Random Data Analysis and Measurement Procedures
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Resonant Nuclear Scattering of 198Hg Gamma-Rays
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1953 Proc. Phys. Soc. A 66 585
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Resonant Nuclear Scattering of 19'Hg Gamma-Rays
BY P. B. MOON AND A. STORRUSTE" Department of Physics, University of Birmingham
MS. received 15th January 1953
Abstract. The resonant scattering has been measured using the original principle ,-,f Doppler shift produced by mechanical motion, but with a quite different experimental arrangement. The intrinsic width of the 0.411 MeV excited state is estimated to be about 5 x 10-6ev, corresponding to a half-life of about 8 x 10-11 second. The difference from the first estimate ( T ~ 1 0 - l ~ sec) is mainly &e to the statistical weight factor of 5 resulting from the now well-established spin (2) of the excited state. This factor causes the resonant-scattering values t o differ considerably from the most recent direct measurement of the half-life, (1.0 i 1-7) x 10-l1 sec, and possible causes of the discrepancy are discussed.
0 1. INTRODUCTION R E V I O U S experiments (Moon 1951) on the scattering in liquid mercury of the 0.411 MeV gamma-rays of 19*Hg showed a small increase of intensity P when the source, carried on a high-speed rotor, approached the scatterer
at a speed such that Doppler effect compensated for energy lost to nuclear recoils and so restored resonance betweeE the energy available from the gamma-ray and the energy required for resonant excitation of the scattering nucleus.
We here describe the confirmatory experiments briefly mentioned in the former paper, and discuss them in the light of more recent information about the nuclear levels.
$2. METHOD OF EXPERIMENT In the earlier experiments a Geiger-Muller counter surrounded by + in. of
lead detected the radiation scattered at an average angle of 115" ; the background due to Compton scattering was several times the irreducible background of elastic electronic (Rayleigh) scattering.
In the present experiments the Compton background was reduced in two alternative ways: by increasing the angle to about 135" and, at a smaller angle of about 106", by using a lead-shielded scintillation counter suitably biased against soft gamma-rays. (With the scintillation counter the Compton background was less than that of Rayleigh scattering, which is a more direct standard against which to measure the resonant scattering ; having the same energy, they are equally attenuated in emerging from the scatterer and passing through the shielding, and they are detected with equal efficiency.)
At the same time a drastic change was made in the geometry of the apparatus, primarily to verify that the effect observed by Moon was not peculiar to his arrangement.
The new arrangement (see figure) had the following advantages : (i) continuous irradiation of the scatterer, which in the old apparatus could 'see' the source for Qnly a fraction of the time; (ii) symmetry about the axis of rotation, a drift of
* Now at Fysisk Institutt, Universitetet, Blindem, pr. Oslo, Norway. PROC. PHYS. SOC. LXVI, 7-A 39
586 P. B. Moon and A. Storruste
which could give only a second-order change in the mean intensity of irradiation; (iii) the possibility of using, at the same time, two detectors at different angles of scattering.
(iv) greater distance of detector from scatterer ; (v) greater sensitivity to changes of length of the rotor; (vi) greater scattering from the coils with which the rotor was electromagnetically driven. This prevented observations during acceleration ; when full speed was reached, the coils were removed by remote control and readings were taken as the rotor slowly decelerated.
These advantages were offset by the following disadvantages :
(a) Ver t i ca l Section
R S A 1,s L
%l T sc
Rotor Sources Collimator Lead Shot Solid Lead Mercury Geiger-muif er Counter Table Scintillation Counter
Vertical and horizontal sections of the apparatus are shown, arrangements for driving and stabilizing the rotor being omitted. The gamma-rays travel obliquely to the planes shown in the figure.
After some preliminary tests in which only the Geiger counter was used, three runs were made with both counters in use, interspersed with blank runs in which either the direction of rotation was reversed or the mercury scatterer was replaced by a geometrically similar scatterer of lead. T o counteract any effects due to diurnal drifts of temperature or of counter voltages, care was taken to distribute forward and blank runs evenly between morning and afternoon, the photomultiplier case was water-cooled and extra stabilization of mains voltage was provided.
