Neutron evaporation spectra

Nuclear Physics 42 (1963) 2 6 4 - - 2 7 9 ; @ North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

NEUTRON EVAPORATION SPECTRA C. H. H O L B R O W t a n d H. H. B A R S C H A L L

University of Wisconsin, Madison, Wisconsin tt Received 5 N o v e m b e r 1962 Abstract: T h i n targets o f Ni, Rh, T a a n d A u were b o m b a r d e d with p r o t o n s o f energies between 6 a n d 12 MeV. N e u t r o n s emitted at angles up to 140 ° were observed. T h e n e u t r o n spectra were studied by time-of-flight spectroscopy. Except for Ni, c o n t i n u o u s spectra resulted which h a d a Maxwellian energy distribution. T h e nuclear t e m p e r a t u r e showed, however, an a n o m a l o u s increase with b o m b a r d i n g energy. Results consistent with the statistical theory could be obtained in the case o f R h by taking into a c c o u n t the energy dependence o f the inverse reaction cross section.

1. Introduction

Recent articles by Erba et al. 1) and Bodansky 2) have reviewed the theory and the experimental data on statistical features in nuclear reactions. If in a nuclear reaction many states of the compound nucleus and many states of the residual nucleus are excited, a continuous energy spectrum of the emit,ted particles results. Under the assumptions of the statistical theory this energy spectrum N(E) is, according to Weisskopf 3- 5), related to the level density of the residual nucleus to(U) by N(E) oc a¢(E)Eto(U),

(I)

where E is the energyof the emitted particle, U is the excitationenergyof the residual nucleus, and ac(E) is the inverse reaction cross section, i.e., the cross section for the formation of the compound nucleus when the residual nucleus is bombarded by the emitted particle. Expressions for to(U) have been derived under various assumptions, and the present status of the level density problem has been reviewed by Ericson 6). The expressions with which experimental results are usually compared are either to(U) oc U -2 exp [2(aU)~]

(2)

to(U)oc exp (u/r),

(3)

or

where the constant a is called the level density parameter. The quantity T is called the nuclear temperature and is usually assumed to be independent of U. Eq. (2) is based on the Fermi gas model 7). If T is independent of U, eq. (3) results in a t N o w at Haverford College, Haverford, Pennsylvania. tt W o r k s u p p o r t e d by the U. S. A t o m i c Energy C o m m i s s i o n . 264

265

NEUTRON EVAPORATION SPECTRA

Maxwellian energy distribution of the emitted particles which is the same as that of molecules evaporated from a liquid 3,4). Hurwitz and Bethe s) suggested that for nuclei containing an odd number of nucleons, U should be measured from an energy 6 above the ground state in order to take into account the pairing energy. Values of the pairing energy 6 have been deduced by Cameron9)on the basisofnuclear masses. If ~ is introduced into eq. (2), it becomes co(U) oc ( U - f ) -2 exp

{2[a(U-6)]i}.

(4)

In the present experiments the applicability of the statistical theory to (p, n) reactions was studied. The choice of neutrons as the emitted particles has the advantage that the inverse reaction cross section varies much more slowly with energy than when charged particles are emitted. In fact, neutron spectra have frequently been analysed under the assumption that ire(E) is independent of E. Another advantage of neutrons is that experiments can be performed at low enough bombarding energies that direct interactions and competing reactions would be expected to be unimportant.

2. Experimental Procedure Protons accelerated with a Tandem electrostatic accelerator to energies between 6 and 12 MeV were used to bombard targets of Ni, Rh, Ta and Au. These targets were self-supporting metal foils which were mounted so that they could be remotely moved into, and out of, the proton beam. The target thicknesses were determined by weighing and are listed in table 1. After passing through the target the beam was TABLE I

Targets used in the experiments Element

Thickness (mg/cm~)

Energy loss for 9-MeV protons (keV)

Ni Rh Ta

3.2 7.1 10.7

100 190 220

Au

7.0

140

stopped in backings of natural carbon or of Ni enriched to 99.5 ~ in Ni 5s. These backings were chosen because they produce relatively few neutrons. The proton beam incident on the target was monitored with a current integrator. Neutrons were detected in a liquid scintillator with pulse shape discrimination against gamma-rays. The detector was placed 2 m from the target at angles from 0 ° to 90 ° with respect to the incident protons, and 1.5 m from the target at angles from 90 ° to 140 °. The detector was biased at 0.5 MeV, and its sensitivity as a function of neutron energy was determined with T(p, n) and D(d, n) neutrons as described

