Compound-statistical features of deuteron-induced reactions

2.A.l: I 2.D

]

Nuclear Physics 86 (1966) 417.---.428; (~) North-Holland Publishiny Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

COMPOUND-STATISTICAL FEATURES OF DEUTERON-INDUCED REACTIONS

(I). Radiative Capture of 4-15 M e V Deuterons F. W. PEMENT and R. L. WOLKE Wherrett Laboratory of Nuclear Chemistry, University of Pittsburgh t, Pittsburgh, Pennsylvania 15213 Received 11 March 1966

Abstract: Absolute cross sections and excitation functions for the s°Si(d, 7)a2P and, lasBa(d, 7)~4°La reactions from ~ 4 to 15 MeV have been measured radiochemically using the stacked target technique. The 3°Si(d,7) cross sections above 5 MeV are 110 to 160/~b and exhibit little energy dependence. The laSBa(d, 7) excitation function peaks at ~ 22 #b near 10 MeV. The compound nucleus mechanism, formulated from continuum-theory cross sections and statistical-model calculations using Fermi gas level densities, reproduces both the magnitudes and the dissimilar energy dependences of the two excitation functions. Inverse E1 photonuclear cross sections were calculated both for the giant resonance shape used by Carver and. Jones and for that proposed by Lane and Lynn, the former providing more satisfactory agreement with experiment, especially in the Si reaction. It is concluded that these radiative deuteron capture reactions can be explained in terms of compound nucleus formation followed by statistical de-excitation. E [

[

NUCLEAR REACTIONS a°Si,l~SBa(d,7), E ~ 4-15 MeV; measured or(E). Natural targets.

1. Introduction D e u t e r o n s have been used extensively as projectiles in experimental studies of the stripping a n d p i c k u p reactions, the m o s t widely investigated of the direct interactions at m o d e r a t e energies. Relatively little a t t e n t i o n has been directed, however, to the i n i t i a t i o n by deuterons of nuclear reactions which might proceed by the f o r m a t i o n of a c o m p o u n d nucleus followed by statistical de-excitation. A l t h o u g h a few comparisons (ref. 1)) have been m a d e between statistical-model calculations a n d experimental d e u t e r o n excitation functions, d e u t e r o n - i n d u c e d , c o m p o u n d - s t a t i s t i c a l processes have been neither studied experimentally n o r subjected to theoretical analysis to the extent that p r o t o n - or alpha-particle-induced reactions have been 2). Moreover, n o predictions of the degree of c o m p e t i t i o n between direct interaction (DI) a n d c o m p o u n d - s t a t i s t i c a l (CS) m e c h a n i s m s in the same d e u t e r o n - i n d u c e d reaction have yet been explicitly extracted from the D I a n d CS theories. * This work was supported in part by the U. S. Atomic Energy Commission, and is based on a dissertation submitted by F. W. P. to the University of Pittsburgh in partial fulfillment of the requirements for the Ph.D. degree. 417

418

F.

W.

PEMENT AND

R. L. W O L K E

Among the deuteron-induced reactions which might be expected to exhibit compound-statistical features are radiative deuteron capture and those reactions in which more than one nucleon is emitted. Accordingly, the compound-statistical features of some (d, 7) and (d, 2n) reactions have been examined in this and the following paper, respectively, by comparing experimental excitation functions between 4 and 15 MeV with calculations based on the CS mechanism. TABLE 1 Previously reported (d, 7) observations Reaction all(d, 7)~He aHe(d,y)SLi 7Li(d, T)gBe ~Be(d, )011B 9Be(d, y)XlB alB(d, 7)~3C ~2C(d, 7)~4N ~C(d, 7)1~N 14N(d,

7)160

~GO(d, T)~SF 3°Si(d, 7)32P 54Cr(d, 7)56Mn 5SNi(d, 7)6°Cu ~'4Zn(d, 7)6nGa laSBa(d, 7)14°La ~a~U(d, 7)z36mNp z~U (d, V)e~SNp ~asU(d, ~)~°Np

Deuteron energy (MeV) 0.150-- 1.300 0.2 --2.85 0.35 --0.4 0.5 1.85 0.5 --5.6 1.50 --2.75 0.5 --2 1.2 --2.6 -

0.5

-

-- 5.5

0.45 --3.9 6 -- 10 3.5 --4.5 3.5 4.5 3.5 4.5 21 ~ 1 14.8--20.0 16.7-- 23.4 1.8 --23.4

Cross section a)

Method u)

Ref.

