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[music] stanford university. >> thank you very much [cough] for theintroduction and welcome back, everybody. as margot told you, i'm anexperimentalist. i think this is the first presentationtoday by an experimentalist. and you will see there is a differentviewpoint, on various aspects. i will touch on a couple of things that,robin, showed already this morning. x-ray interaction with, with matter. but, as i said, from an experimentalistpoint of view.

maybe [cough] one or two sentences moreabout, about my, myself. i actually started when i started doingscience, i did atomic physics in hamburg. and then they told me to get out of the gas phase, that's what a phd student theretold me [laugh]. and so i did that, i got out of the gasphase. and i do spectroscopy on many different things biocatalysis, catalysis and many,many other things. a network user in france, so as you, as you know this is supposed to beinteractive.

interactive does not mean i double checkedover lunch again with your organizers. double, interactive does not mean that wewatched the world cup together and bet on thedifferent teams. it means that you were, unfortunately. but it means that you ask me questionsduring the talk so whenever something is not clear, justto ask a question. it also means that i can ask youquestions. there will be little warning, when when i,when i'm ready to ask a question if when i'veprepared something.

so the quiz, i will quiz you and and thiscomes up right? so you will be warned. okay, so what okay. there's some literature actually robintalked this morning already a couple of books, but here i show mypreferences. the x-ray interaction with matter is stillvery nicely done in this old book by sakurai, i like this alot. and then the, one of the latest versionshere, winfried schuelke. who was one of the godfathers of of

photo and [unknown] or photoscopy or photoscattering. this is a wonderful, wonderful book here. if you're interested in the x-rayabsorption spectroscopy that was mentioned thismorning as well. x-ray absorption [unknown]. there's a book, recent book by grantbunker here who's at the iat in chicago. a very good introduction to x-rayabsorption and fine structure. and then there's another book here on,this is more [inaudible] in 3d transition metals by frank de grootand akio kotani.

also quite, quite recent and [cough]gives a very nice overview. over electroscopy and alsophotoelectronscopy, mainly in solid state systems. so, what will i talk about? again, there will be a little bit of anoverlap with what was said this morning. i talk again about the interaction ofx-rays with matter. and then i also talk a little bit abouthow me, as an experimentalist, how i see the,initial spectrum calculated. there are many spectroscopies, because ithink

we will be talking during this schoolhere. i think then mikael will also then go into moredetail here, as a proper theoretician he will probablydo this right. so i just give you a little introductionon how i see how inner shell spectra arecalculated. i talk about x-ray vision spectroscopycatered towards application of free electron lasers because i think this isrelevant to the community here. and i also talk a little bit if time is left about resonant inner elasticx-ray scattering.

okay. so i start with very basic aspects. so why, why do we why do we do x-rayspectroscopy? of course we hope to get information aboutthe electronic structure and the atomic structure andfrom the sample obviously right. and the, the reason why we do inner-shell spectroscopy so hard x-ray photo in andphoto out spectroscopy, its an inner shell spectroscopy. and the, the important point there its,its element specific alright.

that's always the reason if you were writea proposal. and you proposed i want to do inner shellspectroscopy on a certain system. the reason why i do this because itselements select all right. that's the, that's the most importantthing. and here you see the just the theoreticalor the tabulated values for the cross section c and for the range6,000 to 9,000 electron vaults,. and you see the different elements. this is for an example that contains ionand cobalt. and as you know very well you get the

absorption edges at different energies forthe different elements. that's why it's element selective, right? and the x-ray emissions, so thefluorescents, you can call it flourescent that comes out of the sample, is of coursealso element selective, right. so you, the k-alpha lines or the k-betalines from the different elements. they also appear at different energy sources, element selective in the x-rayemission. when you do a hard x-ray, why do we dohard x-ray spectroscopy? we do this because of the large penetrationdepth of the of the x-rays right?

so if you want to do for example,experiments under extreme conditions. so many would, people do a lot, they takea and so, with diamond anvil cells. so they are two diamonds that press thesample together. to, to hundreds of geo-pascals, so theycan study conditions that you find in, insidethe earth. then you need to have x-rays and you can penetrate through the diamond to get thex-rays out again. so this is the reason why do hard x-rayspectroscopy. so it's [unknown] sensitive for thesample, but

you can also do experiments in [unknown]conditions. i want to put this a little bit with context because you will also hearspeakers later this week. who will, i think at least, talk mainlyabout soft x-ray spectroscopy so we have the hard x-raysand the soft x-rays. hard x-rays start usually if it's aconvention, hard x-rays start at about, let's say, 5000electron volts. and soft x-rays are at lower energies. if you want to study the electronicstructure,

in principle you want to use soft x-rays. because the spectra, the line broadeningis smaller when you use soft x-rays. and it's easier to access the electronic structure when you do, soft x-rayspectroscopy. for example, in 3d transition methods youcan see the, the structure of the 3d orbitals directlyby 2p to 3d absorption. and that gives it then directly be the electronic structure of the 3dorbitals. if you, however, as i told you before, ifyou want to do

experiments with a hard x-ray under, in c2conditions, and in extreme conditions. you want to use hard x-rays because theyhave a larger penetration depth. so what are the challenges in the twotechniques? so, if you do soft x-rays, for example,bessy in berlin. where they use mainly soft x-rays. they are they can easily study theelectronic structure of the system. but they have to improve the way, how theycan study a system on in c2 conditions. right, they do very tricky things ifthere, if we're going to do an experiment incatalysis for example.

if you want to study chemical reaction youhave to flow a gas through your sample. and, and this is very difficult for softx-rays. but they're improving those in c2 cellswith various thin windows that are only like a micron orless thick. they're improving the conditioncy andnormalcy here at berkeley at the ans as well. so the soft x-ray people there are workingon improving the in sequential conditions. we have x-ray people, so i belong to thiscommunity on the right. we have to develop techniques.

we have to improve, ourspectroscopic techniques. to better access the the electronicstructure. the information about electronic structurein the sample. and this is kind of my domain so i'mworking on this. trying to develop techniques, where wecan, use hard x-rays, and learn something about the electronicstructure in the system. here, so the energy range in the about1000 electron volts and 5000 electron volts is by some peoplereferred to as the tender x-ray range. it's kind of in between the soft x-rays andthe hard x-rays.

and people like this, i think they, thepeople in paris, they came up with this so it shows that alsoscientists have a heart, romantic streak. anyway, so what i would talk about is x-ray absorption, x-ray absorption and x-rayemission spectroscopy. so how do you measure an absorptionspectrum? you all know this, i repeat it anyway. so you have your x-rays coming from thesource. that maybe the free electron laser canalso be a storage ring. and then you, you pick an energy so you

use a, in the heart x-ray range adouble-crystal monochronometer. so it's silicon, two silicon crystals hereand they select an energy and this energy then hits your sample andgoes through the sample. and then using the beer-lambert law, thisgive you the absorption cross section. at the linear absorption coefficient. and you see here, this is in the chemicalssensitivity, these are two ion compounds, this is theion cage. and you see here this is a high spinsystem, this is a molecular complex, and a lowspin system.

you see depending on the structure and the spin state of the system, you getdifferent data. now you don't only have elementselectivity, on top you have chemical sensitivity,right? it was, robin mentioned this already thismorning, yeah? so it's very important we have chemicalsensitivity so that we learn about the chemicalenvironment of the sample. we can do this now also with the x-raysthat come out from the sample, that are scatteredfrom the sample, right?

so it's the energy out and the intensityout, and in order to analyze the spectrum of the xrays that come out. i again have to analyze the x rays. what i do, i again use a single crystal. in this case we call it an analyzercrystal. it's experimentally a little bitdifferently done than in this case. but again, so i get a spectrum also forthe emitted x rays. and again, i have a chemical sensitivity. yeah, not only in the metal, a selectivityalso, a chemical sensitivity.

so a high spin compound gives me a different spectrum, than a low spincompound. yeah. so for both absorption and emission, i have as well,a chemical sensitivity. that's important. okay, now. how do i see spectroscopy? how do i understand spectros,spectroscopy, in a general, in a general way?

yeah, so now i give you a little, as a, as i said before, an experimentalist's,approach, [cough] to spectroscopy. let's assume. i show here, on the vertical scale, i showthe total energy of the system. let's assume i have a hematomian that ican do, or i can solve the hematominan including allnuclear, all electrons in the system. so the ideal case, which is of course isnot realistic, is assumed it can do this and it gives me a total energyof the system, yeah? so it lowers the energy in the groundstate and it lowers the energy.

and i know of the system that are excited states and higher total energy i haveexcited states, right. i have the sharp excited state, they aresharp in energy or a little bit broader. if you have a band formation for example,then you may have broader states. and the different total energies have allthose states, yeah. and now you wonder how can i, i want to probe the, i want to learn something aboutthe system. so i want to probe a little bit my, myexcited states in the system. okay?

