Polarization of protons from the 9Be(d, p)10Be reaction at Ed = 12.0 MeV

l

2.B

]

Nuclear Physics A195 (1972) 280- 288; (~) North-HollandPublishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

POLARIZATION OF P R O T O N S FROM THE 9Be(d, p)l°Be REACTION AT

Ed =

12.0 MeV

A. BUDZANOWSK[, L. FREINDL, W. KARCZ, J. KU~MINSKI, B. LAZARSKA and W. ZIPPER btstitute of Nuclear Physics, Cracow 23, Poland and

Institute of Physics, Jaqellonian Unit'ersit.v, Cracow and

Institute of Physics, Silesian UniL,ersity, Kato wice, Poland Received

19 June 1972

Abstract: The polarization o f protons from the 9 B e ( d , p ) ~ ° B c reaction at f_.~- 12.0 MeV was measured for the g r o u n d state and first excited state transitions. The results obtained are c o m p a r e d w i t h the predictions of DWBA theory. It was found that better fits to the experimental data can be obtained using v o l u m e absorption in the distorting potential o f the deuteron elastic channel. A c o m p a r i s o n o f the present polarization data with the vector analysing p o w e r for the same reaction and the s a m e incident deuteron energy has also been made.

E[

NUCLEAR REACTIONS 9Be(d, p), E ~ 12.0 MeV; measured P(O).

I. Introduction Measurements of the spin polarization of particles emitted in deuteron stripping can provide information concerning the spin dependence of the interactions in the incoming and outgoing reaction channels ~- 3). One can expect that the comparison of the polarization measurements with the vector analysing power VAP data will give additional insight into the reaction mechanism. Due to the technical progress in the production of polarized beams the number of accurate VAP data concerning the (d, p) reaction has increased considerably ¢-8). It was shown that the sign of the VAP is strongly dependent on the j-value of the transferred neutron. The angular dependence of the V'AP is quite well predicted by the DWBA theory with spin-orbit potentials in both the deuteron and proton channels. The number of polarization data is still scarce, and the agreement with DWBA predictions is rather poor. A comparison of the VAP and polarization data taken at the same deuteron energy has been made so far for one reaction only, namely ~2C(d, p)13C [refs. 9. ~6)]. From these experiments the following conclusions can be drawn: (i) In the case of I = 1 stripping the polarization of protons Pp is proportional to VAP (?d). (ii) In the case of 1 = 0 stripping the separate contributions to the polarization 280

9Be(d, p)l°Be PROTON POLARIZATION

281

from the spin-orbit potential in the deuteron and proton channels are of equal magnitude. In the present experiment the polarization of the outgoing protons from the 9Be (d, p) reaction has been measured for the / = 1 transitions to the ground and first excited states in t °Be. The results are compared with the VAP data obtained by Griffith et al. 5) at E d = 12.0 MeV. An extensive comparison of the experimental data with D W B A predictions is also presented. 2. Experimental procedure The deuteron beam of the U-120 cyclotron of the Institute of Nuclear Physics in Cracow has been used to initiate the stripping reaction. Protons from the 9Be(d, p) reaction were focused by the quadrupole lens system into the centre of the scattering chamber of the helium analyser. The polarization of the protons was calculated from the measured left-right asymmetry in elastic scattering from '*He nuclei. Full details of the experimental arrangement have been described previously 9). A natural beryllium target of thickness 9.0 mg/cm 2 was used. The mid-target deuteron energy was 12.0 MeV. The geometrical asymmetry of scattering ,4 o was measured using an ~-particle beam and gold targets in both scattering chambers (without helium in the second one). The weighted mean value of A 0 was (0.60+_ 1.26) o/ /o. The overall energy resolution was 400 keV FWH M. 3, Results A typical spectrum of protons from the 9Be(d, p) reaction after scattering from helium is shown in fig. I. The peaks Po and Pt correspond to the protons from the

9Be (d,p)

Z

too

3

9

|

0

10

f

20

30

~ 50 60 70 CHANNEL NUIVlSER

80

90

,

100

Fig. i. The spectrum of protons emitted at the reaction angle 0 - 30' as detected after scattering from helium.

