Neutrons from protons on isotopes of tin

2.A.1 : 2.D

Nuclear Physics 71 (1965) 529--545; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

NEUTRONS FROM PROTONS ON ISOTOPES OF TIN R. M. WOOD, R. R. BORCHERS and H. H. BARSCHALL

University of Wisconsin, Madison, Wisconsin t Received 9 April 1965 A b s t r a c t : Neutron spectra resulting from the bombardment of eight isotopes of tin with protons of

energies between 7 and 14 MeV have been obtained at a laboratory angle of 60 °. At 10 and 14 MeV angular distributions were measured. The statistical model of nuclear reactions was used to deduce the dependence of the level densities in the residual nuclei on excitation energy, but contrary to the predictions of the model, the deduced level densities showed an apparent dependence on bombarding energy. The effect of the pairing energy on the neutron spectra from targets containing even and odd numbers of neutrons is discussed.

E

[ N U C L E A R REACTIONS xl~,11,,lx~,11s,lzs, 1~0,122,ls,Sn(p, n), E = 7_14 MeV; measured or(E; En, On). 116,117,ns, l~0Sb deduced levels, level densities. Enriched targets.

I

1. Introduction

Continuous particle spectra produced in nuclear reactions involving intermediate and heavy nuclei have usually been analysed in terms of the statistical model. Bodansky 1), Erba et al. 2), Lang 3) and Ericson 4) have recently reviewed the application of this model to various experimental results. According to the statistical model 5) the differential cross section a(E, 0) for the emission of particles with energy E at an angle 0 with respect to the incident particles is given by a(E, O) = EF(Ep)(.o(U)~e(E , U),

(1)

where affU) is the level density in the residual nucleus at an excitation energy U, and F(Ep) is a function of the bombarding energy Ep and of the identity of the incident particle and the target nucleus. The quantity ae(E, U) is the inverse reaction cross section, i.e., the cross section for the formation of the compound nucleus when the excited residual nucleus is bombarded by a particle of energy E. In the analysis of experimental results two commonly used expressions for the level density are co(U) oc U -2 exp[2~/a-U],

(2)

og(U) oc exp[U/T].

(3)

Eq. (2) is based on a Fermi gas model of the nucleus and the constant a is called the t Work supported in part by the U.S. Atomic Energy Commission. 529

530

R.M. WOODet al.

level density parameter. The quantity T in eq. (3) is called the nuclear temperature and is often assumed to be constant. More generally the nuclear temperature is defined as d

[T(U)] -1 -

In ~o(U).

(4)

dU "Application of definition (4) to eq. (2) yields for the energy dependence of the nuclear temperature in the Fermi gas model IT(U)]-1

=

-

-

_

U _

°

In order to take into account the effect of even and odd nucleon numbers on the level density, Hurwitz and Bethe 6) suggested that the effective excitation energy for nuclei containing even numbers of neutrons or protons be reduced by the pairing energy 3. Cameron 7) has calculated values of the pairing energy. Since the inverse cross section is for particle capture by an excited nucleus, it cannot be measured directly. In the case where the emitted particles are neutrons, however, analyses of the experimental spectra have usually assumed the cross section to be independent of both neutron and excitation energy, or have used optical model calculations for neutron capture by the residual nucleus in its ground state. In earlier experiments at this laboratory, the neutron spectra resulting from the proton bombardment of Rh, Ta, and Au were measured s). It was found that each spectrum could be fitted by the assumption of a constant nuclear temperature, but, contrary to the predictions of the statistical model, the temperatures deduced at a fixed excitation energy in the residual nucleus showed a dependence on bombarding energy. In the Rh data the energy dependence of the temperature could be reduced by using optical model predictions for o-~(E, U). Studies of the (~, n) reaction on several intermediate nuclei by Sidorov 9) and Alevra et al. 1o) also yielded nuclear temperatures which depended on bombarding energy at a given excitation energy in the residual nucleus. In the experiments of Alevra et al., however, the angular distributions of the emitted neutrons were found to be forward peaked, suggesting the presence of direct reactions. Contributions from direct reactions have also been indicated in (p, ~) and (p, p') reactions with intermediate nuclei, but if the anisotropic components were subtracted from the observed spectra 11), the remainder could be described in terms of the statistical model and eq. (3). Extensive studies of inelastic neutron scattering 12, 13) have revealed direct reaction contributions to the observed spectra, but neutrons emitted with low energies were isotropic. The isotropic component appeared to follow statistical predictions, although there was some evidence that the nuclear temperatures deduced at a fixed excitation energy depended on bombarding energy.

