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The potential use of compton scattered gamma rays for nuclear excitation experiments
NUCLEAR
INSTRUMENTS
AND METHODS
23 (1963)
218--224;
NORTH-HOLLAND
PUBLISHING
CO.
THE POTENTIAL USE OF COMPTON SCATTERED GAMMA RAYS FOR NUCLEAR EXCITATION EXPERIMENTS G. B~,CKSTROM
Institute o/ Physics, Uppsala, Sweden Received 21 December 1962
The possibility of using Compton scattered radiation to induce nuclear resonance absorption is discussed. I t is shown t h a t sufficient counting rate m a y be obtained with g a m m a ray sources i~ow in use, if a suitably curved scatterer is used. The energy spread of the secondary radiation is investigated ex-
perimentaily by comparison with mono-energetic g a m m a rays. The method seems promising for level life-times shortec t h a n 10 -is sec. Energies up to 2.5 MeV m a y be produced, and possibly higher energies.
1. Introduction Gamma rays have as yet been comparatively little used for the purpose of producing excited states in nuclei. Perhaps the most serious obstacle to such experiments is the lack of gamma ray sources where the quantum energy is well defined and yet variable over an appreciable energy region. In most cases where such experiments have been successful l) the method has been to utilize the gamma rays emitted in the de-population of a level produced by radioactive decay and to excite with this radiation the corresponding level in the target nuclei. The recoil energy lost to the emitting and absorbing nuclei has been restored by means of one of the following methods: a) Doppler shift induced by mounting the source on the rotor of a centrifuge; b) random Doppler shift produced by heating the source to a high temperature; c) compensating recoil by preceeding radiation in the radioactive decay. There are some obvious limitations with all of these methods. The level has to be populated in a radioactive decay and in such a way that either the transition to the ground state is the highest energy emitted, or else that this transition is the predominant radiation of the nuclide. When these conditions are fulfilled, a method of restoring the recoil energy can not always be found. It must also oe decided to what extent the gamma rays ob-
served from the target result from resonant scattering or from other elastic scattering processes. In the centrifuge method this may be accomplished by variation of the source velocity, but with the other methods a separate experiment with a matched non-resonant target is usually necessary. In short, the radioactive method of resonant scattering is applicable in a rather limited number of cases, and an energy restoring mechanism has to be selected individually for each level under investigation. In practice these methods are restricted to low energies, and measurements have rarely been performed above 1 MeV level energy The usefulness for life-time determinations of the "recoil-less" resonance scattering discovered by M6ssbauer is confined to even lower energies, and the crystal lattices of the source and scatterer have to fulfill certain conditions. An additional possibility of restoring the recoil energy is provided by the bombarding particle in nuclear reactions. In a (p,?) reaction, for instance, one obtains from a given transition different energies depending on the angle of observation. The energy span may even be large enough to include accidentally the level energy of another nucleus, which hence may be excited. Such experiments are not easily performed, as they yield low coupting rates and require rather complicated apparatus.
218
1) F. R. Metzger, Progress in Nuclear Physics 7 (1959) 54. and Proc. Conf. Gatlinburg (1961) 97.
T H E USE OF GAMMA R A Y S
FOR NUCLEAR EXCITATION EXPERIMENTS
The restriction to a series of narrow energy intervals for a given nuclear reaction is of course a serious one.
More general methods of producing resonant absorption of gamma rays have been searched for by several workers. Schiff2) suggested irradiation of nuclei with the continuous energy distribution of bremsstrahlung gamma rays from a betatron. This method has proved successful in many cases of high energy levels, but has only occasionally been used at energies below 2 MeV3). Attempts have been made recently*) to produce resonant scattering by means of a curved crystal monochromator, selecting a narrow energy band from the continuous spectrum of a 250 kV X-ray tube. Levels at 110 keV with a width of approximately 10 -~ eV could be observed with a peak to background ratio of 0.15. Since reflectivity and resolution rapidly become worse as energy increases, it is not probable that this method should prove applicable at as high energy as 1 MeV. This would furthermore seem to require aVandeGraaff machine or a betatron as the gamma ray source.
2. The Compton Scattering Method When a gamma quantum of energy E~ is scattered by an electron, the secondary quantum will have the energy E~ =
E7 1 + E~(1 - cos O)/moc2
where m o is the electron mass and 0 the scattering angle. From a source of monoenergetic gamma rays it is thus possible to obtain a variable photon energy by accepting scattered radiation in a small angular interval A O at various mean scattering angles 0. Obviously the range of variation is appreciable: with E~ = 1 MeV any energy between 0.2 MeV and 1 MeV may be obtained. If this principle can be used for resonant scattering, the same source may thus be utilized for studying levels in a wide energy region. The possibility of using the Compton effect for resonant scattering experiments has certainly been noticed by most workers concerned with this field, but the idea has been rejected on the grounds that the available source strengths would not permit
219
detailed observation of the radiation after two successive scattering processes. It has probably also occurred to many workers, including the author, that the intensity of the secondary radiation may be increased by the use of a suitably shaped scatterer5). If the scattering material is distributed over a surface of revolution, obtained by rotating the circle in fig. 1 around an axis
A
Fig. 1. Geometry of Compton scattering apparatus.
