2.D
[
Nuclear Physics A140 (1970) 23--32; ~) North-Holland Publishing Co., Amsterdam
I
N o t to be r e p r o d u c e d b y p h o t o p r i n t or microfilm without written permission f r o m the publisher
S T A T I S T I C A L E M I S S I O N AND N U C L E A R L E V E L D E N S I T I E S IN (~, n) R E A C T I O N S M. T. MAGDA, A. ALEVRA, INGRID R. LUKAS, D. PLOSTINARU, ELENA TRUTIA and M. MOLEA Institute for Atomic Physics, Bucharest, Romania Received 1 September 1969 Abstract: Neutron spectra from (~, n) reactions were studied by the time-of-flight method. Energy distributions of the neutrons were analysed in the frame of the statistical theory in order to determine the a level-density parameter. The values obtained were compared with the predictions of the Fermi gas model and other existing experimental data and their anomalous dependence on the mass number and the bombarding energy was attributed to the contribution of precompound processes. E
N U C L E A R R E A C T I O N S 27AI, slY, S2Cr, 5SMn, S6Fe, l°3Rh, IXSln, 139La, a°9Bi(e,n), E = 23.4 MeV; measured cr(Eo). S2Cr, S6Fe(~, n), E = 17.0 MeV; measured a(E,, 0). Residual nuclei statistical parameters a, T and ~" deduced. 1. Introduction
The statistical model was checked in the case of many reactions at intermediate energies. Most of the statistical parameters (a level-density parameter, nuclear temperature) have consistent values and the experimental data (energy and angular distributions and excitation functions) agree with the predictions of the model. However, there are some facts which seem to contradict the statistical theory, in spite of the fact that the shape of the spectra of the emitted particles is typically evaporative. These facts are the dependence of the statistical parameters on the bombarding energy and the anomalous variation of the level-density parameter with the mass number, which were first observed in the case of (e, p) and (e, e') reactions (refs. 1-7)) and afterwards in the case of other reactions 8-10). It is important to establish the existence and to explain these anomalies, in order to specify the limits of validity of the statistical model. It is expected that the specified anomalies manifest themselves in the case of (e, n) reactions too, because they are similar to (e, p) reactions but present the advantage of a simpler analysis of the experimental data due to the absence of the Coulomb barrier for the emitted particles. Starting from these considerations we have undertaken a systematical study of (e, n) reactions at intermediate bombarding energies 11 -14). Earlier data obtained from (c~, n) reactions at E~ = 13.6, 17.0 and 19.3 MeV were completed by neutron energy spectra measurements at E~ = 23.4 MeV and by angular distribution measurements in S2Cr(e, n) and S6Fe(c~, n) reactions at E~ = 17.0 MeV. 23
M.T. MAGDAet al.
24
2. Experimental method Neutron spectra were measured by the time-of-flight method at a flight path of 2.89 m. In angular distribution measurements the detector angle was varied from 0 ° to 150 ° in steps of 10 °. The block-scheme of the electronics is shown on fig. 1. For the detection of neutrons N E - 1 0 2 plastic scintillators (4 x 6 cm) coupled to 56 AVP photomultipliers were employed. The second detector was used as a monitor in the case of angular distribution measurements and served also to improve the detection efficiency in the energy distribution measurements. Rapid pulses from both detectors were analysed by a time-to-pulse-height converter 15). A second SA-40 multichannel analyser allowed
Detec/or2 rE.] ~_~ (m°nit°r)l t~-~ cZ /Tar3e~l \1 ./d ~
[i mixer -~ I I I
f 6ate
½
?
Fig. 1. Block diagram of electronics. a continuous determination of the discriminator setting in the slow chain, whose equivalence in neutron energy was employed to calculate the efficiency of the spectrometer. The energy corresponding to the discriminator setting was measured in the usual way with the aid of 7-calibration sources and converted into neutron energies, refs. 16,17). As the neutron energies were higher than 10 MeV the spectrometer efficiencies were calculated taking into account neutron-proton scattering, neutronproton double scattering and neutron-carbon interactions 18). A supplementary pulsing system 19) was used in order to obtain a full display of the neutron spectrum, whose energies range from 1.5 MeV (the bias of the spectrometer) up to 18 MeV and cover a wide interval of time due to the large flightpath.
