An investigation of the 9Be(3He, p)11B reaction at low energies

I

2.B

I

1 I

Nuclear Physics A91 (1967)97--111; (~) North-Holland Publishiny Co., Amsterdam Not to be reproduced by photoprint or microtilm without written permission from the publisher

AN INVESTIGATION OF THE 9Be(3He, p)llB REACTION AT LOW ENERGIES W. R. C O K E R and M. M. D U N C A N

University of Georqia, Athcns, Georgia t J. L. D U G G A N

Oak Ridge Associated Universities, Oak Ridye, Tennessee t* and P. D. M I L L E R

Oak Ridge National Laboratory, Oak Ridye, Tennessee Received I August 1966 Abstract: Angular distributions and excitation functions have been measured for proton groups

leading to the 4.46, 5.03, 7.30, 7.99, 8.57 and 8.92 McV excited states o f X~Busing 3He particles in the energy range 1-3 MeV. The experimental measurements are analysed in terms o f a twoparticle plane wave stripping formalism and a distorted wave Born approximation (DWBA). Results o f both approaches are consistent with investigations which have been made on this reaction at higher energies. Parities assigned are as follows: 4.46 ( - - ) , 5.03 ( - - ) , 7.30 ( - - ) , 7.99 ( - t ) , 8.57 ( - - ) , 8.92 ( - - ) . Ranges o f angular m o m e n t a include previous assignments. E I

N U C L E A R R E A C T I O N S gBe('~He' p)' E - I - 3 M e V ; measured o'(Ep, 0). 1~B deduccd lcvcls J, :r, L.

I

1. Introduction Since the two-nucleon stripping theory of Newns 1) was published it has become evident that a large group of reactions of the type (3He, p) can be described successfully by such a formulation. The success has been so marked that reactions involving the transfer of two nucleons have become a fruitful approach for nuclear spectroscopists. These reactions are also of interest in the study of reaction mechanisms. The work presented in this paper is part of an attempt to evaluate the applicability of double stripping predictions as a function of bombarding energy. In addition, it was thought worthwhile to investigate the D W B A prcdictions for these angular distributions and hence to determine if distorted wave calculations would give the same general results as the plane wave theory. Agreement of the two approaches would certainly give strength to spin and parity assignments which were made on the basis of these calculations. t Work supported in part by the National Science Foundation. tt Research sponsored by the U.S. Atomic Energy Commission under contract with Union Carbide Corporation and Oak Ridge Associated Universities. 97

98

w.R. COKERet

al.

The 9Be(3He, p)l ~B reaction has been studied by several authors. Angular distributions of proton groups corresponding to the ground state and at least the first two excited states of 11B have been measured at 2.0 MeV (ref. 2)); 1.62, 2.03 and 2.51 MeV (ref. 3)); at 4.5 MeV (ref. 4)) and 6.05 MeV (ref. 5)). Angular distributions of proton groups corresponding to the ground state and the first nine excited states of I~B have been measured 6,7) at 5.7, 8.82 and 10.23 MeV. Excitation functions for the ground state and first excited state proton groups have been measured 4) at six 1.25

............ "

~ _ ~

/o 1.oo

-/

2 0.75 . . . . . . . . . . . . . .

. , ~ ~

Y

-<.

~b 0.50

0.25

..........

.

o

1.0

.

.

.

............

- - P3

-------I-

.

1.2

1.4 t.6 ENERGY (MeV)

18

2.0

Fig. 1. Excitation curves at 90° for protons from the ~Be(3He,p)~B reaction to states in HB lying between 5.03 and 8.92 MeV in excitation. angles for bombarding energies from 1.8 to 5.0 MeV. Also at 10 ° and 90 ° excitation functions have been measured 6, 7) in the energy range 5.7-10.2 MeV for the ground state and the first nine excited state proton groups from ~~B. The most complete investigation of this reaction has been carried out by Hinds and Middleton 6, 7). The majority of the angular distributions measured by Hinds and Middleton exhibit strong forward maxima and seem consistent with a predominantly direct reaction mechanism. For the most part, the shapes of the distributions were energy independent