joining the source and the exit hole, the accepted gamma rays will all have been scattered through the same angle. While the principle of resonant scattering by means of Compton scattering has been known for many years, there have been no reports of experiments of this kind, successful or unsuccessful. This has stirred the author's curiosity, and the present investigation was initiated for the purpose of determining whether or not such an experiment is feasible. The possibility of shaping the scatterer as a surface of revolution seems attractive at first, but there are some disadvantages with this arrangement. If good energy resolution is to be achieved, A0 has to be chosen small, and as a consequence of the rotational symmetry the extension of the gamma ray source would have to be limited in all directions, i.e. a "point" source would be required. The exit collimator would have to be of about the same diameter as the source. In order to change the scattering angle one would have to move the source (S) and the collimator (C) along the circle in fig. 1, ~) L. a) O. 4) E. 503. 5) A.
I. Schifl, Phys. Rev. 70 (1946) 761. Beckman and R. SandstrOm, l~ucl. Phys. 5 (1958) 595. J. Seppi a n d F. Boehm, Bull. Am. Phys. Soc. 6 (1961) M. Cormack, Phys, Rev. 96 (1954) 716.
220
G. B X C K S T R ~ M
which implies that the location of the axis of rotation SC would be changed and a new radius of curvature required. A scatterer would thus have to be specially made for each level to be investigated, which is particularly objectionable since such a shaped scatterer would be very difficult to manufacture. The geometry chosen in this investigation is a more realistic one. The horizontal projection of the arrangement is shown in fig. 1. The scatterer consists of a metal strip, bent in one direction only, and with a height which is small compared to the radius of curvature. If the strip is no longer t h a n about half of the arc from S to C, it m a y evidently be a good approximation to the surface of revolution described above. The first advantage with this arrangement is that the scattering angle 0 depends on the source height only to second order. This means that the source height m a y be taken as large
as 5-10 times the source width, or typically one half of the height of the scatterer. A similar situation exists with the size of the exit hole, which m a y now be given the form of a vertical slit. Part of the reduction in scatterer weight is thus recovered due to the larger collection solid angle, and since the specific activity of the source in practice is limited, the increase in source height m a y be equally valuable. Apart from being simple to build, this apparatus has the advantage over the previous alternative that the spread in scattering angle is, in principle, maintained at a small value at all energies. In practice, the size of the scatterer has to be approximately matched to the scattering angle, but it is at least possible to work over a large energy region with a given scatterer. The mechanical construction is understood from fig. 1 and fig. 2. The positions of source and coll i m a t o r slit are defined by means of the two verti-
Fig. 2. Simple apparatus for investigation of the cnergy spread of scattered quanta.
THE
USE OF GAMMA RAYS FOR NUCLEAR
cal rods S and C, each of which is joined by means of two horizontal rods to a central axle A. The scatterer is fixed at the same distance from this central axle by means of four radial rods, located well above and below the scattering plane. By means of an extra radial rod, connected to A, it m a y easily be determined to what accuracy source, scatterer and collimator are located on a circle. It is a convenient property of this arrangement that the scattering angle 0 becomes one half of the angle SAC. The practicability of resonant scattering experiments using the Compton effect first became appearent to the author through the work of Beckman et al.3), where a continuous X-ray spectrum was used for the excitation of the 477 keV level of LIT). The scintillation spectrum of the scattered radiation showed, in this experiment, only a small (18%) resonance peak on a strongly sloping background. Since the region of the resonance could not contain any Compton scattered quanta, and since most of the background was found to vanish when the Li scatterer was removed, one would believe the background to be produced by non-resonant elastic scattering. Of the elastic scattering processes, Rayleigh scattering is the one responsible for the energy variation of the cross section. Extrapolating the background in Beckman's spectrum from high energies to lower using the Rayleigh factor E - 3 , it becomes evident that the background must have been of other origin, most probably resulting from pile-up of the enormous number of low energy g a m m a rays present in the spectrum. In fact, with proper electronic equipment and better shielding the peak to background ratio in this experiment might have been larger than unity. In a Compton scattering experiment the ratio of the resonant scattering counting rate to the nonresonant background would be more favourable than when bremsstrahlung continua are used. In the latter type of experiment energy selection is provided only by the detector, a NaI crystal which accepts approximately a 10% energy interval. Better resolution m a y be obtained at a well-defined Compton scattering angle, but since the photon intensity decreases rapidly as the angular interval
EXCITATION
EXPERIMENTS
22I
is made smaller, it must be investigated what resolution can be achieved if the counting rate is to be well above room background. For comparison purposes, suppose that the 477 keV level of Li T is to be investigated by means of Compton scattered radiation from the 1332 keV g a m m a ray of Co 6°. This requires a scattering angle of 72 °, which corresponds to the situation in fig. 1. The scatterer is assumed to subtend half of the angle SAC, to have a radius of curvature of 100 cm and a height of 6 cm. A copper plate of 0.3 cm thickness is used as a scatterer. The size of source and exit slit is taken to be 0.6 x 3 cm 2. The difference of the largest and the smallest scattering angle m a y now be calculated to be 0.85 ~, which would imply a total energy spread of 6 keV or 1.3 % of the secondary quantum energy. From this total energy spread one obtains AE/E = 0.65 % as the relative half-width of the line, assuming that it possesses a triangular shape. The number of quanta accepted per second by the exit slit in the above geometry m a y easily be estimated by the use of the differential cross section for the Compton effect6). The probability of a quantum being scattered by the copper sheet into the exit slit C is found to be 5 x 10 -9. If a 3.8 kcurie source of Co 6° were available, a source used in this country for radiological purposes, as much as 7 x 105 quanta per second could thus be obtained with an energy half-width of 3 keV. In the experiment with continuous bremsstrahlung reported by Beckman3), on the other hand, the number of quanta at the target was 15 x 105/sec over a corresponding energy interval. This difference in number of quanta is more than compensated by the fact that in a Compton experiment, where the background in the vicinity of the beam would be low, a larger solid angle could be us~,d from the target to the scintillation detector. These estimates thus strongly indicate that a resonance scattering experiment could be performed at a reasonable counting rate and that the resonance to background ratio would be better than 10 in the case of Li 7. 6) C. M. D a v i s s o n a n d R. D. E v a n s , Revs. Modern P h y s . 24 (1952) 79. 7) O. Klein a n d Y. Nishina, Z. P h y s i k 52 (1929) 853.