(~) n) REACTIONS
25
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Fig. 2. R e d u c e d n e u t r o n s )ectra f r o m (c(, n) reactions at E~ = 23.4 MeV.
~
~.o o
°°
°° o
3.0t6
°°°
2.02.'2 2.~V'ff'(MeV)z'z I
1,8
Fig. 3. R e d u c e d n e u t r o n spectra f r o m (c(, n) reactions at E~ = 23.4 MeV.
26
M.T. MAGDA e t a l .
3. Results and discussion
Some typical energy spectra of neutrons emitted in (~, n) reactions on ZTA1, SXV, 52Cr, SSMn, S6Fe, l°3Rh, 11Sin, 139La and 2°9Bi, at E~ = 23.4 MeV and a laboratory angle of 90 ° are represented in figs. 2 and 3. Experimental continuous spectra of neutrons were used in the usual manner io-13) and put into the form of reduced spectra, from which the statistical parameters were determined. Except the S2Cr(~, n), 56Fe(~, n) and 2°9Bi(~, n) reactions, the energy range of (~, n) neutrons was narrow 26
a (MeV)-/
2~
• E~ =/3.6Me/ E~ =/7.8 MeV " Eo~=/9.3 PleV o Y~ -23.4 MeV
22 2O /6 f6 IX,
t /8 (3 6 4
T
lq_
T
....
2I
20 30
I
P
~O 50
~
I
I
60 70 80
90 /00 /I0 /23 /3Y /~0 /50 /80 /70 A
Fig. 4. Level density parameter versus mass n u m b e r A.
(a few time-channels) and it was necessary to take into account in the analysis the (e, pn) and (e, 2n) neutrons too. The experimental energy distribution was compared to the theoretical formula given by Le Couteur 2o): 020"
-c~QOEn
5/1J
E, exp ( - E . / T x ) .
(1)
(The nuclear temperature T is given by T =Ta-az T1.) Because (e, n) neutrons emitted in the case of S2Cr(c~,n) and S6Fe(~, n) reactions were displayed on many time-channels, an alternative calculation was possible using the usual expression: 02ff ,~ E . a j , v p ( E * ) , (2) OQaE.
(ct, n) REACTIONS
27
(E. = neutron energy, p = level density in the residual nucleus at E* excitation energy, and ai. , = the inverse reaction cross section).
~0 30
20 • AE'-34/YeV o AE'-~-5MeV
I0 I
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2 0 ° 4,0° $0 ° 80* 100 ° 120 ° I/~0" f60"/80" ~,,¢
Fig. 5. Centre-of-mass angular distribution o f the neutrons 17.0 MeV. The error bars indicate statistical errors only. The fits o f the experimental points with the expression W(O) = and 4-5 MeV) and W(O) = c%q-~2 cos 2 0 (AE*
f r o m S2Cr(~, n)55Fe reaction at E~ = solid curves represent the least-squares ~'oq-~'x cos 0q-~'2 cos 2 0 (,dE* = 3--4 = 5-6; 6-7 and 7-8 MeV).
The a-parameters resulting from both calculations agreed. This fact justified a reliable comparison of the a-values presented in this paper with our earlier results
(refs. 11,12,14)).
28
M.T. MAGDAet aL
The a-values versus mass n u m b e r A are represented o n fig. 4. Earlier results, o b t a i n e d for other b o m b a r d i n g energies (circles, triangles a n d squares) are given too.
