Rudolf Mößbauer (1968) - Resonance Spectroscopy of Gamma Rays and its Application on Problems of Solid State Physics (German Presentation)

Ladies and gentlemen, I feel I am here in a somewhat difficult position, since I am a little too young and don’t really know where I belong, whether I still belong to the group of the students or whether I already belong to the establishment. So I feel a little bit uncertain. I am also a bit uncertain about my lecture today, partly because my youth means I am not yet in a position to recount anything to you about a long history, but also because we are working with modern methods after all. So I will try to report a bit from our field of work, while, as I said, wishing to leave history in the background this time. I would like to talk a bit today about recoilless nuclear resonance absorption of gamma radiation, and in particular to stress the applications of this method. I cannot of course go into the details of what has become an enormously wide field. The method has in recent years shown its fertility in the area of solid state physics in the broadest sense of the term, or I should rather say in solid state research. So this covers a range from chemistry, to real solid state physics and into biology and medicine. The great significance that the method of recoilless nuclear absorption has acquired in experimental areas comes largely from the fact that this method has made it possible to perform high resolution resonance spectroscopy with gamma rays. Previously that was not possible due to the fact that gamma rays exhibit an extraordinarily great line width. The gamma lines are always enormously widened by the Doppler Effect. With the help of the method of recoilless nuclear absorption – the first slide please – it has now become possible to overcome this Doppler widening of the gamma lines at a stroke with the result that we now have lines available whose frequency is up to 10 to the power of 10 more sharply defined than is normally the case with gamma rays. I would like as an introduction to recapitulate very briefly what these gamma lines look like. In this case it is a matter of this dotted, this dotted emission spectrum – a gamma emission spectrum which is emitted in the transition from an excited to the ground state of a nucleus But if we move to special conditions, and use particularly low-energy gamma rays, say less than 150 keV, and if we also build the nuclei which emit this radiation into crystals, then this simple structure of this spectrum gets much more complicated; here we have this solid line, which has a complicated structure, where the point that interests us today is just that this structure also contains a part which is expressed here. A part, which occurs exactly at the resonance energy position, that is this transition energy here, and a part which possesses a line width which is no longer characterized by the Doppler width, which would be about this width here, but which is now characterized by the natural line width of this excited nuclear state. I already mentioned that this means that these natural lines are in many cases up to 10 to the power of 10 times narrower than is the case with Doppler lines. Now, this remainder which you can still see here, in this spectrum, I’d like to refer to that today as the background, that is the fraction of gamma quanta which are emitted in the crystal and which are simultaneously accompanied by internal changes in the crystal, by internal changes in energy. That could for example be changes in the internal vibration state of the crystal and so on and so forth. But none of that need interest us today. All I want to say it that this method, this embedding of the nuclei in crystals, provides the possibility of obtaining these sharp lines here, among others. And that, both in the emission spectrum and the absorption spectrum. And here too, this extraordinarily sharp peak appears. So that is the important result of the method, whose details I won’t go into, and in the next slide I would like to show you how one can actually measure these rays with their extremely sharply defined frequency, how one can really observe the lines here experimentally. This is also fortunately possible in a very simple way, which is to take the radioactive source that emits gammas in the transition from the excited state to the ground state, and use an absorber, a resonance absorber, which consists of nuclei that are identical with those which decay in the source. When this radiation, which comes out of here, penetrates this absorber, as we have just seen in the previous slide, that the emission and absorption frequencies are exactly the same, this means that the nuclei here and there are exactly in resonance. This means that this resonance absorber will absorb this radiation very strongly and very little radiation will penetrate further. This detector will sense very little radiation. But that changes immediately if we destroy the perfect resonance between source and absorber here. And destroy it by using the Doppler Effect, in reverse so to speak, by moving the nuclei of the source relative to the absorber. So here you can see a little carriage, we simply move the source to and fro in relation to the absorber, we raise or lower the frequency of the radiation emitted here by the Doppler Effect. The resonance is destroyed here, which means that the radiation, it is no longer absorbed, now it can pass through the absorber; we observe an increase in intensity at the detector which is greater the higher the speed is. This leads to the observation of curves of the kind that you can see here, where the speed is always shown in this direction here, you can see it is a few cm per second in this example. And so here either the absorption or the transmission or something of the kind is recorded. You see that when the relative speed is null you get perfect resonance, minimal transmission