 Okay, let's talk a little bit more about spin-orbit interaction, then we'll try to sweep everything and come to databases. So you remember that we had that ion charge scaling that tells us that you increase charge and your energies kind of increase as well. Spin orbit actually depends on the nuclear charge. If you look at neutral atoms, just going from lower nuclear charge to higher nuclear charge, you will see increase in the spin orbit splitting. So what's here is again kind of rescaled structure for configuration NS and P for different ends. So this is 2S2P for neutral beryllium, 3S3P for neutral magnesium, and so on and so forth, ending here with neutral mercury with configuration 6S6P. So again, at low end we have pure LS coupling and so we cannot even resolve the triplet P0 triplet P1 triplet P2 here, but for neutral mercury we resolve them very nicely and if we apply that semi-theoretical and the formula that I mentioned at the beginning, you will see that it gives you values for spin orbit splitting of this size which more or less agrees with the measured values. Now here's the question. This is neutral mercury. Can we find any lines of neutral mercury around us in the nature? Yes? Yes. The answer is yes we can. All these lamps have neutral mercury and if you use this direction vision spectrometer and look you will see a very nice blue line at 435 nanometers. You can look and then give it, you don't want. Try to look up and you actually, there are two lamps at the back that have just continued. No, you have, okay let me show you what to do. So there is a split here on this side that you can make smaller and bigger and you look this side and you can change focus but pulling and pushing it and if you look upstairs you will see a very nice wonderful spectrum that comes from the fluorescent lamp and the line, the blue line all the way to the left if you look this side would be mercury one. Okay now if you take this same direct vision spectroscope outside and look not at the sun of course but just direction of the sky you will see a wonderful continuous spectrum with dark lines which are known to be the absorption lines in solar atmosphere and these lines are called Fraunhofer absorption lines discovered by Fraunhofer in German inside it's long on the go and this is postal stamp and one of the most famous lines in the spectrum is the doublet of two lines in neutral sodium. This is called D-doublet because simply Fraunhofer named them A, B, C, D and D fells here and these are two very close lines. They come from the 3S 3P transition in neutral sodium and 3P has very small spin orbit split and therefore two lines are very close 5890 angstrom 5896 angstrom so they're really close. Now again you go along isoelectronic sequence and this relative split in between 3P one half and 3P three halves increases dramatically so that at high nuclear on the order of 80 the difference between 3S and 3P one half is four times smaller than difference between 3S and 3P three halves and this is something that we measure in our experiments if we try to look at the same D-doublet in sodium like high Z ions for instance of tungsten other heavy elements you will immediately find that one D line is around eight nanometers and this is the line in the middle here here here and here the other D line sits all the way back to shorter wavelengths around approximately two nanometers the same factor of four that that we expect. Now in addition to LS and JJ Coughlin there are other types of Coughlin when neither electron electron nor spin orbit interactions are much stronger and one of this thing is called Jake K. Coughlin normally excited states in neutral noble cases are described by this type of coupling so you take one electron from the fully closed P6 shell and bring it up. Now it turns out that the hole in NP6 and of course we know that if you have a closed shell and take one electron out the remaining hole behaves like an electron has the same quantum numbers so this hole has very strong spin orbit interaction and therefore it characterized immediately by the total J value that for P electron can only be one half or three halves. Then to get your final total angular total angular momentum value you have to sum up this J value with the orbital momentum of this excited valence electron into the new number which is called K and then finally to take K and add the remaining unaccounted for angle momentum which is spin of this outermost electron S to get the total angle momentum and this type of coupling is very clearly seen in neutral noble cases and some other systems as well. Now a few words about super configurations we remember we started with a picture of average atom that becomes more and more detailed and on the way one of the options to build your collisional relative model upon is to use super configurations so we know what configurations are 2P5, 3S, 2P5, 3P and so on and so forth. Now in multi-electron ions especially in in dense plasma through you have to include many many excitations that are important for the total population kinetics the number of configurations not even speaking about number of level becomes extremely higher and in that case it may be beneficial to use this more general combined representation of super configurations which basically corresponds to the case when you instead of using detailed description for each of these configurations represent them by one super configuration where you simply say that you have two electrons with n equals one then seven electrons in n equals two without specifying how these electrons are distributed how many are in 2S how