T 26
~
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0 ° / 6 '0 '° 180°BcM
Fig. 6. Centre-of-mass angular distribution of the neutrons from 56Fe(~, n)SgNi reaction at Ea = 17.0 MeV. The error bars indicate statistical errors only. The solid curves represent the least-squares fits of the experimental points with the expression W(O) = ~'o-k~'l cos 0-k~'2 cosz 0 ( A E * = 3-4 and 4-5) and W(O) = ~o-k~2 cos 2 0 ( A E * ~ 5-6; 6-7 and 7-8 MeV). We m e n t i o n that the a-parameters were determined for the same excitation energy interval in the residual nucleus, n a m e l y 4 - 7 MeV. The full curve represents the values of the level-density parameter calculated by the e q u a t i o n given by A b d e l m a l e k a n d
(0~, n) REACTIONS
29
Stavinsky 21); the dotted curve was drawn only to guide the eye. One sees that the a-parameters extracted from (or, n) reactions at higher energies present the above mentioned anomalies: the dependence on the bombarding energy and the nonlinear dependence on the mass number. We remark that for the energy of 19.3 MeV a deviation from the linear dependence on the mass number becomes visible for mass numbers larger than 100, in accord with the results obtained by Hurwitz et aL 4) from (~, p) reactions, for the same bombarding energies. In exchange, the aparameters resulted at E~ = 13.6 and 17.0 MeV have the same values in the limits of experimental error and follow the Abdelmalek-Stavinsky curve well. It is interesting to note that the a-parameters for 13.6 and 17.0 MeV agree with those determined from neutron r e s o n a n c e s 22). One concludes that (0~,n) reactions for 0c-energies around 15 MeV are going through compound nucleus formation followed by the statistical emission. This conclusion is confirmed by the angular distributions of the evaporation neutrons. Angular distributions of the neutrons emitted in (0q n) reactions on 52Cr and 56Fe at E~ = 17.0 MeV are represented in figs. 5 and 6. Excitation energies in residual nuclei, corresponding to various groups of neutrons are labelled by dE*. In the case of excitation energies below 4 MeV, the angular distributions present characteristics of direct interactions forward peaking, while the angular distributions corresponding to excitations of 4-8 MeV are symmetrical around 90 ° as predicted by the statistical theory. Earlier we obtained similar results concerning angular distributions of the neutrons emitted in the 5 SMn(~ ' n) reaction at E~ = 13.6 and 17.0 MeV [ref. 23)]. The symmetry around the 90 ° in angular distributions was compared with the distribution: W(O) = Co+e2 cos z 0 (3) and the ~o, 0~2 coefficients were determined by the least-squares method of Rose 24). In order to check the symmetry of the angular distribution data a first fit was performed using the distribution:
W(O) = ~ + ~ cos 0 + ~ cos 2 0
(4)
and the ~" coefficients were determined in the same manner. The values c~ and ~ are collected in tables 1 and 2. From the angular distributions of the neutron groups corresponding to 5-8 MeV residual excitations the moments of inertia of the 5 SFe and 59Ni nuclei were deduced using the semi-classical approximation of Ericson and Strutinsky 25) (table 3). One can see that the values of nuclear moments of inertia ( J ) obtained are smaller than the moments of inertia of the nucleus considered as a rigid body (Jr.b.), in accordance with existing data resulting from isomer ratio and statistical angular distribution data z 6). Therefore the angular distributions and the a-parameters obtained from (~, n) reactions at lower bombarding energies agree well with the predictions of the statisti-
M . T . MAGDA et al.
30
cal t h e o r y . T h e s i t u a t i o n is s o m w e h a t d i f f e r e n t as c o n c e r n s (~, n ) r e a c t i o n s a t h i g h e r bombarding
energies. There were many attempts to explain the occurring anomalies.
There was a trial assignment to the approximations
which are usually performed in
TABLE 1 Angular distribution coefficients AE*
3-4 4-5 5--6 6-7 7-8
W(O) = ~ ' o 4 - ~ ' I c o s 04-1~' 2 c o s 2 0