266

C. H. HOLBROW AND H. H. BAI~CHALL

previously 1o). Because of the steepness of the sensitivity curve near the bias energy, the detection efficiency for neutrons below 1 MeV energy was considered too unreliable for determining energy spectra. Neutron spectra were determined by time-of-flight spectrometry using a vernier :hronotron 1~) and a klystron beam buncher in the system described earlier 12). Neutron backgrounds produced by the proton beam were determined by moving the target foil out of the beam. Backgrounds caused by room scattering were measured by shielding the detector from the target with a brass shadow bar. Conversions of the time spectra to energy spectra, as well as corrections for detector efficiency and backgrounds, were performed with the aid of an IBM 704 computer as described previously 13). The computer also calculated differential cross sections and integrated them over neutron energy. Only spectra in the laboratory system are presented, because, for emission angles other than 0 °, different parts of the spectra correspond to different c.m. angles• The conversions to the c.m. system would produce changes which are within the experimental uncertainty. 20£ -

5040 30 -'~ ,

-

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Q=-69 MeV

15C

~0

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~ ~ Q:-75 MQV

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30 40

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60 80 90 iO0 I10 120 130 CHANNEL NUMBER

Fig. I. T i m e - o f - f l i g h t s p e c t r u m ( c o r r e c t e d f o r d e t e c t o r e f f i c i e n c y ) o f n e u t r o n s f r o m the N i ( p , n) re-

action at a bombarding energy of 9 MeV and a neutron emission angle of 0°. 3. Results 3.1. N I C K E L

Fig. 1 shows a time spectrum obtained at 0 ° neutron emission angle when the Ni target was bombarded with 9 MeV protons. This spectrum exhibits several pronounced peaks• It is clear, therefore, that it cannot be interpreted in terms of the statistical theory• Since the bombarding energy is below the threshold for the NiSa(p, n) reaction and Ni 6° is seven times more abundant than any of the remaining isotopes, the peaks are probably due to the Ni6°(p, n) reaction. The reaction energies corresponding to the four peaks are shown in fig. 1. No appreciable amount of structure occurred in the spectra obtained with Rh, Au, and Ta targets• 3.2. R H O D I U M

For Rh, data were taken every MeV from 6 to 12 MeV proton energy and, except

NEUTRON

EVAPORATION

267

SPECTRA

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6

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t:

',

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Fig. 3. Spectra of neutrons from the Rh(p, n) reaction at a neutron emission angle of 80 c and at the bombarding energies Ep. Nuclear temperatures T of Pd 10~ are given for each plot. T h e three triangles in the lower left hand plot indicate the energy resolution of the spectrometer. The arrows indicate the m a x i m u m energy of neutrons from the (p, 2n) reaction.

at 6 MeV, at angles of 0% 40 °, 80 ° and 120 °. Measurements at additional angles were performed at 7 and 8 MeV proton energy. In fig. 2 the results obtained at a fixed bombarding energy of 7 MeV are shown for different angles; in fig. 3 results obtained at a fixed angle of 80 ° are presented for different bombarding energies. In each case log [N(E,)/E,] is plotted against the neutron energy E.. The energy resolution of the neutron spectrometer and its variation with energy is shown b y the resolution triangles in the graph for 10 MeV protons in fig. 3. The same resolution was used in all the experiments. The neutron energy E. is related to the excitation energy U by U = Ep+Q-E.,

(5)