many are in 2P and one electron in n equals three so you replace this six with just one which makes your model much more easy to work with of course you lose some detail but there are statistical methods that were developed specifically to derive spectra from super configuration approach and by the way two of the codes that you will learn over this week fly check and critter are heavily based on super configuration approach now here is an example of why super configurations are not bad at all this example of calculation of photo absorption cross-section in in summands of gallium at relatively high temperature now the upper spectrum is determined in collision-vehicle model that is typically called detailed detailed level accounting which means that you build your model in terms of level and you see really you have thousands and thousands of lines here this is the result of the same type of calculation performed with super configuration simply it shifted so you can see the difference but it more or less goes over the detailed spectrum and of course the computational efforts doing super configuration calculations is I wouldn't say infinitely smaller than this one but literally orders of magnitude and I think you will show you this a few words about ionization potentials importance of ionization potentials is related to the fact that they are directly connected with ionization distributions in plasmas and therefore it's always good to know whether we can easily determine what the ionization potentials are and whether we do this correctly so in general ionization potentials is an ionization potential obviously it's calculated we take one electron and bring it high and high to high and high ends and we know already from scaling that all this should scale like z squared with z spectroscopic charge what you see here is the data for ionization potentials of nil-like ions with the ground state 2p6 and the red dotted dashed line is the result of the feed with the leading term z squared so you see it really nicely agrees now the blue points from our database in this range were determined from the experiment and you can do it for low charge ions then these numbers were determined from interpolation or extrapolation and the highest were determined from theory because basically there is no experimental data whatsoever to try to get but nonetheless you see everything changes very smoothly and nicely goes like z squared and you can use this information to calculate or determine ionization potential now unfortunately sometimes even theorists can forget some peculiarities for this type of calculation so this is a table from a paper that was published in 2004 big paper that contains ionization potentials for all ions of all atoms and unfortunately most of this data in that paper is incorrect simply because the authors didn't probably forgot about the fact that with higher z everything becomes more and more hydrogenic now let's let's look actually what what happened so if we look at this nice table this is an isochronic sequence this is range of nuclear charges and this is the configuration that was used to describe this particular ion all these results are incorrect and why they are incorrect we can easily see on the example of xenon like isochronic sequence so the neutral xenon is a noble gas very stable atom that has ion structure which is 4010 5s squared 5p6 closed shell d closed shell 5s closed shell 5p and this is what the authors use for all ions of the isochronic sequence but we remember that you go to higher z 4f may become more preferential the 5 and this is what happens for z this is exactly what happened here and when you take your ion charge to higher and higher values xenon like ion becomes more and more 4010 4f8 instead of 5s 2 5p6 which simply means that unfortunately all those results were incorrect once again ionization potential scale z squared but don't forget to think what the actual ground state can be now in a plasma ionization potential is actually a function of plasma condition high line states excited states are no longer bound because of interaction with the atoms ions and electrons in plasmas now let's take a simple example let's take neutral hydrogen if neutral hydrogen atom sits here where will be electron with n 300 000 well we can calculate the orbit radius goes approximately as boron radius times n squared so take n 300 000 make it square and you will see that this electron will see it somewhere there around four and a half meters and of course you understand that even in the in the air there are so many particles in between that electrons at four and a half meters knows nothing about the nucleus even more so in plasma where you have charged particles flying around you take your electron higher and higher further and further away from your nucleus it gets screened by particles in plasma and even potential for the particles sitting next to this particular nucleus changes as well so if we look at isolated atom again this is just one over x potential for neutral hydrogen we have lower state at one readberg n equals two three four so on so forth and then continuum and if we put another hydrogen atom nearby let's say we put another one atom here at at three another one minus three certainly the total potential that electron sitting here sees is not only potential related to the to its original nucleus it will also feel the other nucleus nearby and therefore potential becomes like this red curve which means that if we had these states from n three and four bound in the first case and this is the potential now these these states sit above the top of the