The polarization of the neutrons from the 10B(d, n0)11C reaction for deuteron energies below 3.0 MeV

I

2.B

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Nuclear Physics A121 (1968) 224---232; (~) North-Holland Publishing Co., Amsterdam N o t to be reproduced by p h o t o p r i n t or microfilm without written permission f r o m the publisher

THE POLARIZATION

OF THE NEUTRONS

FROM

T H E l°B(d, no)11C R E A C T I O N F O R D E U T E R O N E N E R G I E S B E L O W 3.0 M e V R. BRUNING, F. W. BI~SSER, H. DUBENKROPP and F. NIEBERGALL

II. Institut fiir Experimentalphysik, Hamburg, Germany and J. CHRISTIANSEN

Hahn-Meitner Institut, Berlin, Germany Received 25 June 1968 Abstract: The angular distributions of the polarization of the neutrons from the l°B(d, n0)taC reaction were investigated at average deuteron bombarding energies of 1.20, 1.65, 2.05, 2.50 and 2.90 MeV. The asymmetry of the neutrons scattered by helium was measured using a telescope of parallel-plate avalanche counters. The polarization was determined from the asymmetry values by means of the phase shifts for n
NUCLEAR REACTION l°B(d, no), E = 1.20 to 2.90 MeV; measured n-polarization (E; 0), tr(E; 0). Enriched target.

!

[

I

1. Introduction T o study the r e a c t i o n m e c h a n i s m o f A ( d , n)B reactions, p o l a r i z a t i o n m e a s u r e m e n t s o f the o u t g o i n g nucleons have to be carried o u t in a d d i t i o n to a n g u l a r d i s t r i b u t i o n m e a s u r e m e n t s o f the differential cross section a n d excitation curves. A t b o m b a r d i n g energies higher t h a n 7 MeV, A ( d , n)B reactions proceed m a i n l y t h r o u g h the direct channel. I n m o s t cases, they have been a n a l y s e d using the dist 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 ) . The D W B A t h e o r y has been very successful in calculating cross sections a n d predicting spectroscopic factors. H o w e v e r , the p o l a r i z a t i o n o f the nucleons emitted in such reactions can r a r e l y be explained by this theory. M a n y a t t e m p t s have been m a d e to analyse A ( d , n)B reactions by m e a n s o f the D W B A t h e o r y at b o m b a r d i n g energies below 7.0 M e V in o r d e r to decide w h e t h e r the reactions are m a i n l y direct o r whether c o m p o u n d nucleus processes are present. Some a u t h o r s 1.2) have tried to calculate the cross sections o f these r e a c t i o n s at lower b o m b a r d i n g energies b y c o m b i n i n g the D W B A t h e o r y a n d the statistical t h e o r y due to H a u s e r a n d F e s h b a c h 3). 224

l°B(d, n0)llc REACTION

225

To obtain further information about these reactions at low bombarding energies, it is important to know the polarization of the outgoing nucleons. Compared to the available experimental data on differential cross section and excitation functions, the information on the polarization of the emitted nucleon is still small. We measured the polarization of the neutrons from the l°B(d, n)llC reaction leading to the ground state of 11C at average bombarding energies of 1.20, 1.65, 2.05, 2.50 and 2.90 MeV. The reaction 1°B(d, no)11C has a Q-value of 6.47 MeV. The spins of the ground states are 3 + for 10B and 32- for l 1C. Since the proton is captured into the lp shell 4), only the v a l u e j = 32 for this transition is possible. Extensive measurements of the differential cross section for the same neutron group at bombarding energies below 3.0 MeV were published by Siemssen et al. 4, 5). They found that the angular distributions vary rapidly with bombarding energy, but the change in shape is smooth. The excitation curves of Siemssen et al. 4,5) and of Marion and Weber 6), who have investigated the corresponding proton group of the mirror reaction l°B(d, p)llB, show no strong fluctuations. The authors conclude that the reaction is mainly direct. The knowledge of the neutron polarization over a large energy range might help to clarify this question. In the experiment described below, the polarization of the neutrons was determined by a measurement of the left-right asymmetry after scattering the neutrons by helium gas.

