Search for Ay = 1 and Ayy = 1 points in the 6Li(d, α)4He reaction

2.B: 2.G [

Nuclear Physics A315 (1979) 3 1 0 - 3 1 6 ; ( ~ North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

SEARCH FOR Ay = 1 AND Ayy = 1 POINTS IN THE 6Li(d, o04He REACTION R. R1SLER, W. GRI~IEBLER, P. A. S C H M E L Z B A C H , B. JENNY, V. K O N I G , J. N U R Z Y N S K I * and H. R. BI~RG1

Laboratorium ./~ir Kernphysik, Eid.q. Technische Hochschule, 8093 Zt~)~ich, Switzerland Received 20 January 1977 (Revised 20 October 1978) Abstract: A search for vector analysing power A~. = t and tensor analysing power Ay~. = 1 values of the 6Li(d, ~)4He reaction in the energy region between 5.0 and 6.5 MeV as well as between 8.0 and 10.0 MeV was performed experimentally. Two A,. m a x i m a which are compatible with unity were found. No A~. = 1 point could be detected. The precise energies and angles for the maxima were determined by interpolation of the experimental data.

N U C L E A R R E A C T I O N 6Li(polarised d, ~), E = 5.0-6.5, 8.(~10.0 MeV; measured A(O, E) a n d A (O, E).

I. Introduction The motivation and interest in the search for points at which a component of the analysing power reaches its theoretical maximum value are discussed in a recent publication t). It was found that such maxima exist not only in elastic scattering but also in nuclear reactions induced by polarized deuterons. The present measurements have been carried out in the framework of a systematic search for maxima in nuclear reactions with light target nuclei. Inspection of analysing powers Tkq of the 6Li(~, ~)4He reaction below 12 MeV incident deuteron energy 2) suggests the possibility of maxima for the analysing power A.,,~, (in cartesian notation) near 6 MeV (0 .... = 30°) and 9 MeV (0 .... = 90 o) 3). Since in the region of 6 MeV all analysing power components undergo rapid changes and near 30 ° A~, is large and positive, the existence of a possible A~. = 1 point was also investigated. 2. Experimental procedure The general experimental arrangement and procedure of the measurements are described in ref. t). A self-supporting 6Li foil, enriched to 96 ~o, with a thickness of about 300 #g/cm 2 was used as target. The detection of the emitted a-particles is favoured by the high Q-value of 22.374 * On leave from the Australian National University, Canberra, Australia. 310

A~, =

1 AND

Ayy =

1 POINTS

31t

MeV. By adjusting the sensitive depth of the surface barrier detectors the background under the a-peaks could be reduced to only a few percent. However, the cross section is very small ( ~ 0.3 mb/sr) compared with that for the elastically scattered deuterons. This is particularly true for forward angles, where the Coulomb cross section is about three orders of magnitudes larger than the reaction cross section. For this reason electronic pile-up effects could not be prevented in all cases and have to be carefully considered in the analysis of the data. These effects are discussed in sect. 4. The components Ay and A;.~,were measured between 5.00 MeV and 6,50 MeV in an angular range of 20 ° to 50° in the c.m. system. Data were obtained in energy steps between 100 and 500 keV. Another investigation was performed between 8.00 and 10.00 MeV in steps of 0.5 MeV. The c.m. angular range measured in this case was 60 ° to 105 °. Because of the identical particles in the exit channel for the 6Li(d, ~)4He reaction A,. must be symmetric and A), has to be antisymmetric about 90° in the c.m. system. 3. Results

The data obtained at the lower energy are presented in figs. 1 and 2. The statistical errors are smaller than the dot size. The data are not corrected for finite geometry and electronic effects. The solid lines in fig. 1 are polynomial curves fitted to the data in order to obtain the local maximum. It is clear from fig. 2 that no A~, = 1 point exists since it must appear at the same angle and energy as an absolute maximum in A,, [ref. 3)]. Results at the higher energy are shown in figs. 3 and 4. The Ay data behave as expected, namely crossing the zero line at 90 °. The A,, results reach nearly unity. The curves are again polynomial fits for finding the local maximum. While the vector component data show that in the investigated energy regions no values of A~, near the theoretical maximum are found, the situation is clearly different for A,,, which component reaches in two energy regions values near unity. 4. Determination of the maxima