NEUTRON SPECTRA

531

Neutron spectra resulting from proton bombardment, on the other hand, have shown no evidence for contributions from direct reaotions 14-27). Individual spectra a, 14, 16) could usually be fitted with eq. (1) together with eqs. (2) or (3). In some cases, however, the deduced values of T or a were found to vary with bombarding energy s). The present experiment was undertaken to explore further the apparent bombarding energy dependence of the nuclear temperatures deduced at a fixed excitation energy in the residual nuclei. The tin isotopes were chosen as targets because for the bombarding energies available at this laboratory they afford large ranges of excitation energy free of second neutrons from the (p, 2n) reaction which is not described by eq. (1). Furthermore, the series of isotopes should give information about odd-even effects.

2. Experimental Procedure Protons were accelerated by a tandem electrostatic accelerator to energies between 7 and 14 MeV. Neutron energy spectra were measured with a pulsed beam time-offlight spectrometer 28) using a 175 cm flight path. Neutrons with energies above 450 keV were detected in a liquid scintillator, and pulse shape discrimination was TABLE 1 The targets studied and some of their properties Target

Isotopic purity

11zSn

70.05 %

116Sn

95.74 %

lXTSn

89.2 ~o

xlaSn xlgSn

97.15 % 89.8 %

az°Sn xz2Sn

98.39 % 90.8 9/oo

l~Sn

92.8 ~o

Major isotopic impurities

120(8.82 9/0) 118(7.01%) 116(5.19 %) 119(2.14 ~o) 118(1.49 ~o) 120(1.06 %) 117(1.02 %) 118(4.5 %) 116(2.34 %) 120(2.16 %) 1190.I2%) 120(1.2 %) 120(5.34 Yo) 118(3.01%) 120(3.75 ~o) 118(1.91%) 124(1.16 %)

Areal density (nuclei/cm ~ × 10-19)

Energy loss of 10 MeV proton (keV)

(p, n) reaction Q value

Neutron separation energy

(MeV)

(MeV)

1.74

73

--7.72*

9.04*

1.71

72

--5.33

7.87

1.61

68

--2.60

9.90

1.63 2.10

69 89

--4.67 --1.36

7.18 9.90

1.58 1.98

67 84

--3.51 --2.37

7.09 6.80

2.00

84

--1.38

6.45

116(1.01%) 120(2.49 %) 118(1.75 %)

532

R.M. WOOD e t al.