intensity, a minimum of the intensity. With increasing relative speed – positive or negative – here increasing destruction of the resonance, reduction of absorption and corresponding increase of the transmission intensity, as you can see here for positive and negative speeds. Now these spectra have the great advantage that they are extremely easy to interpret. Unlike in many areas of resonance spectroscopy where one has to consider what mechanisms underlie the production of this particular spectrum, here one has, so to say, a direct visible image of what is happening, so one can interpret this spectrum with very little difficulty. So now what you can see here is such a line, one can for example immediately read out how wide the line is, which is expressed here in units of speed, but if you take V divided by 10 times the energy, then you have the units of energy here and you can immediately confirm with this, that here we are dealing with lines with the natural line width. That these lines are so enormously sharp, you can see immediately from the fact that it is enough to use speeds of a few cm per second to make measurable changes to the energy or frequency of quanta which move at the speed of light. In actual fact we are working today, I will show you an example at the end, we are working with speeds in the range of thousandths of a mm per second. So the resolution here is not yet so good at all, today we can do that a lot better in the case of other transitions. Now I would like to show you the next slide with another example of how such an apparatus looks in practice. You can see that this is a relatively simple system here. We have here the heart of the apparatus, a low temperature cryostat, many of our experiments take place at very low temperatures, a low temperature cryostat, here at the point of the cryostat sits the heart of the apparatus, this brass tube which you can see here. It contains a drive mechanism to provide us with these relative speeds between source and absorber. In principle what we have here is two coupled loudspeakers which vibrate to and fro, and we can then decompose the vibrations, we can analyse them, we can map each individual element to a speed interval and can then very easily register that with some rather clever electronics. Now, this structure oscillates to and fro, here in its heart it carries a long pipe at the lower end of which, about here, the radioactive source is located. This source, and that is the reason, is cooled in this cryostat, generally with liquid helium. In the direct vicinity of this source the resonance absorber is also located, and it uses the opportunity to be cooled as well, and here below is situated a detector, we generally use solid state detectors these days, which are equally in need of cooling, and so it is supplied here from below with a nitrogen container. So this is approximately how the apparatus looks. I mean the rest is just the recording electronics and the vacuum equipment and the low temperature equipment which we need for operation. But as I said, the heart of the apparatus is this drive system, at the lower end of which, here, the movable source is located. Now I would like to show you the next slide with an overview of that element, and this overview is shown on the background of the periodic system here. An overview of those elements with which we have succeeded up to now in observing the phenomenon of recoilless nuclear resonance absorption. You can see that this goes more or less right across the periodic table, though with the exception in particular of the very light nuclei. With the very light nuclei it has not yet worked and will not work even in the medium term, because the case here is that nuclear transitions possess extraordinarily higher energies, and with these higher energies it is not possible to obtain a reasonable effective cross-section for nuclear resonance absorption. Also the light masses of these nuclei, that is also unfavourable in this respect. You can see though that, apart from these light nuclei, there is a whole range of elements right across the periodic table. Actually in all interesting groups, where interesting means especially in the group of transition metals, the 3D, 4D, 5D series, also here below the 4F electrons in the rare earths are very well represented. Just recently we have found resonance in the case of Neodymium, which is not yet recorded here. I would also like to stress that the actual figure for gamma transitions is about a factor of 2 higher than what you see here, since for many of these elements we have more than one isotope with which we can carry out experiments, so that the number already increases for this reason alone. And then it is also the case that for some isotopes we have more than one gamma transition which we can use for our experiments. Now, after this brief introduction, I would like to sketch the essentials of the main application area which is based on the method of resonance absorption today. And here it mainly concerns measurements of hyperfine structure splitting which, I would say, make up 90% of all experiments which are carried out in this area. May I ask for the next slide, where I give you an overview of the kind of hyperfine structure that we can study today with this method. It is essentially a matter of three groups of such hyperfine structures. The electric monopole interaction, the magnetic dipole interaction, the electric quadrupole interaction. The first group here gives rise to what today is called isomer shift, which is essentially a matter of the electrostatic interaction between atomic nuclei and the electron shells. Of course that is primarily the normal Coulomb interaction where we can assume as a first approximation that the atom, the atomic charge can be regarded as a point. But if we examine it a little more closely, then we have to take into account the finite dimensions of the nuclei, the finite