222
G. BACKSTR~M
It must be kept in mind, however, that the above result was arrived at by the use of a theory which applies only to free electrons, while the majority of the electrons in any scattering material are bound. This means that the differential cross sections calculated by Klein and Nishina v) m a y not be accurate. There are, however, no reasons to believe that a correction for electron binding would appreciably modify our intensity estimates, which admittedly are quite coarse, since the total crosssections seem to be so well predicted by the free electron theory. It is probably much more serious in this connection to neglect electron binding when calculating the secondary photon energy versus scattering angie, as high accuracy is required of this relationship. Evidently, the energy spread caused by the binding energy itself is unimportant. I n copper, for example, all except two of the 29 electrons have a binding energy of 1.1 keV or less. However since mom,:ntum m a y be imparted to the atom m the scattering process, and since this m o m e n t u m m a y be of any direction, new degrees of freedom exist, and the energy is no longer a unique function of the scattering angle. The recoil energy of the nucleus is negligibly small, being only a few eV even if the total m o m e n t u m of a 1 MeV q u a n t u m were absorbed. With a given energy partition between the secondary electron and the photon the angles of emission are therefore largely determined by the m o m e n t u m taken up by the atom. As far as we know, no calculations have been carried out on Compton scattering by bound electrons. A minim u m value of the m o m e n t u m transfer to the atom m a y be obtained by considering only the mom e n t u m of the electron "hole" after the emission. Neglecting the single loosely bound N-electron in Cu, there are ten M-electrons of about 10 eV energy and eight M-electrons with roughly 100 eV. The m o m e n t a of these electrons are equivalent to those of g a m m a rays with an energy of 3 keV and I0 keV respectively and the associated angular spread d 0 for collision in these shells thus becomes approximately + 0 3 ° and 4- 1° in the Co6°-Li ~ example. The eight L-electrons would by the same estimate yield AO = 4- 3 °. Accordingly it seems that only about 30% of the Cu electrons would
yield a sufficiently sharp secondary g a m m a ray energy at a given angle to permit experiments at 1% resolution. Little would be gained, in this respect, by resorting to a lower atomic number; in fact aluminium, fcr instance, would be worse at this resolution, apart from having a lower electron density. On the other hand, a heavy material such as tungsten would probably be more favourable at higher energies, where the photoelectric absorption is negligible. Since the atomic number probably does not much affect the scattenng properties, copper appears to be a good choice, as it has high density and is readily workable. A detailed calculation of the intensity and the line shape of the secondary radiation in the Compton scattering arrangement described above would be very complicated, and because of the limited validity of the theory would not yield reliable results. The rough estimates of the recoil m o m e n t u m made above m a y prove to be much too low, involving as they do a rather arbitrary assumption about the m o m e n t u m transfer. For this reason, and also since the principle had not been previously used in spite of being well known, it was found worthwhile to build a simple scattering apparatus and to investigate as far as possible the line width and intensity before attempting an actual nuclear fluorescence experiment. The complete apparatus is shown in fig. 2. The size of the copper scatterer is 90 x 6 cm 2, the thickness 0.3 cm, and the radius of curvature 100 cm. The source shield to the left is open in the figure to show the position of the source and the colhmator. The lead shield to the right houses a 3" x 3" NaI crystal with a matched photomultiplier. The front shield consists of tungsten blocks. Zn *s was used as the source of primary gamma rays. This nuclide was preferred to Co 6°, because it emits only one g a m m a ray the energy being 1112 keV. This source had a gamma ray strength of 33 mC, a width of 0.2 cm and a height of 2 cm. A scattering angle of 0 = 46 ° was chosen, yielding an energy of 662 keV for the scattered quanta. After the pulse height spectrum had been recorded by means of a multichannel analyser, a background spectrum was taken under identi al
THE
USE OF GAMMA RAYS FOR NUCLEAR
EXCITATION
EXPERIMENTS
223