60 /~b 5 0 ~ 1 0 /zb

/ ?, /

") ~) s)

6.5 c2.0 /~b 0.65 #b/sr (at 90 °) 0.50 #b/sr 0.6±0.2 #b 5--10 # b 0.62 /*b/sr (at 90 °) 0.1 25 /~b 0.1--1 mb 80--295 /~b 17--61 # b 27--80 #b 65:k10 ,ub 440±100 #b 1.38±0.34 mb 1.63 mb

7 7 y 7 A 7 A A A A A A A A A

~') 111)

~o) ~) 1at 1,,) 12) la) 1~) 1~) 1% ~) ~) lrt ~7)

a) Maximum value, unless otherwise noted. ~) 7 = observation o f capture gamma rays. A -- observation of residual nucleus by activation methods.

The radiative capture processes which have been studied most extensively are the thermal and fast (n, 7) reactions. While the former is well understood in terms of CS theory, it has been suggested 3) that a direct capture mechanism must be postulated in order to account for the magnitudes of (n, 7) cross sections above about 4 MeV, especially in heavier elements. Although the capture of charged particles has been studied less extensively, the results of some (p, 3') studies 4) have been qualitatively similar to those of neutron capture; the few (e, 7) reactions which have been analysed are consistent with the CS mechanism 5). Few (d, 7) reactions have been observed in sufficient detail so that comparisons between theory and experiment can be made over a significant range of bombarding energy. The principal reported observations 6 - 17) on targets ofA > 2 are summarized in table 1. In addition, several unsuccessful searches for (d, 7) reactions have been reported, so that upper limits are known for a number of (d, 7) cross sections 13, ts).

DEUTERON-INDUCED REACTIONS (1)

419

Carver and Jones 14.15) have found that the cross sections of 54Cr, 5SNi and 64Zn for the radiative capture of deuterons between 3.5 and 4.5 MeV can be well accounted for by the CS model, with no necessity of invoking other capture mechanisms. Recently, Owens and Winter i2) have obtained evidence for CS processes in the 160( d, 7) reaction up to ~ 4 MeV. The 14C(d, ]2) reaction at 1.2 to 2.6 MeV shows similar behaviour 1~). These studies, however, do not cover very wide ranges of bombarding energy, nor are the maximum bombarding energies as high as in the reported (p, 7) and (z, ]2) studies. The present work was undertaken to extend some radiative deuteron capture excitation functions over much wider ranges of target mass and incident deuteron energy in an attempt to provide a more revealing comparison between CS theory and experiment. In the study of reactions of small cross section by the radiochemical activation method, the choice of possible target nucleides is severely limited by the production of contaminating activities. These can arise either from different reactions of various nucleides in the target which produce the same product, or simply from a more prolific reaction yielding products which are isotopic with the sought radionucleide and which mask the sought radiations in the post-chemistry counting. The former type of contamination was avoided in the present work by seeking the (d, ]2) products of either mono-isotopic targets or of the heaviest isotopes of polyisotopic elements. The latter type of contamination, however, was found to preclude observation of the reactions 88Sr(d, ]2)90m, g y , 1 3 3 C s ( d ' ]2)135tuBa ' 11 opd(d ' ]2)II 2 A g ' 1 3 0 y e ( d ' ]2)132 I and ~s6W(d, 7)I88Re because of large (d, xn) yields, in spite of isotopic enrichment of the latter three targets. The two radiative capture reactions which were found to be sufficiently free of contamination to be studied in detail are 3°Si(d, 7)32p and 13SBa(d ' 7)14OLa.

2. Experimental Proeedures 2.1. G E N E R A L T E C H N I Q U E S

Stacks of targets at the centre of a scattering chamber were bombarded normally with 0.1 to 1.0 /~A beams of 14.9+0.12 MeV deuterons from the University of Pittsburgh cyclotron. The bombarding energy at each target in the stack was calculated from a range-energy relationship 19) based on the ranges of deuterons in air zo). Day-to-day fluctuations of + 0.2 MeV in the mean incident beam energy were compounded by degradation to an uncertainty of ___0.5 MeV at 4 MeV; the inclusion of beam straggling effects 2~) could approximately double this energy uncertainty. The integrated beam intensity during each bombardment was determined by counting the gross ]/-activity induced in a 10 mg/cm 2 Ta foil placed at the head of each target stack. In a series of separate bombardments, the Ta monitors were calibrated against the charge accumulated by a Faraday cage connected to a precision current integrator. The overall accuracy of the Ta monitoring method was ___5 ~o and was independent of incident deuteron energy from 14.3 to 14.9 MeV.

