Proton energy and angular distributions from (n, p) and (n, np) reactions

1•

Nuclear Physics A195 (I 972) 2 8 9 - 301; (~) North-Holland Publishing Co., Amsterdam

Not to be reproduced by photoprint or microfilmwithout written permissionfrom the publisher

PROTON ENERGY AND ANGULAR DISTRIBUTIONS F R O M (n, p) and (n, np) R E A C T I O N S K. R. ALVAR t Department of Physics, Brown Unit'ersity, Proridence, Rhode Island 02912 ~'

Received 26 June 1972 Abstract: The proton energy and angular distributions from (n, p) and (n, rip) reactions on 2;AI, 32S, SgCo and. ~SNi have been measured for 14.1 MeV neutrons. The proton detection threshold was approximately 2 MeV and the reaction angles from 0 ° to 120 ~ were used in 20 ° increments. Thin isotopically pure targets and particle discrimination were used. The leveldensity parameters, nuclear temperatures and total I'n, p) and (n, np) cross sections are reported. Direct contributions are estimated. NUCLEAR REACTIONS ~TA1, 32S, 59Co and SSNi(n,p) and (n, np) E : 14.1 MeV; measured o'(E~, 0); deduced level-density parameters and nuclear temperatures. Enriched targets.

1. Introduction Studies o f (n, p) reactions yield information a b o u t the p a r a m e t e r i z a t i o n o f the level-density formulae and a b o u t the usefulness o f the statistical theory itself. In m a n y cases the interpretation o f the d a t a o f earlier (n, p) experiments was a m b i g u o u s due to the c o n t r i b u t i o n s from (n, d) reactions which were not separated from the yield. This a m b i g u i t y has been eliminated in the present work by the use o f particle disc r i m i n a t i o n . The (n, p) and (n, np) reactions were studied with 27AI, 32S, 5"~Coanti 5SNi as targets for 14.1 MeV neutrons. As the result o f the use o f thin isotopically pure targets, coincidence requirements and particle discrimination, the p r o t o n energy spectra and angular distributions for 32S(n, p)32p have been measured in this w o r k for the first time without the (n, d) c o n t r i b u t i o n . The d a t a for 59Co(n, p)'~gFe are the first for neutrons at 14.1 MeV m e a s u r e d with g o o d particle discrimination for p r o t o n s down to 2 MeV. The spin cut-off factor t ) for 5SCo was estimated from the 5SNi experiment using an isotopically p u r e target and g o o d particle discrimination. N u c l e a r t e m p e r a t u r e s and leveldensity p a r a m e t e r s were extracted for each reaction and the (n, p) and (n, np) cross sections were estimated as were the possible direct c o n t r i b u t i o n s to the total cross sections. * Corinna Borden Keen Research Fellow. Present address, Department of Physics, Rutgers University, New Brunswick, New Jersey 08903. "* Work supported in part by the US Atomic Energy Commission. Submitted in partial fJlfillment of the requirements for the Ph.D. degree at Brown University. 289

290

K.R. ALVAR

2. Experimental and data analysis procedures A 360 keV linear accelerator was used to produce a 14.1 MeV neutron flux at 9 0 via the 2H(d, n)4He reaction. The flux, typically 10 '~ s e c i into 4n st, was generated by accelerating deuterons onto a tritiated titanium-zirconium target and monitored by the associated ~-particle method. The counter telescope used in this work was designed by Wagner 2) and consisted of two proportional counters and a CsI(TI) crystal for the A E and E detectors, respectively. The proportional counter gas was argon-carbon dioxide ( 9 6 - 4 ",i) at 152 mm Hg pressure. Lead telescope liners replaced those of carbon used earlier. The telescope was used in conjunction with a triple coincidence requirement and an electronic particle discrimination system 3) to reduce background and to separate the various particle types by the E" d E / d x method. The data were taken at seven counter telescope settings, 0 ~ to 120 ° in 20 ~ increments. At each angle 3.23x 1013 neutrons into 4n sr were generated for the foreground and background data with a source-to-target distance of 8 cm. The range-energy tables of Janni 4) were utilized in the corrections of the energy scale and energy and angular distributions for energy losses in the target, proportional counter gas and the thin aluminum foil covering the Csi(TI) crystal. All of the laboratory and c.m. cross-section calculations were performed in the absolute sense given the geometrical configuration, target thickness, etc., and also in the relative sense, relative to the known n-p elastic scattering cross section. The agreement in all cases was within about 5 %. The total cross sections were taken from plots of the gross angular distributions by use of a planimeter. All of the data presented later were derived from the relative cross-section calculations. The part of the proton energy distribution d a / d E for residual nucleus excitations below the (n, np) threshold was fit by least squares with the formula da dE

-- A O ' i n v ( E ) E w ( U - A ).