282

A. B U D Z A N O W S K I e t a l . TAnLE 1 Polarization of protons from the 9Be(d, p)~°Be reaction / ~ 1 g r o u n d state transition 0c.m.

l

polarization

32.6 44.6 55.5 66.2 76.7 87.1 97.2 107.1

-i 0.06.: 0.07 - 0 . 1 9 : 0.12 --0.17--0.11 - 0 . 0 2 { 0.08 0.12 t:0.07 0.15_. 0.09 -0.22 :~zO.I0 --0.107t-0.14

I 3.37 MeV state transition

0,.m.

polarization

34.0 45.2 56.2 67.0 77.6

- 0 . 2 1 .: 0.09 --0.14-'0.19 - 0 . 2 7 =_0.10 --0.20_! 0.21 --0.05 :-0.16

P'/o 50

P) lOBe

9Be(d

In-I

gd st

4O 30 20

,o 0

I

~

I

I

t

I

I

t

I

I

~

t

-10 -20 -30 -40 -50 -60 -70 -80 I

i

10o

l

ZO°

30 o

i

z

40 °

i

50 o

60 °

1°8e"

In-1

t

i

70 o

i

80o

t

90 o

100°

I

i

110o

OCM

120o

P% 40

98e(d,p)

337MeV

st

2(3 0

|

I

J

i

I

=

i

0

I

I

~

0

i

I

I

i

-40 -60 -80 I

20 °

40 °

I

60 °

1

80 °

I

100°

I

120°

Fig. 2. The experimental results f o r the p o l a r i z a t i o n o f protons f r o m the 9Be(d, p)S °Be reaction at E,) -

12.0 MeV: (a) ground state 1 -

I transition; (b) 3.37 MeV excited state / = l transition.

9Be(d, p)'°Be PROTON POLARIZATION

283

l°Be ground state and first excited state at 3.37 MeV respectively. The separation of the background was performed by a least-square programme PEAK 3 written for the ODRA 1003 computer. The polarization in the elastic scattering from helium nuclei and the effective analysing power of the polarimeter (Pite) were calculated in the same way as described previously 9). The values of (PHe) as a function of the incident proton energy covered the range from - 0 . 4 7 to - 0 . 6 5 and from - 0 . 6 3 to - 0 . 7 0 for the proton groups of the ground and first excited states respectively. The sign of the polarization is in accordance with the Basel convention. The experimental results are listed in table 1 and are shown in fig. 2. The quoted errors include: statistical errors, errors arising from the separation of proton groups from the background, the error of the measured value of the geometrical asymmetry Ao and the error of the effective analysing power of the helium analyser which was estimated to be less than 5 ~ .

4. Discussion

In fig. 3 the polarization results obtained in the present investigation are compared to those obtained so far by other authors at various incident deuteron energies I 0 - t 6). The following features can be noticed: (i) The values of the polarization in the broad deuteron energy range 2.5-23 MeV are confined between the limits + 33 ~o for both groups. (ii) Below E = 10 MeV the polarization depends strongly on the energy of the incident deuterons. Above 12 MeV the polarization seems not to vary appreciably with the energy of deuterons; the only exception occurs for the 13.8 MeV data of Pasetschnik et al. ~6). It is interesting to mention that in the 9Be(d, p)t OBe reaction the neutron is captured in the lp~ level whereas in the 12C(d, p)13C reaction it is captured in the lp~ level. The DWBA approximation with pure central distorting potentials predicts for the ratio of the absolute values of the polarization IP~I/IP½1 = ~.. Indeed the comparison of the maximum absolute value of the polarization from the ~2C(d, p) reaction (70 ')o) as obtained by Budzanowski et al. ~) at 12.4 MeV with the present data for OBe(d, p) (33 '~o) leads to the conclusion that this simple prediction of the pure central DWBA theory is valid although the value of the polarization itself is not correctly predicted. The weak energy dependence of the polarization above 12 MeV suggested the use of DWBA theory for the analysis of the experinaental data. The DWBA calculations were carried out using the Colorado programme DWUCK written by Kunz t7). Spin-orbit coupling was included in both the proton and deuteron channels. The optical-model potentials assumed were of the Saxon-Woods type with volume (W) and surface derivative ( W ' ) absorption. The neutron was assumed to be captured in a potential well of the Saxon-Woods form with the spin-orbit potential of the Thomas type. The well-depth parameter was adjusted to give the proper neutron binding energy. The parameters of the optical-model potentials are collected in table 2. The

