Angular distributions for the 160Gd(d,t) 159Gd reaction

Nuclear Physics A96 (1967) 52--64; ~ ) North-Holland Publishing Co., Amsterdam

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

ANGULAR DISTRIBUTIONS

F O R T H E 16°Gd(d, t)~59Gd R E A C T I O N

M. JASKOLA t, K. NYBO tt, p. O. TJ~M ttt, and B. ELBEK The Niels Bohr Institute, University of Copenhagen, Denmark

Received 6 December 1966 Abstract: The angular distributions for triton groups from the le°Gd(d, t) reaction have been measured at a deuteron energy of 12.1 MeV. The Nilsson assignments which were known for a considerable number of levels in 15'Gd made it possible to intercompare the distributions for selected groups with l = 0, 1, 2, 3, 4, 5 and 6. An optical-model triton potential was found which gave a good fit to the data at forward angles. Deviations at backward angles indicate that the cross sections depend on the total angular momentum j of the transferred neutron. NUCLEAR REACTIONS Xe°Gd(d,t), E = 12.1 MeV; measured a(Et, 0). lSgGd deduced levels, J, g, L Enriched target.

1. Introduction I t has been s h o w n t h a t the a n g u l a r d i s t r i b u t i o n s for the (d, p ) r e a c t i o n can be very useful for d e t e r m i n i n g the a n g u l a r m o m e n t u m o f the transferred n e u t r o n . I n s o m e cases, the a n g u l a r d i s t r i b u t i o n s are also 1, 2) sensitive to the c h a n g e in the t o t a l a n g u l a r m o m e n t u m j . F o r nuclei in the r a r e - e a r t h region, a few (d, p ) a n g u l a r d i s t r i b u t i o n s have been p u b l i s h e d 3 - 7 ) , b u t no (d, t) a n g u l a r d i s t r i b u t i o n s have been r e p o r t e d thus far. T h e (d, t) r e a c t i o n is a v a l u a b l e spectroscopic t o o l for the study o f energy levels in d e f o r m e d nuclei. I t is therefore o f s o m e interest to investigate w h e t h e r the a n g u l a r d i s t r i b u t i o n s , at t h e b o m b a r d i n g energies available w i t h t a n d e m accelerators, are sufficiently sensitive to the a n g u l a r m o m e n t u m o f the n e u t r o n p i c k e d u p to assist in a s s i g n i n g / - v a l u e s . F o r heavy nuclei the t r i t o n o p t i c a l - m o d e l p a r a m e t e r s are p o o r l y k n o w n . I t was t h e r e f o r e also p a r t o f this w o r k to find a r e a s o n a b l e fit to the e x p e r i m e n t a l a n g u l a r d i s t r i b u t i o n w i t h a d i s t o r t e d wave B o r n a p p r o x i m a t i o n ( D W B A ) calculation. W e have c h o s e n to investigate the 16°Gd(d, t) r e a c t i o n because a c o n s i d e r a b l e a m o u n t o f i n f o r m a t i o n is available a b o u t the levels in 159Gd f r o m a study o f the (d, p ) a n d (d, t) reactions a). These m e a s u r e m e n t s are, however, restricted to a few angles. t On leave from the Institute of Nuclear Research, Polish Academy of Science, Warsaw, Poland. tt On leave from the University of Bergen, Norway. ttt On leave from the University of Oslo, Norway. 52