used to distinguish between neutrons and 2, rays. The dependence of the detector sensitivity on neutron energy was measured using the T(p, n) and D(d, n) reactions following the procedure used previously at this laboratory 19). Self-supporting targets t of metallic tin were obtained in the form of rolled foils 1.2 cm in diam. Some of the properties of these targets are listed in table 1. According to spectroscopic analysis carried out by the supplier, elements other than tin accounted for less than 1 ~ of each sample. The percentage by weight of the predominating isotope in each sample is listed in column two of the table. Column three lists the tin isotopes which are the major impurities. The number of nuclei per cm 2 in each target, listed in column four of the table, was determined by measuring with a solid state detector the energy width of the group of protons elastically scattered by the targets through 150 °. Atomic stopping cross sections compiled by Bichsel 20) were used to calculate the areal densities from the measured energy losses. The uncertainty in the measured thickness is estimated to be 5 ~o. In column five the target thickness is expressed in terms of the energy loss of 10 MeV protons. The Q values for the (p, n) reaction with the targets are listed in column six of the table; column seven contains the binding energy of the last neutron in the final nucleus. Both Q values and binding energies were calculated from tables of masses compiled by Ktinig et al. 21) and Seeger 22). Entries in columns six and seven marked by asterisks are based on the second reference. A modified version of the low mass target chamber described by Dagley et al. 2a) was used. After passing through the target, the proton beam entered a short extension of the chamber and was stopped approximately 25 cm from the target in a shielded cup. For protons below 10 MeV a disc of 5SNi mounted on gold was used as a beamstop, while at higher energies an ice beamstop was chosen 24). The use of the ice beamstop prevented measurements at angles of less than 30 °. Neutron energy spectra were measured at a laboratory angle of 60 °. In addition, angular distributions were determined for all targets at bombarding energies of 10 and 14 MeV. At each angle and energy, background spectra were measured by removing the target from the path of the beam. By placing a brass shadow bar between the target and the detector, it was found that room scattered neutrons arrived at the detector with little or no time correlation. Backgrounds were subtracted and the resulting time spectra were reduced to energy spectra and cross sections with the aid of a CDC 1604 computer. Because the conversion from time to energy is nonlinear, all channels in the time spectrum were not of equal width on an energy scale. At low neutron energies the channels become quite narrow, and groups of channels with a total width of less than 35 keV were combined. Fig. 1 is a plot of the neutron energy spectrum obtained from the bombardment of 1lSSn with 14 MeV protons. The smooth and continuous nature of the spectrum is typical of the spectra from all of the targets. Only at the lowest bombarding energies * Supplied by Oak Ridge National Laboratory.

NmUTRON SPZCa'RA

533

were individual peaks caused by low-lying states in the product nucleus resolved. In this figure, as well as in the subsequent figures, the neutron energy E and the emission angle 0 are measured in the laboratory system. The difference between the values in the laboratory and c.m. system is slight for all the present experiments. The triangles shown in fig. 1 give an indication of the variation of the spectrometer resolution with neutron energy. The width of the triangles is determined by the thickness of the target and the time resolution of the spectrometer. Since all data were collected under the same conditions, the resolution triangles shown apply to all the spectra. [

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3. R ~ d ~

In figs. 2 and 3 In[tr(0, E)/E] is plotted as a function of the excitation energy U in the residual nucleus for the reactions 116Sn(p, n)116Sb and alSSn(p, n)118Sb. The excitation energy was calculated taking into account the recoil of the Sb nucleus. The first number which appears near the top of each set of data denotes the energy of the incident protons. This energy differs from the average proton energy in the target by less than about 50 keV in all cases (see column 5 of table 1). The number in parentheses after the bombarding energy indicates the amount by which the set

534

R. M. wooD er aI.

of points has been shifted upwards to separate adjacent spectra. Thus in the case of the spectrum corresponding to 13 MeV bombarding energy, In [a(0, E)/E] + 1 rather than ln[o(B, E)/E] is plotted against U. The results for other isotopes of tin are very similar. Because of the similarity of the spectra no attempt was made to correct any of the results for the presence of impurities of other isotopes. The error bars shown in the 10, 12 and 14 MeV spectra of fig. 2 are typical and include uncertainties caused by counting statistics, background subtraction and bias 12

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drifts, but not uncertainties in the target thickness and detector efficiency. The relative importance of each of the first three factors mentioned depends on neutron energy, and the combined effect of all three is greatest at the high and low energy ends of the spectra. For example, in the 14 MeV measurements statistical errors are about 7 % at neutron energies below 1 MeV, 4 % at energies around 3 MeV, and 10% at neutron energies above 4 MeV.

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536

WOOD e t al.

R.M.

