Nuclear spectroscopy with energy resolution of a part per million

Volume 17, number 2

PHYSICS

--

LETTERS

V’, like V diagonalizes A+A. If we introduce the left-cosets of the elements of T, and the associated invariant measure on the manifold of these cosets, the entire procedure of Bronk’s paper [5], can be applied and the result is given by (10). So, the single level distribution for the asymptotic case of large m and n, is given by the formula (68) of ref. 5 where 2 = i(m-n-l). The same general method can be applied if A is a real matrix. The joint eigenvalue distribution obtained in this case, if var(Aij) = $, is cn)deldc2.. . de, =

P(E19..

=Kexp

[

-isci

1

matrices. The distribution of the eigenvalue of AA+ is in this case a Porter Thomas distribution with u (number of degrees of freedom) = 2 m in the complex case and v = m in the real case. Although various shapes of distribution may be obtained in this way, it seems that there is not a simple criterion giving an exponential trend similar to that of the experimental level density.

References 1. F. J.Dyeon, J.Math.Phys. 3 (1962) 140;

03)

nt~~-~~~j(ti-~j)d~ldr2...

1 July 1965

M. L. Methaand M.Gaudin, Nucl. Phys. 18 (1960)420. 2. I.I.Gurevich and M. I.Pevzner, Journ.Exp.Theor. Phys.31 (1956) 162; D . J. Hughes, Proc. GatlinburgConf. on Neutron physics by time of flight, ORNL 2309 (1956)p.48; J.B.Garg, J.Rainwater, J.5.PetersenandW.W. HavensJr., Phys.Rev. 134-5B (1964) 985, 3, E . P . Wigner , Proc . GatlinburgConf. on Neutron physics by time of flight, ORNL 2309 (1956)p. 67. 4. T. Ericson, Phil. Mag.Suppl.9 (1960)425. 5. B.V.Bronk, J.Math,Phye.6(1966) 228.

de,.

To show, as an example, how various different shapes of distributions can be obtained we give in the fig. 2 the results of some Montecarlo calculations with real matrices A. As a particular case, we can consider the case n = 1 and m arbitrary for complex and real +***t

NUCLEAR

SPECTROSCOPY OF A PART

WITH ENERGY RESOLUTION PER MILLION *t

J. A. MCINTYRE and J. D. RANDALL Texas A and M University College Station, Texas Received 4 June 1965

Recent advances in nuclear physics have been closely associated with improved techniques in exciting nuclear energy levels. However, with the exception of one technique, the closely spaced energy levels near the particle thresholds of nuclei have remained inaccessible for careful study. The exceptional technique which has provided a “window” into this region, is, of course, the technique of slow neutron absorption. With this technique, levels separated in energy by tens of electron-volts are easily resolved and studied. However, this “window” is limited in its application to an energy region extending some few keV above the neutron threshold. It is the purpose of this note to describe a technique for exciting nuclei to energies between 6 and 10 MeV which also has an energy resolution of a few electron-volts. In addition, the nuclear excitation is accomplished

using electromagnetic &radiation; such excitation then permits the determination of the fundamental electromagnetic transition rates of the levels excited. The excellent energy resolution ( -1:106) of neutron-capture gamma rays has been utilized in constructing the spectrometer for making these studies. Referring to fig. 1, the neutrons for the (n,r) reaction in the source were supplied by the 100 kW Texas A and M research reactor. About 1012 neutrons set-lcm-2 were obtained at the 14-cm diameter iron source which was separated from the core by a 15-cm thick bismuth shield that was used for stopping reactor core gamma * Supported by the Rbbert A. Welch Foundation.

t This material has been submitted by J. D. Randall as part of a dissertation for the degree of Doctor of Philosophy at Texas A and M University.

137

Volume

1’7,

number 2

PHYSICS

LETTERS

1 July 1965

Delecfor

d J+_-

!

Absorber

8 I? 16 20 LNERDY SWIFTIN .”

0 I

e

Typical Spectrum

Fig. 1. Schematic diagram of the apparatus. An imaginary “typical” spectrum is shown at the lower right.

rays. The iron neutron-capture gamma rays were collimated to a 5 X 5 cm2 beam at the exit 6f the six-foot thick shield wall. A 50-cm thick paraffin plug containing boric acid was placed in the beam pipe to stop neutrons. The target was a 5-cm diameter by 2-cm thick piece of lead. This target material was used since it has been shown [I] that the 7.28 MeV iron gamma ray scatters elastically from lead by resonance scattering with a l-barn cross section. A J-inch diameter by 3inch thick NaI (Tl) scintillator placed 170 cm from the target was used as the gamma ray detector. Lead collimation between the target and the detector reduced the exposed area of the detector in the horizontal direction to 5 cm. The energy resolution for the detection of the scattered gamma rays can be calculated using the Compton scattering kinematic relations with the exception that the mass of the lead nucleus is used instead of the mass of the electron. The energy spread of the scattered gamma rays corresponding to a gamma ray of energy of 7.28 MeV being scattered by lead may thus be expressed as dE/dB = 4.8 sin 0 eV/degree The energy spread at the 5-cm wide detector therefore varies from zero at B = Oo to 8 eV at 6 = 900. The total energy variation in the 1800 range of scattering angld is 550 eV. The absorber shown in fig. 1 contains the nuclei to be studied. As the angle B for the detector is varied, the counting rate will change smoothly until an angle is reached such that a energy level is excited in the absorber nuclei. At this angle there will be a sharp increase in absorption with a corresponding decrease in counting rate as shown schematically 138