2. Experimental procedure The investigations were performed with a 3 MV Van de Graaff accelerator. A parallel-plate counter telescope was used as a polarimeter. This method is based on the measurement of the energy and direction of the recoil a-particles. A detailed description of this method is given in ref. 7). The main features of the polarimeter are illustrated in fig. 1. It contains both the helium scattering volume and the detection device, i.e., three parallel-plate transmission counters CrC~TI. The telescope was filled with a self-quenching mixture of helium and an organic vapour (25 Torr ethylalcohol). The helium pressure was varied from 0.4 to 1.0 arm and the depth of the scattering volume from 3 to 4 cm depending on the energy of the recoil ~-particles. The electrodes of the counters (E 1 to Es) consisted of nickel foils (0.6/~m), the gap between the electrodes was 5 mm. An angular filter was mounted between the systems C I and Cxx to select the recoil ~particles of the desired direction. The aperture of the filter was _ 7.5 ° in the plane of the (d, n) reaction and + 2 6 ° in the plane perpendicular to this. For background measurements, a piston was mounted in front of the scattering volume; it could be pushed towards the first electrode E 1 . A mean scattering angle of 142 ° c.m. for the neutrons was chosen; it corresponded to a scattering angle of the ~-particles of Oo ---- 19 ° in the lab system. The recoil a-particles were registered as events of a sixfold coincidence of three

226

R. BRONIr~G et al.

fast coincidence signals (i.e., between every two of three counters) and the signals of the three slow circuits. The target was 96 ~ enriched X°B on a tantalum backing and contained 2 ~ XlB. This was checked by time-of-flight measurements. The thickness of the target caused an energy loss of 220 and 400 keV for bombarding energies of 2.90 and 1.20 MeV, respectively. The target was water cooled, and currents of 150/~A were used. The measurements were performed in open geometry. The angle subtended by the polarimeter at the neutron source was 12 °.

angular filter

scattering piston

E~ ! 4E5

-counter electrodes -counte

,~ ~ I i g axisof telescope the

I target" ~

neutron~

'

~

toamplifier highvoltage

deuteronbecarn Fig. 1. Schematic diagram of the experimental set-up. The telescope contains the scattering volume and the detection device, i.e., three parallel-plate avalanche counters CI-CIII and an angular filter. The piston is used for background measurements. On refers to the reaction angle and O0 to the mean scattering angle of the recoil ~-particles.

The left-right asymmetry was determined as the mean of four independent measurements, i.e., at reaction angles O , "left" and "right" to the deuteron beam and further after rotating the telescope around its axis by 180 ° . The background was measured in the same way. The differential cross section was measured at the same bombarding energies with the same targets using a time-of-flight spectrometer. The results are in agreement with those of ref. 4).

227

l°B(d, n o ) l l c REACTION

0.10

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60 °

t I i rr 9'0 ° 1i 0 ° On

I

I

(c.m.)

30*

60*

90*

120"

e~(c.m.)

Fig. 2. Polarization and differential cross section o f the neutrons as a function of the reaction angle @a (c.m.) at five different b o m b a r d i n g energies. The solid curves are s m o o t h curves connecting the experimental points.

228

R. BRiJNING et al.

3. Correction of experimental data and results The experimental asymmetry values have been corrected for finite geometry. The phase shifts for the calculation of the analysing power of helium were from ref. 8). A further correction was necessary. Since the first excited state of ~ C lies only 1,99 MeV above the ground state, it was not possible to separate completely the neutron groups no and nl leading to the ground state and first excited state of I~C at the higher bombarding energies because of the dE/dx resolution of the counter telescope. To estimate the percentage of the recoil e-particles, which corresponded to the neutrons of the nl group and could not be separated, a measurement was performed with neutrons from the reaction 14N(d, no)lSO using the same counter arrangement.