9Be(aHI,,

p)llB

99

REACTION

except for the systematic tendency for the forward maxima to move toward smaller angles. The excitation functions measured by these workers were smooth with no pronounced structure, consistent with measurements at lower bombarding energies 2,4). The angular distributions of the proton groups from the ground state and first few excited states at these lower energies were more complex in nature and certainly energy dependent. In view of these results it was decided to obtain angular distributions for the proton groups corresponding to the higher excited states of 11B for bombarding energies from 1 to 3 MeV in order to ascertain if these groups had distributions of a complexity consistent with that reported for the lower states in this energy range. Q100

. , i i 9Be (3He' '02) ItB AT E3H e = i MeV'

I {

~

THEORETICAL CURVE I J n ( k r o)

o 0,5

o o~o ....

t_-~ ..'~,~.. . . . . . . . .

12 ÷ 4 . t 2

0 0z5 !

,.__1_!. }1}\~

i

j ~

{

:

.~{_~_L ....

o ,5

~o5o

L

!

[

:

~

i

:-- l

- ....

?

I [

i .....

t.5 IVev :

~

i .........

.

.

; ........ i

, F ' - -

i

i

:

" , ~ ~

t.00

o.25 .......................

I

:

•

:

,, •

L__.

i

0.75

0.50 [ I

• :

i :

j

' I

o. ~50 - 2~- ~ b - ~ o - ~ 6 ~ o o

eb~-ZO % 0 ~8o

8C. ~ (deg)

Fig. 2. Angular distributions of protons from the reaction 9Be(3He,p,)'B* leaving "B in its 4.46 MeV, second excited state. 2. Experimental procedure The l, 1.5 and 2 MeV measurements were made with the 2 MeV Van de Graaff at the University of Georgia, and the 3 MeV measurements with the 5.5 MeV machine at O R N L . Solid state detectors were used to measure the charged particle spectra for all of the data. For each data point two charged-particle spectra were taken. One detector was rotated to measure the angular distributions, while the other detector was a fixed monitor. The monitor spectra were used to analyse the general condition of the 9Be target through the series of runs. With the monitor spectra, 9Be evapora-

100

w . R . COKER et al.

tion and t2C buildup on the target could be determined. As a further monitor, proton groups from the 12C(3He, p)t4N reaction were periodically analysed from the carbon backing of the 9Be targets. The angular distributions for these groups were in good agreement with the work of Johnston et al. 8) for this reaction. For each system charge-sensitive preamplifiers, main amplifiers and biased post 9Be(3He'P3)llB

ATE3He=IMeV

THEORETICAL. CuRvE [Jo(kro)l IJz (*fo)l 2 , "o = 7"/,. o,oo

..........

I

•

j

o.oso

w ....

' .

/

,

o.o25

t

.

r

.

"

.

.

.

.

.

100

• :

'

I (

•

..............

.

~_.,{

i--,~' .....

tt ~

~

I x,-I ......

--~

F--"~--

t i

............ .

0.75

.~=-

"~ o.so

•

o 2.5, •

~

--i

i

I

i

-

~

....

i

. ~

!J ~

:

!

!

F':v"~ . ......... \,

-4, /

~_

....

!

i ~. ,

.

~.

.

3 MeV

~; ~.51,l....

.

-': 1.0 .

.

.

.

II

.

c.5 i .

,

.

.

.

.

.

.

'

.

.

I

I O

.

2o~

0.50

0

.

,--~-

. . . . . . . . . . ................

.

.

~ , .... r...........

2 MeV

0.25

i '

............

,oor-,

o.75

i i i

i

-

oi

I

~

/

< ~

! I 5MeV

(

.

:

.....

.

'

z +13.*

L 20

40

60

80

.. 100

8C.V. ( d e g )

~20

140

160 ~ 0

O

_. 0

20

40

60

80

'00

t20

140

I~3

'8. L~

6Cte (deg)

Fig. 3. Angular distributions of protons from the reaction aBe(aHe, p3)HB * leaving HB in its 5.03 MeV, third excited state.

amplifiers were used. The outputs of the postamplifiers were analysed in spectra with at least 400 channels. This channel capacity was necessary in order that the many groups present could be observed with sufficient system resolution. Silicon surface barrier detectors with resolution capabilities of 30 keV were used. The elastically

tBe(aHe, p ) l l f l

REACTION

|0|

scattered 3He particles were stopped by placing appropriate Ni foils over the detectors. These foils plus target thickness and other sources of energy spread gave overall system resolutions of between 45 and 60 keV. The aBe targets were prepared by the Isotopes Division of ORNL. 9Be metal of thickness about 20/~g/cm 2 was evaporated on 15 F g / cm 2 12C foils. I i gBe ( } H e , p 6 ) l ~ B

ATE3H = 1 MeV

[

THEO~ETIC/kL CURVE I d ~ ( k f o ) i z +3.1 ">

o. oo

i'' .... '

, .........