dimensions of the nuclear charge - and finite dimensions of the nuclear charge means that particular electrons, in particular the S electrons, can penetrate the nucleus which produces a small modification of the electrostatic interaction as compared with the point model. It is this small modification, this small correction to the Coulomb interaction which gives rise to what is known as Isomer Shift of spectral lines, which leads to a slight shift in the energy of these gamma transitions, one of which is shown here. Here, slight means something like one part in 10^12, to give you an idea. So these are extraordinarily slight shifts which occur there, but as I said, the extreme sharpness of the frequency of these spectral lines still allows these incredibly small shifts to be measured. This has the effect that when we have such an isomer shift between a source and an absorber, between the nuclei in a source and the nuclei in an absorber, that the resonance, the maximum of the resonance or the minimum of the intensity no longer occurs here with the relative velocity of null, but is somewhat shifted. Here you can see, perhaps even from your seats, that a slight shift is present here, that this line is shifted a little towards lower speeds. This shift is the Isomer Shift and what we can learn from it is indicated here above. A factor of nuclear physics has an influence, that is essentially the radius of the nuclei in the excited state and in the ground state, or more precisely the difference of these two, and a solid state physics factor is also relevant, namely the density of the electrons at the nucleus. Of course it is only the product of these two quantities which we measure here. Now the second interaction which is of significance, that is the magnetic dipole interaction. The interaction of the dipole moments of the nuclei µ with an external field h. Now, an external field means the field which affects the nuclei and what it usually is, is not a matter of a field which we use in the laboratory, but a field which exists anyway in magnetic substances at the location of the nuclei, so something that exists in the crystal in any case. This interaction does not just give rise to a shift, but to a splitting of the individual nuclear levels, such a splitting is indicated here and here, for a practical example, that would be a nuclear spin of ½ here, that would be a nuclear spin of 3/2 here, then we get a split of this kind, and this leads to our observing not just a single spectral line, but whole series of such spectral lines. An example is provided here, that is the well-known Iron 57 resonance, with which the majority of the experiments are performed, even today. Now, the reason why we can directly resolve these spectral lines nowadays, that is of course based on recoilless nuclear resonance absorption, that was not possible before. And impossible for the reason that these splits here are drawn on a completely false scale. They are in fact extremely small, these splits, compared with the total energy of these transitions. And they are in fact so small that when we work with normal Doppler-widened gamma lines, that these splits disappear completely in the line width. Here it is only possible to resolve these individual lines with the method of recoilless nuclear resonance absorption, because namely the width of these individual lines, which is actually the natural line width, this width is generally smaller than these splits and so these splits are now visible in the spectrum. Now, the third group of interactions which we can observe today, that is the electric quadrupole interaction, the interaction between the quadrupole moments of the nuclei Q in these states and electric field gradients involved which influence these nuclei in the crystal, and especially if we don’t have cubic symmetry. So those are the three sorts of interaction which we can observe and I would like to point out that each of these interactions has a nuclear physics factor, to be specific here – the mean nuclear radii, here – the magnetic moments of the nuclei, here – the quadrupole moments of the nuclei; and a solid state physics factor, that is the electron density at the nucleus, the electric field gradients around the nucleus. So we can determine these quantities directly from such measurements, measurements of these products here, here and there, that is these splits which can be directly read from these spectra very nicely, we can determine these measurements and so learn something about nuclear physics and learn something about solid state physics. But it is quite clear that the solid state physics applications are extraordinarily richer than those in nuclear physics. And for the reason that we only have a limited number of nuclear levels, as I showed or indicated earlier, with the help of which we can carry out such investigations. When we know the nuclear radii, the magnetic moments and the quadrupole moments of these nuclear states, then we are just about finished with the nuclear physics. But that is not quite correct, what I am saying here, there is still a whole range of sophisticated experiments which we can carry out. Nevertheless, there is only a limited number of nuclear physical properties which we can study with this method, at least at the moment. That does not apply to solid state physics. I mean that in solid state physics it is the case that these few nuclei which we have, these perhaps 50 different transitions which we can use for measurements, these few nuclei, they can be brought into an almost limitless multiplicity of different chemical environments. So we could, for instance, diffuse them into metals, diffuse them into alloys, we can produce the most varied chemical compounds. We, that is the chemists who we go to. And that means that we can study an almost unlimited multiplicity of different environments, and also S-electron densities, inner fields of this