The experimental mapping of the two regions was followed with an interpolation procedure. For this calculation each single angular distribution was fitted locally with a polynomial, the order of which was determined by the largest probability of the fit to the data. For this fit, the rough data without correction were used. Finally the same interpolation method was applied to all local maxima t o determine the absolute maximum and its energy and angle. The local maximum between 5.0 and 6.5 MeV, which is at a small scattering angle, requires due to the finite solid angle, an A~,~,correction of + 1.2 %. An additional correction is necessary because of the electronic pile-up effects caused by the much higher counting rate of the elastically scattered deuterons. An investigation, simu-

312

R. R 1 S L E R

1,0 0.9.t 0.8-

et al.

i

O.E

MeV

0.4

o•

500

•

500 MeV

I.O

02

0.9-

0.8

5.25

MeV

0.0

1.0 0.9-

I

I

m•

0.8 ~, 1.0 0.90.8 1.0

5.50

I

I

550 MeV

06

MeV

0.4 5.65

MeV

Q2 Ay

AyYO.9

0.8 1.0 0.9-

5.75

MeV

Q8

5.85

MeV

II

0.0 0.6

I

I

°Oo

I

600M~

0.4 • o

1.0 "

0.2

0.9-

o8

~,

6.00

MeV

0.0 0.6

1.0

t

I III

I

I

• • •

6,50

I MoV

0.90.8

6.25

~

6.50

MeV i

0.4

l.O ;~ 0.9 0.8

0.2 /

0.7' '~ i

20 °

,,'0 °

5'0 °

Fig. 1. The tensor analysing power A~.r between 5.0 and 6.5 MeV. The statistical errors are smaller than the dot size. The curves are polynomial fits.

0.¢

~*

60*

Fig. 2. The vector analysing power A~,between 5.0 and 6.5 MeV. The statistical errors are smaller than the dot size.

lating the electronic situation using two r a n d o m pulse generators with pulse heights and pulse rates c o r r e s p o n d i n g to the scattered deuterons and the alphas from the reaction, results in a 3.5 % c o u n t i n g loss in the simulated a-peak in the spectrum and creates an additional b a c k g r o u n d on b o t h sides of the peak. in spite o f this large loss in the n u m b e r o f counts the calculated correction to the analysing powers is only 0.7 % as the experimental a r r a n g e m e n t used is insensitive in first order to such effects 6). At the higher energy where the m a x i m a are near 90 ° the calculated correction from solid angle geometry is only + 0 . 5 %. Because o f the m u c h smaller elastic deuteron cross section no pile-up loss correction was necessary. The final absolute calibration at the m a x i m a f o u n d at 5.55 and 8.80 MeV was m a d e with a beam calibrated directly with analytically proved Ary = 1 points in d-~ scattering s). This final calibration included also the measurement o f the quantities Axx and A=. The relation Axx + Ayy + Azz = 0 can then be used as a consistency check o f the data. The resulting sums are 0.0030_+0.0150 and -0.0018+_0.0094

Ay = 1 AND A~.r = 1 POINTS j

i

ee '~joe°

0.0

~y

oo

• oo

-0.2 I

800

MeV

I

I

I

,

,

Q2 0.0 -0.2

313

o •

,-

f

oo . •

"

8.50

MeV

I

I

0.2

,

, •

0.0

•"

I

I

"01

-0.

1.0

9.00 MeV

I°

I

I

ilf°° :

_

,,°

I

0.2 O0

.50 MeV

I

I

,

f

,•

•o

•

-0.2 " o • . •

60 °

I

I

... 0

I

80*

I

1.0

.

.

.

.

MeV

I

I00°

Fig. 3. The tensor analysing power Art between 8.0 and 10.0 MeV. The statistical errors are smaller than the dot size. The curves are polynomial fits.