le°od(d, t)15°Gd REACTION

5~

2. Experimental procedure The 12 MeV deuteron beam used in the experiments was obtained from the Niels Bohr Institute Tandem Accelerator. Samples of 16 OGd' isotopically enriched to 94 70, were provided as oxides from the Oak Ridge National Laboratory and were reduced by lanthanum to gadolinium metal 9). The metal was then evaporated in vacuo onto thin carbon foils to produce targets with a thickness of g 200 #g/cm 2. The first measurements of the triton angular distributions were performed by means of a solid-state counter telescope consisting of a 200 pm thick AE counter and a 2000 #m thick E counter. In order to separate the reaction products according to their mass, the counters were operated in the usual E, E x AE mode. A 4096-channel pulseheight analyser recorded simultaneously the particle groups from the (d, p), (d, d') and (d, t) reactions. Due to imperfections in the particle identification system, the strong elastic deuteron groups appeared as weak groups in the triton spectra, but they could be identified and subtracted by means of the recorded deuteron spectrum. The energy resolutions in the triton spectra were from 35 keV to 55 keV, somewhat dependent on the scattering angle and the counting rate. The beam current was measured by a Faraday cup behind the target. In view of the limited energy resolution, the counter telescope could be used only to record the distributions for the four strong groups marked 1, 2, 10 and 14 in fig. 1. Furthermore, the large intensities of the elastically scattered groups from 16°Gd and target impurities limited the angular range to from 50 ° until 160 °. To avoid the ditticulties mentioned above, the measurements were continued in a single-gap magnetic spectrograph 1o) with photographic plate recording. The spectrograph was operated with somewhat less than maximum resolution, which made it possible to use relatively large apertures and thick targets. The final resolution was from about 11 keV at forward angles to about 17 keV at backward angles, where the target was viewed in reflection and therefore gave a considerable line broadening. The exposure time required was about 40 min with an 0.7/~A deuteron beam; however, at extreme forward and backward angles, the low triton intensities required somewhat longer exposures. The total charge for each exposure was measured by a Faraday cup and, simultaneously, a solid-state detector was used to monitor the intensity of scattered deuterons at 45 °. The two monitoring systems were in agreement within 2 70. For an initial series of exposures the Faraday cup had to be removed at 15°, 10° and 5°; otherwise it would have covered the entrance aperture to the spectrograph. Therefore, at these angles only the counter monitor could be used. The spectra at 5 ° showed a large background of doubly scattered deuterons and were not analysed. Later, a smaller Faraday cup was constructed which obstructed only the angular range from + 2 ° to - 2 °. Also the system of anti-scattering baffles in the spectrograph was improved, which resulted in an essentially background-free triton spectrum also at 5 °. At angles from 5 ° to 35 °, a spectrum was recorded at 5 ° intervals and then at 10° intervals until 70 °. For these measurements the target was left in the same position and the

54

aL

M. JASKOLA e t

CHANNEL

100

0

100

200

[

I

I

NUMBER 300

400

I

I

1~

500 i

COUNTER TELESCOPE

600

16°Gd (d ,t) ~SgGd 12

Ed =12 1 HeY e

90

=11o °

4000 ~c J

uJ z z

80

< -1- 70 (.J 6O nLU

m

50

or)

~-

40

o

30

Z

(J

I 0

20

o~

10

°o~ o,o~ o

o~Oo e°

o e

0

I

I

I

I

¢

2000

I

I

I

I

i

1500 EXCITATION

600

2000 ,

. . . . .

1500 -~---,

I

SPECTROGRAPH

o

o k

I

1000 ENERGY ,-

0

o~o

500

0

(keV)

1000 ,

,

14

12

500 i

0 i

i

,

~

I

16OGd (d,t)159Gd E u = 12,1

MeV

e = 90"

500

1o 0o0 ~c

~00

E 300 E w

I?

200

5 10

100

18

•r - Y , - . i ± ' - ' ~ . : , ~ " ~ - " ~

BO

i " \~-'~'~'~':'

85 DISTANCE

ALONG

9O PLATE

95 (cm)

Fig. 1. T r i t o n spectra f r o m t h e 160 G d ( d , t) 159 G d reaction at E d = 12.1 M c V o b t a i n e d with t h e counter telescope a n d t h e m a g n e t i c spectrograph.

55

16°Gd(d, t)lSSGd REACTION TABLE 1 Energy levels studied in a ' G d Peak no.