so, my photon comes in, so i put energyinto the system. the energy's absorbed by the system. and, and then i reach those excitedstates. and the probability for reaching thoseexcited states is this matrix element, so the transitionmatrix element. so it gives me the the velocitatorstrength. the probability of reaching this intermediatestate i call this n here. and this is an excited state, the excited state lives for a certain time, thelifetime [unknown].

and then will decay. there are many different decay channelsnow, it can be a radiative decay, it can be a nonradiative decay. the non radiative decay would be raydecay. i worry about radiative decay because italk about photon-in, photon-out spectroscopy right, thephoton-out is the radiative decay, yeah? so, this excited state now. the decays into those, other excitedstates. at lower energies relative to the originalcase, right.

and, what is important here i may, it insome cases may be possible to reach those excited statesalter directly from the common state. okay, so then i have two ways of probingthe same state. either i give through like this, so in atwo step process, or directly, okay? now, so going back, i just talked aboutthose states in a very general. so, i solved the schroedinger equation andi obtain all of those excited states, andthen. i say i can reach with my spectroscopy, i can reach the states, with a certainprobability.

now, we go to the one electron picturethat was mentioned this morning as well, by robyn, and i want to givenames to those states. just having a state is not very helpful, iwant to discuss science, i want to, in a paper, i want to, i wantto write something. i reach the state, i want to give a nameto the state, right? and in a one, one electron picture, whichis an approximation, right? so i, i'm entering, now, an approximation. i, i give names to the states. so, in this case, if i do hard x-rayspectroscopy, let's say, on an ion system.

i reach an intermediate state where i takeone s electron out. so, in the ground state, i have one istwo. i take an electron out, and put anadditional electron into the 3d [unknown]. so i start in the ground state of 3d5. and then go to an intermediate state, andhave [unknown]. okay, if i go to higher energies, i have,i take one valence electron out, and i putanother electron into p state. it was also discussed this morning, but inconcept, in the context of [unknown]. where do i put my electron?

so i put it into, well, it becomes maybe[unknown] electron which has p symmetry with respect to theabsorbing atom, right? relative to the absorbing atom. and then i have the lower energies. i have, i replace the 1s hole with the 2phole. so the configuration here is 2p5, 3d5, andthen the electrons in valence shell. there are kind of spectators that don't doanything. all they do here is replace the 1s holewith the 2p hole and a 3p hole. and i can go to lower total energies.

in this case actually i have a hole thenin and that would be molecular that i would callthis molecular orbital. so you have a hole in the orbital that is[cough] within the valence shell. and what is interesting now, i told you, ican, i can, well first i give names now, this is the k-alphaline, and this is the k-beta line. so you heard about the fluorescence lines thatcome out of your sample. alpha lines, you find those in the, in thebook, for example, in this nice, orange book, aberkeley book. you find the energies for thoseconditions.

k-alpha line, k-beta line. and and here in this case we call this transition here valence to coretransition. because an electron from a valence orbitalactually fills the 1s hole in this case. now i told you i can reach those finalstates as well directly, and this would be, in thiscase it's the k. i'm sorry i didn't write this. this would be the k absorption edge. and lower energy is the l-edge or them-edge.

so in principle, i have two ways of, ofreaching those states. here, either way via the k-edge or directly via the one photon process,directly. and that would be then the l-edge and them-edge. and down here, at the lowest energies youeven have uv spectroscopy, this would not be aninner shell spectroscopy. this is what you do mainly. maybe some of you did this already in thelab. you read this spectrometer and if you havethis, you probe those states down there.

yeah? so what is important about this? it's the total energy diagram thatconsiders all multi, all electron multielectroneffects in principle. the states here are or the names that igive to the states here are mighty electron states, so iconsider all electrons of the system. that's important as well. it observes energy conservation and inprinciple, what is nice about a mighty electron picturelike

this, a total energy diagram like this, i can put all my spectroscopies in onediagram. right? so i see my cuba vista spectroscopy, andthe heart x-ray spectroscopies. and of course if i have a radioactive decay then of course the, the energy comesout. okay, now since this is, this is important to me, this important point this mightyelectron diagram. i do a little, we do, we play a littlequiz we do, a little, little game now.

what you're probably familiar with is thisone-electron diagram. i mean, most of you probably see this whenyou, i don't know, when you study. you see, if, if somebody explains to you, what, what, what are the differenttransitions in spectroscopy? they, usually, they draw the differentorbitals here. so that's not a multi electron diagram,right? so one electron. so we have the 1s shell here and then theelectron goes out. this is what you see in, in many books andyeah.

so either the electron goes way above thefermi level, this is the fermi energy, or it'll go just aboveinto a 3d level. and then have to decay, i have a k betaline, 3p of opera. 3p to 1s. so i can call this non resident k data orresident k data if i excite it into a letter just above the the fermi energy that would be resident excitation and theresident capetenine. so now what we like to do, what i wouldlike to do with you, is we translate this diagramagain into a multielectron diagram.

so now i need your participation, so wehave the total energy diagram. so, we start at the ground state. so where, where do i put the ground state? do i put the ground state up here? any comments? so i put the ground state down there,okay? do you agree? excellent we start at the ground site. 1 is 2, 3dn.

now i excite my system, so if i have a oneedge to let's say continuum excitation. what would be, what name do i give to thisexcitation there? how many, how many electron's doi have here? >> one. >> one, excellent, one is one. and, the electron goes to let's say, sidekind of so 3dn and they're call this epson-p-epson,would mean a continuum electron, okay? and, again we have then the the resonate excitation we say we put the 1s electron and put the 1s electron in the3d shell so 3d and plus 1.

transition maybe worry about selectionrules. that exists, we can observe this. now for this decay. so what would be my i hope doesn't showup. now i have the k bit at k, so what is theconfiguration there of the final state? where, where is my co-hole? i don't have 1 is 1, i have 3p5. at 3p5, and the electron i carry it on,right? the epson p spectator, it stays up therein 3dn.

and the same, is for the resonantexcitation here down here. it goes, i replace the 1 s over the 3 p. so this is the difference. one electron diagram and multi electrondiagram. if you want to understand spectroscopy, i recommend that you use this diagrambecause it's, it's more physically [laugh] butthey, it's a, as i said observes energyconservation. you can really understand processes ofmulti electron excitation.

this is qualitative, right? so it shows you qualitatively what isgoing on. but some processes are very difficult toexplain in a multi, in a one electron diagram likethis. and i will show you a little bit laterwhen this is the case. okay, electromagnetic radiation, i thinkthis was already addressed this morning. i don't have to go too much into detail. we do, scattering photon in andphoton out spectroscopies. so we look at the scattering of photons,right.

so we have a photon coming in with energyof frequency, a k vector and polarization andthen is scattered. this angle here is my scattering angleand, the, the vector here is the so-called, is themomentum transfer. it's the difference between the incomingand the outcoming, photon k vector of your, of the photon,right. scattering angle here and the differencebetween the two energies is the energy transfer,okay? so i describe my as was shown thismorning, i

describe my photon with a, with a vectorfield here. and what is important was mentioned then,i have two terms that are important. they are the a squared term, and the p.aterm. everything, the, the, the theory behindthis was explained this morning. for me now, just, we just remember that wehave the a squared term and the a.p term. as an experimentalist, i should not showthose scary diagrams, [laugh], but still i findit useful. what is important is for this a squaredterm, i do not create intermediate states. so, i have my ground set coming here, myphoton coming here,

the photon is scattered by the way,without creating intermediate state. if i have the p.a term, i i have my groundstate here, my photon coming and then i create an intermediate statethat lives for a certain time, the lifetimetau. and then at the final state going on and aphoton coming out. what is, so let's look first at the asquared term. so actually i have to say, what, what,what i do here is maybe theoretically not entirelyexact, because the two terms they interfere, the correct formulas were shownthis morning, but the two

terms appear within the square of themodulus, and i separate them. i consider now the case that either one of the two terms dominate, so i neglect theother one. so if i look only first at the a squaredterm, then my, the scattering intensity isproportional to this term here, right? so i have the ratio between the energies out and in, i have the polarization here,.product. and i have all this, this is the matrix element between your grounds andthe final state.

and this is the energy conservation. and this part here is called the dynamicstructure factor. it tells you about, it gives you information about the electronic structurein your system. the response of your system to your preservation of the using the photon,okay? now, i have various terms here, this is a historically, the, the differentnames popped up, because the different people here they

discovered different aspects of thescattering cross section. so thomson scattering and bragg scatteringare so called elastic scattering where the incoming and outcoming energiesare identical, are equal, yeah? so thomson bragg. these two cases are inelastic scattering, is raman scattering and comptonscattering. these are the two inelastic scatteringprocesses that are based on this a square term, yeah? what is important now is this, thisoperator.