On(l) = 30" 2.05

2.50 1.65

13

2.90

"~ 3.0" 1.20

"6 2.01.0 ~

!

t0

2.0

3.0 deuteron energy ( M e V )

Fig. 3. Differential yield curve in arbitrary units for t h e reaction X°B(d, na)11C at t h e lab reaction angle o f 30 ° constructed f r o m ref. 4). T h e arrows indicate t h e m e a n b o m b a r d i n g energies at w h i c h the a n g u l a r distributions o f the differential cross section a n d polarization were m e a s u r e d . The h a t c h e d

regions indicate the energy ranges averaged over target thickness. When choosing the appropriate bombarding energy and reaction angle, the neutrons had the same energy as those of the nl group of the reaction l°B(d, n t ) t l C . Since the first excited state of ~SO lies 5.2 MeV above the ground state no further neutron groups from the reaction ~4N(d, n)~50 disturbed. With these measurements and the measurement of the ratio of the differential cross sections for the neutrons of the nl and no groups from the reaction a°B(d, n ) H C , the percentage of the recoil e-particles from nt neutrons could be determined. The results show that less than 1.5 ~ of the coincidences is caused by the neutrons leading to the excited state of ~1C. Assuming that the neutrons of the n~ group are polarized to _+0.5, the error for the polarization of the neutrons of the no group was increased accordingly to a maximum of 0.8 ~ .

10B(d, no)llc REACTION

229

The admixture of 2 ~ of taB in the target material did not disturb as time-offlight measurements showed. TABLE 1 E x p e r i m e n t a l r e s u l t s a t five d i f f e r e n t b o m b a r d i n g e n e r g i e s .Ea as a f u n c t i o n o f t h e l a b o r a t o r y r e a c t i o n a n g l e On (lab)

Ea ( M e V ) On (lab) (deg) 10 20 30 40 50 60 70 80 90 100 110 120

1.20

1.65

e(On)

,de

(}o~)

(%)

- - 9.1 --12.3 -- 5.5 -- 4.3 - - 2.5 .1. 4.5 0.0 .1. 4.3 .1. 8.3 .1.12.6

3.9 3.1 3.0 3.0 3.3 2.6 2.3 2.8 3.3 3.0

2.05

2.50

P(On) (~)

LIe

/'(On) (~)

,de

(~)

6.0 .1. 1.5 .1. 1.8 .1. 5.9 .1.10.2 ,1,1,16.4 .1.18.1 .1.13.2 +15.2 .1.15.9 .1.14.8 +15.9

2.9 2.6 2.7 2.4 2.0 2.9 2.4 3.1 3.0 3.0 3.1 3.0

.1. 0.8 - - 1.0 -- 2.1 -- 1.8 ,1,10.3 .1.13.6 .1.11.6 +11.8 .1.1.10.4 .1.1.15.0 .1. 0.3 -- 6.8

2.3 2.3 2.3 2.9 2.7 2.1 2.3 2.7 2.6 2.3 2.6 3.6

-

-

P(On) (~)

(~)

4.8 - - 3.7 - - 1.5 -I- 2.5 -}- 4.7 +10.4 .1. 9.3 .1. 1.7 - - 2.1 - - 0.3 .1. 0.9 -- 6.8 -

-

2.90

AP (~o) 2.5 2.0 2.1 2.3 2.1 2.8 3.0 2.9 2.7 2.6 2.8 4.5

P(On) (~) .1. .1. .1. .1. .1. .1. .1. .1. ---.1.