420

F. W. PEMENT AND R. L. WOLKE

After each bombardment, the targets in the stack were subjected to radiochemical separations. The resultant samples of reaction-product nucleides, mounted as circular precipitates of known area under mylar coverings, were then counted absolutely, either with a 4n methane-flow proportional counter or with a 7.6 c m x 7.6 cm NaI(T1) scintillator and a 512-channel pulse-height analyser. The 4n beta counter was calibrated for various mean/%energies by the method of Bayhurst and Prestwood 22). Errors in the measured absolute B-disintegration rates amounted to _+6.9 ~ . The scintillation spectrometer was calibrated with standard sources, the resultant calibration curves being drawn parallel to the calculated efficiency curves of Vegors, Marsden and Heath 2 3 ) . Errors in the measured absolute 7-disintegration rates were +_7.4 ~ . 2.2. THE 3°Si(d, 7)3~P REACTION The targets were prepared from Merck electronic-grade Si containing < 2.1 × 10-7 atom percent of phosphorus and less than one part in 109 of other, electrically active impurities. The Si powder was deposited by sedimentation from triply-distilled, de-ionized water ( > 1.2 × 106 • • cm resistivity) onto 0.025 mm AI foils of > 99.99 purity. Precautions were taken during this procedure to avoid the introduction of any P, S or C1 which, if present at levels of the order of 10 ppm, could be activated by deuterons or fast neutrons to yield 32p in amounts comparable to those produced by the 3°Si(d, y) reaction. The deposits were dried, weighed, covered with 99.99 ~o A1 foil, compacted by pressing, stacked and mounted in rigid frames for bombardment. Typical targets contained 10 to 20 mg Si/cm 2. After the bombardments, phosphorus was chemically separated by dissolving the Si powder in HF-HNO3 in the presence of PO 3- carrier and KMnO4, the purpose of the latter being to prevent the loss of phosphorus as PH 3. Ammonium phosphomolybdate was precipitated once and MgNH4PO4" 6 H 2 0 was precipitated twice from citric acid solution containing Na and Fe holdback carriers 24). The final MgNH4PO4 " 6 H 2 0 precipitates were counted for about a week, after which their radiochemical purity was tested by redissolving them, passing their solutions through Dowex 50W-X12 cation exchange columns and reprecipitating. No changes in the specific activities were observed. The chemical yields ranged from 70 to 85 ~ . The yield of 32p was determined by 4n counting its 1.711 MeV ft. The decay curves were consistent with the known half-life of 14.1 d. 2.3. THE 138Ba(d,7)14°La REACTION "Specpure" BaCO3 powder from Johnson, Matthey and Co. was filtered from suspension in pure ether onto Whatman No. 50 filter paper discs. The resultant targets were dried, weighed, sealed in place with a mylar-base tape about 7 mg/cm 2 thick and then sandwiched tightly between A1 foils. Irradiated "blank" sandwiches, containing tape and paper but no BaCO 3, yielded no detectable 7-activity which followed the La chemistry. Neutron activation analysis of the BaCO3 target material showed < 0.019 ppm of La, < 1 ppm of Ce and < 0.18 ppm of Pr, elements which

421

DEUTERON-INDUCED REACTIONS (I)

could give rise to 14°La by the (d, p), (d, 2p) or (d, ~) and (d, 3p) reactions, respectively. It is estimated that these three elements, if present at the stated levels, could together have produced less than 0.1% of the observed ~4°La activity. Lanthanum was separated from the targets after the bombardments by several hydroxide precipitations interspersed with BaSO4 and AgC1 scavenges, following which LaF a was precipitated and mounted for counting25). The chemical yields were > 70 %. Only lanthanum gamma rays were present in the spectra, as illustrated 1061

LQ135 0481

LFBox,oy t

Zz,,--I

I1

IF

Z::D

~\

/ ~.~ofier 2.4 d

E 03~ 049k^ :