i actually i have a quiz again. so the question here, i'm anexperimentalist. and now i wonder, i, i can change thisangle there in my experiment, right? and let's say assume i want to minimizethis term because i don't want to see it. i want to see all other terms. what, what experimental configurationwould you recommend to me? when, when, when does this, this term hereis, is minimal. it's even zero the way it's written there. any idea?

in the case, i'm sorry i didn't tell youthat, so it's a hint, well i have to tell youthat. incoming light is linear polarized likethis. so the incoming light is linear polarized,so at what scattering angle theta here is my intensity zero, the scatteredintensity? ed? >> 90 degrees. >> ed 90 degrees.

if i look here, if theta goes to 90, because of the .product here, it goes to0, yeah? it is important, everything, all thosescattering parts here they go to 0 if we look at 90 degrees. so i don't see them anymore. that's a nice way, and we do this all the time, if i measure the experiments florescence detectedabsorption spectroscopy whatever. we always measure 90 degrees because inthis

case we are not interested in this term. other people at other experiments areinterested in the term. they should not measure at 90 degrees,yeah? okay so. next, now we have to worry about thisoperator. and this operator here that connects the ground server with the factor is veryinteresting. because it contains, this is the momentumtransfer as i told you before. so the, the momentum transfer is insidethis operator.

which is a very interesting phenomenon. and this is the case, i'm sorry, this isthe case for, for raman scattering. by varying the momentum transfer here, ican change the selection rules. i can change my transition matrix element here by varying the scattering angleshere. and, and that is very interesting. in the so-called, the, it's techniquecalled x-ray raman scattering. so actually i start with all the spectroscopies, i start with the mostesoteric one.

then there is something called, based on this a-squared term, called the x-rayraman spectroscopy. and i'll show you here, this is done by,by a colleague of mine, simo huotari, who isnow in, in helsinki. he did beautiful wrote beautiful paperson, on, on this kind of spectroscopy. so what you see here is the energytransfer, so the energy transfer to the sample when we the, whenthe photons are scattered. and what you see here is the comptonpeak, right? and you know with increasing momentumtransfer, the

compton peak moves out to higher energytransfer, yeah? you see, so what, what you see here forthe different colors and momentum. momentum plans for changes and on top ofthe compton peak, you see a line here, does anybodyknow what that could be? what the, what the edge, the edge that yousee what this could be, any idea? >> it's the carbon. what you see is the carbon kh. so you see at a fixed energy transfer, yousee the carbon kh coming up. the spectrum we measured, so just to makethis clear to you.

so you come in, you hit your sample, let'ssay with 10,000 electron bolts. a photon that has 10,000 electron volts. then you measure the scattered x-rays at10,000 minus, let's say roughly 200, or 280, let's say roughly300 electron volts. so at 9,700 electron volts. you measure your scattered x-ray's. so the energy transfer is roughly 300electron volts, which corresponds, to the 1s observed binding energy of theone is electron in a carbon atom. so that's a, they call this a lowspectroscopy, yeah.

so it's a hard x-ray technique, becausethey go in with hard x-ray's, go out with hardx-ray's. but i measured the edge at 280 electronvolts. so, i measured the edge of a low z element in the, that is usually in the soft x-rayrange. it's called x-ray raman spectroscopy. why am i showing you this? because it's, it's an interesting optionalso for free electron lasers. because i, in order to measure thespectrum, i can scan, the emitted.

i can scan the my, my, emissionsspectrometer. so the, the analyzer that i showed youbefore. so it's not the incident energy that ihave to scan. it's the or i can, i don't have to scanthe incident energy. i can scan the energy of my emissionspectrometer. so the energy that is scattered from thesample. so, i think to date it has not been usedat the free electron laser. it's more and more used at, at synchrotronradiation sources. because, i can, for example, study water.

so there are many people, i think mikhailwas involved as well, and other speakers. [cough] here, they started the oxygen khin water using this kind of technique. because they can use hot x-rays. well, hot x-rays in general are more suit, suitable to study liquids than softx-rays. so it's a very beautiful technique. and another publication here by, byseymour. he combines this x-ray ramans scatteringtechnique together with imaging. so what he did, he put graphite, diamonds,diamond into graphite.

and, as you know, both are made of carbonbut the bonding is different, right? so they give you different spectroscopicsignal, right? so if you look, diamond gives you, this is the carbon kh again, you see here 280, 290electrovolts. diamond gives you a different spectrumthan graphite at the carbon h. and he used a very small beam, and builtthis spectrum, that he used, he had positionresolution as well. and then he turned his sample, so he didsomething like tomography, on this sample. and he get a three dimensional image ofthe diamond, inside the carbon.

beautiful experiment, and, used, and it'sonly possible to do this if you use hard x-rays. because if they go with 10,000 ev insidethe sample, i penetrate the sample sufficiently in order to be able todo this kind of of imaging. a beautiful experiment and a niceapplication of this x-ray raman technique. >> now you presented that the hard x-rayis necessarily the method of choice. of course, since it's, it's penetratingbetter if you have a really thin sample because it means you get wayless signal out of nothing. >> it's true.

>> because it's not efficient. >> yeah, yeah, yeah. of course. what x-rays they use depends on manyaspects and if you have a very thin sample of course, you may want to dothis imaging using soft x-rays. but they absorb quite enormously. you, the sense, is thinner than a micronright that i have to make in many cases. well it depends on what element you lookat. and now it gets very technical as well.

another aspect of this x-ray ramanscattering is that, if i, again, if i change the momentum transfer here, i canexpand the exponential function here. if i vary the momentum transfer, i change the selection rules within thismatrix elements. so i can access different parts of my electronic structure as a function of themomentum transfer. as you see here, this is a very nicepublication by the people here. so here they vary the momentum transfer inthe spectrum changes dramatically. the reason is that this transitionoperated changes

as the function of momentum transfer andit reach different final states depending onwhat terms dominating here in my, in my expansion. just imagine if i, normally if i look at atransition from a 2p orbital, i brought the d density ofstates or d orbitals right? using the, this technique i can instead ofgoing to d, i can go to f directly from p, right? and i learn, i get a more complete pictureof the electronic structure of my system. and so this is the the beauty of of x-rayraman spectroscopy.

okay, so we move on. we go now to the a.p term that appearshere. and the kramers-heisenberg equation. it was shown already before. so your ground state transition operatorintermediate state. it also corresponds to the diagram that ishowed you before. so intermediate state, and here. again transition operate and the finalstate. again, now the transitional operator herenow

does not contain the momentum transfer,right? what you see here, is the photon vectorthe, the vector for the electron position and momentum and theprioritization of your, of your x-rays. you can expand it as well, this gives youthen the dipole and quarter-pole selection rules, i don't want to go intodetails there, because you can find it on wikipedia yeah, so this part here is then responsible, it gives the, is, is, is dueto the a.p term in your, a treatment of the of the preservationhematonian. okay, what you can do now, if you imagine,if this scattering angle now goes to zero.

and it appears to be forward scattering,which is, absorption. so, coherent forward scattering can beviewed. as for so its clear for, for what itsgetting, that means that the phase is preserved,and the its elastic scattering, elastic forwardscattering polarization is preserved as well, and it leads to the total absorption atthe end. so you can view, you can view absorptionas a photon in, photon out process but the photon hits thesample and comes out again,.

and in this case yeah. if you, if you view absorptionspectroscopy as a photon in and photo out process, it'selastic forward scattering. and we can treat, it on the same footinghere, on the same theoretical framework. again here now, now because i try to simplify the kramers-heisenbergequation here. do you know, yeah? >> i, i didn't understand the last partwith the v forwards scattering things as options because to dophoton terms and the

photon is kind of destroyed, it's notscattered to lower energy. >> this is a di, discussion maybe we canleave maybe on the, on the road i have been discussing a lot of this, this point with, with differenttheoreticians. if you, i have this from sakurai. sakurai treats it like this and, and ilike it for several reasons. in principle, the way i argue is if you,if a photon is absorbed, you have reached an excite, an excited state thatlives for a certain time and it has to decay.

so, if i only observe the absorptionprocess, i do not care about the decay afterwards,right. you can say i, i, just neglect it, yeah. then i would say to p.a in the firstorder term, i hesitate a little bit to, to accept this, because i can't just forget what happens after the absorptionprocess, right. it decays after a certain time. and if i look at the radiation decay, i have a photon out, photon in, photon outprocess.