potential which means they're now in continuum and then is an effective ionization potential lord to approximately this way and this is called ionization potential depression there are many different formulas how you can determine and it seems that right now in dense plasma physics we do have problem because the results of advanced experiments advanced calculations show some significant mismatch of course even these states here are not completely bound because if the potential bearer is not too wide you may easily have quantum mechanical tunnel and that brings electron from here to here so there is a lot happening in plasmas okay we have approximately 25 minutes so i will try you i will try to show you a few features of the atomic spectra database that we develop at nist you can access it at this address physics that means that gov slash ast extensive list of atomic atomic databases is available at the plasma gate site at weitzman institute there are actually quite a few other collections of basic atomic spectroscopic data vault which is vienna atomic line database primarily for spectroscopic purposes now sits primarily in obsola sweden with mirror in moscow russia there is a spectra w three in russia a chinese atomic and molecular database kianti which is combination of basic atomic data and collision related modeling model for astrophysics corutz databases in the united states ia has some data on atomic structure and so on so forth but probably it's fair to say that on the nist has evaluated and recommended data on atomic structure so let me let me show you a few features of of the database okay so this is the you can you can access from the address that i gave you on the prius page it will redirect you over here right now we have already version five it provides interface to date on spectral lines and energy levels as well as ground states and ionization energies now let's start with general overview of what we actually have so here's link that's called list of spectra no thank you so let's see what we have for energy levels okay now of course this periodic table looks a little bit different from what you have not in terms of elements but in colors and different colors show you how many levels are actually available for one or another element or ion so looking at the elements you see okay this color show that there is between 2000 and 5000 angel levels and the iron group elements are represented the best than molybdenum tungsten and molybdenum tungsten are very much used in magnetic fusion that's why they're so well studied and iron group elements are used everywhere particularly in astrophysics as well neon so again different colors mean different number of levels what you see on the right is the same information but showing you how much is available for each particular ion so there are two axes this axis is the nuclear charge so we go from hydrogen which is z1 to darmstadtium which is z 110 and this axis is ion charge and again different colors tell you how much you have for each ion that corresponds to a small square here let me just make it a little bit bigger okay and a little more okay so if you put your mouse over any square here it will tell you so this is for instance molybdenum 23 22 times ionize has only three levels you move to something like iron 2 it has thousand levels and from here you can directly go to the data for particular ion so if I click somewhere here it brings me to chromium 9 with 49 levels it shows you which is electronic sequence it belongs to in this case itself and then this is the list of levels that we have in the database in some cases we do not have as complete spectroscopic information as we'd like to have for instance we know that because anatomic states characterized by j and parity and all other things are not exact in principle the state can be linear combination of different contributions so for instance a state in helium like ion 1 s2p with j equals 1 has contribution for both triplets and singlet which means we would like certainly to have information about the weight and coefficients from this basis function we don't have them for this particular case but in general in many cases we do so for instance if we go to neutral iron okay it's a long list you see in some cases there is information about contribution of different components so for instance configuration 3d7 for s with term for f for the 3d7 electrons these levels was j equals 4 3 and 2 have small contribution with different 3f term also there is information on the one there factor that is used to calculate split in magnetic field of course in many cases we have information about the source of data and this is very important as well for levels of course you can choose different units again center inverse centimeters electron walls readberg if you want to look just at some part of levels in the ion you can use additional criteria so for instance iron one as you saw has 847 levels in the database if you want to look at one particular configuration you click this button then it gives you the list of available configuration and terms you choose whatever you want and then this is what you get only 12 levels for this particular case okay now here you see examples where you have really really strong interaction between different terms in this case so for instance 3d1 level for this configuration has only 45 percent contribution from real 3d but then it has 35 percent coming from single p and so on so forth and this information is certainly crucial when you try to understand what the radiative probabilities can be now going to the lines again here you can enter