(1)

The parameter A was an adjustable parameter, a~, v the inverse cross section taken from Mani et al. 5), E the c.m. proton energy, U the rcsidual nucleus excitation energy and o 9 ( U - A ) the level density with an energy shift. Two forms were used for the level density, the constant-temperature form e v/' and that given by Gilbert and Cameron: ~ ( V ) oc U - ~le2*~c.

(2)

Here, t the statistical temperature and a the level-density parameter were found as part of the least-squares fitting procedure. For the Gilbert and Cameron form, the observable level density was used, taking the energy dependence of the spin cut-off factor into account. The energy shifts A = 0.0 MeV, A = 1.45 MeV given by Cameron 7) and A = 1.54 MeV given by Gilbert and Cameron were used in the analysis of the 5~Co(n, p)5'~Fe results. The shift was also used for the other reactions

(n,p) AND 01, np) REACTIONS

291

tO see how the results changed when the data for the first MeV of excitation (A = 1.0 MeV) were omitted, to delete possible "direct" effects. Once the least-squares calculation was completed, the expression for da,/dE was extrapolated to excitation energies above the (n, np) threshold. The (n, p) and (n, np) total cross sections could then be calculated in a straightforward manner and will be given later as percentages of the total (n, n + np) cross section. To take into account the resolution of the energy detector for the higher-energy protons and the energy smearing of the lower-energy protons by the finite target thickness, the proton energy' distributions were also calculated using an averaging technique. A running average was taken over the data for each set of angular data, the data for a given channel being summed with that for each of the two channels below and above, the result being divided by five. The smoothed data then were used for the calculation of the energy distribution. Statistical calculations were done for both the unsmoothed and smoothed data, but only the unsmoothed data will be presented in figures given later. The values of a obtained from experiment may be compared to empirical values calculated by Newton 8). For comparison with the statistical temperatures, the integral temperatures ~) were calculated using the known level schemes 10). The plot of the number of levels per ½ MeV v e r s u s energy was tit with an exponential and the integral temperature t extracted. While it is not possible experimentally to separate direct and compound contributions to the gross angular distributions, an estimate of each was made for comparison with the calculations of Brown and Muirhead 11). For simplicity the assumptions were made here that the compound contribution was isotropic and that the lowest point of the gross angular distribution had no direct contribution. The value at that point was used to find the total statistical contribution. The direct part then was given by subtraction of the statistical cross section from the total cross section. The validity of these simplifications will be discussed later.

3. Results

The gross angular distributions are given in fig. I, the proton energy distributions in figs. 2-5, and the angular distribution for the 32S target in fig. 6. In all figures the vertical error bars are statistical standard deviations only. In fig. 6 the horizontal bars give the spread of the c.m. response of the counter telescope. The data show two features not seen in earlier studies. The first is the large cross section for the transitions in the first MeV of excitation of 32P and the second, the very low cross section at 120 '' for the cobalt reaction. The data for 58Ni. although taken with a lower proton energy threshold than previously, 1.92 MeV in the c.m., were not much different from that seen before.

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80;-

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.......

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12

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16

(MeV)

Fig. 2. Proton energy distribution from 32S(n, p + n p ) reactions. See sect. 2 l'or explanation o f the statistical theory fit go the data.