okay, i neglect the non-radiat, radiat,radiated decays. and i come up, if it's in the forwarddirection. if it's elastic, then it becomesabsorption. so then, absorption becomes the photon in,photon out process. another view, what some people write inthe books is that... observe or consider the absorption processas the, the beams that attenuated right? in, in your sample, so it's partly, partly constructive, destructive interferencebetween the, between two waves. >> but

is it having the [laugh], the, >> it, exactly, that's, [laugh] the,that's. if you have an already decay happening,process happening, then you probably have to look at it morecarefully. still, it's a two-step process. we have an excited state and a decay sentfurther. if i consider the p.a term onlyin first order, i still don't, care about what happensafter my excited state. >> and what more fundamental processestake?

the photon number isconserved. >> that is if you consider, exactly if,well... >> well, if you, if you say, it will be elastic, part of the elastic schedulingprocess then photon comes in. if you think about it as absorption, yourpicture will get shifted. but i can, i can count the number ofphotons that go through a sample. >> if you have less photons afterwards,the photon, the photon number is after. that is exactly. in this view, in this view i, i struggle a

little bit as well to, to bring this toterms. but, in the terms of, if you look at it in a wave, the continuation of a wave, then itdoes make sense. it also makes sense that i do have forwardscattering, right? this process is not but we can discuss this maybe later. as i said i, i, followed here thediscussion by, for example sakurai and other,people in another book. but if you view as a, as a number of countthe number of photons.

that suddenly disappears. still you can not argue with my argument that you have an excited state thatdecays, and if it decays very actively somethinghas to happen to the, to the excited state. but anyway, we, we will discuss later. it may be nice, it's, it's nice exerciseto think about this and to [laugh] many different decay paths, that's true. okay, so let's look at the interferenceterms here.

so what, what does interference mean? do you know what interference means? how can i. how does interference show up here in thisin this equation? does anybody so, you have a sum within thesquare, right? so, that means you have the square, eachterm squared, plus cross terms between thedifferent matrix elements, right? because you have, and the sum, and thenyou square the sum, right? so you always sum sum deviance, yeah?

so if you, let's try to simplify the kramers-heisenberg equation here by firstneglecting interference terms. interference would happen between if gofrom the, from the grounds state of decay to the samefinal state. and those let's say, assume those are theintermediate states that interfere, okay? now we ignore the interference effects and then it becomes we ignore all interferenceterms. and then the equation becomes becomes likethis. so i have the square of the matrixelements divided

by this denominator that is too big forthe resonance. if i, if i look at this note carefully, iobserve that i just have the product between absorption,because i take the square now, between absorptionand emission. if i, in the next step, that makeseverything much, much easier, right? because i can calculate my absorptioncross section, and calculate the emission, and i don't need to know thephase between them. because i take the square. and the problem is much, much easier toaddress theoretically.

and the question is now, how far do we get by, by, by using this assumption, thissimplification? if i now, and in certain cases i can do this, and this is actually what is done inmany cases. when absorptions spectra are calculated, iapproximate my transition metrics element by the electron density inthe system. that's a very harsh approximation, and inthe upright theoritation will rebel against this, butthis is what i understand in many cases, just because wehave to do

it, we have no other way of addressingthis problem. so, the transition matrix elements here isapproximated by the electron density. principal is another radial matrix elementbefore that i'm neglecting here. you do this for the absorption process andfor the for the emission process. you approximate the matrix element usingthe density of states of the occupi, unoccupied statesand the occupied states. and then this equation reads like this. so this step, i will address this later aswell, this step neglects all electron, electron interactions ormany

multi electron excitation's itneglects as well. partly the cohort potentials, so there aremany, many approximations there. but, it works, i will show you, in somecases, or many cases. and then i get a very simple equationhere. the kramers-heisenberg equation. it was published already it, in 99 bythose people here. where my scattering intensity is proportionate simply to convolutionbetween the density of occupied and unoccupied statesdivided by this term here.

this is due to the lifetime growing. so, the, the question is [unknown] it's kind of, we approached this, we tryout how far we get by approximating our matrix solution, the absorptionprocess, the absorption spectrum by the density ofstates, yeah? and this is here for, i show you for an experimental spectrum at the oxygenk-edge. in, in silicon dioxide, this is theexperimental spectrum. and this is the calculated density ofstates.

and you see in this case, it works quitenicely, so indeed i can, in certain cases, i can approximate my absorption matrix element by the densityof states. one has to be very careful. it does not work. for example when,and it will be, it will be discussed later during thisweek. but if excitations into the 3d orbitals of3d transition metals. so iron, manganese and then the the

l-edges of 3d transition methods thisdoesn't work. and people will discuss this afterwardlater this week. also when i look, look at rare earths fourf orbitals are the valence orbitals and bare earths. also this approach doesn't work. and also in cortical x-ray emissionsspectroscopy approach doesn't work and i will address this in a little bit. just to, to show you a little bit, giveyou a feeling of how you can approach this problem of,of calculating initial spectrum. okay, summary slides, so for the residentterm, i have here

the, the resident part of the heisenberg equation but this transition operator. so, this is what we are mainly concernedwith when we do element selective spectroscopy, and then we havethe thomson scattering term, and i showed you this scattering term here is due toall those raman spectroscopy that i showed you before where you can changethe transition matrix elements. the two terms interfere and neglect this,i put this here in vacant. you may wonder what is resonant? it's also an interesting question to, tocontemplate it a little bit. it, i think, also this morning robinmentioned

this a little bit there was a questionhere. what, what is actually resonant? in principal, when you look at theliterature, you say resonance are excitation's close to anabsorption edge, right? they are sharp resonances in a system,right? but, in principle, i could say also when iexcite one electron from the one s-shell into the continuum, right,it become a free electron, the principlesalso. a resonance within this continuum state,yeah, so, a

strict definition of resonance is verydifficult to do. in principle you could say, the mostgeneral definition is that whenever i use thiskramers-heisenberg term, i have a resonance excitation, and thatwould actually refer to all to most, to allelement-selective spectroscopies. apart from the x-ray raman spectroscopythat i showed you before. yeah, that would be very generaldefinition of of resonance. okay, so the next question, what caninertial spectral do, do for you? in principle, you want to learn what itell, told you before.

we want to learn about electronictransitions and thus the electron density and electronconfiguration. this will tell you, as, as robin mentionedalready before about bond distances, so you have anabsolving atom here, you have bond distances, you have bondangles, and it would, may tell you about the type ofnumber of beacon. so this is exo spectroscopy. what is important is that in principlespectroscopy, using this lecture rules, spectroscopy issymmetry selective, yeah?

it will tell you about the symmetry aroundthe ground state. so, how, how many of you are familiar withthis, with term here? this is the spin orbital, 2s plus 1l, soyou are familiar with multiplets, atomic multiplets, yeah, so iuse this term in, in a certain coupling scheme, i use this term inorder to describe the symmetry of my ground state, and based on theselection rules, i will then. can only reach certain excited states. and the excited state is what i probe inmy spectroscopy. so that means i probe what i getinformation about as symmetry.

the ls term of the ground state. so it's very important to remember that a, that a spectroscopy is symmetry selectedon the outside. probe symmetry of my ground state. i added this slide now because there was this discussion on what, what do imeasure? can i measure oxidation states, or ratherhow much does a k-edge shift as a measure of theoxidation state? that's a very fundamental question thatpeople discuss all the time.

and my reply to this question will alwaysbe the oxidation state is not an observable, it's not a quantitythat i can measure. oxidation state is a, is a chemicalconcept that helps you to predict certainstoichiometries in your chemical equation. but it's not really a quantity that iwould i like measure. if you try to translate this into aquantity that you can measure, it would somehow relate tothe charge per atom. assume if ever, if ever an ion in oxy,oxy, oxidation states three that means i have a3d5 configuration.

that means i would translate the conceptof oxidation state into a number of electrons, that i have onmy atom. but this is a tricky question, right? if you look for a time, this is amolecule, and this the electron density map for, someenergies that are important. there's manganese here in the middle, andthen there's the electron density around. now, i have to assign electron densityhere, to a certain atom. and you see it's a tricky business. i have to come up with a certain scheme,and

then many sophisticated schemes, in orderto assign the electron density. to a certain to a certain atom. but there's, its, its, there's no strictprocedures. so it's not a strict observable how muchcharge i have on an atom, yeah. so one has to be very careful when i ask aquestion or when, or when, when i tell somebody i can, i cantell you if i do my spectroscopy, i can tell you howmuch, how many electrons i have on my absorbing atom methods not really what i, what i can measure.