Drifts in detector bias are important only at neutron energies below 1.5 MeV where the detector sensitivity is rapidly changing with neutron energy. Such shifts causeuncertainties ranging from about 15 ~o at the lowest neutron energies to less than 5 ~o at neutron energies of about 1.5 MeV. Errors in background subtraction are significant only at high neutron energies where the yield is low and amount to less than 10 Yo. The vertical dashed lines in figs. 2 and 3 are drawn at the excitation energies at which it becomes energetically possible for a neutron to be emitted by 116Sb and

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11SSb, respectively. Above these excitation energies second neutrons from the (p, 2n) reaction can contribute to the spectra so that eq. (1) will not apply. Arrows in figs. 2 and 3 indicate the excitation energy above which neutrons from the (p, p'n) reaction could contribute to the observed spectra. Since the Coulomb barrier is about 9.5 MeV in Sn, the (p, p'n) reaction is not expected to compete appreciably with the (p, n) reaction. Fig. 4 shows data from the reaction l~aSn(p, n)~aSb measured at a bombarding energy of 10 MeV at several angles. The notation used is the same as that in figs. 2 and 3 except that the first number which appears at the top of each curve denotes the reaction angle.

NEUTRON SPECTRA

537

Numerical integration of the measured energy spectra for this isotope as well as for all the other tin isotopes that were investigated showed that the yield of all neutrons with energies greater than 1 MeV was isotropic to within the accuracy of the experiment for the angular range studied. Fig. 5 illustrates this result for 117Sn(p, n) lt7Sb at a proton energy of 14 MeV. It shows the cross section for the production of neutrons in three energy ranges as a function of angle. Error bars represent statistical uncertainties and possible errors in background subtraction. 4. Discussion

4.1. STATES IN Sb ISOTOPES Peaks observed in the neutron energy spectra correspond to states or groups of states in the residual nuclei. Peaks were found, for example, in the 7, 8 and 9 MeV spectra of fig. 2. The energies of these levels as well as the others observed in this experiment are listed in table 2. The accuracy of the energy assignments is limited by the accuracy of the Q values used in the calculation of the excitation energies. TABLE 2 Excitation energy of states observed in antimony isotopes Isotope

State (MeV)

lxeSb

0.35 0.73

1175b

0.75

11sSb l~°Sb

1.5 1.15 0.16 1.17

1.67

The 0.33 MeV state in 116Sb is probably the 60 min isomeric state observed by Temmer 25) and Aten et aL 26). The state in 117Sb at 0.75 MeV occurs near the excitation energy of 0.72 MeV assigned to a state in 1t 7Sb by Fink 27) in his study of the decay of 117Te. Other states in t17Sb observed by Fink at 1.29, 1.72, 2.24 and 2.8 MeV were not observed in this experiment. 4.2. COMPARISON TO THE STATISTICAL MODEL In order to deduce level densities from the experimental data it is convenient to eliminate the dependence of the differential cross section a(0, E) on E v. This can be accomplished by taking the derivative of In [tr(0, E)/E] with respect to the excitation energy. According to eqs. (1) and (4) d 1 - - In[a(0, E)/E] = - -

~u

T(U)

a + - - In at(E, U).

~U

(6)

538

R.M. wood e t al.

The left h a n d side can be f o u n d b y t a k i n g the slopes o f the curves in figs. 2 a n d 3. The reciprocals o f these e x p e r i m e n t a l l y d e t e r m i n e d slopes will be d e n o t e d b y O. F r e q u e n t l y 6) has been called the nuclear t e m p e r a t u r e , b u t it is clear f r o m eq. (6) t h a t (9 is e q u a l to T o n l y if the s e c o n d t e r m on the right o f e q . (6) can be neglected, i.e., if ~rc(E, U) varies sufficiently slowly with U a n d E. It s h o u l d be e m p h a s i z e d t h a t even if this is the case, the nuclear t e m p e r a t u r e is a physically m e a n i n g f u l nuclear p r o p e r t y only if it turns o u t to d e p e n d on U b u t n o t on Ep. 21Sn~a I'I

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Fig. 6. Plots of ~9 against the excitation energy in the residual nucleus for each target. The separate curves within each plot were deduced from measurements made at the different bombarding energies which are noted in the figure. All measurements were made at a laboratory reaction angle of 60 °. The dotted curve in each plot is drawn according to eq. (5), and the numbers given for a are those which give the best fit to measured values of (9 at a neutron energy of 1.5 MeV. This neutron energy is marked on each experimental curve by a vertical line. I f the energy d e p e n d e n c e o f the inverse cross section can be neglected, plots o f O against U should yield the same curve for all values o f Ep for a given final nucleus.