(1.004-0.07)+(0.594-0.06) (1.004-0.05)4-(0.294-0.05) (1.004-0.04)+(0.154-0.04) (1.004-0.03)+(0.054-0.03) (1.00+0.03)+(0.054-0.03)
cos 0+(0.564-0.13) cos 04-(0.60220.10) cos 0+(0.434-0.08) cos 0+(0.344-0.06) cos 0+(0.244-0.05)
W(O) = (Xo4-~ 2 c o s 2 0
cos 2 0 cos 2 0 cos 2 0 cos a 0 cos 2 0
(1.004-0.05)+(0.524-0.09) cos 2 0 (1.004-0.03)4-(0.374-0.06) cos 2 0 (1.004-0.03)4-(0.274-0.05) cos 2 0
The coefficients of the angular distribution of neutrons from 52Cr(c~, n)55Fe reaction at E~ = 17.0 MeV and for different intervals of excitation energies dE* = 3--4 MeV, 4--5 MeV, 5-6 MeV, 6-7 MeV and 7-8 MeV. (The coefficients were normalized to an c% coefficient equal to unity.) TABLE 2 Angular distribution coefficients
AE* 3-4 4-5 5-6 6-7 7-8
W(O) = e'o+C61 cos +~'2 cos 2 0 (1.004-0.08)+(0.27-t-0.09) (1.004-0.05)+(0.11 4-0.06) (1.004-0.04)+(0.064-0.04) (1.004-0.02)+(0.024-0.03) (1.004-0.02)+(0.064-0.02)
cos 0+(0.884-0.02) cos 04-(0.574-0.11) cos 0+(0.424-0.07) cos 0-t-(0.234-0.02) cos 04-(0.124-0.04)
W(O) = Co+e2 cos 2 0 cos 2 0 cos 2 0 cos 2 0 cos 2 0 cos 2 0
(1.004-0.04)+(0.46-t-0.07) cos 2 0 (1.004-0.02)+(0.21 4-0.04) cos 2 0 (1.004-0.02)+(0.074-0.04) cos 2 0
The coefficients of the angular distribution of neutrons from S6Cr(% n)59Ni reaction at E~ = 17.0 MeV and for different intervals of excitation energies AE* = 3-4 MeV, 4-5 MeV, 5-6 MeV, 6-7 MeV and 7-8 MeV. (The coefficients were normalized to an ~o coefficient equal to unity.) TABLE 3
The R = ..¢/--~r.b. ratio for the 5SFe and S9Ni nuclei
AE*
J/Jr.~.
J/Jr.b.
(MeV)
(s 5Fe nucleus)
(s 9Ni nucleus)
5-6 6-7 7-8
0.33 4-0.03 0.334-0.03 0.324-0.03
0.374-0.04 0.424-0.05 0.55±0.15
the statistical analysis of data: the neglect of the angular momentum sumption
a n d t h e as-
that the inverse reaction cross sections for the excited nuclei are equal
t o t h o s e o f t h e n u c l e u s i n t h e g r o u n d state. T h e a n g u l a r m o m e n t u m effect w a s e x t e n s i v e l y d i s c u s s e d b y T h o m a s 27) a n d T h o m a s a n d W i l l i a m s o n 28); t h e y t o o k i n t o
(~x,n) REACTIONS
31
consideration the reactions we have studied and concluded that the above mentioned anomalies are not explained by introducing angular m o m e n t a in the calculations. We have determined more exactly the a-parameters after a suggestion o f Gadioli and Zetta 2 9) but the level-density parameters so obtained differ too slightly f r o m the previous ones to justify the observed variations. On the other hand, it is very improbable that in the n a r r o w range o f excitation energies for which we performed the analysis, the inverse reaction cross section has such a large variation as to modify the a-parameter. o,"
(ar6ilrory
on#s) Z5
,/oo
20
.~,,e j .
Z5
Z..*__,:,.._..~.°d"% o
o
o
10 Excitalion I
0.5
I
2
I
#
3
I
5
I
I
8
I
7
6 eneJ'gg(MeV)
Fig. 7. Comparison of precompound distribution to the neutron spectrum from 52Cr(~, n) reaction at E~ = 17.0 MeV. (arbi/~ry 3.5 F
~, /
un//'s) 30 t
°~"~*"~/ o *z* ~
2.5 ~ ZO ~5 ;{0
f
051
/~° . -I
2
,2,/"°
-.;z. I
3
* i
I
z~ 5
I
G
°"
I
7
i Exc/falz~n
8 ener~ (HEY)
Fig. 8. Comparison of precompound distribution to the neutron spectrum from 56Fe(cc,n) reaction at E~ = 17.0 MeV. The anomalous behaviour of the statistical parameters could be explained by the contribution o f p r e c o m p o u n d processes, as it was suggested by Griffin for the case o f (p, n) reactions. We have c o m p a r e d the experimental energy distribution ( N ' ) of the neutrons emitted in S6Fe(e, n) and S2Cr(e, n) reactions at E~ = 17.0 MeV to the p r e c o m p o u n d distribution (Wp) given by Griffin's theory 3o) (figs. 7 and 8). In the calculation o f the p r e c o m p o u n d distribution the n -- 3 residual states were included, considering that the first p r e c o m p o u n d state is a three-particle zero-hole state, formed by a t w o - b o d y reaction a m o n g two nucleons in the e-particle *. One t We are indebted to Professor Griffin for having pointed out in a private letter the importance of n = 3 residual states for the calculation of the precompound distribution in the case of (~, n) reactions.