and a little philosophical intermezzo ifound there are two provocations here, one by, byrobert parr, who is very famous for coming up with exchange function, indensity functiontheory, and in a publication he was asking what is an atom in amolecule, and and what he writes then it says that a mol, an atom in a molecule isa noumenon in the sense of kant. i'm not asking you what a noumenon is. i had to look it up myself. wikipedia says, it's an object knowable bythe mind or intellect, not by the senses.

so that's bad news for the intriguerspectostrophist. because we claim we do element selectivespectrosopies. anyway, so, but there is a point i toldyou, i showed you this electron density map, so this iswhere they're coming from. they say well i have to look at the entire molecule and my electrons are distributedover the entire molecule. it doesn't really make sense, that's theway i understand it in layman's terms; it doesn't really make sense totalk about an atom and a molecule. there was a reply right away, as you can

imagine, to this paper by the group ofrichard beta. richard beta wrote a famous book, atomsand molecules, and came up with a way of projecting the electron density onthe mole, on the, on the atoms. and they reply, of course, anexperimentalist has no doubt the he or she is measuring the properties of asingle atom. we cannot solve this issue, but i'mshowing you this in order to, i dont know, sensitize you a little bit tothis, to this problem. i mean, what are the properties that weactually measure? in principle, you read a publication.

people like to write about 4p and 3d, andbut, this doesn't really exist, right? i don't have spherical symmetry in mysystem. so there are no 3d orbitals in principle. yeah, it's very difficult, very difficultto find a language how we discuss electronic structure and how do i present my scientific results, spectroscopic resultsto a scientific community. what language do i use there? and that's tricky.

so we have to find observically reallyobservables that are probe in my spectroscopy in order to thencommunicate my results to the community. and that's a very difficult task that icannot solve here. okay, just, i want to point some moreproblems out to you. [cough] when i do intershell spectroscopy. yeah, so i remove the electron here,that's one less electron, so this is a very simple pictureof an atom. yeah, nucleus here, i take the one1s orbital out. what happens is that i have one 1selectron less,

so the nuclear charge is screened by oneelectron less. so all other electrons in the field change their potential, obviously, theywill relax, right? so the, the, the energy levels will relax. what can happen if i have this relaxation,that not only i remove one s electron, another electron, so when those, those shells, say theycollapse a little bit, they react to the newpotential, another electron is excited from an occupied level to an unoccupied

level, so that would be multi-electronexcitation. so, that means. what i told you before and was, wasdiscussed this morning. discussing spectros we using only oneelectron. and assuming all other electrons are kindof spectators is a tricky business and may not work in manycases, yeah? so when i, when i calculate my, my absorption projection here i, i assume thematrix elements of these i assume that thosestates

are mighty electron states in the mostgeneral case. i can use many electron, like a wavefunction. i can approximate this, and this is whatis done if i then ultimately do my calculations using the electron density, using densityfunction theory. so i approximate this multi-electrontransition matrix element by using one electron wave functions as wasshown this morning. and, what i can do, in order to somehowtake care of the multi-electron processes, i can scale thismatrix a little bit by a prefactor.

but this is kind of, this is andapproximation, yeah? in this case, i have one electron wavefunctions and then i can use density function theory inorder to. calculate my, my absorption spectra. so that's again, is my experiment withpoint of view how the two different ways of, of trying tocalculate inner-shelf spectra. i can start, with a nine, so i neglect allthe ligands. i have an absorber, and iron absorber inmy system. i neglect all the ligands, so there's nooxygen nothing.

i just look, it's an ion because maybe ican remove two electrons, because i assume it's anoxidation state too, yeah? and then i have a wave function that is later determined that describes mysystem, right? what i can do then, artificially, i can gofrom the spherical symmetry here to the local symmetry, so i have six oxygen lignds around, i have octahedralsymmetry. and this, i can simulate, by assigning newsymmetries to my 3d objects. so, my, they're not 3d anymore, theybecome t2 orbiters, or t2g orbiters, eg

orbiters, according to, the symmetry thati may have in the real system, yeah? and this is kind of done empirically, andi can split the orbiter, the field splittingthe orbiters. i can also include covalency by mixingthem in several configurations. so in this case, i, i, i treat all the,the, the effect of the ligens i treat in anempirical way. and but what's the advantage here? i can treat in principle multi electronexcitations in an accurate way.

and i also can include the interaction ofthe core wall with the valence electrons in a, in arather accurate way. and this is the ligenfute margin ratetheory. some of you may have heard about thisbefore. and it starts, as i say, it starts with afree ion. alternately, i. start with the whole structure so i am notincluding only the ion, but all my deletings around so the chemicalenvironment is included and in this case it will density function theoryand i calculate the electron density.

then there ways of including the corehole. i say he approximative way that maybe somepeople are insulted but anyway i can include some of the the cohold andinclude my electocitations as well. in this case i have a good treatment obviously i have a good treatment of ofthe legans in long range order because this is all considered in the in the in thecalculations. but, it's more difficult to treatthe multi electron excitations and, and treat the interactions of the valenceelectrons with the cohort, yeah?

so these are roughly the, the twoapproaches, the way i see it. there's enormous work at the moment tosomehow merge the two, approaches. it's kind of the holy grail of initial spectroscopy, they're calledappanesio maltiplets that means you calculate the electronic structureusing all ligands and have all the multiplet structurebecause of all the electron interactionsincluded, so we are called appanesio multiplets and they'reenormous, there's enormous progress that, i thinkmikael,

will talk about later, laterthis week. this is just to illustrate to you thefundamental problem. yes another problem in inner shellspectroscopy. what i told you already about thosemulti electron expectations. so to give you an example, this is the l 3absorption edge. so i excited 2 p 3 hops electron in serumdioxide. what you see here experimental spectrumthe red line and the blue line here are one-electron calculations. so what do you see what i used here is

the 5th code some of you maybe familiarwith that. the 5th code is density functionaltheory code that approximates the obsorbtion spectrumusing a one-electron transitions. and what you see, those features here aremissing, they're not coming on. the rest comes on quite nicely but thosefeatures are missing, just plain missing, because it'sa one electron code, yeah. then there's another code which is calledthe single impurity anderson model, and, and this code gets those multi-electron excitations, they get itquite nicely.

but one has to say that this splittinghere. which comes out in the one electroncalculations. this splitting here is introduced in this code empirically, so it's kind ofcheating, right? so this splitting comes from theprogrammer, the programmer puts the splitting in here. while in this calculations the splittinghere comes out up in issue from the calculations, so that nicely illustrates the advantages anddisadvantages.

of the off these different approaches. so here, the fine structure off this casein this is the 5t band. the fine structure comes out of thecalculations, but i do not have them out here exertations but inthis case i do have the molecular excitations, butthe fine structure i have to put in by hand into thecalculations, yeah? so again, what we would like to do in the future is have those two approachescombine, so i have. the correct fine structure and the multielectron excitation in one go.

>> excellent, very good, so you paidattention. i was hoping nobody would pay attention. no but, you did and these are, so i toldyou, this is the 5t band. so these are transitions from 2p to 4f. and in order to get them out from thecalculations, er, you have to do some tricks that i have to admitthat i was not aware. it's not only you have to include transitions obviously,but they also send tricks to 4f orbitals in thosecalculations and those on the right.

position so we have to tweak a little bitthe calculations to get your four propertiesin the right spot. which i didn't do back then. that's a simple explanation. still a good question. okay. there's one, one thing i would like tomention, the multiplet theory because i'm not sure to what extent, well theother speakers might address this as well. just to a little, to give you the ideawhat multiple theory means.

there some, a lot of little, this i don't have to go through it. you will have the slides. so the fundamental problem is, i have my3d orbitals that say in a 3d transition metal. if i have only one 3d electron, it's easy. my total energy is just mg of all theother electrons. the rest. and, and plus the energy of this electronthat we show. if i have two 3d electrons, how do i treatthis?

that's a good question. it's not twice the energy, it's not thatsimple unfortunately. what we have to do is treat theinteraction between those two electrons, there is the combinedaction between those two electrons. and they come up with the two electronoperator. i get matrix elements for this twoelectron operator, and what comes out then is the so called the direct termand the exchange term. yeah it's the direct coulomb term and theexchange term. and the exchange term is a exchange intoaction that is zero in the spins of

the two electrons are anti parallel and itkicks in if the spin of the two electrons. it's parallel, and it enters the totalenergy with a minus sign here, so when the two electrons are parallel, then i get a finite value here, so the total energy, isdecreased. it's hanh's rule, basically, so, yeah. and those terms are the slater integrals or racah parameters, as you may haveheard. and about, okay? so, what does it mean for my, for

my system where i have two, 3d electrons,right? so, i have to couple the angular momentumof the two, of the two electrons. and to couple the orbital angularmomentum, and i have to couple the spin, which i didn'tshow here, these are the standard rules for thecoupling of angular momentum which you have probablylearned in quantum mechanics. so i don't have to. had to repeat this and, so i couple themand then i have also have to observe the heisenberg

the i'm sorry the pounding exclusionprincipal. and what i find, if i go through all thequantum mechanics here what i find that for a 3d toolconfiguration, i have all those states. yeah, that comes out of multiple theory,atomic multiple theory. so, i don't have just a, maybe you learned, i dunno, you learned the clusterfield splitting, or whatever, you have to observe also theelectron elegant interactions that give you allthose different terms. there are five different energy levels for3d2 configuration, yeah.