$3, RESULTS Detailed plots of the variation of counting rate with speed have been given
by Storruste (1951). Table 1 shows the percentage excess of the average counting rate at speeds
above 4 x lo4 cmsec-l over the counting rate at lower speeds. I t is seen that a positive effect occurs even with the reverse and dummy experiments. Much of this is due to stretching of the rotor at high speeds, a s was shown by an experiment in which a stationary rotor with a source at one end only was set UP
Resonant Nuclear Scattering of lS8Hg Gamma-Rays 587
in the normal position and then given various radial displacements. The back- ground of the scintillation counter increased by 10% for each millimetre of
Calculation showed rhat the half-length of the rotor was 0.2 mm greater at an average 'high' speed that at an average low speed, SO that a 2% change of counting rate is to be expected. Thermal contraction of the lead shot as the apparatus cools during deceleration, giving improved shielding against direct rays, accounts for about 0.2 % ; the remainder, if real, may be due to a temperature coefficient of the phosphor (CaWO,).
Table 1. Ratio of Mean Counting Rates at Source Speeds above and below 4 x IO4 cm sec-1
H g Hg Hg Pb Hg Hg forward backward forward forward forward backward (a.m.) (p.m.) (p.m.) (a.m.) (p.m.) (a.m.) 1.048 1.023 1.043 1.028 1.068 1.035 Scintillation counter (106")
1.038 1.019 Geiger counter (135)" 1.077 1.053 1.055 1.034
Next it will be seen that for each of the six pairs of results the 'forward' one shows a greater effect than the ' reverse ' or ' dummy'. The same was true of the two pairs taken with the earlier apparatus, and of the three pairs that constituted the preliminary tests of the present apparatus. These eleven pairs, involving two kinds of counter, two forms of ' blank' experiment and two quite different geometrical arrangements, leave no doubt of the existence of the resonant scattering.
$4. ANALYSIS OF RESULTS In estimating the actual intensity of the resonant scattering, the measurements
with the scintillation counter should be superior because of the higher rate of counting as well as for the reasons given in $2. The method of analysis will therefore be illustrated with reference to these results rather than those obtained with the Geiger counter.
An experimental analysis was first made of the various contributions to the low-speed counting rate. The percentages were as follows : counter background, 8%; radiation penetrating directly through shielding, 24 % ; scattering from collimator, walls and floor of room, ctc., 34%; scattering from mercury, 34%.
A theoretical analysis was then made of the various components of scattering from the mercury, including that due to the weak high energy gamma-rays from lg8Hg. Each entry of table 2 shows the cross section per unit solid angle (at the mean angle of 106") for the process in question, multiplied by its relative chance of penetrating the lead shield and being detected by the scintillation counter, this chance being takeii as unity for elastic scattering.
Table 2. Effective Cross Sections for Various Components of Secondary Radiation
Primary Effective cross section (cmz sterad-l at 106") x Process ?-ray (MeV)
0.41 Elastic scattering (Rayleigh and Thomson) 10 0.41 Compton scattering 5.9
1 .OS Compton scattering 1 *4
0.41 Bremsstrahlung from photoelectrons 0.4 0.67 Compton scattering 1.3
Total 19.0 3 5-2
588 P. B. Moon and A. Storruste
The total of 19 x l e 2 ' cm2 steradu1 thus represents the cross section for a fictitious elastic scattering process that would give the same counting rate as all the actual processes (except resonant scattering) that occur in the scatterer, These, as stated above, were responsible for 34% of the total background, so if the resonant scattering at some particular rotor speed is X% of the background, its equivalent cross section is (x/34) x 19 x
Taking the detailed plots of counting rate against rotor speed, averaging the 'real' and 'blank' experiments separately and subtracting their ordinates, we obtained the experimental resonant-scattering cross section as a function of rotor speed. It is not, of course, a nuclear constant, but it may be useful to mention that at the highest speed (7.5 x lO4cmsec-l) it was found to be about 2 x 10-2' cm2 sterad-I, which may be compared with Compton and Rayleigh cross sections of about 10-24 and 10-*6 cm2 sterad-l respectively.
If the Doppler shift added to the energy E of the y-ray by the velocity U of the rotor tip were simply Eulc, the cross section should theoretically be
where I is the isotopic abundance of the resonantly scattering isotope, A its (conventional) atomic weight, ga and g b the multiplicities of the excited and ground states respectively, and T the mean of the temperatures of the source and the scatterer ; U is the actual speed of approach of source to scatterer, lcm is the optimum speed of approach (for Ig8Hg, 6.7 x lo4 cm sec-I) and f(0) is the angular distribution factor, normalized so as to be equal to unity for isotropic scattering. I? is the width of the excited state and, like E, is measured in electron volts.