conditions but with the scatterer removed. The somewhat fortuitous agreement with the experispectrum of the scattered radiation was obtained ment. Since it is shown beyond doubt that the energy by subtracting this relatively small background. In order to determine the energy homogeneity of width of Compton scattered radiation may be far the scattered radiation a comparison was made smaller than the energy "window" of a scintillation with the spectrum from mono-energetic gamma counter, and since the intensity estimates are born rays. A source of Cs 13~, emitting a gamma ray of out by experiment, it is clear that a resonance 662 keV, was fixed at the former position of the fluorescence experiment with Li T could be successscatterer by means of a radial rod and was moved fully performed. It is true that the shielding along a circle during the measurement in order to against direct radiation would have to be improved simulate radiation from a curved scatterer. Ex- by a factor of 105, but this is equivalent to about periments were made at various sizes of the slit. 22 cm of lead, pile-up neglected, and there is ample The results obtained with a slit of 0.3 x 3 cm 2 are space for shielding between the source and the shown in fig. 3. The peak obtained with the Cs detector. The relative half-width is in this case estimated source (upper curve) had a half-width of 9.4%, which is larger than the nominal value of 8.5 % for to be AE/E - 1.1%, still on the basis of the free this equipment because of scattering by the slit electron formula for E~. This is not necessarily in edges. The peak from the scattered radiation, how- quantitative agreement with the difference in ever, possessed a half-width of 10.3 %. The count- width found for the scintillation peaks in fig. 3 ing rate under this peak was 20/sec, which means (0.9 %), because the energy spread of the gamma that the number of scattered quanta per primary rays would combine quadratically rather than quantum was 1.6 x 10 -6 in this case. Computing linearly with the inherent width of the scintillaUon as before the solid angles involved and using the spectrometer. The experiment actually indicates Klein-Nishina cross'sections one obtains for the an energy spread of a few percent. It was not same ratio the value 1.8 x 10 -8, in presumably found worthwhile, with this material, to extend the
Counts//10rain
[: ,
it
Compton scattered
I~
200
C'~37-'--"
Zn gamma rays
o
3oo0
I'll
oo
o
zo~
o
o o
"
io
'
~'o
'
6'o
'
8'o
'
~o
' ~o"
~
~ ~ m ' = ' ~ - ' ~ m Chen~l ncJm~r
Fig. 3. Scintillation s p e c t r a of C o m p t o n s c a t t e r e d g a m m a r a y s f r o m Zn ~ a n d of direct r a d i a t i o n f r o m Cs 137.
224
G. B X C K S T R ~ M
analysis by a folding procedure in order to determine more accurately the energy distribution, because a closer study of Compton scattering by bound electrons should be made at low energy, preferably with a curved clystal diffraction spectrom e t e r - o r indeed by means of nuclear resonance scattering. It had been planned that the potentiality of the Compton scattering method of nuclear resonance scattering would next be investigated in full scale, using a Co 6° source and the 477 keV level of Li T. At this stage, however, it was brought to the author's attention that a similar experiment had been successfully made elsewhere and that the result is under publicationS). In this situation there remains only to summarize the virtues of the Compton scattering method and to discuss its scope of application for life-time measurements. 1. The most important advantage is that the same source m a y be used for the study of levels in a wide region of energies, while most other methods require a special arrangement for each level to be investigated. The useful range of a Co 6° source is approximately 0.3-1.2 MeV. The range m a y be extended to somewhat higher energies by the use of Eu 1s2 which also has some other advantages over Co 6° in this application. It seems possible to reach 2.5 MeV by means of a source of Na 24 (15 hours) but the apparatus has then to be attached to a high flux nuclear reactor, where the source m a y be repeatedly irradiated. In order to increase the maximum energy further one might consider using the prompt g a m m a rays arising in neutron capture. An element yielding a prominent maximum-energy transition would then have to be irradiated continuously in a reactor. The background of fast neutrons may be a problem in this scheme, however. 2. The background counting rate in this type of 5) W. L. Mouton, J. P. F. Sellschop and G. Wiechers, Phys. Rev., 119 (1963) 361.
resonance scattering experiment will vary only slowly with the angle 0 and m a y quite accurately be subtracted from the total to yield the resonant counting rate. An increase in counting rate of only a few percent should be sufficient for the measurement of a resonance. The determination of the level life-time generally requires knowledge of the spectral composition of the exciting radiation. A calibration in terms of strong resonances, where the line shape m a y be examined in detail, then suggests itself, and as a second solution the self-absorption technique m a y be used. 3. It is important to estimate how m a n y levels that m a y be excited by the Compton method. The 477 keV state in Li T is a rather favourable case, as it involves a mean life of 10 -13 sec and such low atomic number that non-resonant elastic scattering becomes negligible. Assuming a standard Compton energy spread of 2 % one obtains for the crosssections of resonant and Rayleigh scattering a(r)/a(R) = l O - S / z Z 3
where z is the mean life of the level in seconds. F r o m the point of view of this ratio, the method seems rather generally applicable in the region of 1 0 - 1 , sec, and since levels of this life-time are expected to be quite abundant at energies of 1-2 MeV, a number of cases m a y certainly be studied. 4. The secondary beam is partially polarized. It is not probable, however, that the intensity will permit one to take advantage of this feature.