and it's very important to considerbecause you observe, actually, those levels, when youdo spectrocity. so when you do ligenfield, mind you, thetheory, the program codes you may have heard of the code that is, managed in germany so the code does, it starts with atomiccalculations, introduces then the chemical environment that i wouldtold you before. it branches to the appropriate asymmetry. and then i can somehow consider, ishouldn't

write here hybridization, sorry, it shouldbe orbital mixing. so it considers somehow the orbits of theligands as well, and i can, i can mix the different, bymixing different configurations. so, i told you i started with a 3d2 configuration. and then i have those five levels, just bylooking at the atomic multiplets. on top of this now, i have the, the, thecrystal field of the ligands. so i have an additional splitting on top. and yet, this, all this combined. it's shown in the so called tanabe-suganodiagram.

who has heard of a tanabe-sugano diagram? okay, that's very nice. some people at least. it's usually important and i'm surprisedthat this is not generally taught at universities, it's, asi said, usually important if you want to understand electronicstructure in, for example, 3d transition methods, because this is what reallyhappens in your sample, yeah? so i don't know, when you get the changelook up ten other tanabe-sugano diagrams, becausethis

is important to electronic structure,okay? so this was just a littler... i, i was a digressed a little bit [cough]to address this point and i give you now some well some examples for x-ray emissionspectroscopy. okay, i showed this diagram before verybusy diagram i make it easier now to understand i want to look now atthe capital lines, yeah. so i remove a 1s electron, have an excitedstate here, it decays. and then i have the capital line comingout. as i replace the 1s hole over the 3p hole.

in a one electron diagram, it's atransition from 3p to 1s. and i show you here so in the context of the other fluorescence lines coming out of magnese. if the k-alpha line's here, the k-betalines then, and these lines, i will addresslater, the core lines. so what can i learn, what is the, what isthe sensitivity of those lines, and and what i can, what cani learn about my sample? using those present lines. so first i look at the spins, right?

i start out, i have a 3d5 configuration. so in the ground state. my l-s term, l a twist, was one. l term is [unknown] s. right, it's a it's a 0 anglum momentum andi have five spins pointing up, right. and then i, photo ionize so i put oneelectron into into continuum with the p symmetry, and what remains, isa [unknown] or [unknown] s state. so that you have to count the spin here in the one estro together with the spins inthe 3d show.

so this spin here and the, and the corehole can point up or down, can be parallel to the 3d electrons or anti-parallel to the 3delectrons, okay? and, so one gives you of course, this is intercepted, and this is the quintetstate. and by the way, i indicated this a littlebit. so this state is a little bit lower inenergy than this state. it's only 50 million [unknown], but it'sstill lower because of the hans rule, because of this exchangeinteractions between space.

so now let's take this study case. and you keep the spin orientation of theelectron of the, in the core hole, no you keep it, and then you reachreceptive p in the final state. and in this case, you reach a quinted pin the final state okay? and again, you have the interaction the,the energy difference here again is the exchangeinteraction between the 3p electron here and the 3d electron here,it's again the exchange term that i explainedto you before. and the exchange energy lowers thisenergy, so it's lower,

the septed p is lower than thequinted p, okay? so that's very nice, so we have now atomic multiplied theory, and this can explainthe k beta lines to us. so this is not experimental spectrum, thisis the manganese. k beta line, and you see, indeed, a lowerenergy, a lower emission energy. so that means the energy difference heregives you the emission energy. so the quinted p [cough] is at lowerenergies. it's here. so this corresponds to this configuration.

and at higher energies, i have the septetp. so now we have the, the, the roughelectronic or spectral shape we have explained, using very simple, atomic multiplets theory,arguments. and what is important is here, theorientation of the unpaired spin in the, in the 3p shell,yeah? so you realize already this spectroscopyis sensitive to the spin state, right, because there arespins interacting here. but you see there's the shoulder.

the shoulder here i have not explainedyet. but we can explain it. so what may happen, and that's why it'simportant to consider all electrons or manyelectrons in your system. what can happen is when you have thisdecay is that one spin the 3d shell flips over. you can calculate this very accurately. these are the so-called non-diagonalmatrix elements. slate already in the 60s was able tocalculate this.

and there's a certain probably, a verystrong probability actually, that this spin in the 3d shell flips over when ithas a 1s 2, 3b condition. and what you see if you count the spinsnow, or if you look at the ls term it's also a quinted p term, so the ls term of the entire configuration here isquinted p. also, this, so you can realize a quintet p final state using twodifferent configurations. and that's very important because when ihave the same total ls term, those those statesinterfere.

and that, that is part of the reason why iget this intensity so strong for this, forthis configuration here, yeah. and this spin-flip explains the shoulderhere. so the shoulder b here is the spin-flip. and it shows you that the shoulder is verypronounced. and it shows you that the, the probabilityfor this spin-flip is very high. what i want to show you in this slidehere, is that, the equivalence between the manganese k beta lines, thathave a 3p whole in the final state. and 3p x ray photo emission.

because, in both techniques, you reach thesame final state. in one case, i first created one as whole. and then the one as whole is replacedby a 3p hole, right? so i have a 3p hole in the final state. in the other case i do photo emission. i take the 3p hole out right away. at the end i have the same final states,and i com-, compare them, and indeed i turned thisaround because the electron, photo electron people they like to plot itthe other way round.

so that's why it's here. mirror, mirror written. and yeah, but you get the same, you getthe same state. this is peak a, this is septed peak,quintet peak quintet p. right, you get the same states in k betaas in photo electron spectroscopy. the spec, the instrumental resolution is much better in photo electronspectroscopy. but, this is a hard... now the chemicals entity.

we explained now the spectral shape of thek beta lines. are there questions actually because thisis quite important. questions they is all clear? i guess not. so, so what is the chemical sensitivity, where does the chemical sensitivity comefrom? so, i told you, it's a, it's a, it'selected to the spin, right? it's a, it's an exchange into action. if i now change the spin state in myvalence

shell i will get different energies, theyalso configurations, right? just because i have different exchangeenergies. yeah, so if i have a manganese 3+ and amanganese 4+ will give me different spectrum, yeah,so, the chemical sensitivity. and this is true,this is an experimentaldata now. if i change now the formula of the oxidation state of the manganese withdifferent fluorides, i see how the k beta line changes, it moves here to lower energies with increasingoxidation state.

just because the spin state in my valenceshell, the spin in the valence shell, changes as a function of the oxidation state, yeah. so, that's how i'm chemically sensitive,i'm sensitive to the spin state. >> so, what is the contribution of theover charge. is their contribution at all of the charge? the charge, is that the atomic route butthe charge moves somehow right? so how much contribution purely from thecharge. if you could neglect the spin, how muchcontribution would you have in the energy shape?

>> that is a very good question again. it's a topic of discussion. they have various publications that cameout recently and another one coming out now very soon. their people investigated to an extentk beta lines changes because of the charge. this one aspect that i haven't mentionedyet. or i think it's robin mentioned thismorning the reason why line of flourcene line or real line may changeis because of screening effects. if my valance valance electron densitychanges.

you can say but of the electrons that arevalance shell they also have a certain probability of being close to the nucleus right because the radialdistribution. it's not a delta function. it has a extend, right? so also, the electrons in the valence shell,they screen electrons in the 3p shell, or even the 2p,right? so if i remove, an electron from thevalence shell. even my core levels, 2p or 3p.

they will sh, they will move a little bit. the question is, by how much? or you could ask a question by how muchdoes my charge actually change when i change myoxidation state? people did calculations, and it'ssurprisingly little. the real charge, depending on how youproject your charge on your ion. the charge, by how much it changes. so we, we don't have a really ionicpicture. we don't have a manganese four plus ionthere.

that's, that's... that is not true, right? the real charge between thedifferent oxidation state doesn't change very much. so, people recently, there's also rubinmunheim from maser, they investigated to what extentthe k beta line shifts. because of changes of the charge densityit's very little. it's really, to a large extent, the spin state that causes the spectralchanges, surprisingly.