or that sort on a large scale. And I would like to show you a few examples of this quite briefly, about them, a few examples which illustrate a bit, what one can really learn from such measurements. Firstly, in connection with the isomer shift; it is clear that here one, if one knows this factor somewhat, and that still remains quite an achievement these days, because the theoreticians are not in a position, in most cases, to make reasonably sensible and consistent statements about these quantities which are very hard to calculate. But now we also have meson atom measurements, which could contribute something to an improvement in the near future. So far they have not done so, because the meson people naturally first measure the nuclei which are easy, and they are mostly the ones which are of no interest to us, but that may improve in future. But in any case, when one obtains these values, and we have fairly sophisticated methods for the independent experimental confirmation of these values, then it is this value here, the density of electrons at the nucleus, which we can deduce primarily from such measurements. This is a value which has great importance, especially for chemistry. Because these densities of S-electrons which we are measuring here, they are strictly speaking differences in S-electron densities for the various chemical compounds which we use in source and absorber. And these differences, they are naturally, since they are only differences, not the inner S-electrons, but especially those S-electrons which are situated in the outer shells of the atoms, that is the valence electrons, and so we learn something directly about the chemical valence from such measurements. Now, there is an extraordinarily rich field of activity, a lot has already happened in this area, but I would still like to assert that this procedure is actually right at the beginning, this application of isomer shift measurements, in order to learn something about the chemical valences. Actually, we don’t only learn about chemical valences from measurements of these isomer shifts which tell us about S-electron densities, we also learn something about chemical valences from these quadrupole splits that we often observe, and for this reason, that these electric field gradients don't affect the S-electrons but primarily, if they are present, the P-electrons, so that we learn something here about the S-electrons, and here something about the P-electrons. And the nice thing with this is especially that these measurements don’t require any difficult interpretation, it is awfully trivial, in my opinion, to evaluate these shifts here or these splits there. Here it is not so easy to make mistakes, unlike other resonance methods such as electro-paramagnetic resonance or nuclear magnetic resonance, the interpretation of which is very often quite difficult, because there are many cases where one does not know how the signals are produced. The advantage of these gamma resonance methods arise from the fact that the frequency of the gamma rays used are so extraordinarily high that they are enormously higher than all other frequencies in the atom, so that we are not disturbed at all by the presence of these other frequencies. But that is not the case. With many other resonance procedures, slight shifts of the resonance frequencies can occur in uncontrollable ways and that then makes the interpretation of these other experiments extraordinarily difficult. We have in actual fact recently found, in particular with the especially interesting intermetallic compounds and alloys, a whole range of discrepancies between our measurements and other resonance measurements, which have essentially shown that this interpretation of other resonance measurements is much more difficult after all, than we used to believe. That is of course also very fruitful, because one can now consider what might be happening with the signals and with the frequencies in other resonance experiments. It is not always easy to interpret these gamma resonance spectra here. Here, too, almost anything is possible. But on average one can get a far better grasp on them because of the high frequency of the gamma rays employed. Now, I would like to show you a few examples of isomer shift measurements. And I don’t intend to show you the kind of measurements which used to be made at one time, where one chemical compound was measured against another chemical compound. There, of course, you generally find an isomer shift, but then you have, so to speak, one piece of information yet you are describing a system here which is generally characterized by many, many parameters. What I mean is, the chemical compound is not usually so simple to characterize that we use only one parameter, but we actually measure only one quantity. The reason, of course, is that when we change from one chemical compound to another, that we influence many electrons in the many shells involved in a more or less uncontrollable manner. So the target, which we are striving for more and more, and we are doing that primarily in Munich, that we are trying to get away from this discrete step, to change from one compound to another compound, that we are trying rather to modify some parameter continuously. And we can do that, for example, by making measurements with one and the same compound and now applying high pressure to this compound. Then we can study the isomer shift for instance as a function of pressure, and hope that the wave functions of the electrons involved change in a continuous manner. We might of course have natural phase changes now and then, but in general that may be a step which could allow a more direct theoretical interpretation. And with the next slide I would like to show you briefly the construction of our high pressure apparatus. This is an apparatus with which we can apply pressures up to about 100,000 atmospheres. And the heart of the apparatus is