NEUTRON SPECTRA

539

The curve should be a horizontal line if the level density is represented by eq. (3) or should follow eq. (5) if the level density is given by eq. (2). Irrespective of the functional form of the level density, however, O measured at a fixed U should not depend on Ep. In fig. 6 0 is plotted against U for each of the targets studied. The values of O were calculated from the slope of tangents drawn to curves like those in figs. 2 and 3. The determination of these slopes has an uncertainty of the order of 6 ~o at neutron energies below 3 MeV and of the order of 10 7o above that energy. Fig. 6 shows that the values of O deduced from measurements at different bombarding energies do not fall on the same curve. In earlier measurements at this laboratory of the Rh(p, n) reaction 8), the dependence of O on Ep could be explained by using for at(E, U) optical model cross sections for neutron capture by the final nucleus in its ground state. In a comparable analysis o f data from the bombardment of Ta and Au, however, use of optical model cross sections did not significantly reduce the apparent dependence of the temperature T(U) on bombarding energy. Similarly the dependence of T(U) on bombarding energy in the present data is not removed by the use of optical model cross sections. The energy dependence of the derivative with respect to neutron energy, of the optical model cross sections for tin are too small by a factor of five to ten to account for the observed variation of O. In fact, in the mass range 80 < A < 150 none of the optical model cross sections tabulated in refs. 2a, 29) show sufficient variation with energy to account for the bombarding energy dependence of O in the tin data. In an attempt to take into account a possible explicit dependence of ac(E, U) on U, Zhmailo ao) obtained the expression

a~(E, U) = ac(E)+alU (1- E l ,

E< U,

(7)

where ac(E) is the usual optical model capture cross section and al is a constant equal to 1 b/MeV. Use of eq. (7) in the data analysis had little effect on the variation of temperature with bombarding energy. As before, the second derivative of ao(E, U)with respect to energy was too small to account for the observed variation in O. If it is assumed that the statistical model does apply to the present data and that the functional dependence of the level density is given by eq. (2), it is possible to deduce the energy dependence of a¢(E, U) from the data. The dotted curves in fig. 6 are calculated from eq. (5) for constant a. The inverse cross section needed to produce agreement between the dotted curves and the observed data would have to vary exponentially with neutron energy. Furthermore, the energy dependence of a¢(E, U) needed to account for the data is different at different bombarding energies, indicating that ao(E, U) must depend on U as well as on E. Another factor which may affect the analysis of the neutron spectra is the dependence of the level density on angular momentum. Thomas a a) has recently investigated

540

g.M. WOODet al.

the role of angular momentum in determining the shape of neutron spectra. His procedure was to calculate a number of evaporation spectra according to the statistical model with angular momentum effects included, and then analyse them as if they were experimental measurements. He concluded that the failure to consider angular momentum is not responsible for the observed dependence of T or a on bombarding energy. The same conclusion has been reached by others 32). If the temperature anomaly cannot be explained by considering different inverse cross sections or angular momentum effects, one has to conclude that eq. (1) does not fit the data. The most frequently cited explanation for the inapplicability of eq. (1) in (p, n) and similar reactions is that direct reactions occur in competition with compound nucleus formation. A method of distinguishing between the two reaction mechanisms is to examine the angular distribution of the emitted particles. The statistical model predicts that the distribution should be symmetric about 90 °, while direct reactions usually produce yields which are forward peaked. Figs. 4 and 5 show that the angular distributions of neutrons from tin are isotropic within the experimental accuracy. This result is consistent with other measurements of neutron spectra from (p, n) reactions on intermediate nuclei 8,14, 16). Since symmetry about 90 ° is a necessary but not a sufficient condition for concluding that the reaction proceeds through compound nucleus formation, it is only possible to say that there is no evidence that direct reactions contribute to the spectra measured in this experiment. Another possible explanation of the inapplicability of eq. (1) is that the compound nucleus does not live long enough for the energy carried by the bombarding particle to be shared by all the degrees of freedom of the compound nucleus. Arguments 1, 9) for this suggestion envisage an intermediate process such that the particle spectra might still exhibit the symmetry predicted by the statistical model and yet disagree with the basic assumptions of the model. For the statistical model to be applicable the level density in the residual nucleus must be large. The observation of individual levels at the lowest excitation energies in the present experiments might raise the question whether this condition is satisfied. On the basis of the experiments of Jackson and Bollinger aa) on resonances in the interaction of slow neutrons with Sb one can estimate that the average spacing o f levels formed by s wave neutrons is of the order of 20 eV at an excitation energy around 6.5 MeV. If the level density is described by eq. (2), this would correspond to an average level spacing of the order of 60 keV at an excitation energy of 2 MeV, and of the order of 10 keV at 3 MeV. With the energy resolution of the present experiment the statistical treatment of energy levels should therefore be a good approximation above 3 MeV excitation energy. Because of the possibility of direct reactions or the possible failure of the compound nucleus to reach thermal equilibrium, it has been suggested that the statistical model should be applied only to the low-energy neutrons in each spectrum. Wong et al. ~6),