NEUTRON EVAPORATION SPECTRA

269

where Ep is the proton energy, and Q is the reaction energy. Therefore, if the spectrum can be described by eq. (1) and the level density varies according to eq. (3) and if the energy dependence of the inverse reaction cross section is negligible, the plots o f figs. 2 and 3 yield curves the slope of which determines the nuclear temperature 7". All the data up to proton bombarding energies of 10 MeV can be fitted fairly well with straight lines indicating that T is a constant for each spectrum. All the spectra taken at 11 and 12 MeV show, however, marked deviations from straight lines for the lower neutron energies. The arrows in fig. 3 indicate the maximum energy of neutrons from the Rh(p, 2n) reaction. Since the breaks in the straight lines occur just at the energies indicated by the arrows, it is believed that below these energies neutrons from the Rh(p, 2n) reaction contribute to the spectrum. Because of the Coulomb barrier the (p, pn) reaction should not produce an appreciable number of neutrons. All the solid lines drawn through the experimental points in fig. 2 have, within the accuracy of the experiment, the same slope. The resulting temperatures T are indicated for each angle. At other bombarding energies the slopes were likewise the same at all angles. This would be expected if the statistical theory is applicable. At each bombarding energy the differential cross section for neutron emission was, within the accuracy of the measurement of about 15 ~o, independent of angle. If the reaction proceeds through a compound nucleus, the angular distribution should be symmetric about 90 °. The observed angular distributions were in fact isotropic. The observed symmetry about 90 ° of the angular distribution indicates that direct interactions do not contribute appreciably to the neutron emission. In table 2 the cross sections for the emission of neutrons of energy greater than 0.5 MeV are listed in the third column for different bombarding energies. These TABLE 2 Cross section for neutron production Element

Rh

Ta

Au

Ep (MeV)

Cross section for production o f neutrons with E n > 0.5 MeV (rob)

Cross section for (n, p) reaction (rob)

Results o f refs.14, is) (rob)

7 8 9 10 11 12 8 9 10 11 12 9 10 1! 12

130 250 500 750 950 1100 50 160 400 750 1000 60 250 500 630

150 310 450 660 640 630 40 140 160

230 400 550 700

60 200

60 100

45 100 110

C. H. HOLBROWANDH. H. ItAEHALL

270

cross sections include neutrons from the Rh(p, 2n) reaction and are integrated over all angles. In the fourth column of table 2 the cross sections for the Rh(p, n) reaction are given. These cross sections do not include the Rh(p, 2n) reaction and were obtained by extrapolating the solid lines, shown in figs. 2 and 3, to E, = 0. For comparison, results for the total cross section obtained by Hansen and Albert ~4) are shown in the last column. In the experiment of Hansen and Albert the flux of all emitted neutrons was measured with a long counter. Although the latter experiments give higher value than the present measurements of the (p, n) cross section, the results are probably within the experimental uncertainty. To~l(p,n)W fSI £p • ~0 MeV

LO7

io7 k

8 • 0°

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x~%

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4

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7

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1

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£n(MeV)

Fig. 4. Spectra of neutrons from the Ta(p, n) reaction at a bombarding energy of 10 MeV, 0 is the neutron emission angle, and T is the nuclear temperature of W I~1 determined from the slope of the solid line. The arrows indicate the maximum energy of neutrons from the (p, 2n) reactions.

3.3TANTALUM .

Fig. 4 shows neutron spectra obtained when Ta was bombarded with 10 MeV protons for emission angles of 0 °, 40 °, 80 ° and 120 °. Because of the low neutron yield compared to the background the spectra could be measured only up to an energy of about 4 MeV. In fig. 5 spectra are shown which were obtained at 0 ° and different

NEUTRON

EVAIN)RATION

271

SPECTRA

proton energies• All the plots are presented in the same way as the Rh data. From the slopes of the solid lines the indicated temperatures were deduced. The solid lines were drawn through the points at neutron energies where only the Ta(p, n) reaction is energetically possible. Spectra were also taken at other angles at 8 and 9 MeV proton energy. Within the rather large statistical uncertainty, temperatures were again independent of emission angle, and the neutron emission was isotropic. In table 2 cross sections, obtained in the same way as those for Rh, are given for Ta. For proton energies of 11 and 12 MeV the cross section for the Ta(p, n) Tol~(p, n)wlgl 8,0"

i@

ioz EP • 8

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MeV

•

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4

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2

3

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6

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E n (MW)

Fig. 5. Neutron spectra from the Ta(p, n) reaction at a neutron emission angle of 0 ° and at the bombarding energiea Ep. The quantity T is the nuclear temperature of W m.

reaction alone could not be determined because of the small number of neutrons emitted in the energy region where only the (p, n) reaction is energetically possible. The last column of table 2 compares the Ta(p, n) cross sections with those obtained by Hansen et al. is) using an activation method. 3.4. GOLD

Spectra of neutrons emitted in the proton bombardment of Au 197 are shown in

272

c.H.

HOLBROW

AND

H.

H.