here. Here is situated the resonance absorber or the source, in most cases it is a source which we subject to pressure, it is basically pressed together by two pistons here, where the trick to the whole thing is that one must ensure that the source does not take this as an opportunity to fly out sideways. The difficulty is that the pressures are very high and that we cannot extend the pressure cells so that our samples are enclosed on all sides in a sensible way. Because we still have to get our relatively soft gamma radiation in and out. The reason why we generally worked with sources before was that we then only had to get them out and not both in and out. That is experimentally somewhat simpler, but we have learned in the meantime to perform through-radiation. At the moment we are mainly involved with running these apparatuses at low temperatures, which is a very complicated technology that takes time to learn, but we have made quite a lot of progress in this area recently. Here you can see the heart of this apparatus drawn on a larger scale. So it consists essentially of such a plate which is generally made from some kind of resin or some boron compound. In the middle, a section which is relatively thin, the whole plate is only 0.7mm thick. Here we place the source, here near the edge in the form of a thin sheet, in this case we are performing measurements on metallic tin, and the rest is then filled up with a resin. That has the advantage, if we then compress this plate between the two pistons here, which are shown here and here, then the material flows and we then have a more or less hydrostatic pressure and not a uniaxial pressure, which then becomes apparent in this way at the location of the nuclei and leads, so to say, to the S-electrons being pressed into the nucleus or else the non-S-electrons being pressed into the nucleus. Which one happens to be dominant is determined by the sign in front of our isomer shift. If it is the S-electrons that are mainly pressed in, then the isomer shift will have a particular sign. If we press in the non-S-electrons, then we are shielding the S-electrons, and then the isomer shift has the opposite sign. I would like to show you an example of such a measurement in the next slide. Just to show the magnitude of such shifts, which is really slight you would say, here we have one curve for the pressure, for the application of no external pressure, and the second curve for a pressure of around 100,000 atmospheres. The substance is a tin compound, which is unimportant at the moment. You can see that the application of this pressure causes a significant shift of these lines, the real picture is somewhat better in that it is now trivially easy for us today to measure a shift of about a hundredth to a thousandth of the line width, so that this shift which you can see here represents an enormously large and very easily measurable shift. In the next slide I would like to show you a few of the curves which we recorded in the case of tin compounds. Here you can see essentially the isomer shift and to the side the pressure. These are pressures which once again range up to around 100,000 atmospheres. You can see up here, for example, beta tin, metallic tin, then tin sulphate and some, an alloy here. The interesting case here is, for example, tin-magnesium-II, I would like, perhaps, to say very briefly how this curve arose, without going into detail. What makes it so interesting is that is actually the first example for a nonlinear dependence of the isomer shift on pressure. These curves up here, you see, you can understand them simply by saying yes, here the S-electron densities are either raised or lowered and the whole thing is simply proportional to the volume. Then you get this kind of linear dependency. Here, however, it is obviously significantly more complicated and what happens here in fact, and that has been supported by many further experiments, is, that this compound here below is a semiconductor when no external pressure is applied and that this compound then changes to the metallic state here, which is the interpretation of this fall in the curve, whereas this renewed increase which you can see up here has the same cause which led to the rise in this curve which you can see above. So that is an example here for such a continuous measurement of the isomer shift, that is for the principle, that one now takes care to vary one or other of the parameters continuously in order to arrive at a better interpretation of the isomer shift. Apart from these measurements of the isomer shift, of particular interest at the moment is the measurement of magnetic hyperfine interactions. The quadrupole interactions, I don’t want to pay special attention to them, they mainly occur as an incidental side effect, when we are dealing with non-cubic crystals. We have, incidentally, recently found quadrupole splitting in a whole range of cubic crystals. They shouldn’t really be there, since the electric field gradient disappears when we have a cubically symmetrical environment, but we can still have a crystallographic cubically symmetrical environment and beneath it a magnetic non-cubic symmetry. When we have magnetically aligned states, we have now directly obtained quadrupole splitting in many cases. But the really interesting area at the moment is, besides these isomer shift measurements, the application of the method to the study of magnetic problems. These are in particular the intermetallic compounds and the alloys which are at the focus of interest currently especially in connection with the Kondo effect there is tremendous interest in dilute magnetic substances, where one adds particular transition elements to particular metallic matrices as dilute substances, and then asks the question whether these impurities have a magnetic moment or not and how they behave with temperature and so on and so forth. I would just like to show you here