NEUTRON SPECTRA

541

for example, interpret their experiments by neglecting neutrons of high energy and assuming that the excitation energies at which the nuclear temperatures are evaluated are different at the different bombarding energies. They find that the dependence of the experimentally determined nuclear temperatures on U is that of eq. (5) with constant a, and conclude, therefore, that the statistical model and the Fermi gas level density adequately describe the data. The parallel of Wong's analysis in the case of the present data is illustrated in fig. 6. The lowest neutron energy at which a reliable value of O could be determined is slightly above 1 MeV. In fig. 6 1.5 MeV neutron energy is indicated on each curve by a vertical line except in cases where at this energy (p, 2n) reactions are energetically possible. The values of a corresponding to each of the values of O deduced at 1.5 MeV neutron energy were calculated using eq. (5). It was found, in agreement with the results of Wong et al., that the values of a so deduced were the same at all bombarding energies for a given isotope within the experimental uncertainty. The average values of a for E = 1.5 MeV are listed for each isotope in fig. 6, and the dotted curves were calculated according to eq. (5) for the listed values of a. The values of a would have been different if the same procedure had been followed for a different choice of neutron energy. An increase of a by 1 MeV- ~ moves the curve of constant a down by only about 20 keV. It is clear, therefore, that the values of a are quite uncertain. The values of a deduced in this experiment range from 17 MeV -1 to 24 MeV -1 for the different antimony isotopes. Measurements by Thomson 12) of the inelastic scattering of neutrons by natural antimony yielded a values of 24.9 M e V - ~ at an incident neutron energy of 7 MeV, and 31.3 M e V - ~ at an incident neutron energy of 4 MeV. Buccino et al. 13) deduced from their study of inelastic neutron scattering by antimony an a value of 16.1 MeV -~ at neutron bombarding energies from 4.0 to 6.5 MeV. Measurements on the (n, 2n) reaction for natural antimony by Plattner et al. 34) yielded a nuclear temperature of 890 keV at an incident neutron energy of 14 MeV, corresponding to an a value of approximately 15 MeV-1 Calculation of a from an expression given by Newton 35) as modified by Lang 3) gives values around 17 MeV- ~ for all the isotopes studied in reasonable agreement with the values deduced from fig. 6. Similar values have been obtained by Abdelmalek and Stavinsky 36) and by Gilbert and Cameron 37). 4.3. THE

ODD-EVEN

EFFECT

When the present experiments were undertaken, it had been hoped that the choice of odd and even isotopes would yield information about the pairing energy. The difficulty in fitting the data using the statistical theory makes it doubtful that any reliable conclusions regarding the effect of pairing energy can be drawn from the data. A possible way in which such information might be obtained, is to compare values of the level density parameter a obtained from fig. 6 for the various isotopes. In view of the poor fit of the data to eq. (5), conclusions drawn from such a comparison are obviously very uncertain. Nevertheless, there is an indication that the values of a

542

R.M. WOODe t

al.