However, the velocity component of the source towards the scatterer is equal t o the speed of the source only for those gamma-rays which leave the source exactly in the direction of its motion ; the coarse structure of the collimator and the incomplete opacity of its fins to the gamma-rays together allow a considerable spread of angle in the horizontal plane, while in the vertical plane the considerable height of the cylindrical scatterer has to be taken into account. An estimate of the corrections to be applied was first made (Storruste 1951) by calculations in which the scatterer was imagined split into several sections. The correction has since been determined experimentally by placing a scintillation counter at various heights representing the various sections of the scatterer and, for each of these positions, placing a stationary l9*Hg source in a series of positions round the circle described by the rotor tip. From the measured relative intensities and the angles, combined with the theoretical variation of resonant scattering with velocity of approach, it was found (for example) that at the rotor tip speed nominally corresponding to resonance (6.7 x 104 cm sec-1) the spread of velocity components would reduce the actual resonant scattering to 0.30 of the ideal maximum. Correcting in this manner the cross sections observed at various source speeds, and comparing them with eqn. (l) , we find the mean value, in electron volts, for 0 = 106" :
, . . . * (2) T h e Geiger counter at 135" gave an identical result.
T h e expression given by Moon (1951, eqn. (7)) was for the total cross section without statistical weights ; the factor 3 .O x lobg was accidentally omitted from this equation only.
Resonant Nuclear Scattering of 19SHg Gamma-Rays
5 . DISCUSSION
Owing to the smallness of the effect and the complexity of the corrections, the above result might easily be in error by a factor of two ; it is in reasonable agreement with Moon's estimate of 3 x and with the 3.9 x 10-5 obtained recently by Malmfors (1952), who has observed resonant scattering by raising the Source of gamma-rays to a high temperature.
It is now almost certain from internal conversion measurements (Siegbahn and Hedgran 1949, Elliott and Wolfson 1951) that the transition in question is an electric quadrupole one between a ground state of spin zero and an upper state of spin 2, and this agrees with the general rule for even-even nuclei (Goldhaber and Sunyar 1951). If so, the factorgb/g, is + and f ( 0 ) at 106" is close to unity, while at 135"f(8) is 8. The width I? as obtained from the scintillation counter would then be about 4 x 10-sev, corresponding to a half-life of about 10-10 sec, while the Geiger counter gives .F = 6 x ev, TI,, = 6 x 10-11 second.
Graham and Bell (1951) have looked for the half-life directly, finding (1.0 1.7) x second. Though the various experimental results might be strained to fit a value of TI/, in the neighbourhood of 4 x 10-11 sec, it is necessary to consider whether the discrepancy may be due to the use of eqn. (1). The basic equation for resonant scattering, including the statistical factor g,/gb, is securely linked to Einstein's detailed-balancing derivation of Planck's law, but eqn. (1) involves the additional assumptions that the @-ray recoil has been dissipated by collisions before the y-ray is emitted, and that the initial velocity of y-ray recoil is to be calculated for free nuclei unaffected by their surrounding electrons and neighbouring atoms, but having thermal velocities as in a gas.
In support of the first assumption it may be mentioned that the mean delay between ,B and y emission is much greater than the time required for the recoiling nucleus to travel an interatomic distance, while the Debye frequency v,,, for gold corresponds to an energy hv, of about 1.5 x lO-,ev, so there should be little quantum restriction upon transfer of energy to the lattice. The low Debye temperature (175"~) makes ' gaseous ' thermal velocities a good approximation.
The assumption of free y-ray recoil rests upon the conception of emission, absorption and re-emission of the photon as three separate instantaneous acts, collisions made by the scattering nucleus while in the excited state affecting the exact energy of the scattered photon but not retrospectively affecting the process of excitation. More experimental evidence-particularly a test of whether the maximum scattering occurs at the predicted relative velocity of source and scatterer-is needed to determine whether recoil is, in fact, free.
the speed of the rotor during the experiments. obtained with the aid of a Royal Society Government Grant.
The authors are grateful to Mr. '1'. ri. su l l for controlling and measuring Part of the apparatus was
REFERENCES ELLIOTT, L. G., and WOLFSON, J. L., 1951, Phys. Rev., 82, 333. GOLDHABER, M., and SUNYAR, A. W., 1951, Phys. Rev., 83, 906. GRAHAM, R. L., and BELL, R. E., 1951, Phys. Rev., 84, 380. MALMFORS, K. G., 1952, A r k . Fys., 6, 49. MOON, P. B., 1951, Proc. Phys. Soc. A, 64, 76. SIEGBAHN, K., and HEDGRAN, A., 1949, Phys. Rev., 75, 523. STOR~USTE, A., 1951, Thesis, University of Oslo.