0.8

~ 80 °

~

0~

J

I00"

120"

Fig. 4. The vector analysing power A~. between 8.0 and 10.0 MeV. The statistical errors are smaller than the dot size.

respectively. A l t h o u g h this r e l a t i o n d o e s n o t check the a b s o l u t e value o f the c a l i b r a tion it d e m o n s t r a t e s the stability o f the b e a m p o l a r i z a t i o n with respect to c h a n g e s o f the spin angle a n d c o r r e l a t e d c h a n g e s in the b e a m optics. T h e fits o f the i n t e r p o l a t e d m a x i m a are s h o w n in figs. 5 a n d 6. T h e d o t s with e r r o r b a r s are the c o r r e c t e d a n d a b s o l u t e l y c a l i b r a t e d results for the different energies. T h e o p e n circles r e p r e s e n t the final c a l i b r a t i o n m e a s u r e m e n t d e r i v e d f r o m d-~ elastic scattering. T h e t h i c k solid line is the fit as a f u n c t i o n o f energy a n d the s h a d e d b a n d indicates the u n c e r t a i n t y o f this fit d u e to statistical e r r o r s o f the m e a s u r e m e n t s . A n a d d i t i o n a l u n c e r t a i n t y o f 0.007 m a i n l y c a u s e d by the u n r e l i a b l e b a c k g r o u n d s u b t r a c t i o n a n d the u n c e r t a i n t y in the c o r r e c t i o n for p i l e - u p losses m u s t be a p p l i e d to the results at 5.55 M e V . This is s h o w n in fig. 5 by the d a s h e d curves. T h e s e uncertainties d o n o t include an u n c e r t a i n t y d u e to the a b s o l u t e d e t e r m i n a t i o n o f the b e a m

R. RISLER et al.

314 1.0

I

I

Ayy

I

I

. - -..

u-~2~o,nty__u~ - - ~ : - "-~ u'.~-u_-_m -_-_- -

/'~."T,

T polarization

1.0 Ayy

0.95

!

I

0.95

"':'::i:

I

--

~u_ncerlam~y

I

of b e a m

yio

I

0.90

i 5D

i 5.5

i 6.0

J 6.5

O9C

do

,do Ed MeV

Ed MeV Fig. 5. Polynomial fit of the maxima found by interpolation of the experimental data between 5.0 and 6.5 MeV. The curves are explained in the text.

Fig. 6. Polynomial fit of the maxima found by interpolation of the experimental data between 8.0 and 10.0 MeV. The curves are explained in the text.

polarization. The energy of the accelerator has to be changed from the d-~ calibration points to the 6Li(d, ~)4He maxima, and hence a slight change in the beam optics and a corresponding deviation of the beam polarization must be taken into account. The total uncertainty of the calibration procedure is estimated to be at most 1 o;. This uncertainty is shown in figs. 5 and 6 by the horizontal band below Ay3. = 1. 5. Discussion

The results at both energies are compatible within the assumed errors with an Ay3 = 1 ~alue. The energies and angles found in the analysis are listed in table 1. It is obvious from the experimental difficulties that the 5.55 MeV point at least is not suitable for the calibration of polarized deuteron beams. TABLE ]

Location of A~.~. Ed. lab (MeV) 01.h (deg) 0 .... (deg)

1 points in the 6Li(d, :04He reaction 5.55 _+0.12 24.2 + 1.0 29.7 _+ 1.0

8.80 + 0.25 76.8 _+ 1.0 90.0 + 1.0

While the shape of A~,y as a function of angle and energy near the maximum at 5.55 MeV is smooth and simple, the behaviour of the same component around the 8.80 MeV maximum is more complex. Near this energy the angular distribution changes from one maximum at 90 ° to two maxima, which appear symmetrically around a dip at 90 °. This more complicated situation is shown in fig. 7. Since the A~,~, = 1 surface is flat over a large energy and angular range the energy of the maximum is not well determined. One may speculate that the absolute maximum occurs at the forking point of the local maxima.

A r = 1 AND 1.0

Ar), = 1 P O I N T S

315

MAXIMUM

Ayy 0.8

0.6

0.4

0.2

8,0

70-

Fig. 7. T h r e e - d i m e n s i o n a l r e p r e s e n t a t i o n of the

90-

0~

A~,~, surface

II0-

between 8.0 and 10.0 MeV.

Considering the experimental difficulties and hence the remaining uncertainty of Ayy = 1 points in the 6Li(c[, ~)4He an analytical proof would be highly desirable. For a reaction with the spin structure 1 + 1 ~ 0 + 0 the necessary and sufficient condition for the M-matrix elements in order to obtain A~,y equal unity is 3)

M11,00"~- M1-

1,oo =

O.