284

A. B U D Z A N O W S K I e t al.

100j P 9Be (d. p) 1°Be g d st.

1"8011 t

60 i-

IF- &OMe~ \

"

...........

/I/r,~.~

-60 -80 .

-100'

,

213°

100 P%

,

,

40 ° -,-

80J-

.

,

60 °

,

,

80°

,

,

•

,

,

,

,

100°

120°

140°

160° ~:.

,6o0'

,~'

1~o0'

,~'

-,

98e (d. p) 1°8e* 337MeV st

6O

.

-20 -40 I -60 --80

-loo[

' 2~'

'° 40

' ~oo'

8'oo'

Oc."

Fig. 3. The polarization o f protons from the 9Be(d, p ) ' ° B e reaction at different energies: (a) ground state transition; (b) first excited state transition.

"FABLE 2 Vah, es of the parameters used in the D W B A calculations for the 9Be(d,p)~°Be reaction at L"d -~ 12.0 MeV

A B C D E F

Reaction channel

I/R (MeV)

ro (fm)

a (fro)

deuteron deuteron deuteron proton proton proton

118 118 45.62 45 54.42 55.66

0.886 0.869 1.633 1.32 1.17 1.17

0.907 1.01 0.792 0.57 0.75 0.75

W W' (MeV) (MeV) 6.3 6.87 20.76 II 10.2 11.2

r'o (fro)

a' (fro)

I/,.,,. (MeV)

r"o (fro)

a'" (fro)

rc (fm)

1.77 1.68 1.628 1.32 1.32 1.32

0.66 0.879 0.288 0.345 0.65 0.65

5.8 6.0 15.15 5.0 6.2 6.2

ro ro 1.528 ro 1.01 1.01

a a 0.81 a a a

1.3 1.3 1.3 1.3 1.25 1.25

9Be(d ' p)t OBe PROTON POLARIZATION

285

p r o t o n p a r a m e t e r s were taken from the work o f Schiffer ~8) and Greenlees a n d Becchetti ~9). The deuteron o p t i c a l - m o d e l p a r a m e t e r s were taken from Fitz et al. 2o), Schiffer ~a) and Grifl~th et al. 5). It should be mentioned that the p r o t o n and deuteron p a r a m e t e r s o f Schiffer et al. and Fitz et al. were o b t a i n e d f r o m the best fits to the elastic scattering a n g u l a r distributions. The p r o t o n p a r a m e t e r s q u o t e d from Greenlees and Becchetti were o b t a i n e d from the expression given by these a u t h o r s for the P°/. i 80::

9Be(d.p) '°Be g s.

60-

l- 1

}°3/2

40:20 L

c~ o, 3,~

o~---~--~., ~

J

~-

T ~ ' "

....

-60 r-80~ -1001

100

,

,

20° r

_.: ....

~

40*

,

~

~ - - - - T - - ~ - - ' ~ "

~oo' ~ o ° ' --~ . . . . . .

~2oo . . . ~4oo .