Energy (keY)

Nilsson assignment

dtr/dsQ 90 ° (/zb/sr)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

0 120 146 184 226 327 371 455 506 681 704 743 780 973 999 1109 1143 1960

] :~- [521 ] ~ ~-[521 ] ~ ]-[523] ~ ~+[642] ~ ~- [523] ] ~-[523] ~ ~+ [642] ~ ~-[523] ~ ½-[521] 4~ ~--[505] ~ ½-[521] ~ ~+[402]

191 219 27 86 118 25 71 18 80 102 26 613 195 584 114 54 219 104

} }+[400] ~ }+[400]? t }-[530] ~ ½+[404]

1

1 3 3 4 3 5 6 5 1 5 3 2 0 s) 0 2 s) 1 s) 1 ,) 4

=) Assignment made on the basis of the angular distribution measured in this experiment.

,soGd (d.t)ISgGd

S P E C T R O G R A P H

•

COUNTER

O ~

L=O

n," m

10~

,g

I

10 0 °

30 °

I

I

I

60 ° 90 ° 120 o LABORATORY ANGLE

I

150 °

180 o

Fig. 2. Angular distributions for triton groups with l ---- 0. The assignment for the 973 keV level is fairly certain whereas the Nflsson state corresponding to the level at 780 keV is not known. The solid line shows the result of a D W B A calculation with the parameters listed in table 2.

M. JASKOLA et aL

56 I03L

l

/ L

{

y

I

.=

/..Z~,

"

= J ,,o Gd(d,t),,,Gd

....

. oo,,ER '

SPECTROGRAPH

o

10z

=< ,< z C~ 101

lool ,l 0°

,

30 o

,

,

,

,

60 o 90 ° 120" LABORATORY ANGLE

150 o

180=

Fig. 3. Angular distributions fbr triton groups with l = 1.

103

I

I

I

I

I

~6oGd (d,t)1~9 Gd •

COUNTER

O SPECTROGRAPH 1=2 O

$

102

b--

.< _z ~10'~

10o 0=

~

30*

60 ° 90 = 120 ° LABORATORY ANGLE

~

150=

180 =

Fig. 4. Angular distributions for triton groups with l = 2.

lS°Gd(d, t)lS°od REACTION

57

absolute cross sections were obtained by normalization to an elastic cross section of 350 mb/sr at 60 °. At 90 °, 105 °, 125 ° and 150 ° the spectra were individually normalized to elastic cross sections o f 45 mb/sr, 20.5 mb/sr, 9.6 mb/sr and 5.8 mb/sr, respectively. 3. Experimental results Examples o f the spectra observed at 90 ° by means o f the magnetic spectrograph and at 110 ° by means of the solid-state counter telescope are shown in fig. 1. The angular distributions were measured for the transitions to the levels in lS9Gd listed in table 1 which also gives the Nilsson assignment and the absolute 90 ° cross section. 103

i

i

I

103'

J

I

~,oGd(d.t)'SgGd • COUNTER

]

I

1

~S°Gd ( d , t )~S~Gd

NO 2

O3 2

102

< <

I-m

NOS

:

i

y

~ - Es23]

< z

10 ~

g

fl, 100,o

1 30 °

60 ° 90 ° LABORATORY

120" ANGLE

150"

180 c

Fig. 5a. Angular distributions for triton groups with l = 3 .

P

i

10ol O°

30 o

: I 50 ° 90 ° 120 o LABORATORY ANGLE

150 °

180 °

Fig. 5b. Angular distributions for triton groups with l = 3.

The data in this table are from ref. s). The corresponding angular distributions are presented in figs. 2-8. The error bars in the figures refer to statistical errors only. The agreement between the angular distributions obtained from the magnetic spectrograph measurements and from the solid-state counter measurements is satisfactory in the angular range from 60 ° to 130 ° . The solid curves are angular distributions obtained by D W B A calculations. The angular distribution for the level at 973 keV, which has been assigned as the ½ ½+ [400] Nilsson state, is shown in fig. 2. It has a pronounced minimum at ~ 20 °. A similar shape was observed for an unassigned level at 780 keV, and, as the l = 0

58

M.