3.7 0.2 0.3 2.8 5.5 5.5 6.4 0.5 5.9 4.9 1.7 3.3

`de (~;) 3.0 2.6 2.4 2.5 2.4 2.7 2.8 3.2 2.9 3.0 4.5 4.0

T h e p o l a r i z a t i o n v a l u e s c a l c u l a t e d b y m e a n s o f the n-ct s c a t t e r i n g p h a s e shifts o f H o o p a n d B a r s c h a l l (ref. 8)) f r o m t h e m e a s u r e d a s y m m e t r i e s are l i s t e d in t h e c o l u m n P ( O n ) . I n t h e c o l u m n AP, s t a t i s t i c a l e r r o r s a n d c o r r e c t i o n s d u e t o t h e n e u t r o n s l e a d i n g to the first e x c i t e d s t a t e o f 1~C h a v e b e e n t a k e n i n t o a c c o u n t . T h e s i g n o f the p o l a r i z a t i o n w a s t a k e n a c c o r d i n g to t h e B a s l e c o n v e n t i o n .

In fig. 2, the corrected values of the polarization of the neutrons from the reaction 10B(d, no)l 1C are plotted against the reaction angle On (c.m.). The errors include the statistical errors and those in the corrections mentioned above. Furthermore fig. 2 shows the angular distributions of the differential cross section in arbitrary units. The statistical errors are smaller than the size of the symbols. The quoted energies are mean energies taking into account target thickness. The sign of the polarization was chosen according to the Basle convention. In table 1 the corrected polarizations and their errors are listed for the different bombarding energies and lab reaction angles O . (lab). Fig. 3 shows the excitation function for the reaction t°B(d, n o ) t i C at the lab reaction angle of 30 ° based on the measurements of ref. 4). The arrows indicate the mean bombarding energies at which the angular distributions of the differential cross section and polarization were measured. The hatched regions indicate the energy ranges averaged due to target thickness. 4. Discussion

The excitation curve in fig. 2 shows no strong fluctuations, only a wide maximum at the bombarding energy of 2.05 MeV. The angular distributions of the differential

230

R. BR'U'NINGet al.

cross sections change rapidly, but the variation from one distribution to the other is smooth. These facts indicate that the reaction l°B(d, no)11C is mainly direct. The measurements on the mirror reaction l°B(d, p)llB by Marion and Weber 6) and Breuer 9) show results similar to those for the reaction ~°B(d, no)~C. Breuer 9) reported a weak resonance at 2.3 MeV in the reaction 10B(d, p)l lB. Siemssen et al. 5) performed DWBA calculations for the reaction l°B(d, no)llC assuming that this reaction is dominated by a direct process. They reproduce the experimentally observed over-all shape of the transition when a cut-off radius is used. The angular distributions of the polarization of the neutrons show strong variations with bombarding energy. The outstanding characteristic of the polarization is the strong fluctuation at higher bombarding energies. The highest polarization occurs at the lower bombarding energies; at higher bombarding energies the polarization decreases and at 2.9 MeV it is near zero. These relatively large variations of the polarization indicate that the ~°B(d, n 0 ) ~ C reaction is not purely direct, but compound nucleus processes may contribute. Recent measurements on the polarization of the protons from the mirror reaction ~°B(d, po)l~B at bombarding energies below 2.0 MeV by Stahl and Dietze lO) show the same characteristics. At 1.35, 1.60 and 2.05 MeV, the results agree within the experimental errors with those in the reaction 10B(d, no)l 1C. There is not much point in trying DWBA calculations for the polarization measurements at each bombarding energy. In order to test how well the polarizations and differential cross-sections can be calculated by DWBA theory, we averaged the measured angular distributions of the differential cross section and polarization over the interval of bombarding energies between 1.2 and 2.9 MeV. When averaging the polarization values, they were weighted according to the differential cross section. Since the compound-nucleus contributions can change rapidly with bombarding energy, they partly cancel. The differential cross section contribution from direct process should change slowly with energy. For the averaged angular distributions of the differential cross section and polarization, a code developed by Macefield ~ ) was used for the calculations. For the calculations, the following potential was used: V(r) = Vc(r ) - U f ( r ) - i W g ( r ) -

Uz~(r)l " s,

where f(r) =

1+ exp

g(r) = 4exp

1+ exp ~---d-)] ,

h(r) = (h/m~c)2(1/r) d / d r ( f (r)), R = ro A~.

l°B(d, no)UC REACTION

231

For the Coulomb potential Vc(r), the potential of a uniformly charged sphere was taken. The bound-state wave function is calculated in the program of Macefield from a real Woods-Saxon potential; a spin-orbit term was included. The best fit is shown in fig. 4. The scale for the differential cross section is in arbitrary units. Since no absolute measurements of the cross-section were carried out,

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120" 150" ®n (c.m.)