Physically, this means that the absolute values of the amplitudes with parallel and antiparallel spins in the entrance channel should be equal; however, they should have opposite signs. The study of the behaviour of this complex function will decide analytically about the existence of such maxima. The procedure is in principle the same as that used in the elastic d-~ scattering 5); the calculation, however, is more complex. Unfortunately such an analysis is not yet available. From the existence ofAr~, = 1 points in deuteron elastic scattering 5) and deuteron induced reactions 1) arises the question about the physical significance of such maxima. A systematic discussion about conditions for the M-matrix elements for different spin structures has been given in refs. 1,7). In ref. 1) the correlation of Ary -- 1 values with compound nucleus resonances has been suggested. Table 2 is a compilation of information about Art -- 1 values near resonant

316

R. RISLER et al. TABLE 2 Compound nucleus resonances near A . , = 1

Reaction

Ed Comp. E x (MeV) nucl. (MeV)

Resonant reaction matrix element

s

s"

AI

(l's'J ~ IR IlsJ ~)

3He(d, p)4He

9.3

5Li

22

(4 ½ ~+lRI2 ~2 ~+)

½,

6Li(d, o04He

5.5

8Be

26

(4 0 4 + IRI2 2 4 +)

0, 1, 2

0

2

6Li(d, ct)4He

8.8

8Be

29

(6 0 6+1RI4 2 6 +)

0, 1, 2

0

2

a) Ref. 1o).

2

Further evidence for a J~ resonance from other reactions p-:t scattering, 267. 2 resonance a) ct-:t scattering, 64 resonance b) ~-ct scattering, 6~, resonance b)

b) Ref. 11).

reaction matrix elements (l's'J"lRllsJ"). It has been found in analyses of the corresponding reactions that these reaction matrix elements are important in this energy region 8,9) and that they fulfil some special linear relations relevant to the corresponding resonance 8). It is interesting to notice that all resonant reaction matrix elements found change the orbital angular momentum by two units from the entrance to the exit channels. Such a coupling can only be achieved by tensor forces. Tensor forces can cause strong spin flip, which is a necessary condition of the M-matrix elements for Ary equal to unit~¢. This view supports the idea suggested 1) for the origin of analysing power maxima. It would make the search for such maxima even more interesting as a tool for the investigation of broad and highly excited levels in light nuclei. We are greatly indebted to the Swiss National Foundation for its financial support.

References 1) W. Griiebler, P. A. Schmelzbach, V. K6nig, B. Jenny, R. Risler, H. R. Biirgi and J. Nurzynski, Nucl. Phys. A271 (1976) 29 2) R. Risler, W. Griiebler, A. A. Debenham, V. K6nig, P. A. Schmelzbach and D. O. Boerma, Nucl. Phys. A286 (1977) 115 3) F. Seller, F. N. Rad, H. E. Conzett and R. Roy, Proc. Fourth Int. Symp. on polarization phenomena in nuclear reaction, ZiJrich, ed. W. Griiebler and V. K6nig (Birkh~iuser Verlag, Basel, 1976) pp. 587,897 4) P. A. Schmelzbach, W. Griiebler, V. K6nig, R. Risler, D. O. Boerma and B. Jenny, Nucl. Phys. A264 (1976) 45 5) W. Griiebler, P. A. Schmelzbach, V. K6nig, R. Risler, B. Jenny and D. Boerma, Nucl. Phys. A242 (1975) 285 6) V. Kfnig, W. Griiebler and P. A. Schmelzbach, ref. 3), p. 893 7) H. E. Conzett and F. Seiler, Nucl. Phys. A290 (1977) 93 8) F. Seiler, Nucl. Phys. A157 (1972) 379 9) R. Risler, W. Griiebler, V. K6nig and P. A. Schmelzbach, Nucl. Phys. A286 (1977) 131 10) G. R. Plattner, A. D. Bacher and H. E. Conzett, Phys. Rev. C5 (1972) 1158 11) A.D. Bacher, F. G. Resmini, H. E. Conzett, R. de Swiniarski, H. Meiner and-J. Ernst, Phys. Rev. Lett. 29 (1972) 1331