different different requests for one ion or a group of ion or for instance all are all possible spectrum within a predefined spectral range so in addition you can choose what kind of data you want to get for instance everything that we have or only data where you have transition probabilities for those spectral lines or only those transitions where we do know upper and lower energy level classifications only those transitions that were actually observed in the experiment we also have some tools that allow you to do diagnostics so for instance let's look at i think it would be something like neon 7 let's see yeah so this example of how this database can be directly used for diagnostics of low density plasma because these calculated results that are therefore diagnostics were calculated with kianti code which is astrophysical code so in this case well let's let's go step one step back so total we have um 661 lines for uh six times ionized neon which is very unlike and few of those lines can be used for diagnostic this calculation was died by uh uh john silik's uh colic or ory feldman from the naval research lab so let's look again at what we have for uh diagnostic five lines in the database have information about how they can be used for density and or temperature diagnostic let's take a look at density here's line at 55 99 47 nanometers if we click on density it shows us how ratio of intensities of this line with another line at 56 2992 depends on electron density and again these calculations were performed for low density cases therefore it doesn't go above 10 to the 16 this axis is log of electron density in centimeter minus 3 and obviously you can use this ratio only in the region where the ratio changes the most so it's it would be good to do analysis between let's say 10 and 10 to the 12 and 10 to the 10th in in electron density similar for temperature but a different line here's ratio of 9733 to 89 52 you see the ratio of intensity of this line changes as a function of electron temperature again this is log in kelvin in this case and if the ratio is one tenths you're here and and so on and so forth but from the beginning this databases where this database was developed as the source of data on uh evaluated and recommended uh energy levels and and spectral lines and you can again choose many many different options to find whatever you need you can get output in vacuum or in standard output which has vacuum below 2000 2000 angstrom 200 nanometers air output with account of air refraction index between 200 2000 and vacuum about above 2000 nanometers you can ask for oscillator strength output or log gf you can use you can get only allowed or only forbidden in addition to general output that contains both allowed and forbidden lines and one of the options that you already saw in my presentation is the grotrain diagram so let's take a look at the grotrain diagram that simply shows everything that we would have for neon seven and all possible transition now this tool uses java interface and therefore you need java install on your computer so what you see here is the whole energy structure for the uh for the seventh for for neon seven uh neon six plus again this is the zero energy corresponding to ground state this is the ionization potential and there may be more than one ionization potential depending on uh which electron you bring up and you see there are states above ionization potential and those are authorized on states that uh chef and fritch will be mentioning tomorrow now the axis here corresponds to different series of levels let me just zoom in so that we will see what happens in here okay so if we zoom in yeah the whole the whole picture becomes better seen now what you have here is 2s square 2s 3s 2s 4s 2s 5s and so on this series corresponds to 2s and p so these levels are 2s 2p 3p and so on so forth each level comes from the database and each connected line corresponds to the spectral line that is in the database if you click on the line let's say this one it highlights in red and you get information about the lower and upper level of the transition so this particular line connects ground state to a squared and here's the quantum numbers 1s zero with energy zero with a level 2p 4d term 1p and j of course equals one which is uh located at this energy here you can get information about the line itself here's the wavelengths ritz wavelengths which is the difference of of energies 6.8 nanometers the uh Einstein transition probability value 2.4 10 to the 9 and uh accuracy of these transition probabilities this is what we also try to add to the database we want not only uh the numbers we want to understand how accurate those numbers are because this is where physics is physics is really in uncertainty is not not in the real numbers and you can continue this analysis for all other uh transitions if you just push the space bar you see everything jumps to the next line and so on and so forth you can filter out weak or strong transitions so for instance right now we have on this float all transitions with a values between zero and here's the highest in the right bottom corner shows that the highest value of a transition probability is 3.4 10 to the 11th now let's select only the strongest transitions everything above like say 10 to the 10th so in the minimum a we put one 10 to the 10th submit and these are only the lines with a values 10 to the 10th or higher of course they correspond to the largest energy differences there's a lot more that you can do with the broad term diagrams with the output you can even build sa-ha LP spectra but we will talk about this