(n, p) AND (n, np) REACTIONS

293

3.1. THE a2S(n, p)a2p REACTION The target used was that fabricated by Wagner 2) for his study of 32S(n, d)alP. It was 99.86 % 32S deposited on a clean lead backing and its thickness was 3.044-0.12 mg/cm 2. In all other (n, p) work on sulfur 1:--2o) the large contribution from the 32S(n, d) 31p reaction was evident. These deuterons have been excluded for the first time in this experiment via particle discrimination. The gross angular distribution for 325(n, n -}-rip) is given in fig. 1. Clearly it is neither isotropic nor symmetrical about 90 ° so a spin cut-off factor could not beextracted. The gross angular distribution here is in rough agreement with that of Antolkovic 19) when his deuteron component is subtracted. The upward turn after 90 ° given by him was not seen in this experiment. A strong transition was observed in this experiment for the 0-1 MeV excitation interval of 32p, see fig. 6, which includes the known levels 1o) at 0.0, 0.078 and 0.5 MeV. The data of Eubank et al. 13) were given for a 0.5 MeV energy interval about the ground state with the absolute magnitude not given. However, their results have the same shape as that presented here. Hassler and Peck ts) could not record this peak as their energy detector was not thick enough to stop these protons. The angular distribution given in fig. 6 show a large amount of structure, which is typical for all of the angular distributions measured in this work. The other angular distributions will not be presented. Further theoretical work is needed to understand the structure which occurs in these angular distributions. The energy spectrum is shown in fig. 2 with the curve generated by the statistical calculations for the Gilbert-Cameron level density and A = 0.0 MeV. The value tbr the level-density parameter from Newton's work is 2.08 MeV- ~. The integral temperature was found to be z = i.86+0.08 MeV using the levels given by Endt and Van der Leun 1o). Eubank et al. 13) give t = 2.1 MeV, Hassler and Peck 1a) t = 2.13+0.10 MeV and Antolkovic 12) t = 1.38+0.08 MeV. While the first two values are in good agreement with the present work, the disagreement with the third value reflects the fact that the measured spectra differ. The t-values presented here, table 1, are also in reasonable agreement with the integral value. Agreement is not particularly good for the a-parameter, with the present values being higher than Newton's. Allan 16) found a total (n, p) cross section of 365+25 mb and a total (n, np) cross section of 105+25 mb yielding 470+35 mb for the sum and 77.6 ~o and 22.4 for the (n, p) and (n, np) percentage contributions, respectively. Levkovskii 20) gave a somewhat smaller value for the (n, p) cross section, 220+40 mb. The value found for the total cross section in the present experiment is 400 + 31 mb for the angles measured. This is in favourable agreement with the value given by Allan's work. The percentages given by the statistical calculations, see table 1, are also in similar agreement with the values derived from Allan's cross sections. Direct contributions, table 2, under the simplifying assumptions made earlier,

294

K.R. ALVAR

constitute 48 °o of the total (n, n + np) cross section. This is more than twice as large as the theoretical estimate of 20 ~ . The fact that the direct contribution is this large is rather surprising. If the gross angular distribution turns up after 120 °, then our simplifying assumption of isotropy would be incorrect and the statistical contribution TABLE 1 Level-density p a r a m e t e r s a n d derived cross sections Target .

32S ~'~Co ~aNi ZrAI

t (MeV) ~) .

.

.

.

.

.

.

.

.

2.26 ~_0.19 2.104-0.11 2.26-+0.55 1.37 .'-0.09 1.64-+0.07 1.58-+0.05 2.93.!_0.74 2.01 :: 0.16

r (MeVJ .

.

.

.

.

.

.

.

.

.

a (MeV-I) .

.

1 . 8 6 - 0.08 1.18 !.0.09 0.99 !_0.12 1.78_- 0.08

.

.

.

.

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.

.

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a ( M e V ) ~ - b) .

.

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3.05 ~ 0.23 3.28-+0.16 3.09 !:0.60 4.96 :_0.32 4.17 k0.21 4.36_-t 0.18 2.59-+0.46 3.31 ~.t-0.25

.

.

.

.

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2.08 6.27 5.59 2.61

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tr(n, p) (%) .

.

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ti(n, np) (%) .

65 69 35 50 43 43 33 40

.

.

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35 31 65 50 53 57 67 60

'~) T h e value ,J - 0 was used in the calculations leading to the data presented in this table. T h e s m o o t h e d data results are listed second in the data columns. ") Ref. 8). TABLE 2 Direct a n d total cross sections Target

~(mb) total, exp.