I L;O_.3+. 0

46

Ml 120 ENSROl5HIFT IN lV

160

24

200

L_+__+_+ 40 XAYYERIND ANDLE IN DEDREES

Fig. 2. Angular distribution of the elastically scattered gamma rays. The counting rate has been divided by 1 + cos2 0. The two abscissa scales give the scattering angle and the corresponding shift in gamma ray energy with respect to the beam energy. The insert at the right shows the small angle data in detail. at the lower right in fig. 1. In the experiments reported here, the lead target itself is used as the absorber, i.e. the target is thick enough so that resonance absorption of the scattered gamma rays will attenuate their number by 30%. The detector counting rate is of

the order of one per second. The background was determined by using a matched bismuth target. Except at the smallest scattering angles, the lead target counting rate was a factor of 5 larger than that of the bismuth target. The results obtained are shown in fig. 2. The counting rate at the different angles has been divided by 1 + cos2 0 to give a constant base line. (The dipole property of this scattered radiation has already been determined by Young and Donahue [ 11. ) It is seen in fig. 2 that, except for the smallest angles, there is no sign of a “dip” in the counting rate. This result would indicate‘ that there are no levels that are strongly excited in lead within 200 eV of the beam energy. However, at the small angles there is a dip as would be expected. This small-angle dip occurs because of absorption of the resonance scattered gamma rays by the same excited state in lead that is producing the scattering. Data are not yet obtainable at the smallest angles because of the Compton scattering background. The insert in fig. 2 shows this absorption dip in detail. The curve shown is that expected for a Doppler-broadened line with a Lorentz partial width, ro, of 0.8 eV. A pure Doppler line gives a significantly poorer fit. The data determine I’, to be 0.7 k 0.2 eV in agree-

Volume 1’7, number 2

PHYSICS

1 July 1965

LETTERS

ment with other measurements [ 21. These experimental techniques thus open many new “windows” into the region of the highly excited nuclear states. At least three new lines of investigation can be pursued using these experimental methods. (1) Study of the parameters of the approximately 60 energy levels that have already been excited [3] by neutron capture gamma rays by investigating small angle scattering as described in this paper [4]. (2) Study of the energy levels of the nuclei in different absorbers (see fig. 1) by using the ironlead, or some other appropriate, scattering process as a source of variable energy gamma rays. The relative spacing of the levels will be measured directly by the position of the dips; in addition the partial width of each level will be determined from a measurement of the depth of the absorption dip. (3) Selection of two nuclei for study such that the energy levels excited by the technique in [2]

will correspond to those known from slowneutron spectroscopy. Since the slow-neutron level energies are known to an accuracy of an eV with respect to the neutron threshold, while the gamma ray excitation occurs from the ground state, the relative binding energies of the neutron in the two nuclei can be determined to an accuracy of an eV. References 1. G. Ben-David and B. Huebschmann, Phys, Letters 3 (1962) 87; C.S.YoungandD.J.Donahue, Phys.Rev.132 (1963) 1724. H. H. Fleischmann and F. W.Stanek, Zeit. f. Phys. 2* 175 (1963) 1’72; B. Arad, G. Ben-David and Y. Schlesinger, Phys. Rev. 136 (1964) B370. 3. B. Arad, G. Ben-David, I. Pelah and Y. Schlesinger, 4 Phys. Rev. 133 (1964) B684. Similar information has been obtained by the investigators of ref. 2; Fleischmann and Stanek have varied the temperature of the scatterer while Arad et al. have mounted the scatterer on a rotor,

*****

CORE

POLARIZATION EFFECT IN 2ogPb THE 209Tl - 209Pb DECAY

STUDIED

IN

P. SALLING Institute University

for Theoretical of Copenhagen,

Physics Denmark

Received 4 June 1965

The level structure of 2ogPb has previously been examined in the stripping reaction 208Pb(d, p)20gPb [l] and in the beta decay 2ogT1 2ogPb [2]. In the former process most of the expected single-neutron states are populated, whereas in the 2ogT1 decay the main beta branch leads to a 2.15 MeV $- state of 2ogPb, which, resumably, corresponds to an excitation of the %08Pb core. The f- state, in turn, decays by a gamma cascade passing through the 4s; and 3% single-neutron states to the 2g$ ground state (fig. 1). The half life of the 2.15 MeV state has been reported to be 3.1 ns [2], but no information is available on the E2 rates of the s$ - df and d; - gS transitions. The present study of the 209Tl decay was undertaken with the aim of measuring the rate of the s+ --) df E2 transition, the energy of which is 470 keV. This transition is of

special interest because it provides a direct measure of the polarization of the closed core due to the odd neutron. The measurements were performec -witht4r delayed coincidence setup described in ref. 3. The equipment has been fully transistorized, and the resolving time is 200 ps f.w.h.m. with an exponential slope of 25 ps (measured with a 6oCo source and with the upper 30% of the pulseheight spectra observed with two Natonscintillators). One side of the coincidence detector was triggered by the 120 keV gamma ray. The selectivity for this gamma ray was greatly improved by a 5% lead loaded plastic scintillator * with a resolution x 50% near 100 keV and a photopeak intensity -10% the intensity of the Compton dis* Manufacturedby Pilot Chemicals, Inc. 139