Acknowledgements It is a pleasure to thank Professor Kai Siegbahn for the encouragement given in the course of this work. The friendly interest of Drs. P. Bergvall and O. Beckman is greatly appreciated. Thanks are also due to F. M. Sven A n t m a n for assistance in the experiments. The work was made possible by grants from Svenska Statens Atomr~d and the European Office of Aerospace Research, United States Air Force.
INSTRUMENTS
AND METHODS
23 (1963)
218--224;
NORTH-HOLLAND
PUBLISHING
CO.
THE POTENTIAL USE OF COMPTON SCATTERED GAMMA RAYS FOR NUCLEAR EXCITATION EXPERIMENTS G. B~,CKSTROM
Institute o/ Physics, Uppsala, Sweden Received 21 December 1962
The possibility of using Compton scattered radiation to induce nuclear resonance absorption is discussed. I t is shown t h a t sufficient counting rate m a y be obtained with g a m m a ray sources i~ow in use, if a suitably curved scatterer is used. The energy spread of the secondary radiation is investigated ex-
perimentaily by comparison with mono-energetic g a m m a rays. The method seems promising for level life-times shortec t h a n 10 -is sec. Energies up to 2.5 MeV m a y be produced, and possibly higher energies.
1. Introduction Gamma rays have as yet been comparatively little used for the purpose of producing excited states in nuclei. Perhaps the most serious obstacle to such experiments is the lack of gamma ray sources where the quantum energy is well defined and yet variable over an appreciable energy region. In most cases where such experiments have been successful l) the method has been to utilize the gamma rays emitted in the de-population of a level produced by radioactive decay and to excite with this radiation the corresponding level in the target nuclei. The recoil energy lost to the emitting and absorbing nuclei has been restored by means of one of the following methods: a) Doppler shift induced by mounting the source on the rotor of a centrifuge; b) random Doppler shift produced by heating the source to a high temperature; c) compensating recoil by preceeding radiation in the radioactive decay. There are some obvious limitations with all of these methods. The level has to be populated in a radioactive decay and in such a way that either the transition to the ground state is the highest energy emitted, or else that this transition is the predominant radiation of the nuclide. When these conditions are fulfilled, a method of restoring the recoil energy can not always be found. It must also oe decided to what extent the gamma rays ob-
served from the target result from resonant scattering or from other elastic scattering processes. In the centrifuge method this may be accomplished by variation of the source velocity, but with the other methods a separate experiment with a matched non-resonant target is usually necessary. In short, the radioactive method of resonant scattering is applicable in a rather limited number of cases, and an energy restoring mechanism has to be selected individually for each level under investigation. In practice these methods are restricted to low energies, and measurements have rarely been performed above 1 MeV level energy The usefulness for life-time determinations of the "recoil-less" resonance scattering discovered by M6ssbauer is confined to even lower energies, and the crystal lattices of the source and scatterer have to fulfill certain conditions. An additional possibility of restoring the recoil energy is provided by the bombarding particle in nuclear reactions. In a (p,?) reaction, for instance, one obtains from a given transition different energies depending on the angle of observation. The energy span may even be large enough to include accidentally the level energy of another nucleus, which hence may be excited. Such experiments are not easily performed, as they yield low coupting rates and require rather complicated apparatus.
218
1) F. R. Metzger, Progress in Nuclear Physics 7 (1959) 54. and Proc. Conf. Gatlinburg (1961) 97.
T H E USE OF GAMMA R A Y S
FOR NUCLEAR EXCITATION EXPERIMENTS
The restriction to a series of narrow energy intervals for a given nuclear reaction is of course a serious one.
More general methods of producing resonant absorption of gamma rays have been searched for by several workers. Schiff2) suggested irradiation of nuclei with the continuous energy distribution of bremsstrahlung gamma rays from a betatron. This method has proved successful in many cases of high energy levels, but has only occasionally been used at energies below 2 MeV3). Attempts have been made recently*) to produce resonant scattering by means of a curved crystal monochromator, selecting a narrow energy band from the continuous spectrum of a 250 kV X-ray tube. Levels at 110 keV with a width of approximately 10 -~ eV could be observed with a peak to background ratio of 0.15. Since reflectivity and resolution rapidly become worse as energy increases, it is not probable that this method should prove applicable at as high energy as 1 MeV. This would furthermore seem to require aVandeGraaff machine or a betatron as the gamma ray source.
2. The Compton Scattering Method When a gamma quantum of energy E~ is scattered by an electron, the secondary quantum will have the energy E~ =
E7 1 + E~(1 - cos O)/moc2
where m o is the electron mass and 0 the scattering angle. From a source of monoenergetic gamma rays it is thus possible to obtain a variable photon energy by accepting scattered radiation in a small angular interval A O at various mean scattering angles 0. Obviously the range of variation is appreciable: with E~ = 1 MeV any energy between 0.2 MeV and 1 MeV may be obtained. If this principle can be used for resonant scattering, the same source may thus be utilized for studying levels in a wide energy region. The possibility of using the Compton effect for resonant scattering experiments has certainly been noticed by most workers concerned with this field, but the idea has been rejected on the grounds that the available source strengths would not permit
219
detailed observation of the radiation after two successive scattering processes. It has probably also occurred to many workers, including the author, that the intensity of the secondary radiation may be increased by the use of a suitably shaped scatterer5). If the scattering material is distributed over a surface of revolution, obtained by rotating the circle in fig. 1 around an axis
A
Fig. 1. Geometry of Compton scattering apparatus.