a single example in the next slide of such measurements. This also illustrates the marginal problems a little. That is a measurement carried out on the transition in R466, that is an 80 keV gamma transition with a spin sequence of 02, so that the ground state with spin 0 experiences no splitting, the excited condition with spin 2 shows a total of 2 x 2 + 1 = 5 sublevels, so that we expect 5 gamma lines which you can actually see up here for this transition. That is a measurement at 30°. And if we raise the temperature very slightly in this case, then you can see the occurrence of a fairly dramatic change in this spectrum. And that over a very small temperature range. Here we are at about 35° Kelvin. Now, one might at first suspect, as we always do, that we are dealing here with the contribution of electron relaxation effects. Perhaps you know that in the other resonance methods, electro-paramagnetic resonance as well as nuclear magnetic resonance, such relaxation effects play a really extraordinarily great role. That was not the case in the early years of gamma resonance. But that is now also the case. So now we have many examples where electronic relaxation effects directly influence the gamma lines. That essentially means the following: If you have an electron spin which points upwards, then it produces some kind of magnetic field which generally goes downwards. If this electron spin then turns around for some reason or other, which we call a relaxation, then the magnetic field naturally turns around as well. Now, the nucleus will therefore see a magnetic field directed upwards in one case, and in the other case a magnetic field directed downwards. If you now make this reversal of the spin and so the reversal of the magnetic field fast enough, then in the end the nucleus will no longer know whether the field points upwards or downwards, then the whole hyperfine structure breaks down. In the limiting case where that happens slowly, the nucleus will feel the whole magnetic field, and in the limiting case where it happens very fast, this realignment, this electronic relaxation, then the nucleus feels no field at all. And in between, which is the interesting area, it happens neither fast nor slow, and that results in a complicated structure of the spectra. So initially the suspicion arises that this may be the case here, but the spectra which we then obtain, they look quite different. In particular they don’t look as though all the lines involved change more or less similarly, these outer lines here. You can see what has clearly happened here: That the outer lines stay where they are, but that here in the middle a strong peak develops at the transition to higher temperatures here. In addition, the temperature interval we have here is in principle much too small to suggest relaxation effects. We supposed therefore that we were dealing with a phase transition here, whereby it was not yet quite clear what order of phase transition. The next slide, which I would only like to show very briefly, shows that in actual fact it was a matter of a phase transition of the first order. And here is shown in the group B, the measurement data are shown, the relation of the intensity among the normal outer lines here in comparison with the intensity of the middle components or their reciprocal. The main thing is that we have a sharp decline here, it should actually be vertical, if we had a real phase transition of the first order. But that is always, for a whole host of reasons, it is always blurred, in our case we suppose that the reason for this is that the substances were not totally uniform. This Erbium-Cobalt-II compound that we are dealing with here, with these measurements it is unfortunately at a very unfavourable place in the phase diagram, and it is therefore very difficult to arrive at uniform crystalline conditions. We then in actual fact also measured the latent heat for this phase transition, which exists, and we could then classify the transition as a phase transition. Interestingly, here below there is a record of the quadrupole transition. I would like to perhaps stress that this substance is a case of a cubic substance which should really show no quadrupole splitting and in fact shows none above the phase transition. We have here a further point, here below, the quadrupole split has disappeared here, but at the point of the phase transition it jumps and then we have a roughly constant quadrupole split although the substance is cubic as before. The reason for this is simply that we may be dealing with a crystallographically cubic environmental symmetry here, but that the magnetic environmental symmetry in the magnetically aligned state is no longer cubic. So that is just one example which is representative of, I would say, hundreds of measurements of all kinds which one can perform here. One has here yet again, as I said, the possibility of extremely simply analysing these spectra. It is an extraordinarily direct procedure which gives us very direct indications about what is going on here. Now, I think I would like to omit the next two slides and go straight to the last one. I would like perhaps to say another word about what I have briefly indicated here, that this area of measurement of hyperfine structure splitting of gamma lines, that it is only a subset of the whole area of recoilless nuclear resonance absorption of gamma radiation. I have for example mentioned nothing about the whole problem of lattice dynamics which we can solve here. The intensity of these recoilless lines, known as the Debye-Waller Factor, which is involved here, this provides us with direct information about lattice-dynamics problems. I have also said nothing about the polarization of the gamma radiation. We have today the possibility of generating practically 100% polarized gamma radiation, including both linearly and circularly polarized gamma radiation. All of that has become