uh on on uh Wednesday now let me show you really just for a few minutes uh how you can run uh Cowan's atomic structure code from the Los Alamos uh web interface oh excuse me that's uh okay i bookmarked it somewhere just a second okay so this is the interface to Los Alamos atomic physics code we'll write down the link basically you can not only use it to calculate atomic structure but also to do calculations for different types of cross sections ionization or excitation but if we want to restrict ourselves just to uh atomic structure uh let's start with the okay calculation here it doesn't matter which what we choose for collisions because right now we want to look only at atomic structure so we start the calculations and we have to pick up some ion by default they have carbon two plus okay let's do something different let's do the same neon seven that we had which would be neon six plus and we go to configuration selection so it immediately offers you the ground state which is two s squared and the first excited to s2p well we can take only these two but let's make it a little bit more interesting let's take also other configurations that may that have relatively low uh energy level so we'll have 2p2 and let's take one of the electrons from the uh ground state 2s shell and bring it to n equals 3 so let's add uh 2s1 3s1 2s1 excuse me 2s1 3p1 and 2s1 3d1 okay so we have uh levels within n equals 2 and n equals 3 for completeness we can also add situation when we have one electron n equals 2 and one electron n equals 3 but let's take the low electron not 2s but 2p so we will add 2p1 3s1 2p1 3p1 and 2p1 3d1 okay so we have everything for n equals 2 n equals 3 click and here we have the result of online calculation 46 energy levels were calculated in the output we certainly have the energies right here in electron volts and this is the level notation of course the ground state 2s squared has zero energies and then we go higher and higher let's just quickly compare this calculation with what we have in the atomic spectra database so we take also uh neon seven uh let's take electron volts so we have the same values uh that's it let's let's see what we what we're having okay so the first group of levels in asd for 2s2p is of course the triplet uh we know that triplets are normally uh sitting lower than singlets this is one of the indication of the so-called punz rule in atomic physics and the energies are approximately 13.8 8 and 14 let's see what we get with accounts code it's 13.7 13.8 13.9 so certainly you would not expect to get spectroscopic accuracy from such simple calculations that runs for fraction of a second but at least it gives you reasonable idea where your levels are and how they are arranged but uh you can hardly get the same uh quality for neutrals you go to more highly charged ions it's really the interaction of electrons with the nucleus that becomes stronger you remember the z squared term that it grows faster than other z and other terms but for neutrals uh you may probably not get such good accuracy let's let's do the same calculation but not for uh neon but rather for for neutral beryllium so we do beryllium ion charge zero we go to configuration selection we add all those configurations that we had for uh beryllium like neon okay the same 46 levels because we have the same number of electrons that uh and we cannot get any difference now let's look at what we have for beryllium one okay so for neutral beryllium the lowest energies are 27 for uh for the lowest 2s to p triplet p 2.7 electron volts let's see what we get here well 2.6 something not too bad but not as good as for not as good as for uh uh uh neon if we look at this group of levels this is 2p squared triplet p with 3p zero one and two all sit at 7.3 let's see what we get here 2p squared triplet p 7.4 so 7.3 7.4 the difference is not that that bad but uh it's it's fair to say that for instance count's code would would better work for not so neutral ions but still not going too far in ion charge this is really where relativistic methods and codes uh are becoming uh much more accurate and uh certainly we will hear tomorrow a lot about uh about this uh codes and methods in particular regarding uh radiation and authorization um okay uh finally uh a few words about the database for ionization energies again ionization energies are important because uh really the ionization distribution of uh charge states and plasmas uh certainly depend on on these energies you can get all possible ionization potentials for all ions up to nuclear charge hundreds and tens so for instance if you want to look at what's available for iron this is list of all ionization energies for all ions of iron from neutral to hydrogen like now some of them were determined experimentally and you see these numbers are here those that have uh uh red brackets or parenthesis were either uh extrapolated or theoretically calculated again it's it's really difficult to uh determine ionization potentials for uh highly charged ions and of course literature sources are available for each uh and uh every number here if you want to look what's available not for iron but for all iron like ions you just I think do iron like and then you get everything with the same number of electron for neutral ion synchronized cobalt double nice nickel and so on and so forth so this is kind of databases that uh many atomic spectroscopists use uh regularly but also many plasmas spectroscopy those who work with atomic spectra some plasmas because they really contain a lot of information uh let me stop here and I think we have coffee break okay thank you