~(%) direct, CXl3.

tr(~) direct, theory ~)

3'S 5 "Co ~SNi 27A1

400~32 108 -- 22 422.-16 191 ! 25

48 large 13 38

20 not given 13 57

~) Ref. 1,).

would be larger. However, the data of Hassler and Peck ~a) do not indicate such an upward trend at back angles. Since neither the statistical or direct theories with the simplifying assumptions used earlier can account for the large direct contribution, these simplifications should be examined further. This examination has not been done. Also, a criterion for the experimental identification of direct contributions more meaningful than mere angular asymmetry is needed. 3.2. T H E SOCo(n, p)S'~Fe R E A C T I O N

The cobalt target was 99.9 ')0 pure 59Co purchased commercially with a thickness 9.04+0.18 mg/cm 2. A lead disc 71 mm thick was used as a backing to stop protons from the aluminum target holder and to duplicate conditions under which the background runs were made.

(n, p) AND (n, np) REACTIONS

295

Work has been done on 59C0 by several groups 18,21 -24). Colli et aL 23) investigated only one angular interval 15_ 15°, but this was the only work up to the present using particle discrimination. Jack et aL z2) looked at 0 ° and Storey and Ward 24) at 90 °. For the 0: work it was concluded that the target was contaminated with vacuumpump oil giving a large peak at an energy not allowed kinematically. This peak was not seen in the present work or in the others. The present work represents the first time that the angular distribution has been measured with good particle discrimination. 321-

59Co( n, p)59Fe

/

24-

1

t, = 2.26 t. 0.55 MeV

T E Ld

I 8-

b O1

- 8 - - - -

0

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!

l

2

4

6

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.

Proton

t

8

;

1

I . . . .

I0

12

14

16

Energy (MeV)

Fig. 3. Proton energy distribution from 59Co(n, p ~-np) reactions.

The only other gross angular distribution is that given by Hassler and Peck ta) with which the present work is in rather large disagreement. This is due principally to the fact that the proton threshold in the present experiment was significantly lower than that used in their work. Mohindra and Hans 24) used a 4 MeV proton energy threshold. The gross angular distribution, fig. 1, measured here does not rise after 90 ° and as a result the spin cut-off factor was not calculated. Table 1 gives the results of the statistical calculations and fig. 3 the energy spectrum and the fitted curve. The effect of smoothing is large here because the cross section is smaller resulting in large statistical deviations. The value of the level density parameter from Newton's work is 6.2 MeV- ~. This is higher than either of the values in table I. The integral temperature using the known level scheme 10) is 1.18 4-0.09 MeV, which is slightly lower than the values given here by the statistical calculations. The (,n, p) and (n, np) percentages of the total cross section, measured here to be 1084-22 mb, can not be compared to activation values since the (n, np) reaction has not been studied. The work of Hassler and Peck 18) with a counter telescope and a higher proton threshold give the (n, p) contribution to be greater than 48 4- 5 mb and

296

K.R. ALVAR

about 11 mb for the (n, np) part. Allan 16) and Storey and Ward 21) estimated the (n, p) cross section to be 81 + 10 mb and 75+_ 15 mb respectively. We can estimate here that the (n, np) part is at least 35 mb. Brown and Muirhead did not give a value for direct contributions for this reaction. If we use the simplifying assumptions given earlier we are forced to attribute all of the angular distribution to direct reactions. This is rather unsatisfactory as we expect some of the reaction to be of the statistical type.

Ioo

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58Ni( n, p)58C0 t = 1 . 6 4 + 0 . 0 7 MeV

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, 50

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Energy

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14

16

(MeV)

Fig. 4. Proton energy distribution from SaNi(n, p~ np) reactions.