incredibly simple. But that would go well beyond the framework, the timescale that is available to me here. I would however like to devote at least a word to providing a bit of a view into the future. What hopes we have, how the area will expand further in the future. Now, it will naturally expand along these lines here. I mean that the doctors, the biologists, the chemists, they are leaping at these methods and applying them to their diverse problems. I don’t want to say anything about that because it is, I would say, obvious that development in this direction will continue to progress. But the special hopes that we as physicists have, they are naturally these, that the enormous resolution which we already have today in this area and the relative resolution which we have here, they exceed everything which is usual in any other area of physics or elsewhere. But still we have the hope that we can push this enormous resolution even further in future, that we may still succeed in achieving a leap of a few powers of 10. In recent years we have been working very hard on this. Initially with little success, but recently we have indeed succeeded in making a certain breakthrough. We have actually succeeded in pushing the resolution a little further than was previously the case. The difficulty that we have with this is actually twofold. If we want to have better resolution, then we need gamma lines which possess an even narrower natural line width than is the case with those used up to now. That means that we must use excited nuclear levels which have even longer lifetimes than has been the case so far. Now, the isotope Iron-57 is representative here, with a lifetime of the excited state of 10^-7 seconds, making this the sharpest level with which one has normally worked. Normally means there may be a further example where some sort of really feeble resonance has gone a little better. So the difficulty of making progress means sharper lines, which means longer lifetimes. Now, we can naturally say that there are indeed transitions which live for several hours. But that is hopeless. We can only hope to progress in steps of perhaps 1 or 2 powers of 10. And the reason is simply that we now have such an enormously high resolution that nature more or less defends itself. All the tiny effects which we generally know nothing about today, which can influence things, they rebound on us. We need enormously well-defined crystals. I mean that minute impurities, which are present in the crystal and which vary from place to place, they result in small differences in the environmental symmetry from place to place, which means that field gradients or magnetic fields will differ slightly. This means that we have different hyperfine structure splits from place to place, with the result that our intensity naturally collapses immediately, it will immediately become so weak that we can observe no resonances at all. That is one difficulty, the main one. The second difficulty is that there are unfortunately very few nuclear transitions in the interesting area which have the right lifetimes. We would like to have something perhaps like 10^-5 seconds or even a bit longer, perhaps up to 10^-3 seconds, but there is almost nothing there. So there is, from the practical lower limit at about 10^-7 seconds, from there on to shorter lifetimes we have an enormously large number of transitions and then of course in the area of hours there is also something, but unfortunately there are almost no nuclear transitions in this area in between. Now, almost means that there actually are some, and a particularly interesting transition is the 6 KeV transition in the isotope tantalum-181. A large number of laboratories have committed themselves to this isotope from, I would say, the year 1960. Every now and then a publication would be written where an almost invisible hint of a resonance had been seen but which almost no one believed in principle. Then it improved a little. So what I would call a puny resonance had been discovered, but the experimental difficulties were gigantic to arrive at really sharp lines. We have succeeded this year in Munich in achieving a breakthrough and I would now like to show you in the last slide the resonance of tantalum 181, which we have now obtained. You can see immediately that we are dealing with a sharp line which is relatively large, the intensities here are quite remarkable. We get from 100% here about 94%, so we have about 6% of a resonance, these are for us enormously strong resonances. You can also see that the main speeds here are really low, that is an interval from here to here, of one mm per second, which gives you a direct indication that the resonance here really is very sharp especially when one considers that the energy of this radiation is very low. I mentioned that it is a matter of only about 6 keV. Now, the problems that we had to overcome here with the discovery of this resonance, as I said, they were of a purely experimental nature. One simply had to learn, the tantalum substances, here we worked with tantalum metal, in the case of the absorber and in the case of the source with tungsten in tungsten. The tungsten source here then decays into tantalum 181. The problems which occurred here were mainly of a metallurgical kind. So we had to learn how one can boil out the oxygen loading of tantalum, which is very high, with weeks in extremely high ultra-vacuums, without adding more than one boils out. And it was problems of this kind, problems of diffusion, whose mastery ultimately led us to obtaining this resonance in a very nice form. I must however directly admit that the actual widening of this line still constitutes a factor of 10. That means that we still have a factor of 10 in reserve in this level. We could make this level, which has a lifetime of 10^-5 seconds, we could in principle make it a factor of 10 sharper and we are actually working on doing