Fig. 4. DWBA calculations for the reaction l°B(d, n0)llC° The angular distributions of the differential cross section and polarization have been averaged over the range of bombarding energies between 1.20 and 2.90 MeV. the experimental value for the reaction angle of 40 ° was fitted with the calculated one. The optical-model parameters are listed in table 2. Adopting for the deuteron the parameters of Siemssen et aL 5) and of Maddison 12), we could not reproduce the measured polarizations. F o r the emitted neutron, the depth of the imaginary part of the potential is much smaller than that given by the relations of Wilmore and Hodgson 13). Adopting the non-local optical potential of Perey and Buck 14), Wilmore and Hodgson a 3) calculated distortion parameters for elastic neutron scattering in terms of the

232

R. BRU-NING et al.

e q u i v a l e n t local potential. T h e relations o f ref. 13) yield a d ep t h o f 9.0 M e V for the i m a g i n a r y p a r t o f the potential. All other p a r a m e t e r s f o r the em i t t ed n e u t r o n agree with ref. i 3). In s u m m a r y the results o f the D W B A calculations an d the m e a s u r e m e n t s for the r e a c t i o n 10B(d, n)011C are similar. TABLE2 Optical-model parameters used for the DWBA calculations of the averaged angular distribution of the differential cross section and polarization Potential part

incoming deuteron

Real part V

ro

(MeV)

(fm)

(fin)

64.0

1.20

0.90

1.20

0.60

1.31

0.66

captured proton emitted neutron

Imaginary part

44.8

a

14"

ro

(MeV) (fm)

Spin-orbit part a

(fm)

6.0

1.90

0.65

1.5

1.26

0.48

Uls

ro

(MeV) (fm)

a

(fm)

5.7

1.20

0.60

7.5

1.20

0.60

9.7

1.25

0.50

The potential depth for the captured protons was varied according to the binding energies. T h e au t h o r s w o u l d like to t h a n k Professor Dr. W. Jentschke for his c o n t i n u o u s interest an d s u p p o r t o f this work. T h e s u p p o r t given by the B u n d e s m i n i s t e r i u m fiir wissenschaftliche F o r s c h u n g is gratefully acknowledged.

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

P. E. Hodgson, Advan. Phys. 15 (1966) 329 A. Gallmann, P. Fintz and P. E. Hodgson, Nucl. Phys. 82 (1966) 161 W. Hauser and H. Feshbach, Phys. Rev. 87 (1952) 366 R. H. Siemssen, M. Cosack and R. Felst, Nucl. Phys. 69 (1965) 209 R. H. Siemssen, M. Cosack and R. Felst, Nucl. Phys. 69 (1965) 227 I. B. Marion and G. Weber, Phys. Rev. 103 (1956) 1408 F. W. Buesser, J. Christiansen, H. P. Hermsen, F. Niebergall and S. S6hngen, Z. Phys. 187 (1965) 243 B. Hoop Jr. and H. H. Barschall, Proc. Int. Conf. on polarization phenomena of nucleons, Karlsruhe (1965); Nucl. Phys. 83 (1966) 65 G. Breuer, Z. Phys. 178 (1964) 269 K. D. Stahl and G. Dietze, Phys. Verhandl. 4 (1968) 327 B. E. F. Macefield, private communication R. N. Maddison, Proc. Phys. Soc. 79 (1962) 264 D. Wilmore and P. E. Hodgson, Nucl. Phys. 55 (1964) 673 F. Perey and B. Buck, Nucl. Phys. 32 (1962) 353