~o*L

I

P'Io 80 60

t i t

9Be(d. p) ~°Be* 3.37MeV st I- 1

j-3/2

-i

40 20

o

] cut otf 3~rn

_J

,t

Fig. 4. The DWBA fits to the polarization for the 9Be(d, p)l°Be reaction: (a) ground state transition; (b) first excited state transition. Solid curves are drawn for non-local potentials and finite range; the dashed curves illustrate results for the zero-range local potential with 3 fm cut-off radius. The experimental results are marked by circles and crosses.

average p r o 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 in re('. ~9). The deuteron p a r a m e t e r s given by the B i r m i n g h a m g r o u p s) were o b t a i n e d from the best fit to the elastic scattering cross sections and "gAP data. In the present calculations all possible c o m b i n a t i o n s o f the p r o t o n and deuteron potentials mentioned a b o v e were used. M a r k e d l y better fits

286

A. B U D Z A N O W S K I

et al.

were obtained with the parameters CE (ground state) and CF (first excited state); see table 2. It should be pointed out that the deuteron optical-model potential giving the best fit to our data contains pure volume absorption. This last effect confirms the results o f t h e earlier analyses of Griffith et al. 5) and Haeberli et al. 4). In figs. 4 and 5 the fits for the polarization obtained in the present work and for the differential cross sections taken from Schiffer et al. ~8) are shown. Solid curves represent results of the dcr cl~

do"

g

~-

~ •

oeeo$o

'~

•

•*

° e

o•

%~.

•

ai°*eee°

% .

~'

. ~ %

%% %%

cut ott 3fro

9 B e ( d . p ) ~°Be GROUND STATE

9Be ( d , p )

[ - 1 , j-3/2

i

OcM 0°

' 2 'oo

r

i

40 °

t

0 ° '8' 0 °

1

_1_ °. 100

~

. ° 120

i

i

i

1

. ° . 160. ° 140

f 0°

~°Be'3.37 MeV STATE

I - 1 . j.3C2

1

20 °

,

40 °

J

i

60 °

,

80 °

J

,

100°

,

OCM 1 0o'

' °' I 140

Fig. 5. The D W B A fits to the ditTerentia] cross sections f o r the 9Be(d, p)~°Be reaction: (a) g r o u n d state t r a n s i t i o n ; (b) first excited state transition. Solid curves are d r a w n f o r non-local potentials and finite range; the dashed curves illustrate results f o r the zero-range local potentials w i t h 3 fm

cut-offradius. The points represent experimental results.

calculation in which the non-locality of the distorting and binding potentials and the finite range of the p-n interaction were taken into account. The dashed lines illustrate the results of the zero-range, local-potential-DWBA calculation. It was found that these last calculations gave best fits using the cut-off for the radial integrals at 3 fro. We notice that a fairly good agreement with experiment can be achieved with both local and non-local theories providing that one uses the optical-model potentials obtained from the best fits to the elastic scattering cross sections and polarization. in fig. 6 the polarization results are compared with the existing VAP data for the ground state transition at Ej = 12 MeV taken from Griffith et al. 5). The VAP cal-

o

9Be(d, p ) t ° B e P R O T O N P O L A R I Z A T [ O N

287

cttlated by Griffith et al. 5) is indicated by the dashed line; the solid line represents the polarization calculated in the present work. Except for the one experimental point for the polarization at 32.6 ° the shape of the polarization curve follows that of the VAP although their magnitudes are different. A similar result was found previously ~) for the / = 1 ground state transition in the 1 2 C ( d , p) reaction. P%

'

(tTIl"~(~

,

9Be (d. p ) lOBe Oddst

20

t

:

f" x~.~

//

, I I t-,r__.t

10

--iz[

o

-30

-401 I

I

20 °

,

1

40 °

60 °

I

I

80 °

I

I

100 °

t

I

120 °

Fig. 6, T h e c o m p a r i s o n o f polarization [the circles represent experimental results; the solid line represents the calculated values] with the V A P [the crosses represent experimental data; the dashed curve represents the calculated values ] m a d e at the samc energy Ed = 12.0 MeV for the 9 Be(d, p) 10Be (g.s.) transition. T h e curves were calculated using the s a m e potential taken from ref. s).