BARSCHALL

figs. 6 and 7, and cross sections are summarized in table 2. The same comments apply to these results as to the tantalum results. The last column gives again the activation results o f Hansen et al.lS). 3.5. E X P E R I M E N T A L UNCERTAINTIES

Typical statistical uncertainties are shown in every spectrum. They vary from 3 % to 20 % for the Rh spectra, and from 10 % to 40 % for the Ta and Au data

Au~J7(p,n)Hg197 Fp-I0 MeV I07

107

~\

0,0" T: 860 keV

\\

106 ~

I0 5

0

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• 4o"

T z 820 keV

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O - 80 °

I0 6

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En (MeV) Fig. 6. Spectra o f neutrons from the Au(p, n) reaction at a bombarding energy of 10 MeV for neutron emission angles 0. T h e quantity T is the nuclear temperature of Hgt*L

shown. Another important source o f error is the efficiency determination of the detector which has an uncertainty of the order o f 15 %. For the cross section for production o f neutrons of energy greater than 0.5 MeV given in table 2, the main uncertainty is the 15 % error in detector efficiency. At the highest bombarding energies the statistical uncertainty in the Ta and Au data contributes an additional error. For the total (p, n) cross sections there is a further

273

NEUTRON EVAPORATION SPECTRA

uncertainty because of the extrapolation to zero neutron energy. The total uncertainty in the (p, n) cross section is estimated to be of the order of 30 %. In the determinations of the nuclear temperatures from the slopes, the uncertainties are estimated to be 7 % for Pd 1°3, 10 % for W tSt and 15 9/0 for Hg 197. Although the variation of energy resolution with neutron energy produces some distortion of the spectrum, this introduces a smaller error into the temperature determination than the statistical and efficiency errors. Aulg"~p,n)Pd r03 8 = 40"

i06~'N ° I

IO7

rp = 9 MeV

"X~.

~',

Ep • I0 MeV T • 820 keY

T" 960 keY

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2

3

4

5

6

10 4

7

~o71~ N

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2

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107 :,\

Ep= II MeV

,

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5

6

7

~p= 12 MeV

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N

°~.

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3

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5

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2

3

4

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6

7

E n (MeV)

Fig. 7. Spectra of neutrons from the Au(p, n) reaction at a neutron emission angle of 40° and at the bombarding energies Ep. 4. D i s c u s s i o n

Since the Rh data are considerably more accurate than those for Ta and Au, the discussion will be concerned primarily with the neutron spectra from the proton bombardment of Rh. I f the nuclear temperatures obtained for Pd 1°3 from measurements at different angles, but at the same proton energy, are averaged, the values tabulated in the

274

c.H.

HOLBROW AND H. H. BARSCHALL

second column of table 3 and plotted in fig. 8 are obtained. For 11 and 12 MeV proton energy a portion of the spectrum was used for which only the Rh(p, n) reaction is energetically possible. In fig. 8 nuclear temperatures obtained by other authors ,6, ,~) are also shown. The errors for the present measurements are based on the consistency of the determinations at different angles. Although the uncertainties are large, the temperatures appear to increase with bombarding energy. Such an apparent dependence of nuclear temperature on bombarding energy has previously been observed by Sidorov ,s) in his study of (0t, n) reactions. If T is independent of U, as figs. 2-7 appear to indicate, it should, according to eq. (5), also be independent of E o, unless the assumptions of the statistical theory are not right. Sidorov suggested that eq. (1) may be invalid because the compound nucleus does not live long enough to attain statistical equilibrium. In the following, alternative explanations of the anomalous temperature behaviour are examined. t2 • BRAMBLETT and BONNER x ALBERT el oL • PRESENT DATA

I.I

1.0

t

>- 0.9 b-

T

t

OB

tt! t{

07 0.6 O~

[ 5

i 6

1 7

t

I

8 9 Ep (NN~V)

I I0

iii

I 12

13

Fig. 8. T h e v a r i a t i o n o f the nuclear t e m p e r a t u r e T o f P d tos a v e r a g e d o v e r angles for each b o m b a r d i n g energy, as a f u n c t i o n o f p r o t o n b o m b a r d i n g energy.