32
M.T. MAGDAet al.
can see on the figures that the ratio N ' / W p
is equal to unity for excitation energies
up to 4.5 M e V an d grows rapidly at larger excitation energies due to the c o m p o u n d neutrons co n t r i b ut io n . 4, Conclusions Th e a level-density p a r a m e t e r s o b t a i n e d f r o m (~, n) reactions at lower b o m b a r d i n g energies present the dependence on the mass n u m b e r predicted by the F e r m i gas m o d e l and are in a g r e e m e n t with the values determined f r o m n e u t r o n resonances or other methods. This fact and the shape o f the an g u l ar distributions o f the neutrons too, show that (~, n) reactions at lower energies are well described by the statistical model. A t higher b o m b a r d i n g energies the s - p a r a m e t e r s resulting f r o m (~, n) reactions have an a n o m a l o u s variation with the mass n u m b er , indicating the presence o f p r e c o m p o u n d processes. It is a pleasure for us to t h a n k Felicia Stan for her help while this w o r k was carried out, and the crew o f the I.A.P. cyclotron.
References 1) D. Bodansky, Proc. Conf. direct interactions and nuclear reaction mechanism, eds. E. Clemmentel, C. Villi; p. 23 2) R. M. Eisberg, G. Igo and H. E. Wegner, Phys. Rev. 100 (1955) 1309 3) G. Igo and H. E. Wegner, Phys. Rev. 102 (1956) 1364 4) C. I-Iurwitz et aL, Nucl. Phys. 54 (1964) 65 5) L. W. Swenson and N. Cindro, Phys. Rev. 123 (1961) 910 6) L. W. Swenson and C. R. Gruhn, Phys. Rev. 146 (1966) 886 7) N. O. Lassen and V. A. Sidorov, Nucl. Phys. 19 (1960) 579 8) C. H. I-Iolbrow and I-I. H. Barschall, Nucl. Phys. 42 (1963) 264; 71 (1965) 529 9) V. A. Sidorov, Nucl. Phys. 35 (1962) 253 10) A. Alevra et aL, Nucl. Phys. 58 (1964) 108 11) M. T. Magda et al., Rev. Roum. Phys. 11 (1966) 241 12) M. T. Magda et aL, Rev. Roum. Phys. 12 (1967) 235 13) M. T. Magda et al., Rev. Roum. Phys. 13 (1968) 179 14) M. T. Magda et aL, Rev. Roum. Phys. 14 (1969) 3 15) M. Molea, preprint IFA-CRD-38 (1968) 16) H. C. Evans and E. H. Bellamy, Proc. Phys. Soc. 74 (1959) 483 17) M. Gettner and W. Selove, Rev. Sci. Instr. 31 (1960) 450 18) J. E. Hardy, Rev. Sci. Instr. 29 (1958) 705 19) S. Papureanu, P. Andruscenco, M. Macovei, M. Molea, P. Moteca, Gh. Pascovici and V. Stancu, Rev. Roum. Phys., to be published 20) K. J. Le Couteur, Proc. Phys. Soc. A63 (1950) 259; A65 (1952) 718 21) N. N. Abdelmalek and V. S. Stavinsky, Nucl. Phys. 51 (1964) 601 22) U. Facchini and E. Saetta-Menichella, Energia Nucleare 15 (1968) 64 23) A. Alevra et al., Nucl. Phys. 72 (1965) 209 24) M. E. Rose, Phys. Rev. 91 (1953) 610 25) T. Ericson and V. Strutinsky, Nucl. Phys. 8 (1958) 284 26) M. Bormann and H. Neuert, Fortschr. Phys. 11 (1963) 277 27) T. D. Thomas, Nucl. Phys. 53 (1964) 558, 577 28) D. C. Williamson and T. D. Thomas, Nucl. Phys. A107 (1968) 552 29) E. Gadioli and L. Zetta, Nuovo Cim. 51A (1967) 1074 30) J. J. Griffin, Phys. Rev. Lett. 17 (1966) 478