joining the source and the exit hole, the accepted gamma rays will all have been scattered through the same angle. While the principle of resonant scattering by means of Compton scattering has been known for many years, there have been no reports of experiments of this kind, successful or unsuccessful. This has stirred the author's curiosity, and the present investigation was initiated for the purpose of determining whether or not such an experiment is feasible. The possibility of shaping the scatterer as a surface of revolution seems attractive at first, but there are some disadvantages with this arrangement. If good energy resolution is to be achieved, A0 has to be chosen small, and as a consequence of the rotational symmetry the extension of the gamma ray source would have to be limited in all directions, i.e. a "point" source would be required. The exit collimator would have to be of about the same diameter as the source. In order to change the scattering angle one would have to move the source (S) and the collimator (C) along the circle in fig. 1, ~) L. a) O. 4) E. 503. 5) A.
I. Schifl, Phys. Rev. 70 (1946) 761. Beckman and R. SandstrOm, l~ucl. Phys. 5 (1958) 595. J. Seppi a n d F. Boehm, Bull. Am. Phys. Soc. 6 (1961) M. Cormack, Phys, Rev. 96 (1954) 716.
220
G. B X C K S T R ~ M
which implies that the location of the axis of rotation SC would be changed and a new radius of curvature required. A scatterer would thus have to be specially made for each level to be investigated, which is particularly objectionable since such a shaped scatterer would be very difficult to manufacture. The geometry chosen in this investigation is a more realistic one. The horizontal projection of the arrangement is shown in fig. 1. The scatterer consists of a metal strip, bent in one direction only, and with a height which is small compared to the radius of curvature. If the strip is no longer t h a n about half of the arc from S to C, it m a y evidently be a good approximation to the surface of revolution described above. The first advantage with this arrangement is that the scattering angle 0 depends on the source height only to second order. This means that the source height m a y be taken as large
as 5-10 times the source width, or typically one half of the height of the scatterer. A similar situation exists with the size of the exit hole, which m a y now be given the form of a vertical slit. Part of the reduction in scatterer weight is thus recovered due to the larger collection solid angle, and since the specific activity of the source in practice is limited, the increase in source height m a y be equally valuable. Apart from being simple to build, this apparatus has the advantage over the previous alternative that the spread in scattering angle is, in principle, maintained at a small value at all energies. In practice, the size of the scatterer has to be approximately matched to the scattering angle, but it is at least possible to work over a large energy region with a given scatterer. The mechanical construction is understood from fig. 1 and fig. 2. The positions of source and coll i m a t o r slit are defined by means of the two verti-
Fig. 2. Simple apparatus for investigation of the cnergy spread of scattered quanta.
THE
USE OF GAMMA RAYS FOR NUCLEAR
cal rods S and C, each of which is joined by means of two horizontal rods to a central axle A. The scatterer is fixed at the same distance from this central axle by means of four radial rods, located well above and below the scattering plane. By means of an extra radial rod, connected to A, it m a y easily be determined to what accuracy source, scatterer and collimator are located on a circle. It is a convenient property of this arrangement that the scattering angle 0 becomes one half of the angle SAC. The practicability of resonant scattering experiments using the Compton effect first became appearent to the author through the work of Beckman et al.3), where a continuous X-ray spectrum was used for the excitation of the 477 keV level of LIT). The scintillation spectrum of the scattered radiation showed, in this experiment, only a small (18%) resonance peak on a strongly sloping background. Since the region of the resonance could not contain any Compton scattered quanta, and since most of the background was found to vanish when the Li scatterer was removed, one would believe the background to be produced by non-resonant elastic scattering. Of the elastic scattering processes, Rayleigh scattering is the one responsible for the energy variation of the cross section. Extrapolating the background in Beckman's spectrum from high energies to lower using the Rayleigh factor E - 3 , it becomes evident that the background must have been of other origin, most probably resulting from pile-up of the enormous number of low energy g a m m a rays present in the spectrum. In fact, with proper electronic equipment and better shielding the peak to background ratio in this experiment might have been larger than unity. In a Compton scattering experiment the ratio of the resonant scattering counting rate to the nonresonant background would be more favourable than when bremsstrahlung continua are used. In the latter type of experiment energy selection is provided only by the detector, a NaI crystal which accepts approximately a 10% energy interval. Better resolution m a y be obtained at a well-defined Compton scattering angle, but since the photon intensity decreases rapidly as the angular interval
EXCITATION
EXPERIMENTS
22I
is made smaller, it must be investigated what resolution can be achieved if the counting rate is to be well above room background. For comparison purposes, suppose that the 477 keV level of Li T is to be investigated by means of Compton scattered radiation from the 1332 keV g a m m a ray of Co 6°. This requires a scattering angle of 72 °, which corresponds to the situation in fig. 1. The scatterer is assumed to subtend half of the angle SAC, to have a radius of curvature of 100 cm and a height of 6 cm. A copper plate of 0.3 cm thickness is used as a scatterer. The size of source and exit slit is taken to be 0.6 x 3 cm 2. The difference of the largest and the smallest scattering angle m a y now be calculated to be 0.85 ~, which would imply a total energy spread of 6 keV or 1.3 % of the secondary quantum energy. From this total energy spread one obtains AE/E = 0.65 % as the relative half-width of the line, assuming that it possesses a triangular shape. The number of quanta accepted per second by the exit slit in the above geometry m a y easily be estimated by the use of the differential cross section for the Compton effect6). The probability of a quantum being scattered by the copper sheet into the exit slit C is found to be 5 x 10 -9. If a 3.8 kcurie source of Co 6° were available, a source used in this country for radiological purposes, as much as 7 x 105 quanta per second could thus be obtained with an energy half-width of 3 keV. In the experiment with continuous bremsstrahlung reported by Beckman3), on the other hand, the number of quanta at the target was 15 x 105/sec over a corresponding energy interval. This difference in number of quanta is more than compensated by the fact that in a Compton experiment, where the background in the vicinity of the beam would be low, a larger solid angle could be us~,d from the target to the scintillation detector. These estimates thus strongly indicate that a resonance scattering experiment could be performed at a reasonable counting rate and that the resonance to background ratio would be better than 10 in the case of Li 7. 6) C. M. D a v i s s o n a n d R. D. E v a n s , Revs. Modern P h y s . 24 (1952) 79. 7) O. Klein a n d Y. Nishina, Z. P h y s i k 52 (1929) 853.