TABLE 3 N u c l e a r temperatures (in MeV) Ep

pdl0 s

7

0.74

(MeV)

WIBI

8

0.77

0.64

9

0.83

0.70

10

0.86

0.78

11

0.94

12

1.04

Hgll7

0.8 0.8 0.9

In fig. 9 the Rh data taken at 8, 9, 10 and 11 MeV proton energy are plotted to investigate how well the level density expression (2) fits the data. In fig. 9

N E U T R O N EVAI~RATION SPECTRA

log

[U2N(E,)/E,] is

27~

p l o t t e d against U*. T h e curves were n o r m a l i z e d to the s a m e

o r d i n a t e at U = 4 M e V . I f eq. (2) h o l d s , a single straight line s h o u l d result. N o

IOlO, iO9

/ ///• /x

//./ ;~hlO3(P,n ) pdl03

,,~, ,/

[08

"

,

//2". / d,

L,jc

¢..

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106

2"

.,2

7"

. . . . . . .

Ep

........

£p'9

,/

MeV

MeV

E p " I 0 MeV

,7 . . . . . .

/

10'12

• 8

14

16

18

20

22

Ep,II

24

MeV

26

30

UI/2 (MeVl/2}

Fig. 9. Neutron spectra from the Rh(p, n) reaction plotted to test the fit of the Fermi gas formula to the data. I0 8

,

,

,

,

,

,

+

,

i

,

+

i

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/j/" /

106

./

.... .

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. L4

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.

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.

.

.,,.v .

.

.

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10 5

.

Ep- II MI~'

,

, 22

,

i

,

Z.4

uu'z o ~ v ~

Fig. 10. Neutron spectra from the Rh(p, n) re,action plotted to test the fit of the Fermi gas formula to the data when the variation of a c with E n is taken into account.

C. H. HOLBROW AND H. H. BARSCI-L~LL

27~

points are shown in fig. 9, because spectra obtained at different angles were averaged. The curves in fig. 9 are neither coincident nor straight. This result is consistent with the observation that the nuclear temperatures depend on bombarding energy. It would appear that eq. (3) fits the data better than eq. (2). So far it has been assumed that tr¢ in eq. (I) is independent of E,. As a next step, the variation of trc with E, was taken into account by using reaction cross sections @'[

107

Rh~(p,n) pdm

rx, x

I0"~ ~

T-740keV

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3 4 5 £. (MeV)

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F.I =7MeV, e=8o-

103

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4

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Fig. 11. Spectra of n e u t r o n s f r o m the R h ( p , n) reaction at a n e u t r o n emission a ngl e o f 80 ° a nd at the b o m b a r d i n g energies indicated by Ep. A c o r r e c t i o n has been m a d e for the v a r i a t i o n o f a c with E,. The nuclear t e m p e r a t u r e s T of Pd t°s are deduced from the solid lines t h r o u g h the points.

based on the optical model. Although ac is the cross section for the bombardment of the residual nucleus in an excited state, it is assumed that this cross section is the same as that for the residual nucleus in its ground state. The optical model cross sections tabulated by Campbell et al. 19) were used. These are based on a SaxonWoods potential

NEUTRON

I/=

EVAPORATION

277

SPECTRA

- I/0 (1 + i~)r i + exp [ 2 ( r - R)/d]] -i

(6)

with the parameters Vo = 52 MeV, ~ = 0.06, d = 1.04 fm and R = (1.15A t +0.4)fm. In fig. 10 the curves of fig. 9 are replotted after dividing by the ac so obtained. These curves are straighter and more nearly parallel than those in fig. 9. If the data in fig. 3 are replotted after dividing by Go one obtains the curves of fig. 11. The variation of temperature with bombarding energy has become smaller and may in part be due to the fact that all the points do not lie on a straight line. If other parameters had been used for the optical model potential, it might have been possible 108

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.