listed in fig. 6 for the odd isotopes of tin (corresponding to even neutron numbers in Sb) are about 4 M e V - ~ higher than for the even Sn isotopes. I f the excitation energy is reduced by the pairing energy 7), the calculated values of a for the Sb isotopes with even neutron numbers are reduced by about 4 M e V - 1 bringing them closer to those for the odd isotopes. In most treatments of the pairing energy, a is expected to be the same for even and odd isotopes if the pairing energy is taken into account, except that Abdelmalek and Stavinsky obtain lower values of a for even neutron numbers than for odd neutron numbers after application of the pairing energy correction. The present experiments give no evidence for such a variation. i A

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Fig. 7. The differential cross section for the production of neutrons with energies greater than 1 MeV in the (p, n) reaction on tin as a function of target mass number. Measurements were made at a reaction angle of 60° and a bombarding energy of 10 MeV. As has been pointed out by Ericson 4), odd-even effects should not affect the cross section for the production of neutrons integrated over all neutron energies. In fig. 7 the differential cross section for the production of neutrons with energies greater than 1 MeV is plotte d as a function of the target mass number. The points shown were calculated by numerical integration of the spectra obtained at 60 ° with 10 MeV protons. The figure shows that the cross section varies smoothly with mass number and shows no odd-even effect. The typical error bars in the figure include the 5 estimated uncertainty in measurements of target thickness and the 5 ~ uncertainty owing to counting statistics and background subtraction. At bombarding energies above 10 MeV the presence of neutrons from the (p, 2n) reaction makes similar comparisons less reliable. 4.4-. INTEGRATED CROSS SECTIONS In fig. 8 the cross section for production of neutrons with energies greater than 1 MeV is plotted as a function of bombarding energy for each of the targets studied. The differential cross sections were obtained by numerical integration of the neutron spectra measured at a laboratory angle of 60 °. Typical uncertainties indicated by error bars include statistical uncertainties and errors in background subtraction,

NEUTRON SPECTRA

543

but not errors in detector efficiency and target thickness. The combined error caused by statistics and background subtraction is estimated to be about 5 ~o. These cross sections were computed without taking into account the effect of second neutrons from (p, 2n) reactions and are therefore larger than the sum of the cross sections for the (p, n) and the (p, 2n) reactions at bombarding energies at which (p, 2n) reactions Occur.

There are few published data with which the results of this experiment can be compared. Blaser et al. as) measured the (p, n) cross section of 117Sn, 12°Sn and 60

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122Sn at a proton energy of 6.3 MeV by activation analysis. If isotropy is assumed for the emitted neutrons, and if allowance is made for the fact that the present experiment measured only neutrons with energies greater than 1 MeV, the activation measurements are consistent with the present results. The cross section for the formation of the compound nucleus when tin is bombarded by protons has been calculated by Shapiro 39). Under the assumption that neutrons are emitted isotropically, and that approximately one third have energies less than 1 MeV, the cross sections deduced from the present measurements are 20 to 50 larger than those calculated by Shapiro for an interaction radius of 1.5A¢ fro. For a given isotope the measured yield shows about the same dependence on proton

544

R. ra. WOODet al.

energy as do the calculations. O n the other h a n d , at fixed b o m b a r d i n g energy the dependence of the measured cross section on atomic weight is a b o u t five times that given by A ~r. Part of the observed variation is p r o b a b l y caused by the effect o f the different Q values for the (p, n ) reactions o n the different Sn isotopes a n d the resulting variation of the probability of competing modes of decay of the c o m p o u n d nucleus. 4.5. SUMMARY The present m e a s u r e m e n t s disagree with predictions of the statistical model. I n particular, the a p p a r e n t b o m b a r d i n g energy dependence o f the level density in the residual nucleus disagrees with the basic assumptions o f the model. It is unlikely that this difficulty can be explained by including a n g u l a r m o m e n t u m effects in the analysis or by using a n y presently available inverse cross section. There is n o evidence o f n e u t r o n s from direct reactions in the m e a s u r e d spectra. I f it is assumed that the statistical m o d e l applies only to the emission of low energy neutrons, values of the level p a r a m e t e r m a y be o b t a i n e d which are consistent with previous experiments a n d with theoretical estimates.