"' v\\

~x

A ' ~/

0f, er

t~ /1

6.2d

l;?l

',,

,d

pure LC}I40~'~,~ I01

I

I

20

I

I

I

I

I

I

40 60 80 CHANNEL NUMBER

~

I I

I00

Fig. 1. Gamma spectra of La activities from the deuteron bombardment of Ba. in fig. 1. The yield of 14°La was determined by stripping its 1.60 MeV photopeak, the decay of which was followed over five 40 h half-lives. It was assumed that the 1.60 MeV transition accompanies 95.6 % of the 14°La disintegrations 26), although an abundance of 88.2 % has also been reported 27). The experimental results are presented in sect. 4, where they are compared with theoretical calculations. The calculations are described in the following section. 3. Statistical-Model Calculations of the Capture Cross Sections 3.1. INTRODUCTION

The cross section for a (d, 7) reaction may be expressed in compound nucleus formalism as 2s) o'(d, 7) = a~(d)G~(7),

(1)

422

F.W.

PEMENT AND R. L. WOLKE

in which a~(d) is the cross section for the formation of a compound nucleus by deuterons as a function of energy and G¢(7) the independent probability that the excited compound nucleus will decay by photon emission to a bound state. Following Lane and Lynn 3), Go(7) may be written as

Q(~)

r~ (l+x)rn

(2)

where F~ is the photon emission width, F, the neutron emission width and x the contribution of charged particles to the total emission width. For most nuclei, x << 1. The widths F~ and F, were obtained by integrating a generalized Weisskopf expression 2 9 ) for the probability that an excited nucleus will emit a particle i of energy between ~i and e i + d e i. Such an expression is 28' 3o)

Pi(ei)dei -- gik2 ¢r,(ei) Pi(-Ei) dei, 2rr 2

(3)

pc(Ec)

where E~ and E,. are the excitation energies of the compound nucleus and of the residual nucleus formed by the emission of particle i, respectively, Pc and pi the respective level densities, ~r~(e~)the inverse compound nucleus formation cross section for particle i incident on the excited residual nucleus, k; the wave number of the emitted particle and 9~ the statistical weighting factor. The energy E~ is equal to Ea + Qa,-~ where E a is the bombarding energy in the centre-of-mass system and Qd, ~. the deuteron binding energy in the target nucleus. The energy E~ is E~-Q~-~.~, Q~ being the separation energy of particle i in the compound nucleus. If s and m denote spin and mass, respectively, /(2si+

9ik2

=

1)(2migi)/h

12(r.i/hC) 2

2

if i is a nuclear particle; if i is a photon s o l

(4)

The integrated emission probabilities, then, depend upon al, P and the limits of integration chosen for eq. (3). These quantities are discussed briefly below. 3.2. C O M P O U N D NUCLEUS F O R M A T I O N CROSS SECTIONS

For both deuterons and neutrons, cross sections derived frona continuum theory were used. Shapiro's numerical values 31) for at(d) were substituted directly into eq. (1). For ~rj(e,), however, the approximation which has been developed 3z) for Monte Carlo calculations was used: at(c,,) = zRZ~.(I +/~/en),

(5)

where ~ = 0.76+2.2A -~, /~ = (2.12A-~-0.050)/:~, and R is the nuclear radius, R o A ~. The excited-state cross sections have been approximated by the corresponding ground-state values. The inverse photon absorption cross sections were calculated on the assumption of E1 absorption by the ground-state nuclei. The area under the

DEUTERON-INDUCED REACTIONS (1)

423

photonuclear giant resonance peak is thus given by the dipole sum rule

fo

aV(er)de v = 2rcZ N Z eEh (1 +0.8x), A Mc

33) (6)

and ranges from 0.0812 NZ/A M e V . b if x (the fraction of the neutron-proton force with exchange character) is assigned a value of 0.5, down to 0.058 NZ/A MeV • b if the exchange contribution is neglected. Two expressions describing the shapes of the giant resonances have been used in statistical-model calculations. The Lorentz form of Steinwedel and Jensen 34), used by Carver and Jones 14, 15) and by Khulelidze et al. 5) may be written

al(er) = 2

FRe ~

2 2 + (/'R~) z (~2 --~R)

f:

ar(e~)der.