that. Now, what is interesting about such measurements? In my opinion it is first of all a matter of sport, in that, as an experimental physicist, one is naturally glad to set some records and say: Here you are, that is the sharpest resonance in existence. But of course that is no aim in itself. The actual aim which we have here, that is expressed very nicely by this figure here. You see, here we have tungsten, or essentially I should say tantalum in tungsten, that is what is employed in the experiment, against tantalum. So we measure here, so to speak, an isomer shift, the line is certainly displaced, there is an enormous isomer shift here. An isomer shift of tantalum metal against tungsten metal. The two substances, however, we would expect, should be very similar to one another. That means, we see, that in this case enormously large isomer shifts appear even with quite similar substances and here we expect that we now, if we use chemical compounds, that we get isomer shifts of perhaps 10^3 to 10^4 times the line width, and that would mean that we could study details of the chemical bond to an extent which has not been possible up to now. In actual fact, I have recently, in the last two years I would say, been cooperating with various German chemical institutes, which means that I asked them to send me extremely pure tantalum compounds, which they also did. We measured them, we never found a resonance and of course my attitude was initially that this was because the chemists did not understand chemistry well enough, the compounds were faulty. I don’t believe that this is the case anymore, now that we have carried out this measurement. I believe that the resonances are located entirely outside the speed range which we covered. We covered perhaps 100 to 1,000 line widths, but these resonances are probably located in the area of 10,000 or more line widths. This means that have hope here of being able to study directly the details of chemical bonds to a previously unimaginable extent. That is one thing. The second is of course, that one always keeps half an eye on the general theory of relativity, that one hopes that in the course of time it might be possible to carry out terrestrial experiments which really involve the field equations as such. Indeed gravitational red-shift experiments have already been carried out. In fact, we can, with this resonance now, in principle, construct the famous experiment of Pound and Rebka as a student exercise. We only need relatively small differences in the Earth’s gravitational field in order to obtain a measurable shift. But we are still relatively far removed from being able to apply these experiments directly for gravitational tests of a general kind. Perhaps I should give a few figures in this connection. The experimental accuracy we have here is: We can measure an energy shift here of about 1 part in 10^15. So that is, in order to express this on a human scale, this would mean that we can measure the distance from Lindau to Munich with an accuracy of about a millionth of an mm. So that is approximately the accuracy available here. But that is still not enough to be able to attack the general theory of relativity in a terrestrial manner, to test it. We need here precision of perhaps a factor of 10^3 higher than has been the case up to now. But now that we have put the first 15 powers of 10 behind us, it is perhaps not entirely unthinkable that we may also master the remaining 3 powers of 10. But, as I said, that goes far into the future and so I believe that this would be a good place to finish this lecture. Thank you very much.

Rudolf Mößbauer (1968)

Resonance Spectroscopy of Gamma Rays and its Application on Problems of Solid State Physics (German Presentation)

Rudolf Mößbauer (1968)

Resonance Spectroscopy of Gamma Rays and its Application on Problems of Solid State Physics (German Presentation)

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When Rudolf Mößbauer received his Nobel Prize in Physics 1961, he was only 31 years old. Since the Lindau meetings had already started some ten years earlier, he could look forward to many invitations, not only to the meetings in physics, but to all meetings. In the beginning he chose the physics ones and mostly lectured on what is named after him, the Mößbauer effect, and its applications. The present lecture is his second at Lindau and mainly concerns the applications of this effect in the general area of solid-state physics. Most atomic nuclei can absorb and emit high-energy electromagnetic radiation of extremely well defined frequency, so called characteristic gamma rays. But the frequencies are generally shifted due to the Doppler effect, which becomes active because of the nuclear recoil, and so the frequencies become smeared. What Mößbauer found was that if the atoms are bound in crystal lattices, the nuclear recoil energy can be shared among all the atoms of the crystal. This means that the Doppler effect becomes negligible and the frequencies well defined. Using one crystal for emission and another one for absorption, it becomes possible to measure extremely small frequency shifts. These could derive from moving the whole crystal with velocities down to millimetres per hour or even from changes in the gravitational potential between emitter and absorber (according to the general theory of relativity). The main use of the method, as described by Mößbauer, is to measure the so-called hyperfine effects. These are small shifts of the gamma frequencies that depend on the local fields at the atomic nuclei. These fields can derive from the electronic and magnetic properties of the electron clouds and the shifts also depend on the shape of the atomic nuclei. So measuring these effects can give important information both on the electronic structure of the atoms in the crystals and on their nuclei.

Anders Bárány

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