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,

2_4

(u- ~p'Z(MeVO'2) Fig. 12. N e u t r o n spectra f r o m the R h ( p , n) reaction plotted to test the fit o f the Fermi gas f o r m u l a to t h e d a t a w h e n b o t h the pairing energy a n d t h e variation o f a c with E n are t a k e n into account.

to obtain straight parallel lines in fig. 10 and to remove the apparent remaining variation of temperature with bombarding energy in fig. 11. As an additional parameter one can introduce the pairing energy 6. Using Cameron's value of ~ = 1.4 MeV, the curves of fig. 10 were replotted in fig. 12 so that straight parallel lines should be obtained if eq. (4) held for the level density. The curves in fig. 12 are indeed almost coincident and straight. The results on Ta and Au are not sufficiently accurate nor do they cover a sufficiently wide range of bombarding energies to draw definite conclusions. In table 3 nuclear temperatures averaged over angles are given in columns three and four for W lsl and n g 197, respectively. Although these temperatures also appear to increase

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C. H. HOLBROW AND H. H. BARSCHALL

with bombarding energy, the variation is not clearly outside the experimental uncertainty. When the data on Ta were plotted in the same way as fig. 9, the resulting curves likewise, were neither straight nor parallel. Taking into account the pairing energy and the variation of ac with energy, however, failed, to improve the situation markedly in this case. This may in part be due to the uncertainty in the data. In the literature values of the level density parameter a are frequently quoted. These values are usually deduced from the slopes of plots similar to those of fig. 9, i.e., without taking into account either the pairing energy or the variation of ac with energy. Because each curve of fig. 9 has a varying slope, a is not well defined and can be given only with an uncertainty of the order of 25 %. Typical values of a are 12 MeV -1 for P d 1°3 and 18 MeV -1 for W ls~ and Hg 197. Other authors have given values of a with much smaller errors, but the present values are consistent with those found in the literature. At neutron energies at which the (p, 2n) reaction is energetically possible, straight dashed lines are drawn through the experimental points in figs. 3-7. In principle, it would be possible to obtain the spectrum of the second neutrons by taking the difference between the dashed and solid lines. These differences have, however, such large statistical uncertainties that the results were not significant. The energy distribution of the second neutrons cannot be expressed in a simple way like eq. (1), and it is not expected that it can be described in terms o f one simple parameter like a or T.

5. Summary The present measurements give spectra which have the form of evaporation spectra, but, contrary to the assumption of the statistical model, yield nuclear temperatures which depend on bombarding energy. This anomalous temperature dependence may in part be due to the variation of the inverse reaction cross section with energy and to the use of too simplified expressions for the level density as a function of excitation energy. In the case of the Rh(p, n) reaction corrections for these effects yielded results consistent with the statistical theory. We wish to thank Dr. J. C. Overley for his help in performing the experiment and Dr. R. R. Borchers for his assistance in operating the spectrometer.

References I) 2) 3) 4) 5) 6) 7) 8) 9)

E. Erba, U. Facchini and Eo S. Menichella, Nuovo Cim. 22 (1961) 1237 D. Bodansky, Ann. Rev. Nuclear Sci., 12 (1962) 79 V. F. Weisskopf, Phys. Rev. 52 (1937) 295 J. M. Blatt and V. F. Weisskopf, Theoretical nuclear physics (John Wiley and Sons, New York, 1952) V. F. Weisskopf and D. H. Ewing, Phys. Rev. 57 (1940) 472 T. Ericson, Advances in Physics 9 (1960) 425 H. A. Bethe, Revs. Mod. Phys. 9 (1937) 69 H. Hurwitz and H. A. Bethe, Phys. Rev. 81 (1951) 898 A. G. W. Cameron, Can. J. Phys. 36 (1958) 1040

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10) I 1) 12) 13) 14) 15) 16) 17) 18) 19)

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C. H. Poppe, C. H. Holbrow and R. R. Borchers, Phys. Rev., to be published H . W . Lefevre and J. T. Russell, Rev. Sci. Instr. 30 (1959) 159 H. W. Lefevre, R. R. Borchers and C. H. Poppe, Rev. Sci. Instr., 33 (1962) 1231 H. W. Lefevr¢, R. R. Borchers and C. H. Poppe, Phys. Rev., 128 (1962) 1328 L. F. Hansen and R. D. Albert, Phys. Key., 128 (1962) 291 L. F. Hansen, R. C. Jopson, Hans Mark and C. D. Swift, Nuclear Physics 30 (1962) 389 R. D. Albert, J. D. Anderson and C. Wong, Phys. Rev. 120 (1960) 2149 R. L. Bramblett and T. W. Bonner, Nuclear Physics 20 (1960) 395 V. A. Sidorov, Nuclear Physics 35 (1962) 253 E. J. Campbell, H. Feshbach, C. E. Porter and V. F. Weisskopf, MIT Laboratory for Nuclear Science, Technical Report No. 73 (1960)