which is good for us, because we aremainly interested in the spin state. and this has been used here around the corner, at the free electron laserat lcls. so, what people do, they, they, looked,you saw these images probably before. if you look at protein, protein crystals. you well, you excite them with the laser that can be important to reach excitementstate obviously a near-field lcls pulse and thenthey use a x-ray spectrometer here that isdispersive.

that means the x-rays that come from thesample, they hit this this spectrometer and they hitthe position-sensitive detector. that then gives you, [cough] the k betalines, right. so the sample comes here, the x-rayshit the spectrometer, the analyzer crystal here, and then on the two-dimensional detector, i get myk beta lines. and they change as a function of oxidationstate, yeah, and the people who have done this a lot in, in, in proteinsin order to redox mechanisms. in proteins.

but, what i wonder here, and there was an honest discussion, i think, especiallyin stanford, in my free electron laser with thisenormous brilliance. am i, should i, am i able to measure, kbeta lines over an intact sample. why i'm asking this, you, you also open. you also, those, pictures, of the coulombexplosion, right. you've all seen this before. if i have a coulomb explosion, and thisis, i, i don't know the answer, but to just to, just forthe poetry maybe.

if i have a coulomb explosion, would i beable to measure. in the flourescence line, that is reallyreflect the ground state electronic properties or,that corresponds to flourescence line that it would measure atthe sunkatoon variation source where i don't have thishigh brilliance. the argument there is that, i have, i have my lifetime, the lifetime of theexcited state. well, the coulomb explosion, i'll tell youmy reasoning. the coulomb explosion happens, correct meif

i'm wrong, i strip off the electrons,right? and i have many charged particles, ions,and the whole thing falls apart because they, repulsive forcebetween the different, between the ions. of course, the, the argument there is that the, the atoms they start moving after imeasured my deflection pattern, so i detect andthen destroy, but the electrons they, they react muchfaster no? they should, react to the to thepulse, to the electromagnetic wave for my for my free electron lasem on theon an attosecond time scale.

the lifetime of the intermediate state. is a femtosecond roughly, so my electronicstructure should be destroyed, much faster than, my fluorescence decay occurs. so strictly speaking i should not be able to measure my fluorescence line. the fact that we can do, may indicate thatwe do not have, exposure. maybe, under the conditions. but this is not entirely clear. >> so when, when you do this experiment,the spectrocity experiment at

the lcls, you don't need to focus thebeams that hard, right? your effective fluence would be as lowas with a synchrotron? >> well, it is the one shot that isimportant, right? i was one short of one molecule. >> it wasn't a molecule, but it wasnano-crystals or whatever you want to, the focus, the beam wasfocused as much as possible. the question, of course, the question isdo i have an explosion or not, and >> in principle, you asked the question, with lcls examples, the answer isdepends.

[laugh] but if you really focus hard, oryou if you focus loosely, then for all techniques youneed to focus hard. so for spectroscopy, if you combine itwith like a diffraction method [crosstalk] >> exactly, but the goals. spectroscopy very well. >> you, exactly, you're right, but forthis experiment the goal was to combine it with therefraction, right? okay, but i am showing this to point out that that the conditions forspectroscopy, of course,

different than for, diffraction in orderto discuss whether i can measure an intact sample or not,right? because in spectroscopy, i'm sensitive to the electron's, the electronicconfiguration that may react much faster than thecoulomb exposition occurs, right. okay, another experiment that was donehere actually some examples, here at the lcls is the on the spin cross-over system. that can go by excitation of light, i cango from a ground state, which is a low spin term, singlet a 1

i know something funny happens here, it'snot entirely clear. i may go to a triplet state, and thenfinally go down to a quintet state. this state here was probed at synchrotron radiationfacilities already extensively. and this works. but the big question was what is happeninghere? is there really a triplet state inbetween? and and i'm not sure what i want to do. aya exactly. now we raise a very obvious question, whatkind of spectroscopy

would you choose to study the spin stateof the system? well, it's obvious but tell me anyways[laugh]. huh? epr? well, it's [laugh] it's one possibility. i would propose k beta spectroscopy,because it's so nice and sensitive to the spin state,right, the exchange interaction. okay, so in in's system as well, if you gofrom high spin to low spin, these experimentaldata, these are calculated data.

if i go from heisman concentration, that'sthe black line here, to a low spin concentration asthe green line here. i'm very sensitive to the spin state usingthis k beta spectroscopy as i pointed out to you before. okay, and there's a publication that justcame out recently. i think the pi here is kelly gaffney. and they, they, these are again the k betalines for. ein and different, spin states, right? singlets, triplets, quartet, quintet, it'dbe nice to see

the changes then, and these are differentspectra, right? because they like to emit a transientspectra, at, at pump and prob experiments. and, these are different spectra between,you know doublet minus singlet, minus singletquintet minus singlet. and then they compare those specter inmotor systems. they compare those data then to thespectrum that they measured at a time delay between the x-rayprobe of 50 femtoseconds. and what they write to you in the paper isthat this spectrum here proofs really that i observes andable to observe the triplet stage.

at 50 femtoseconds after the light andexertation. so that's just to, to show you an examplethere. so the k beta lines are very sensative, and i can study, spin crossover systems very nicely using, usingthis technique. let's see. i don't have so, so much time left, so letme skip a couple of things here. and i want to there's another nicetechnique that has not been used yet at the free electron laser, but will, ithink, very soon, will be very soon. and that's, these are those lines, right?

again, i go to my removed 1s electron. and then i look, the final step is i lookat is has a hole in the valence shell. so this, as i told you i, i probeexcitations that can also, also observe in principlewith a uv spectrometer. i observe excitations within the valenceshell. so it tells me directly about thevalence-electron configuration which is a very powerfultechnique yeah. if you look in the one electron diagramagain. you see transitions from the valence shelldown to the 1s shell.

and they are just here, you can imaginethe fermi energy would be here. so it, just below the fermi level. >> why is it so weak? is it because of electronic overlap? >> em, i tell you why, in a, in a minute. you can imagine already, because, what,what, what orbit, what orbitance do i have in the valence shell of the 3dtransition metal? it's a 3d transition made up of 3dorbitals in the valence , that's right? a 3d to 1s transition is not dipoleallowed.

it's only quadrupole allowed. so it would be from this point of viewalready extremely weak. but i can tell you already we don't see 3dorbitals in those transitions. and i will tell you in the next step whatwe see. so transitions from the valence shell downto the 1s, yeah? the transitions, where do they come from? so i do not see the 3d orbitals [cough]. what can happen is that the orbitals thatare on the ligands. so i have here a metal center, and i haveeight i'm sorry, six ligands around.

so ungerade symmetry. six ligands around. then i have the p orbitals of the ligandsin the two results. those p orbiters or s orbiters, they canform the molecular orbiters. so i can do a linear combination of atomicorbiter to construct a molecular orbiter. and this molecular orbiter has unevenungerade, uneven symmetry with respect to the metalside. that means we do an inversion, i, iproject the object onto itself, but with anegative sign.

and so it's uneven negative parity,basically yeah, uneven symmetry. and the transition form such a molecularorbiter, to the 1s shell of the metal is dipoleallowed. yeah, and these are the transitions wesee. so in this, in this we call this valenceto coil mission spectroscopy. so emission lines just below the fermilevel are i am sensitive to the electrons that are onthe ligand. so i don't see my 3d orbitals in this vdtransition metal. so that's bad news if i want to study my3d levels.

but if i'm interested in to, in theligand, what kind of ligands i have, then it'sgood news. and as shown here if i, i, i look here forchromium, for example. so i have a chromium metal, that's a blackline here. if i now put different ligands on mychromium. oxygen, carbon, chlorine, nitrogen, i seethe, the ligand comes with a tag. i can, i can see from the, from the emission line here, i see what ligand ihave. that's fantastic, so i have an elementselective

probe that tells me what kind of ligand ihave. there's, to my knowledge, no othertechnique that can do this. access cannot do this, because the, theligands are too similar in atomic number, and it's a, it's a very nice, it'sa very nice technique. it's very, weak lines, weak line as youpointed out, so very difficult to do. but i think there are experiments plannedhere at the lcls where they will use those mission lines to study theligand environment in, in proteins. so this, this is coming up. and the beauty, another wonderful thingabout this, this approach,

is i can model those data using groundstate density theory calculations. i told you a little bit about the, the,the problems i have. when i, when i model inertial spectra, ihave to worry about the core-hole, i have to worry about modulated effects,electron-electron interactions. in this case, because the transitionsmainly arise from electrons that are in molecular orbiters that are, thelocalized on the ligands. i get very far with density functiontheory. and that's very nice.