10 ~

,

e t al.

JASKOLA

~

I F

.o ,n i -}+[~o~1

~'

n102 NO 4

}

<

}+£6423

t

eY m

z

10 ~

,,OGd(d,t)~5,G d o SPECTROGRAPH t=4 10 o 0o

30 =

60 = 90 ° LABORATORY

120 ° ANGLE

150 °

180 =

Fig. 6. Angular distributions for triton groups with l = 4.

1031

t NO. 10

t I--

i

NO

-~ 102

+

8

B23]

-

>DC ,< I.-N

,

~---

NO.

10 ~

6

~-~- [5231

i

~OGd(d,t),s~Gd o

SPECTROGRAPH t=5

I

101o '

0o

30 °

I

I

60 ° 90 ° 120 ° LABORATORY ANGL-E

I

150 °

180 °

Fig. 7. Angular distributions for triton groups with 1 = 5.

59

le°Gd(d, t)X69Gd REACTION

distributions are distinctly different from other distributions, a spin assignment of ½+ for the 780 keV level is almost certain. The distributions for four transitions with l = 1 are shown in fig. 3. They appear to be fairly typical, with a small secondary m a x i m u m between 15 ° and 20 °. At forward angles the shapes are almost the same. The differences at back angles will be discussed in sect. 5. For l = 2 and l = 3 the observed distributions shown in figs. 4 and 5, respectively, are quite similar. The maxima seem to occur at slightly lower angles for the l = 2 distributions than the l = 3 distributions.

1°3l

I

I

i

t

I

,~Gd (d,t)~'Gd 0 SPECTROGRAPH

E

L=6

102 >-

d

or-

J

rn n-

101

J

TO O

0*

I

30*

60"

i

90"

LABORATORY

r

120"

I

150"

r

180"

ANGLE

Fig. 8. A n g u l a r d i s t r i b u t i o n f o r a t r i t o n g r o u p w i t h ! = 6.

The l = 4 distributions shown in fig. 6 again peak at a somewhat larger angle than the l = 2 distributions and also fall off quite steeply at forwar(i angles. The very large difference between the two distributions in fig. 6 will be discussed in sect. 5. The distributions corresponding to l = 5 are shown in fig. 7. One of them shows a slight increase at forward angles in contrast to the sharp decrease found for l = 3 and 4. Finally, one distribution with l = 6 was measured. As shown in fig. 8, it has a sharp decrease at forward angles, in contrast to the result from the D W B A which shows an almost constant cross section at small angles.

60

M. SASKO~,Aet aL

4. DWBA analysis of the data The triton angular distribution data have been analysed in terms of the distorted wave Born approximation by means of a GIER-ALGOL computer program 12) which used a formalism similar to that of the well-known code SALLY t a). The bound state wave functions for the neutron were evaluated for a Saxon-Woods well at a binding energy (in MeV) B = 6.26-Q. The radius parameter r 0 and the diffuseness parameter a were 1.25 fm and 0.65 fro, respectively. All the DWBA calculations were performed with deuteron and triton surface absorption potentials and without lower cut-off. The deuteron optical parameters used are listed in table 2. They have been successfully applied for analyses of (d, p) reactions on Yb targets a. 14) and are essentially in agreement with the standard deuteron parameters given by Percy and Percy 11). TABLE 2 Optical-model parameters for deuterons and tritons V (MeV)

W (MeV)

ro (fro)

a (fro)

r'o (fm)

a' (fm)

86

12

1.15

0.87

1.37

0.7

Triton optical parameters

154

1~

1.10

0.75

1.40

0.65

Triton optical parameters ~)

155

10

1.20

0.70

1.30

0.65

Deuteron optical parameters

~) Ref. is).