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It must be kept in mind, however, that the above result was arrived at by the use of a theory which applies only to free electrons, while the majority of the electrons in any scattering material are bound. This means that the differential cross sections calculated by Klein and Nishina v) m a y not be accurate. There are, however, no reasons to believe that a correction for electron binding would appreciably modify our intensity estimates, which admittedly are quite coarse, since the total crosssections seem to be so well predicted by the free electron theory. It is probably much more serious in this connection to neglect electron binding when calculating the secondary photon energy versus scattering angie, as high accuracy is required of this relationship. Evidently, the energy spread caused by the binding energy itself is unimportant. I n copper, for example, all except two of the 29 electrons have a binding energy of 1.1 keV or less. However since mom,:ntum m a y be imparted to the atom m the scattering process, and since this m o m e n t u m m a y be of any direction, new degrees of freedom exist, and the energy is no longer a unique function of the scattering angle. The recoil energy of the nucleus is negligibly small, being only a few eV even if the total m o m e n t u m of a 1 MeV q u a n t u m were absorbed. With a given energy partition between the secondary electron and the photon the angles of emission are therefore largely determined by the m o m e n t u m taken up by the atom. As far as we know, no calculations have been carried out on Compton scattering by bound electrons. A minim u m value of the m o m e n t u m transfer to the atom m a y be obtained by considering only the mom e n t u m of the electron "hole" after the emission. Neglecting the single loosely bound N-electron in Cu, there are ten M-electrons of about 10 eV energy and eight M-electrons with roughly 100 eV. The m o m e n t a of these electrons are equivalent to those of g a m m a rays with an energy of 3 keV and I0 keV respectively and the associated angular spread d 0 for collision in these shells thus becomes approximately + 0 3 ° and 4- 1° in the Co6°-Li ~ example. The eight L-electrons would by the same estimate yield AO = 4- 3 °. Accordingly it seems that only about 30% of the Cu electrons would
yield a sufficiently sharp secondary g a m m a ray energy at a given angle to permit experiments at 1% resolution. Little would be gained, in this respect, by resorting to a lower atomic number; in fact aluminium, fcr instance, would be worse at this resolution, apart from having a lower electron density. On the other hand, a heavy material such as tungsten would probably be more favourable at higher energies, where the photoelectric absorption is negligible. Since the atomic number probably does not much affect the scattenng properties, copper appears to be a good choice, as it has high density and is readily workable. A detailed calculation of the intensity and the line shape of the secondary radiation in the Compton scattering arrangement described above would be very complicated, and because of the limited validity of the theory would not yield reliable results. The rough estimates of the recoil m o m e n t u m made above m a y prove to be much too low, involving as they do a rather arbitrary assumption about the m o m e n t u m transfer. For this reason, and also since the principle had not been previously used in spite of being well known, it was found worthwhile to build a simple scattering apparatus and to investigate as far as possible the line width and intensity before attempting an actual nuclear fluorescence experiment. The complete apparatus is shown in fig. 2. The size of the copper scatterer is 90 x 6 cm 2, the thickness 0.3 cm, and the radius of curvature 100 cm. The source shield to the left is open in the figure to show the position of the source and the colhmator. The lead shield to the right houses a 3" x 3" NaI crystal with a matched photomultiplier. The front shield consists of tungsten blocks. Zn *s was used as the source of primary gamma rays. This nuclide was preferred to Co 6°, because it emits only one g a m m a ray the energy being 1112 keV. This source had a gamma ray strength of 33 mC, a width of 0.2 cm and a height of 2 cm. A scattering angle of 0 = 46 ° was chosen, yielding an energy of 662 keV for the scattered quanta. After the pulse height spectrum had been recorded by means of a multichannel analyser, a background spectrum was taken under identi al
THE
USE OF GAMMA RAYS FOR NUCLEAR
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EXPERIMENTS
223