so, what i do, i put the electronic structure of the molecule into my dftcode. i calculate the electron density. and you may notice you have kohn-shamorbitals, we have something coming out, orbitals comingout of your calculations. ground state calculations, so nothingfancy, anybody can do this. they are codes you can download from theinternet. and then you just found the matrixelement. one electron matrix elements, dipoleoperator between the 1s

shell of your, of your metal, iron ormanganese. and, any field molecular orbital. and, and this is what comes out to theblack dots here. so this is titanium silicalite. so it's titanium in the silicalite, in thesilicon oxide, okay? and so the black dots here areexperimental spectrum and the red line is the did you see the six here, arethe calculations. and you see you get a very nice agreement. main problem here is this intensity isoverestimated.

we don't really know why, we're strugglingto find out. still, the correspondence between thecalculations and the experimental data is very nice. when initial spectroscopy this is a, youalready very happy with this, yeah? as you can learn now, since thecalculations work quite nice. we can learn many things enormously about your about the electronic structuralsystem. and you can find out what ligands youhave. you can distinguish between an oxygen

legand and a hydrogen, hydro, hydroxidelegands. so it's a very powerful, it's a very powerful technique that normal peopleare using. and i'm sure in the future, alsoat the free electron laser. so i think five minutes, or something, just briefly, resonantinelastic x-ray scattering. i cannot say, it is a huge field. i cannot cover everything. i just want to give you a little flavorof.

so what do you do? i showed you this diagram already manytimes before. so, i start at the ground state and i hadtwo, let's say, discrete excitations here. i have a continuing excitation there. i have the lifetime for the, for theintermediate state and then state decays and at the final state herethat is still an excited state. it also has a certain lifetime. they will begin to cascade, decay,ultimately it will thermalize, to the groundstatement, okay?

so the, the difference between incidentand emitted energy is the energy transfer,right? so let's see energy that remains in the sample if you consider the final statethere. okay now again, we play a little game. we try now to translate this energydiagram there, that i show you before. we translate this now into, into aspectrum, yeah. when i measure rixs, i have two energiesthat i vary. i have the energy of the incoming light,that would be my incoming monochromator.

and there also is the energy of the finalstate. that would be my secondary spectrometer. you remember in the beginning i showed wehave an analyzer crystal you know to analyzethe x-rays coming out, yeah? so we have two energy scales, the incidentenergy, yeah, and the energy transfer. so now we try to understand, we try to translate this energy diagram there into arixs flame. so i start to give you the first point. i have an absorption here, so that meansthat at a certain

incident energy and this intermediatestate now decays into a finer state there. and i chose the finer state energy here. okay, now i have to see that if i.....i didn't want this anyway. [laugh] anyway, so if you're, now you sawit anyway. but the idea is, if i, if thisintermediate state now decays also to the second finalstate, right? so it's possible that one intermediatestates decays into two final states. so the question is, where would i see thistransition? so, i think you saw it already, it's at

the same incident energy, but a differentfinal state energy. it's clear? yeah, so this is how you translate yourenergy diagram into. usually you do it differently you measurethis and translate it [laugh] okay. but as a first step, i think it's easierthis way. now in the next step let's say we go to the next higher, inter, intermediatestate. and this intermediate state now it is caseto the state. where would this point be?

here? here? actually. ahh, one line is missing, i'msorry. that disappeared in the, in thepresentation. there should be a line here, i'm sorry, itwas supposed to be the high energy but for some reason itdisappeared off. yeah, so it's supposed to be a little highenergy transfer. so, it's a high incident and a high energytransfer, yeah?

and, and then we have also the continued excitations, and they interestingly appearas a diagonal streak. yeah, because you vary your incidentenergy continuously and the final state energy variescontinuously as well. so excitations into this band here, theywill appear as a diagonal streak in yourdisplay, okay? >> so, why is it not, how broad is this diagonal streak? >> if you have a frescence line, if you go into a continuum, it's infinitelybroad.

i actually brought along [crosstalk]>> the width? [crosstalk]. >> the maybe, maybe this answer yourquestion? >> i think this answers my question[laugh]. >> yeah, so, so what i, before i onlylooked at the, i neglected all lifetime broadenings, not consideringinstrumental broadenings. but now, i consider my lifetimebroadenings, right? now i see how my lifetime broadeningsextend in the rixs plane.

now, i, oh god, i made this too quickly,now i have to correct this. so this is the intermediate stage, so thisshould be gamma n and gamma f. so the intermediate state lifetime broadening extends here in the horizontaldirection. and the final state lifetime broadeningextends in this direction, yeah? so, this is this is a model system, right? this is, this is not mattered but it tellsyou a little bit how you can translate an energydiagram into into a rxes plane. that you, that you actually measure.

and it's really important that that, tosee how the lifetime broadenings. they shape your, the intensity in thestates. yes? >> does the diagonal engagement show somecorrelation between the manifolds there? >> a correlation between the two manifoldsthere. >> there is a diagonal allocation there? or. so the transitions between those twostates, they give rise to this diagonal there. >> the fact that they areparallel,

they are going to, do some correlationbetween them. can you vary this somehow, or? >> when a principle shows you, that it shows you that you replace one co-holdhere, with another co-hold. in principle, if it shows up diagonallylike this. it shows you that the co-hold does not really interact or it weakly interactswith a photoelectron. if it does interact, you get somenondiagonal effects. if it starts reacting it becomesnon-diagonal.

in principle, you can explain everythingwith a diagram like this. if the co-hold potentials are different inthe two states. you get so called non diagonal features,in your, in your rixs plane. and if there's a strong electron electroninteraction, as well. there are many effects that can give riseto non-diagonal effect. this diagonal streak, now, is, inprinciple, just a fluorescence line. that means you fully ionize your system. and default electron does not interactanymore with your, with the remaining ion. then you have the florescence line.

in this step the florescence line comingout. and and this give you then, then rise tothe diagonal streak. and then again the photo-electron in it'sfinal state is not interacting with theremaining ion. that kind of works, let me show you anexperimental spectrum now. so we are, this is serum dioxide, so wemeasure the obsorbtion spectrum and we have the emissionspectrum, i showed you this before. this is another experimental rixs plane ofserum dioxide, and here it is a little bitmagnified.

so, in this case we have a 2p3 half whole,in this case we have 3d whole. and the life time broadenings of the, ofthe 2p3 updates is horizontal here and the final state is,is vertical here. and what i can do if i take, if i take the integral of all spectral intensity iget a conventional absorption spectrum. if i take a diagonal cut here, i ca, i obtain something called highresolution absorption spectrum. it's not really an absorption spectrum, ithas to be careful. it just a diagonal cut through the rixsplane.

but what is important here, if you comparethe conventional absorption spectrum to thehigh resolution spectrum here. that you, the high resolution spectrum yousee many more spectral features. for example, you see the 4forbiters that we discussed before. we see the here in the high resolutionspectrum the features here. but you don't see this or barely see themin the conventional absorption spectrum. the reason, and that's a very important point, the reason for this sharpeningeffect. it's simply that i move, kind of, at 45

degrees relative to the lifetime broadening in my,in my system. in order to observe the sharpening effectin this, kind of, rixs spectrocity, we do not need interferenceand there's nothing fancy going on. it's simply the effect that my lifetimebroadenings, if i consider properly my lifetimebroadenings right away. is nothing fancy. in principle, you can also consider this,this here, if you, this, this, this is a cross here, youput here. and then, you consider your continuousexcitations as an

infinite number of discrete exaltation'sinfinitely close to each other. you just move, your cross here, you moveit through and ultimately, and then youobtain this band. here. and if you go through the maths, yourealize that the lifetime broadening of yourfluorescence line is the sum. it's the convolution of two, soit's the sum of the lifetime broadenings. so there's nothing fancy in the rixs process that gives rise to this sharpeningeffect.

it's rather banal. if you just look at the heisenberg equationand you can neglect all interference effects, it comesout correctly at the end. well, what, what is interesting in therixs process of course, if you [unknown]. if i reduce the, the, the energy transfer from let's say 1,000electronvolts that i showed you before. to let's say 1 electronvolt, and imentioned this before, i can observe in the rixs process, lowenergy excitations. these can be collective excitations,modern

excitations, dd excitations, chargedones for excitations. this is what many people do using thisrixs process, right? so they would use the energy transferhere. so very small numbers can be used to 50million ev, depending on what ind of excitations youwant to look at, yeah? and that's that's the idea, of the rixsspectroscopy. and just an example, we measure here, thisis chromium, and magnesium chromium oxide. this is the rixs plane here, and the energy transfer is the, of two, three,electron balls.

and we get two excitations here, that youcan then, compare to this spectroscopy. and, it shows you that, that you reach,the same final states in, in rixs or hotx-ray probe. as in uva spectroscopy, you cansee the same excitation's and with this i thank you foryour attention. [noise]. >> for more, please visit us atstanford.edu.