A set of triton parameters which reproduced the observed angular distributions was found essentially by trial and error. Empirical parameters for the 26Mg(t, d) (ref. 15)) and the 2°6pb(t, p) reactions 16) were the starting point for the calculation. The parameters used in ref. 16) are listed in table 2. The position of the minimum at ,~ 20° for the l = 0 distributions was correctly given by the calculation when the value of r o given in ref. 16) was reduced to 1.1 fm. However, for even values of l, the calculated distributions showed violent oscillations, in contrast to the experimental distributions which are smooth within the experimental uncertainties. It was therefore attempted to damp the oscillations in the theoretical distributions by varying the real potential depth V, which appeared to have a marked influence on the strength of the oscillation. A slight increase in V was sufficient to remove the oscillatory structure almost completely. The triton parameters finally selected are listed in table 2 and the calculated angular distributions for these parameters are shown as solid lines in figs. 2-8. Although no very extensive parameter search was made, a reasonably good fit to the observed distributions was obtained for aU/-values, especially at forward angles. It is also gratifying that the parameter set is only slightly different from that of ref. 16). An added argument in favour of the parameter set is that the predicted absolute cross

xa°Od(d, t)X89OdREACTION

51

sections are in good agreement with the observed cross section for several levels in the Gd isotopes where the spectroscopic factor is expected to be near unity s). This comparison was based on a normalization factor N of 3.0 (eft ref. 15)). It is interesting to utilize the triton optical parameters for a calculation of the expected cross-sections and angular distributions for other bombarding energies. In fig. 9, the result of such a calculation is shown for even I at 8, 12 and 16 MeV deuteron energy. 10'

I

I

Ed =8 MeV

L

I

I

I

I

I

I

Ed :12 MeV

I

I

r

Ea:16 MeV

10o

i 10"1 t=2

t=O

10-2 L=2

a__.

t=5

10-3 L=4

10-'

10-5

10-6

P

3O

60

I

i

90 120 150 180

l

0

I

I

I

30

60

90

I

I

I

120 150 180

I

I

30

60

I

I

1

1--

90 130 150 180

e°tab Fig. 9. D W B A calculations with the triton and deuteron optical parameters listed in table 2.

At the lowest energy, the distributions are dearly dominated by the Coulomb effects, and measurable cross sections are found at back angles only. At the highest bombarding energy, chosen to simulate what can be expected from a medium-sized tandem accelerator, the cross sections increase considerably and the angular distributions are more forward peaked. It appears, however, that the difference between the distributions for the different values of l are not more distinct than it was the case for a deuteron energy of 12 MeV.

62

M..IASKOL.A e t al.

5. The j-dependence of cross sections

Whereas the agreement between the calculated and the measured angular distributions is reasonably good at forward angles, there are several cases where, at back angles, the measured cross sections deviate considerably from the calculated values. (Cf., e.g., the distributions for the ½½-[521] l = 1 group and the ~{+[642] l = 4 group on figs. 3 and 6, respectively.) Although the present material comprises only 16 distributions, it seems possible to relate these deviations to the total angular momentum j of the group. The relative deviations between measured and calculated values as function of l are shown in fig. 10. For each/, the cases with the spin of the neutron parallel to the orbital angular momentum are distinguished from those with the spin anti-parallel. •

5.0

t*½FOROOOL-VALUE + + ° G d ( d , t ) m G d RATIO OF 125" CROSS SECTION TO CALCULATED CROSS SECTION

t-{.

•

[+ {

-

v

t-½..