; {-r~

i!

"

~{!{,

,'

-

-

.....

!

;

~

i

{

,

i

i

t

i

!

2.oo

•I

,.75

i

"

{

i 1.5MeV

-; I...... J~

........

i

o.o~'5,~---~

I

~;-~~

t"

........ ;

•

1.5o

. . . . . . . . . . . . . . . .

/ ....

0.025 •"~

t'.

o,

I

"

"~

,

•

l

l

"

J '

:

i '

i i ._

~-~-%,

,oo ~

....

:

o

0.25

:,

,.~o --.;'~ -~

~

'

/ o .....

I i

2 Mev

.: .... :

./,

~ ..... ~*~_~J

60

80

1

, J

• '!

~ i

" 3MeV •

.:~..(.~{{{: ......

~,.o

~_!

~- ,,~--

__~_i .... :.

J . . . . . . .

20 .40

t

.... ,.5 ............. -1-

.

0

~

-! ..... :

'

-

0.75. 0.50

.....

,

~oo 1'

~

100 120 140 160 180

O

11

20

40

60

80

, .....

. . . . . . .

tOO 120 140 160 i S 0

OC.M.(~eg)

8C.~.(deg)

Fig. 4. Angular distributions of protons From the reaction 9Be(3He,p~)HB* leaving HB in its "/.30 MeV, sixth excited state.

3. Results Fig. 1 shows the excitation functions for six groups of protons for this reaction. It can be seen that the yield rises rapidly and smoothly in the energy interval from

102

w.R. qOKER et

al.

1 to 2 MeV. The average increase in cross section between 1 and 2 MeV at a lab angle of 90 ° is 0.7 mb/sr. In general the cross sections seem to level off between 2 and 4.5 MeV and then decrease by the order of 50 % between 4.5 and 5.7 MeV (ref. ,.6)). From 5.7 to 10.2 MeV the cross sections drop 7) by about another 50%. None of the groups studied show any resonance structure in the energy range from 1 to 10 MeV. -

-

~25

I

I

TqEORE TICAL CURVE IJ,(*,o)i 2+ 3.76 :

!

Iv3 k,-o)i 2, to: 7

,

o

'

5f~

. . . . . . . . . . . . . . .

'

,oo

0.040

}

i

i

I

,

"

i-i--

i

[

i

, 0.50

0.030

---

"-

"~

:

-

I

o.olo

I

i

"

o [

t.oo

050 ,' i

02%-

/

I

....... 2 MeV

. . . . . i. . . . . . . . . . . . . . . . . . .

2o 4o 6 o - 8 o

[--T: {

0

20

40

60

80 t 0 0 t 2 0 8C.M(deg )

t40

~60 t80

!1

~&~ ~2o ~4o ,60 ,3c

ec M (deg}

Fig. 5. Angular distributions of protons from the reaction °Be(3He, pT)nB * leaving nB in its 7.99 McV, seventh excited state.

Figs. 2-7 show measured angular distributions of P2, P3, P6, PT, Ps and P9 at l, 1.5, 2 and 3 MeV. The fourth and fifth excited state proton groups were not resolved from one another and hence are not shown. It should be noted that the scale for the 3 MeV data is relative. However, as has been mentioned above, the absolute values at 3 MeV should be within 50 % of the corresponding values at 2 MeV. The second excited state angular distribution is not shown at 3 MeV since some of the protons

°Be(aHe, p)nB REACTION

103

were energetic enough to penetrate completely through the depletion region of the detector before being stopped. However, the angular distribution shown in fig. 2 at 2 MeV does not differ appreciably from that found by Wolicki et aL 4) at an incident energy of 4.5 MeV. The seventh excited state proton group is not shown at 3 MeV since it was obscured by contaminant groups over a large fraction of its angular range. The plane wave attempts at fitting the data are shown also in figs. 2-7. Figs. 8-13 show some of the angular distributions on a semi-log plot with the appropriate DWBA and plane wave fits. Where two L-values were used for the DWBA analysis, these are shown individually and their sum is also given with the indicated 0.t00

. . . . . . . . . . . ( I

'e, .o8 ]

B AT E3H e =

.~ THEORETICAL

CURVE

1.75 -: 1.50r

]Jo(kro)12*3.5

i ..................... . i ;---i" ~ ...............