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13)

D. Bodansky, Ann. Rev. Nucl. Sci. 12 (1962) 79 E. Erba, U. Facchini and E. S. Menichella, Nuovo Cim. 22 0961) 1237 D. W. Lang, Nuclear Physics 26 (1961) 434 T. Ericson, Advan. Phys. 9 (1960) 425 V. F. Weisskopf, Phys. Rev. 52 (1937) 295 H. Hurwitz and H. A. Bethe, Phys. Rev. 81 (1951) 898 A. G. W. Cameron, Can. J. Phys. 36 (1958) 1040 C. H. Holbrow and H. H. Barschall, Nuclear Physics 42 (1963) 264 V. A. Sidorov, Nuclear Physics 35 (1962) 253 A. Alevra et aL, Nuclear Physics 58 (1964) 108 R. Sherr and F. P. Brady, Phys. Rev. 124 (1961) 1928 D. B. Thomson, Phys. Rev. 129 0963) 1649 S. G. Buccino, C. E. Hollandsworth, H. W. Lewis and P. R. Bevington, Nuclear Physics 60 (1964) 17 14) R. D. Albert, J. D. Anderson and C. Wong, Phys. Rev. 120 (1960) 2149 15) L. F. Hansen and R. D. Albert, Phys. Rev. 128 (1962) 291 16) C. Wong, J. D. Anderson, J. W. McClure and B. D. Walker, Nuclear Physics 57 (1964) 515 17) R. R. Borchers, C. H. Holbrow and R. M. Wood, Nuclear Physics, to be published 18) H. W. Lefevre, R. R. Borchers and C. H. Poppe, Rev. Sci. Instr. 33 (1962) 1231 19) C. H. Poppe, C. H. Holbrow, and R. R. Borchers, Phys. Rev. 129 (1963) 733 20) H. Bichsel, American Institute of Physics Handbook, ed. by D. E. Gray (McGraw-Hill Book Co., New York, 1963) 21) L. A. K6nig, J. H. E. Mattauch and A. H. Wapstra, Nuclear Physics 3! (1962) 1 22) P. A. Seeger, Nuclear Physics 25 (1961) 1 23) P. Dagley, W. Haeberli and J. X. Saladin, Nuclear Physics 24 (1961) 353 24) R. R. Borchers, J. C. Overley and R. M. Wood, Nucl. Instr. 30 (1964) 73 25) G. M. Temmer, Phys. Rev. 76 (1949) 424 26) A. H. W. Aten, Jr., J. Manassen and G. D. de Feyfer, Physica 20 (1954) 665 27) R. W. Fink, G. Andersson and J. Kantele, Ark. Fys. 19 (1961) 323

NEUTRON

28) E. J. Campbell,

29) 30) 31) 32) 33) 34) 35) 36) 37) 38) 39)

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H. Feshbach, C. E. Porter and V. F. Weisskopf, MIT Laboratory for Nuclear Science, Technical Report No. 73 (1960) E. H. Auerbach and F. G. J. Perey, Brookhaven National Laboratory, Report No. 765 (T-286) 1962 V. A. Zhmailo, JETP 43 (1962) 473 T. D. Thomas, Nuclear Physics 53 (1964) 558 C. Hurwitz et al., Nuclear Physics 54 (1964) 65 H. E. Jackson and L. M. Bollinger, Phys. Rev. 124 (1961) 1142 R. Plattner, P. Huber, C. Poppelbaum and R. Wagner, Helv. Phys. Acta 36 (1963) 1059 T. D. Newton, Can. J. Phys. 34 (1956) 804 N. N. Abdelmalek and V. S. Stavinsky, Nuclear Physics 58 (1964) 601 A. Gilbert and A. G. W. Cameron, Can. J. of Phys., to be published J. P. Blaser, F. Boehm, P. Marmier and D. C. Peaslee, Helv. Phys. Acta 24 (1951) 3 M. M. Shapiro, Phys. Rev. 90 (1953) 171