A modified Breit-Wigner form due to Lane and Lynn

(7)

3),

FR e~/2rCeR f: a,(e~) = (e _eR)Z+F~/4 exp [(ber--eR)] ar(er)der,

(8)

is more strongly energy dependent and more asymmetric than expression (7). In eqs. (7) and (8), F R is the width of the giant resonance, centred at the energy eR. In eq. (8), b ~ 0.3 MeV -1 and exp [b(eT--eR)] is taken as unity at % > eR" Both the Steinwedel-Jensen and Lane-Lynn forms were used in the present calculations. 3.3. LEVEL DENS[TIES The Fermi gas level density formulation of Weisskopf 29)

p(E) = C e x p [2(aE) ~]

(9)

was used. Significantly better agreement with experiment was obtained when oddeven effects were compensated for by altering the pre-exponential constant C rather than by introducing a pairing energy to give the alternate formulation p(E) = C exp {2[a(E-6)]~}. The constants obtained by Varshni 35) from a least-squares analysis of observed level spacings,

Coati = 2.43 Coda. . . . = 15.05 C .....

(10)

were used in eq. (9) for 14°La; the constants were modified for 32p, as described below. While eq. (3) may be integrated analytically with the use of eq. (9), more complex level density formulations 36) in which C is a function of E or in which the exponential is more complicated require the use of approximations and were not used. There is evidence 37) that the accuracy of statistical-model calculations is not generally improved by the more complex level density expressions.

424

r.W.

PEMENT AND R. L. WOLKE

3.4. CALCULATION OF THE PARTICLE WIDTH The neutron width was calculated by combining eqs. (4), (5) and (9) with eq. (3) and integrating over neutron energy e~ from 0 to (E~-Q~). Writing the level density of the residual nucleus formed by the evaporation of a neutron as p , ( E ~ ) = Cn exp { 2 [ a ( E ~ - Q ~ - e ~ ) ] ~} leads to the integrated form of eq. (3) obtained by Dostrovsky eta[. 32) F~(Ec)-

2

g n m n R ° A ~ o~C. ± ~ 2 exp[2(anRn)~](2a.g.-(~-anfl)[2(a~R.)~-l]} 21r2h2pe(Ee) a n

,

(11)

where R. = E ~ - Qn. Calculations of the proton width from the corresponding expression of Dostrovsky et al. indicated that Fp << F. for both the 3°Si and the 13SBa reactions. Hence x in eq. (2) was taken as zero and /'total ~ F~. 3.5. CALCULATION OF THE PHOTON WIDTH Eq. (3) for P y d ~ was integrated numerically after substitution of eq. (4) to give F~(Ec) -

1 Ec ~, e~a,(e,~)p(E~-e;,)AL,. ~2h2 c2 p~(E~) ~¢=~c-Q,

(12)

In eq. (12), the limits of e~ correspond to single photon transitions directly from the capturing state to bound states of the compound nucleus. This amounts to an assumption that 7 cascading through the continuum contributes negligibly to the cross section because of the strong competition by particle emission in the unbound region. Slightly above the threshold for particle emission, however, photon emission should begin to compete effectively, so that there is some question as to the effective lower limit of e~. Carver and Jones 1 5 ) chose an arbitrary lower limit T, the value of which was close to Qn in their cases. They pointed out that their results were not too sensitive to T, and the use of eq. (12) in the present calculations supported the same general conclusion. The lower limit e~ = E ~ - Q n was therefore used, in accordance with Lane and Lynn 3).

4. Comparison of Statistical Theory with Experiment 4.1. PARAMETERS USED IN THE CALCULATIONS Nucleidic masses for the computation of Q-values were taken from the tables of Mattauch et al. 3s). An Ro of 1.5 fm was used in the calculations of the continuumtheory particle cross sections. It is noted that the experimental values of the integrated photoneutron production cross sections in the neighbouring stable nuclei 31p and 32S are only 20-25 % and 10-14 % of the dipole sum rule, respectively 39). On the assumption that the dipole sum rule might also overestimate the integrated photoneutron cross section for 32p, a value of S~a~(e~)de~ was chosen to fit the magnitudes of the experimental (d, ~/)

DEUTERON-INDUCED REACTIONS (t)