~0.75

0.050 -

i

- .......

:

.~ ~-~

........

;

o

. ...........

~"~ .... i

. . . . . . .

I :

!~

,5

\ ,.o

.

....... ! , ! -: . _ ~ , ~ , ~ _

~

[

I

!

0

20

40

/ 60

80

100 120 140 160 180

j ~

6. A n g u l a r

distributions

of

60

I i

,

....

~

i

i '

40

,

,~.~ ,

i 0

- T--

i i,

....... '

o

"

;-!

8C. M (deg) Fig.

~

i

:'

1.0 "6

'.

-

i ~ 0.25

~v o o 2 5 L

t . 5 Mev i ~ "

80

I

......

I00 120 140

160 180

eC.M (decj)

protons

from

the

reaction

9Be(SHe,

pg)*lB

* leaving

HB

in

its 8.57

MeV, eighth excited state.

mixing. A discussion of the DWBA and the plane wave calculations will be given in the next section. 4. Calculations

The plane wave calculations were made by using the two particle stripping formalism of Newns *). The differential cross section in this formulation is given by da dO

- ~.4Ll.~(Kro)l 2, L

(1)

log

W . R . COKER et al.

where (2)

K = IK3-(Mi/Mf)Kel,

and ro is the stripping radius. The A z are constants which can be determined by fitting the theoretical expression to the experimental points. They are similar to the capture o.~25

[

2.50

I

9Be (3He,P9) nB ATE3~e=' MeV T~HEORETIC&LCURVE jo(A'ro}',2, to= 6fm

0.1C0

~"

,+ .

. . . . .; . . . . . . . . . . . . . . . . .

.... ~ ' - - -

"

.

.

0.075.......

.

.

.........

.

.

.

.

1.75

.

•

......

.

2.00

+i+iill

0.050

0.025

1.5 MeV 2.25 .

i+++

o

~

1.25

"~

t.00

..

0.75 0.50

"", ~ ; . . . . . . . .

tx'-, . , ~ . ,:

-

....... "

~

o__ 2.25

i

.

.

.

.

.!

""

0.25

o .

.

.

.

.

.

.

.

.

. . . . .

t.75

..............

............ ._~

2.o

L .......................

5MeV

. .

.

.

.

.

. "~--"

!+

----~-. . . . 1

, 0.75

i

o.5o

'-

~-

..................

~,{',"~~

.....

• .t\

0

. 0

\

.

20

.

"

+++'-. 40

_I . . . . . . .

I.C

\

. (50

~ •

80

....... ,, '.SO

:20

140

160

=. i.

1 .

.

.

.

. . . ... . . . ..

" ..................

!

.

,= ~

~. . . ... . . . -~. +-

,

', I

.*- . . . . . . .

++

,

180

0.5

.... . . . . ~+

.........

aC.M.(deg)

,

~

i OL ............. 0 20 40

....

I

o

. . . . . . . . . . . .

1.00

i

,

L ....

...........................

1.25

I

.

2MeV 2.00

"

60

80

'~ j '~ + .....

100

120

140

160

180

(~C.p,q. [ de g)

Fig. 7. Angular distributions of protons from the reaction 'Be('~He, pg)nB * leaving nB in its 8.92 MeV, ninth excited state.

probability which occurs in ordinary deuteron stripping, i.e., the probability of finding the captured particle in its captured state at the nuclear surface. The plane wave calculations which were made all involve stripping radii between 5 and 7.5 fm. These

,oo ~_.._ =

'

~

9Be: (3.e.p2) "B AT ~.=,.~Mev PLA,E WAVE

~ ~ "~

l~

2

5 ~ - ~

I ~----

2

....

. . . . . . .