It is interesting to mention that the calculated polarization and VAP distributions are different especially at larger angles, in our case the DWBA fits to the polarization are better than the fits to the VAP data although in both cases the same potential parameters were used. This indicates that the polarization and VAP measurements are not equivalent in the sense that the good DWBA fit to one of these quantities does not necessarily mean an equally good fit to the other. It may be due to the omission in the standard DWBA calculation of some factors such as the d-state in the dettteron wave function, tensor potentials in the input channel, etc. The authors are very grateful to Professor K. Grotowski and Professor A. Strzatkowski for discussion and innumerable useful remarks. Special thanks are due to Dr. S. Roman for sending his potential parameters before publication and Dr. J. Nurzyfiski for performing some part of the DWBA calculations. We are also grateful to the cyclotron staff of the Institute of Nuclear Physics for running the machine. References 1) L. J. B. G o l d f a r b a n d R. C. J o h n s t o n , Nucl. Phys. 18 (1960) 353 2) S. A. H jorth, J. X. Saladin and G. R. Satchler, Phys. Rev. 138 (1965) B1425

288 3) 4) 5) 6) 7) 8) 9) 10) ll) 12) 13) 14) 15)

16)

17) 18) 19) 20)

A. BUDZANOWSKI e t al. L. J. B. Goldfarb and R. G. Seyler, Nucl. Phys. 149 (1970) 545 T. J. Yule and W. Haeberli, Nucl. Phys. Al17 (1968) 1 J. A. Griffith, M. Irshad, O. Karban, S. W. Oh and S. Roman, Nucl. Phys. A167 (1971) 87 A. A. Debenham, J. A. Griltith, M. Irshad, O. Karban and S. Roman, Nucl. Phys. A167 (1971) 289 D. C. Kocher and W. Haeberli, Nucl. Phys. A172 (1971) 652 D. C. Kocher, P. J. Bjorkholm and W. Haeberli, Nucl. Phys. A172 (1971) 663 A. Budzanowski, L. Freindl, W. Karcz, B. Lazarska and W. Zipper, Nucl. Phys. A161 0971) 610 L. H. Reber and J. X. Saladin, Phys. Rev. 133 (1964) B1155 R. A. Blue, K. J. Stout and G. Marr, Nucl. Phys. A90 (1967) 601 J. A. Green and H. C. Parkinson, Phys. Rev. 127 (1962) 926 B. Hird, J. A. Cookson and H. S. Bokkari, Proc. Phys. Soc. 72 (1958) 489 R. G. Alias, R. W. Bercaw and F. B. Schull, Phys. Rev. 127 (1962) 1252 M. V. Pasechnik, L. S. Saltykow and D. J. Tambovtsev, 7.urnal Tieor. i Ekspier. Fiziki 43 (1962) 1575; O. F. Nemets, M. V. Pasechnik and N. N. Putcherov, Nucl. Phys. 45 0963) 1 J. S. Vincent and E. T. Boschitz, Proc. Second Symp. on polarization phcnomena ofnucleons, Karlsruhe, 1965 and Basel-Stuttgart, 1966, p. 427; R. Beuertey, R. Chaminade, A. Falcoz, R. Maillard, T. Mikumo, A. Papineau and J. Thirion, J. de Phys. 24 0963) 1038 P. D. Kunz, D W U C K , a distorted-wave Born approximation program, University of Colorado, 1969, unpublished J. P. Schiffer, G. C. Morrison, R. H. Siemsson and B. Zeidman, Phys. Rev. 164 (1967) 1274 F. D. Becchetti and G. W. Greenlees, Phys. Rev. 182 (1969) 1190 W. Fitz, R. Jahr and R. Santo, Nucl. Phys. AI01 (1967) 449