425

cross sections; a cross section of 0.241 MeV • b, which is 37 % of the sum rule prediction, was required. For ~4°La+y, the sum rule value of S~ar(er)de r = 2.76 MeV • b was used. This is in reasonable agreement with the experimental average 39) of 2.1 MeV • b for 139La+ 7, which may not be a strictly comparable case, however, b e c a u s e 139La contains a closed neutron shell. The resonance widths F R were estimated from Goryachev's tables 39) as 5.6 and 5.2 MeV for 32p and 14°La, respectively, and the respective peak energies eR were obtained from his expression eR = 40.7/A~ as 20.4 and 15.1 MeV. TABLE 2 80Si(d' 7)azp cross sections

TABLE 3 13SBa(d, 7)14°La cross sections

Ed (MeV)

tr (,ub)

Ed (MeV)

tr (/tb)

14.1~0.2 13.9±0.2 12.7±0.2 12.3±0.3 10.9~0.3 10.7±0.3 9.9±0.3 9.1±0.3 8.6±0.3 7.3±0.3 5.4±0.4 3.7±0.4

156--17 157--17 112 -12 130--14 116--13 115 13 157 -17 115 -13 138 15 112--12 130- 14 74± 8

13.9±0.2 13.4±0.2 13.0±0.2 11.9±0.3 10.9±0.3 10.1±0,3 8.5±0,3 8.3±0.3 7.6~0.3 7.4±0.3 5.6±0.4

12.7~1.5 10.1~1.2 11.5~1.3 17.5±2.0 21.9~2.5 21.8±2.5 20.7~2.4 18.1~2.0 18.5~2.1 15.7~1.8 6.0~0.6

The choice of numerical values for the constants C and a in the level density expression (9) was made as follows. In the 3°Si(d, ~)32p calculation, Varshni's relation 35), a = A/11.25, was used. The values of C given by eq. (10), however, have been found 35) to predict densities in 31p (odd mass) at 9-10 MeV and in 32p (odd) at 2-4 MeV which are 316 % and 1 % larger, respectively, than those deduced from experiment. On the supposition that the densities at the excitation energies currently of interest ( ~ 17-28 MeV) bear a similar relationship to one another, C was increased f o r 32p over the value 2.43 Cod d . . . . of eq. (10) by the factor 316/101, to give Cod d ~ 7.60 Cod d . . . . • In the 13SBa(d ' y)140La calculation, the odd-even constants of eq. (10) were used. The level density parameter a, however, was varied to optimize agreement with experiment, a = I ~ A being adopted. In view of the fact that 14°La contains only one neutron in excess of the 82-neutron closed-shell configuration of 139La, a n anomalously small level density, which has been employed in similar instances 4o), is not entirely unexpected. 4.2. RESULTS

The measured cross sections are presented in tables 2 and 3 and are plotted as a function of deuteron energy in figs. 2 and 3. The quoted errors in the cross sections

426

F. W. PEMENT AND R. L. WOLKE

include the contributions of uncertainties in the counting efficiencies, chemical yields, decay scheme parameters, target thicknesses and incident beam intensities. The errors in the deuteron energies represent the uncertainty in the incident beam energy, lO00~--

[

]

g-

T

l

7

.3o p32 S~ ( d , ) ' )

r

ol

SJ

:t-

g Ioo 03 O I1: {D I

I0-2

4

6 8 DEUTERON

I0 12 ENERGY, MeV

14

16

Fig. 2. E x c i t a t i o n f u n c t i o n for the a°Si(d, p)82p r e a c t i o n . T h e d a s h e d line j o i n s t h e e x p e r i m e n t a l p o i n t s . T h e s o l i d lines are f r o m c o m p o u n d - s t a t i s t i c a l c a l c u l a t i o n s , u s i n g R o = 1.5 fro, a - - A l l 1.25, a n d the S t e i n w e d e l - J e n s e n (S J) o r L a n e - L y n n ( L L ) s h a p e s for the i n v e r s e g i a n t r e s o n a n c e .

t Bo~3S(d,7,) Lo~4O

11

z" 0

E; PERIMENT ), / "// {D tO--sJ , o c~

F-

/

~L

-4

i'

4

/

,~, 4~ \', i

/

--

I --

×l ~, '

Zi •

j 4.

S5

t

!