1 ]-

IJo~*~o)l + 4.,2 I-'~ I*~o) I , ~o = s.o~m _

•..... b

ll

5

"

10-2 0

30

60

90

120

150

180

8C.M. ( d e g ) Fig.

8.

A n g u l a r distribution o f p r o t o n s for the 4.46 MeV state in riB, s h o w i n g the c o m p a r i s o n o f plane wave a n d D W B A fits to the data. 2~<10o

9Be(3He, p s ) t t B IAT E3He = :3 MeV ___ :

to 0

_.~,,(.~._~..~.~r

1 V

->

. . . .

b

I \

"~

/ 10 -- t

~

I

/

\

~

"~

t

mI

k ' <

!

~

I

I !,

. . . .

'

- .I

- ~-

!

\

:

II ~

\/!

X'=

i

: :

"PLANE

(2

=

,4"- . . . .

' 30

I II [

//..7 :

0

2)×32

WAVE

I

10-2

....

"

~

[

l]

60

90

- -

I

D.W.B.A..~=0

!

t

t20

t50

t80

eC M (deg) Fig. 9. A n g u l a r distribution o f p r o t o n s for the 5.03 MeV state in riB, s h o w i n g t h e c o m p a r i s o n o f plane wave a n d D W B A fits to the data.

106

w . R . COKER et al. q i t "

_

_

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

___+_ .

.

_ _ - " 9Be (3He..06) "IB

.

.

t

.

.

•

.

.

.

.

.

.

.

.

.

.

.

"

~.T E3H e = 3 . 0 MeV -. .- . . . . . . . . .

!

1

2-'

" - '7-;'~"~'= " ~ i - ' - ~ - - = ! ' ' 1

lo ° i ~

:[,

Pc/

t r / 5

t

i

. ", - ' ~ - - --":"---. : . / . _.._'X~__ ~_

"

;.......

~
"~

- ........

1

D.W.B.A.. SUM \

t

"~.

.

~ -- ....... :

..... _~..~-~-

L=t

-

PLANE - 7 ~ : \ " . . . . . . WAVE . . . . " % - - ~ X : ,~. , . - ; _ _ . "~..~

-D.w.B.~. (L= 3;× 3. 8

.

:_

t

Ii 10-~ . _ _ 0

30

60

90

120

~50

180

8C.M.(de9)

Fig. 10. Angular distribution of protons for the 7.30 MeV state in 11B, showing the comparison of plane wave and DWBA fits to the data. tO o -

........

-

t- .

-

t

• :~K-;/~

,/ //i / , .. . . . . . t ---;

,

_ .f.

_r_~

0

4"

.

.

.

.

=...

.

.

D.W.S.A.

r

. . . . . .

I i

AT EmN e = 1,5 MeV . . . . . . .

,

l

: ~

,o

I

.....

q

S U M s _

.

as:

.......

.....

I....... .,z__ ~ ...... ' "/ . . . . . . . .

.../--A~ _ : ~

~

i WAVE

3

=

,

..... -

D.W.B.A ..... (L=l)x7.5 ........

-

L

~

_

i",.x

i .

"'PLANE

I0-2

---

i

9 B e (3He, p 7 ) ttb

....

....

-"1- . . . . . . .

:, I

I

i

i 50

i 60

90

120

150

180

8C,M.(deg )

Fig. 11. Angular distribution of protons for the 7.99 MeV state in ~IB, showing the comparison o f plane wave and D W B A fits to the data.

9Be(SHe,p)lIB REACTION

107

values are similar to the radii used at higher bombarding energies for this reaction 6.7). "lhc angular momenta L, dctcrmincd from the analysis of thcse data, agree in all cases with those dctermincd at the higher bombarding energies. The D W B A calculations were madc with the distorted wavc codc JULIE 2 i). The optical-model parameters for thc 3He channel wcrc taken from the elastic scattering calculations of Hodgson 9) for the reaction 12C(3He, 3Hc)12C at an incidcnt energy of 5.5 MeV. In this calculation Hodgson attemptcd to fit the cxperimcntal data of t0 t -

.: -

5

.

.

.

.

i 9Be

.

.

.

.

(3He, .

.

.

.

p8 ~ttB .

.

.

AT

.

.

_.

: 3 MeV

;3"e . .

.

--

.

.

] . . . . . . . . .

t

t

-i

. . . . . . . . . .