0

t-

EVEN

2.0 1.0

o

•

•

/x A

0.5

0.2 l

I

L

I

J

J.__

I

0

1

2

3 l

4

5

6

Fig. 10. Relative deviations between m e a s u r e d and calculated values o f the cross section as

function of L The experimental observations at back angles are all consistent with the rule that, for odd l, the j = l - ½ cases have lower cross sections than the j = I+½ cases. The latter are in reasonably good agreement with the DWBA calculation. For even I the situation is just opposite. The direction of this effect is the same as found for the j-dependence in (d, p) stripping 2). 6. Discussion

For the cases studied here it appears difficult to obtain a unique determination of l from the shape of the (d, t) angular distributions alone. For l = 0 and l = 1, the behaviour at small angles is probably sufficiently characteristic to make an assignment

16°Gd(d, t)15°Gd REACTION

63

fairly certain. The differences between the distributions for l = 2, 3 and 4 are, however, small at forward angles, the most noticeable being a shift o f the maximum of the distribution towards higher angles with increasing l and a corresponding increase in slope for the part of the distribution which lies between ~ 20 ° and ~ 60 °. At back angles, the slopes are expected to be decreasing with increasing l (cf. the calculated distributions in figs. 2-8), but the j-dependence discussed in sect. 5 completely dominates the distributions in the backward hemisphere. As mentioned earlier, the observed and calculated distributions for l = 0 and l = 1 show a maximum at small angles. A probably related extremum can be observed as a hump on the distributions for higher values of I. The estimated position of this hump I

I

I

I

I

I

80

70 6O 5O ~0 3O 2O I0 0

I

I

I

I

I

I

1

2

3

~

5

6

t Fig. 11. Position o f the first e x t r e m u m as f u n c t i o n o f l.

is indicated by an arrow in figs. 2-8 and the angles at which it occurs has been plotted as function of I in fig. 11. Perhaps the most reliable determination o f / c a n be obtained from a careful measurement o f the angular distributions in the region where this extremum occurs. Once the l has been determined, then fig. 10 indicates that j can be determined from the angular distributions at back angles.

Note added in proof." A slight error has recently been discovered in the pick-up part of the D W B A code used in this work. Some of the distributions have therefore been recalculated with the Oak Ridge code :rULIE. The changes are all small, the most noticeable being a somewhat improved fit to the experimental data in the angular range from 30 ° to 20 °. We are grateful to dr. Ole Hansen for discussions on this point. One of the authors (M.L) is grateful for a fellowship from the International Atomic Energy Agency. Another (P.O.T.) wishes to acknowledge a grant from "Norges Teknisk-Naturvitenskapelige Forskningsr~d".

64

M. JASKOLAet aL

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16)

R. H. Fulmer and W. W. Daelmick, Phys. Rev. Lett. 12 (1964) 455 L. L. Lee, Jr. and J. P. Schiffer, Phys. Rev. 136 (1964) B405 M. N. Vergnes and R. K. Sheline, Phys. Rev. 132 (1963) 1736 A. Isoya, Phys. Rev. 130 (1963) 234 B. E. F. Macefield and R. Middleton, Nuclear Physics 59 (1964) 561 J. R. Erskine and W. W. Buechner, Phys. Rev. 133 (1964) B370 R. H. Siemssen and J. R. Erskine, Phys. Rev. 146 (1966) 911 P. O. Tjem and B. Elbek, to be published L. Westgaard and S. Bjernholm, Nucl. Instr. 42 (1966) 77 J. Borggreen, B. Elbek and L. Perch Nielsen, Nucl. Instr. 24 (1961) 1 C. M. Percy and F. G. Percy, Phys. Rev. 132 (1963) 755 R. K. Cooper and J. Bang, The Niels Bohr Institute, G.A.P.2 (1965) R. H. Bassel, R. M. Drisko and G. R. Satchler, O R N L 3240 (1962) D. G. Burke et aL, Mat. Fys. Medd. Dan. Vid. Selsk. 35, No. 2 (1966) R. N. Glover, A. D. W. Jones a n d J . R. Rook, Phys. Lett. 13 (1965) 493 R. A. Broglia and C. Riedel, Nuclear Physics A92 (1967) 145