3.3. THE 58Ni(n,p)'~aCo REACTION

The target used in this experiment was two pieces t of 5aNi each 4.00_+ 0.04 mg/cm 2. The target was backed with a 71 mm thick lead blank. The 5aNi(n, p)5aCo reaction has been studied with isotopic targets by many groups [refs. 16, 21--23, 25-28)] with three groups 23, 27, 2a) using particle discrimination. In the three other experiments where particle discrimination was used Colli et al. 23) measured the energy distribution at only one angle 15 + 15°; Glover and Purser [ref. 27)] used 15 MeV neutrons and went out to 130°; and Debertin and Rossle 2a) used 13.1 MeV neutrons to measure the angular distributions out to 150 ° for protons down to about 6 MeV. In the present experiment the 5aNi(n, p)SaCo energy and angular distributions have been measured for 14.1 MeV neutrons with good particle discrimination lbr proton energies down to 2 MeV. The gross angular distribution for this reaction is given in fig. 2. This distribution dips around 90 ° and rises at the back angles. Because of the shape of the distribution * Purchased from the Isotopes Division, Oak Ridge National Laboratory.

(n, p) AND (n, np) REACTIONS

297

the curve for the weak coupling formula l) can be roughly estimated. Such an estimate gives a spin cut-off factor greater than or equal to I. The data from the statistical calculations are given in table 2 and the energy distribution and fit are given in fig. 4. Note that the differences between the smoothed and unsmoothed data in table 2 are much smaller than for the other reactions as the cross section here is larger. In other experiments Glover et al. 2~) give t = 1.36 MeV, Allan 16) t = 1.1 + 0.1 MeV and Debertin and Rossle 2a) give a = 5.9 + 0.4 MeVwith a slightly different to(U). Calculations using the known level scheme to) give z = 0.99_+0.12 MeV. The level-density parameter found from Newton's work is 5.58 MeV -1. The integral temperature agrees with Allah's value but the temperature given here are significantly higher. The (n, p) total cross section for 5aNi has been measured by several investigators with varying results, see for example, the article by Chatterjee 29). Storey and Ward [ref. 21)], Allan 16), and Glover et al. 3o) give 534+ ll0, 440-+27, and 435_+36 mb, respectively. Other values are given by Levkovskii 3t) 380-+57 mb and by Fink et al. 32) 331 -+30 rob. The (n, rip) cross sections are given as 560+_56 mb [ref. 3o)] and 343-+_27 mb [ref. 16)]. The value found here for the (n, p + n p ) cross section is 422+ 16 mb. This is lower than the sum of the appropriate values given above because the angular distribution does not drop off beyond 120 °, this being the largest angle reached in this work. The results of the statistical calculation, table 1, indicate an approximately even division between the (n, p) and (n, np) reactions. With our earlier assumptions the experimentally estimated value for the direct contribution is 13 ',~o and the theoretical estimate is also 13 %. This reaction is the only one studied here which gives a definite indication of an upturn in the angular distribution toward back angles. As a result of this, the experimental estimate may be too large. Such close agreement between the two estimates is not expected in view of the approximations made in the direct theory. 3.4. THE 27Al(n,p)27Mg REACTION The target was a foil purchased commercially, 25-+2/~m thick (6.86 mg/cm 2) and 99.997 % pure in the prefabricated form. The purity of the aluminum in the foil form was not known. This target was also used with a lead backing disc. The number of neutrons generated into 47z sr was 3.23 x l0 la for 0 °, 8.08 × l012 for 20 ° and 100 ~, and 4.04 x 1012 for the other angles. The gross angular distribution is given in fig. I. While 16 other (n, p) experiments have been done on 27AI [see ref. 33) for references to the literature] only two of them have been done using particle discrimination. The work of Glover et al. 2~) was done at 15 MeV and that by Colliet al. 34) used a 4 MeV proton threshold. Because the data for each experiment were presented in a different manner it is difficult to compare results. The statistical calculation results are given in table 1 and the energy spectrum in fig. 5. Since there were few protons at higher energies the evaporation fits are rather

298

K.R. ALVAR

,oo

27A{ ( n, p) 27Mg t, = 2.93 _+0.74 MeV

>~

"E

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Fi

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. . . . . . . 0 2

~. . . . 4

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t 6

.

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l I0

. . . . . . l ..... 12

14

Proton Energy (MeV)

Fig. 5. Proton energy distribution from ZTAl(n, p : np) reactions.

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Fig. 6a. Angular distributions of protons from 32S(n, p-!-np) reactions given in 1 MeV intervals o f excitation o f 32p. Vertical error bars are statistical deviations only. Horizontal bars indicatethe angular spread of the counter telescope. Fig. 6b. Angular distributions of protons from "~2S(n, p : np) reactions. Sce caption o f fig. 6a.