2

1

-

.

.~IIItO0

-=~"J~

--

• -

[-

PLANE

. . . .

-.:

._-~'N,-_Z_..:-.

--

.....

WAVE

!-\/:

-.

-- :

--i

. . . . . . . . . . . . . . .

.....

....

---~

X

~,_--__/0.W.B.A.

:

..._

]

'~',~..~Z~"*,,...... ~ - ~ ,: _ .-,,,,_

v

~

...... /

......

-! e

~

.... ,/

"

"

-

. . . . . . .

.,o-,

:..-4:

......... _.LY;-!

.... ......

,0.2

I

: 0

30

60

,

/i 90

|20

t50

180

8C.M. (deg)

Fig. 12. Angular distribution of protons for the 8.57 MeV state in 1~B, showing the comparison of plane wave and DWBA fits to the data. P a r r y et al. 12) with a c o n v e n t i o n a l optical potential using a W o o d s - S a x o n form factor. A systematic search was p e r f o r m e d to find the best fit optical m o d e l p a r a meters. H o d g s o n ' s p a r a m e t e r s were as follows: - U = 83 MeV, - W = 56 MeV, ro = 1.6 fm, and a = 0.7 fm. These p a r a m e t e r s with re = 1.6 fm were used for all o f the present calculations in the 3He channel, while three different sets were tried for the exit channel. The first set o f p r o t o n p a r a m e t e r s a t t e m p t e d were t a k e n from a 9Be(p, p)gBe fit by Blieden et al. to) at an incident p r o t o n energy o f 6 MeV. F o r

108

w.R.

COKER et al.

this fit the optical model parameters were - V = 53.3 MeV, - W = 20.54 MeV, r o = 1.96 fm and a = 0.48 fm. In addition to these parameters r c was chosen to be 1.6 fin (ref. 13)). Later it was decided to fit the experimental measurements of Kokame et al. 11) for the liB(p, p)~lB reaction at an incident proton energy of 7.36 MeV. It was felt that such a fit might give a better set of optical-model parameters for the exit channel. A search program was used to find the least squares set of parameters for the data. Fig. 14 shows the results with the initial parameter set and with the final set. The initial set of parameters shown in fig. 14 were those of Blieden et al. ~o) modified according to the experience of Bassel and Drisko at ORNL. 2 ×100

9Be(3He, p 9 ) I I B

AT L-3He = ! 5 MeV

t0 o ~ - "-.o'~

I

:

-.[- ~ .

........ ~ ' " \ ...........

/

[

t

! -

-

~---- PLANE WAVE ,~= o

\ ~

~

/ 10_ t

v

.....

~

-

:

.........

It [~

:

..........

\~ ~ It T~-i-'~ .......

i

.......... !.........

-'-~--

~/~ /

"~-~,-/

' ...............

I -t i /

. . . .

,~'~,

. . . . . . . . . . _ _ _ . _ : .............

a

" ~--_~

: ........... i - - : - : i

x',<-

~

/ "C

! .7_-.Y_ !

~.

.......

;

.__

I t ......... /

/ [ i' . . -r--[LT£~ "--g.w-B-A-.-- ............

........ i!

...........

[ ......

i--'.:o ,.:.:.-.~<-

. . . . . . . . . . . . . .

\ ; /

'.

\1:-

- _ _

.

I

..........

t0-2 0

30

60

90 8CM (deg)

420

t50

180

Fig. 13. A n g u l a r distribution o f p r o t o n s for the 8.92 MeV state in riB, s h o w i n g the c o m p a r i s o n o f plane wavc a n d D W B A fits to the data.

DWBA calculations were made for all proton groups using thc final sct of optical parameters. Also, some calculations were made with the initial set to ascertain the sensitivity of the calculation to a change in paramcters. The result, as expected, was that both sets gave approximately the same prediction. To show this, fig. 12 is included with the DWBA results calculated using Blieden's parameters. All other DWBA results shown use the final set of parameters. The similarity of the predictions of the two sets of parameters secms reasonable sincc both sets give a good description of the elastic scattering for the ~lB(p, p)l ~B reaction.