L

I

6 8 t0 12 DEUTERON ENERGY, MeV

i4

16

Fig. 3. E x c i t a t i o n f u n c t i o n for the 13SBa(d, p ) H ° L a r e a c t i o n . T h e d a s h e d line j o i n s the e x p e r i m e n t a l p o i n t s . T h e s o l i d lines are f r o m c o m p o u n d - s t a t i s t i c a l c a l c u l a t i o n s , u s i n g R 0 = 1.5 fm, a = ~oA a n d the S t e i n w e d e l - J e n s e n (SJ) o r L a n e - L y n n ( L L ) s h a p e s for the inverse g i a n t r e s o n a n c e .

compounded by the estimated energy spread during degradation through the target stacks. The a°Si(d, 7)a2P cross section, which had previously been obtained 13) semi-

DEUTERON-INDUCED REACTIONS (I)

427

quantitatively as 0.1-1 mb at 10 MeV, is seen to be approximately constant at ~ 130 /~b between 5 and 14 MeV. Early evidence for the occurrence of the 138Ba(d ' ~)14OLa reaction was presented by Weimer, Pool and Kurbatov 41), and a cross section of 65__+10 #b at 21 ___1 MeV was later reported by Ball, Fairhall and Halpern 16). The present results, however, indicate that the cross section rises from ~ 6/~b at 5.6 MeV to a peak value of ~ 2 2 / t b at ~ 10 MeV and falls off at higher energies. The curves in figs. 2 and 3 are the results of the statistical-model calculations, using the Steinwedel-Jensen (S J) or the Lane-Lynn (LL) forms for the shape of the inverse giant resonance. Although the calculations necessarily include the several approximations and assumptions discussed above, it appears that the compound nucleus mechanism is capable of accounting for the cross section of the (d, y) reactions in 3°Si and 13SBa. That compound nucleus calculations are capable of giving the magnitude of or(d, 7) for medium-mass nuclei and for light nuclei at ~ 4-4.5 MeV has already been shown by Carver and Jones 14. is) and by Owens and Winter 12), respectively. The present results extend this agreement with statistical theory over a wider range of target mass and over a much wider range of deuteron energy. They also show that the shapes of two quite dissimilar excitation functions can be reproduced by the theory, the Steinwedel and Jensen 34) giant resonance shape being somewhat more successful in this respect than the Lane and Lynn 3) giant resonance shape. Any direct mechanisms which might contribute to these radiative deuteron capture reactions are apparently dominated by the compound-statistical mechanism and are not observable in the cross section, at least to the extent that compound nucleus formation and statistical de-excitation can be quantitatively calculated. We wish to thank Dr. J. B. Natowitz for his cooperation in several aspects of this work. The cooperation of Prof. B. L. Cohen and of the crew of the Sarah Mellon Scaife Radiation Laboratory is also appreciated. The silicon samples were kindly furnished by the Westinghouse Electric Corporation. References 1) M. Blann and G. Merkel, Phys. Rev. 131 (1963) 764; R. Bock and R. Rtidel, Z. Phys. 174 (1963) 440; M. Z. Maksirnov, JETP (Soy. Phys.) 6 (1958) 1085 2) D. Bodansky, Ann. Rev. Nucl. Sci. 12 (1962) 79 3) A. M. Lane and J. E. Lynn, Nuclear Physics 11 (1959) 646 4) P. J. Daly and P. F. D. Shaw, Nuclear Physics 56 (1964) 322; P. J. Daly, J. R. Rook and P. E. Hodgson, ibid. 56 (1964) 331; G. E. Brown, ibid. 57 (1964) 339 5) N. T. Porile, Phys. Rev. 115 (1959) 939; D. E. Khulelidze, V. L. Chikhlad.ze, M. Z. Maksimov and V. G. Onufriev, JETP (Soy. Phys.) 20 (1965) 259 6) W. Buss, H. W~iffler and B. Ziegler, Phys. Lett. 4 (1963) 198 7) J. M. Blair, N. M. Hintz and. D. M. Van Patter, Phys. Rev. 96 (1954) 1023; W. E. Kunz, J. W. Butler and. H. D. Holmgren, Phys. Rev. 100 (1955) 1252