(n, p) AND (n, np) REACTIONS

i++ !....

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Fig. 6c. Angular distributions of protons from 32S(n,p-~-np) reactions. See caption of fig. 6a. flat. The integral temperature is !.78+_0.08 MeV, which is lower than the values found in the statistical calculations. The unsmoothed a-value, 2.59_+0.46 MeV - t compares quite favorably with Newton's value of 2.61 M e V - ' . The total cross section (n, p + n p ) was measured to be 191 +_25 mb. Values given for the (n, p) cross section are 90+_ 18 mb [ref. zl)] and 87+_ I I m b [ref. 16)] and for the (n, np) reaction 53_+ I l mb [ref. ,6)]. The percentage contributions given by the statistical calculations, table l, differ from the 62 % (n, p) and 38 % (n, np) contribution calculated from Allan's work 16). The direct component for this reaction was estimated experimentally to be 38 % in comparison to the theoretical value of 57 %. The disagreement here could be a reflection of the model used by Brown and Muirhead or could be due to the fact that the angular distribution may continue to decrease to back angles. No conclusive data have been given for the latter possibility. 4. C o n c l u s i o n s

The comparison of the measured energy spectra and angular distributions with the results of other experiments gives rough agreement overall, when experimental differences are taken into account. Treatment of the energy spectra via the statistical theory with A = 0.0 MeV yielded results, table 1, which were in reasonable agreement with those of earlier

300

K . R . ALVAR

works. The comparison of the t- and z-parameters indicated that they were approximately equal with the difference indicating that the (n, p) reaction does not involve all of the known residual nucleus levels. An arbitrary adjustment of the multiplying constant in Newton's formula a = 0 . 0 6 2 ( j , + j o + 1), (3) would not bring all of the values given by this formula into agreement with those extracted from experiment. This procedure was used in ref. 18) to get better agreement. The (n, p) and (n, rip) total cross sections estimated from the statistical calculations are also given in table 1, expressed as percentages of the total cross sections given in table 2. The percentage error in the temperature or in a is smaller for the smoothed data than for the unsmoothed data. This is not surprising since the smoothing reduces fluctuations in the data. In general, the smoothed data yields smaller temperatures and larger a-values. In addition to A = 0.0 MeV, the energy distribution for each reaction was anal2rzed for A = 1 MeV (A = 1.45, 1.54 MeV for 5SNi), which changed the a- and t-values only slightly. The small changes can equally be attributed to curve-fitting as well as to the omission of possible direct effects. The gross angular distribution of the 5SNi reaction led to the estimation of the spin cut-off factor to be > I, which satisfies the "weak coupling" approximation t). The shape of the gross angular distributions for the other reactions could not be explained on a purely statistical-model basis. An estimate was made of the possible direct components for comparison with the direct-reaction calculations of Brown and Muirhead 1~) and the results are given in table 2. The comparison of the two estimates for 5SNi shows good agreement, for the others agreement is poorer, but no consistent trend is observed. In view of the size of the direct components, it is somewhat surprising that there is reasonable agreement between the statistical calculations, the integral temperature and the known (n, p) and (n, np) cross sections. The agreement may arise from the strong energy dependence of the level density which could dominate the behavior of the energy distributions for both direct and statistical processes for this particular type of reaction. A more satisfactory explanation awaits further theoretical developments. References I) 2) 3) 4) 5) 61 7) 8)

T. Ericson, Adv. in Phys. 9 (1960) 436 R. R. Wagner and R. A. Peck, Jr., Nucl. Phys. A l l 0 (1968) 81 J. M. Kootsey, Nucl. Instr. 35 (1965) 141 J. J. Janni, Air Force Weapons Laboratory technical report 65-150 (1966) G. S. Mani, M. A. Melkanoff and I. lori, CEA report 2379 (1963) A. Gilbert and A. G. W. Cameron, Can. J. Phys. 43 (1965) 1479 A. G. W. Cameron, Can. J. Phys. 36 (1958) 1040 T. D. Newton, Can. J. Phys. 34 (1956) 804

(n, p) AND (n, np) REACTIONS

301

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