conditions but with the scatterer removed. The somewhat fortuitous agreement with the experispectrum of the scattered radiation was obtained ment. Since it is shown beyond doubt that the energy by subtracting this relatively small background. In order to determine the energy homogeneity of width of Compton scattered radiation may be far the scattered radiation a comparison was made smaller than the energy "window" of a scintillation with the spectrum from mono-energetic gamma counter, and since the intensity estimates are born rays. A source of Cs 13~, emitting a gamma ray of out by experiment, it is clear that a resonance 662 keV, was fixed at the former position of the fluorescence experiment with Li T could be successscatterer by means of a radial rod and was moved fully performed. It is true that the shielding along a circle during the measurement in order to against direct radiation would have to be improved simulate radiation from a curved scatterer. Ex- by a factor of 105, but this is equivalent to about periments were made at various sizes of the slit. 22 cm of lead, pile-up neglected, and there is ample The results obtained with a slit of 0.3 x 3 cm 2 are space for shielding between the source and the shown in fig. 3. The peak obtained with the Cs detector. The relative half-width is in this case estimated source (upper curve) had a half-width of 9.4%, which is larger than the nominal value of 8.5 % for to be AE/E - 1.1%, still on the basis of the free this equipment because of scattering by the slit electron formula for E~. This is not necessarily in edges. The peak from the scattered radiation, how- quantitative agreement with the difference in ever, possessed a half-width of 10.3 %. The count- width found for the scintillation peaks in fig. 3 ing rate under this peak was 20/sec, which means (0.9 %), because the energy spread of the gamma that the number of scattered quanta per primary rays would combine quadratically rather than quantum was 1.6 x 10 -6 in this case. Computing linearly with the inherent width of the scintillaUon as before the solid angles involved and using the spectrometer. The experiment actually indicates Klein-Nishina cross'sections one obtains for the an energy spread of a few percent. It was not same ratio the value 1.8 x 10 -8, in presumably found worthwhile, with this material, to extend the
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it
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224
G. B X C K S T R ~ M
analysis by a folding procedure in order to determine more accurately the energy distribution, because a closer study of Compton scattering by bound electrons should be made at low energy, preferably with a curved clystal diffraction spectrom e t e r - o r indeed by means of nuclear resonance scattering. It had been planned that the potentiality of the Compton scattering method of nuclear resonance scattering would next be investigated in full scale, using a Co 6° source and the 477 keV level of Li T. At this stage, however, it was brought to the author's attention that a similar experiment had been successfully made elsewhere and that the result is under publicationS). In this situation there remains only to summarize the virtues of the Compton scattering method and to discuss its scope of application for life-time measurements. 1. The most important advantage is that the same source m a y be used for the study of levels in a wide region of energies, while most other methods require a special arrangement for each level to be investigated. The useful range of a Co 6° source is approximately 0.3-1.2 MeV. The range m a y be extended to somewhat higher energies by the use of Eu 1s2 which also has some other advantages over Co 6° in this application. It seems possible to reach 2.5 MeV by means of a source of Na 24 (15 hours) but the apparatus has then to be attached to a high flux nuclear reactor, where the source m a y be repeatedly irradiated. In order to increase the maximum energy further one might consider using the prompt g a m m a rays arising in neutron capture. An element yielding a prominent maximum-energy transition would then have to be irradiated continuously in a reactor. The background of fast neutrons may be a problem in this scheme, however. 2. The background counting rate in this type of 5) W. L. Mouton, J. P. F. Sellschop and G. Wiechers, Phys. Rev., 119 (1963) 361.
resonance scattering experiment will vary only slowly with the angle 0 and m a y quite accurately be subtracted from the total to yield the resonant counting rate. An increase in counting rate of only a few percent should be sufficient for the measurement of a resonance. The determination of the level life-time generally requires knowledge of the spectral composition of the exciting radiation. A calibration in terms of strong resonances, where the line shape m a y be examined in detail, then suggests itself, and as a second solution the self-absorption technique m a y be used. 3. It is important to estimate how m a n y levels that m a y be excited by the Compton method. The 477 keV state in Li T is a rather favourable case, as it involves a mean life of 10 -13 sec and such low atomic number that non-resonant elastic scattering becomes negligible. Assuming a standard Compton energy spread of 2 % one obtains for the crosssections of resonant and Rayleigh scattering a(r)/a(R) = l O - S / z Z 3
where z is the mean life of the level in seconds. F r o m the point of view of this ratio, the method seems rather generally applicable in the region of 1 0 - 1 , sec, and since levels of this life-time are expected to be quite abundant at energies of 1-2 MeV, a number of cases m a y certainly be studied. 4. The secondary beam is partially polarized. It is not probable, however, that the intensity will permit one to take advantage of this feature.
Acknowledgements It is a pleasure to thank Professor Kai Siegbahn for the encouragement given in the course of this work. The friendly interest of Drs. P. Bergvall and O. Beckman is greatly appreciated. Thanks are also due to F. M. Sven A n t m a n for assistance in the experiments. The work was made possible by grants from Svenska Statens Atomr~d and the European Office of Aerospace Research, United States Air Force.