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8) J. B. Woods and D. H. Wilkinson, Nuclear Physics 61 (1965) 661 9) H. H. Knitter and H. W/iffier, Proc. Rutherford Jubilee Int. Conf. Manchester, (1961) p. 823 10) M. Suffert, G. Costa and D. Magnac-Valette, J. de Phys. 24 (1963) 1029; M. Suffert, D. Magnac-Valette and J. Yoccoz, J. Phys. Rad. 22 (1961) 565 11) J. B. Nelson, E. L. Hudspeth and E. M. Bernstein, Phys. Rev. 136 (1964) BTI 12) R. O. Owens and R. G. Winter, Nuclear Physics 71 (1965) 625; J. W. Butler, Phys. Rev. 99 (1955) 643 13) H. D. Sharma, U. S. Atomic Energy Comm. rept. UCRE-1265 (1951) unpublished 14) J. H. Carver and G. A. Jones, Nuclear Physics 24 (196i) 607 15) J. H. Carver and G. A. Jones, Nuclear Physics l I (1959) 400 16) J. B. Ball, A. W. Fairhall and I. Halpern, Bull. Am. Phys. Soc. 3 (1958) 322 17) R. M. Lessler, U, S. Atomic Energy Comm. rept. UCRL-8439 (1958) unpublished 18) R. M. Sinclair, Phys. Rev. 93 (1954) 1082; G. A. Sawyer and L. C. Burkhardt, ibid. 98 (1955) 1305; H. R. Allan and N. Sarma, Proc. Phys. Soc. 68A (1955) 535 19) G. Friedlander, J. W. Kennedy and J. M. Miller, Nuclear and Radiochemistry (Wiley, New York, 1964) chapt. 4 20) W. A. Axon, B. G, Hoffman and F. C. Williams, U. S. Atomic Energy Comm. rept. AECU-663 (1949) unpublished 21) P. Kafalas and J. W. Irvine, Jr., Phys. Rev. 104 (1956) 703 22) B. P. Bayhurst and R. J. Prestwood, Nucleonics 17, No. 3 (1959) 82 23) S. H. Vegors, Jr., L. L. Marsden and R. L. Heath, U. S. Atomic Energy Comm. rept. [DO-16370 (1958) unpublished 24) W. T. Mullins and G. W. Leddicote, NAS-NS-3056 Nat. Acad. Sci.-Nat. Res. Council, Washington (1962) 25) J. Alstad and A. C. Pappas, J. Inorg. Nucl. Chem. 15 (1960) 220 26) B. S. Dzhelepov, V. P. Prikhodtseva and Yu. V. Khol'nov, Isobaric nuclei with the mass number A = 140 (Macmillan, New York, 1963) 27) R. L. Macklin, N. H. Lazar and W. S. Lyon, Phys. Rev. 107 (1957) 504 28) R. G. Moore, Jr., Revs. l~od. Phys. 32 (1960) 101 29) V. F. Weisskopf, Phys. Rev. 52 (1937) 295 30) H. Bfittner, A. Lindner and H. Meldner, Nuclear Physics 63 (1965) 615 31) M. M. Shapiro, Phys. Rev. 90 (1953) 171 32) I. Dostrovsky, Z. Fraenkel and G. Friedlander, Phys. Rev. 116 (1959) 683 33) J. S. Levinger and H. A. Bethe, Phys. Rev. 78 (1950) 115 34) H. Steinwedel and J. H. D. Jensen, Z. Naturf. 5a (1950) 413; B. B. Kinsey, Handbuch der Physik, ed. by S. Fliagge, vol. 40 (1957) p. 202 35) Y. P. Varshni, Nuovo Cirn. 22 (1961) I45 36) H, A. Bethe, Revs. Mod. Phys. 9 (1937) 69; T. D. Newton, Can. J. Phys. 34 (1956) 804; J. M. B. Lang and K. J. LeCouteur, Proc. Phys. Soc. 67A (1954) 586 37) D, L. Allan, Nuclear Physics 24 (196l) 274; C. S. Khurana and H. S. Hans, ibid. 28 (1961) 560 38) J. H. E. Mattauch, W. Thiele and A. H. Wapstra, Nuclear Physics 67 (1965) 1 39) B. I. Goryachev, Atom. Energ. Rev. 2 (1964) 71 40) I. Dostrovsky, Z. Fraenkel and L. Winsberg, Phys. Rev. 118 (1960) 781 41) K. E. Weimer, M. L. Pool and J. K. Kurbatov, Phys. Rev. 63 (1943) 67