IIBeiaHc, p)UB REACTION

109

5. Conclusion The spin and parity assignments which result from the DWBA and plane wave calculations in this paper will be discussed in the following paragraphs. The 4.46 MeV level in 1, B has been assigned 14) a spin of { - . The angular distributions for protons from this state are shown in figs. 2 and 8, and the theoretical plane

~

- ± ..... "

THEORY

0

~__ •

!. . . . . . . . .

_'-7

EXPERIMENT:

. . . . . . . . . . . . . ............

Q__oo.o. o .

o Oee 0

_ ......

O~l~O • e _ e _ ! °.

• •

FIT

1 S_T

00

• .

.

.

.

.

.

.

V

0

55.0

..

ro

,

o

1.25

•

rc

1.25

-o . . . . . . .

a

0.65

o'

0.60

125 . O. 0. 9 .9 .Q Q. U. I . . . 0. . . . . . . o

z

0 •

~oo

0

"

~

14//

"

"

20.0,

0

(-)iLJJ

......

O

0

t

O3

03 03

~

O

O

rr

FINAL

:.-~ .

.

.

.

.

;~

V .......

-

0

• o@

000 ooo 0

ee

O_

i o ° ° 0° °0,

O

o

~0

"

O

66.2

"o

1.25

rc

1.25

o

0.408

r"

0.437

0 ~

000

w

oe

FiT

/

0.644 37.40

0

30

60

90

120

150

180

8C.~ ' (deg)

Fig. 14. T h c *~B(p, p)*'B angular distribution at Ep = 7.36 MeV. The data are from ref. 11). The upper theoretical curve results from using the optical model parameters similar to those o f ref. ~"). The lower theoretical curve results from a least-squares D W B A fit.

wave mixture of L = 0,2 gives a negative parity assignment and a range of angular momentum which encompasses -~. The angular distributions of protons from the 5.03 MeV levcl of I~B are shown in figs. 3 and 9. The analysis of this state (L = 0,2) gives a negative parity and angular momentum range which includes the J~ values previously assigned to this state ( } - , i}-).

1 10

w . R . COKER et al.

In the past the J~ values for the levels in 11.B at 7.30 and 7.99 MeV have been in a state of confusion. Earlier predictions based on the l°B(d, p)t ~B reaction for these states at an incident deuteron energy of 800 keV by Sjogren 1.s) assigned a negative parity to these states. Also Bilaniuk et al. 16) studied this same reaction at an incident energy of 7.78 MeV and stated that a plane wave fit for the 7.99 MeV level could not be made. Later this reaction was studied at E d = 10.1 MeV by Hinds and Middleton 17), and a tentative assignment of negative parity was made for the 7.30 MeV level. An analysis of the 7.99 MeV state was not attempted by these workers, since it did not show an apparent stripping distribution. The (3He, p) reactions leading to these states have been studied at 5.7 and 10.2 MeV by Hinds and Middleton 6,7). At a 3He energy of 5.7 MeV the double-stripping analysis gave positive parities for the two states. However, at an incident energy of 10.2 MeV the authors indicate that these states do not exhibit good stripping distributions. Ferguson et al. 1.8) from a study of branching ratios, assign a negative parity to the 7.30 MeV level. Recently Olness et al. 1.9) have published a comprehensive study of the ~,transitions in l i B and conclude that the 7.30 MeV level is 3 + or I ÷ and the 7.99 MeV state is 3 +. The measurements presented in this paper indicate, on the basis of both plane wave and DWBA treatments, (figs. 4, 5, 10 and l 1), that the two levels have positive parity and possible angular momenta in agreement with Olness et al. and the 5.7 MeV data of Hinds and Middleton. It should be noted that, although the plane wave calculations do not give striking agreement with the experimental data, the general features are described by the calculations. A problem similar to that for the 7.30 and 7.99 MeV states exists for the 8.57 MeV level. The 1.°B(d, p)1.1.B measurements 1.6,1.7) indicate an L = 2 transfer. This would give even parity to this state since the ground state parity of I°B is even. On the other hand the 9Be(3He, p)1.1.B data of Hinds and Middleton 6,7) at 5.7 and 10.2 MeV is described with an L = 0 transfer and thus a negative parity for the level. This is in agreement with the assignment J~ = { - which has been given by Olness et al. 1.9). The measurements presented here (figs. 6 and 12) also confirm a negative parity for this state. All assignments of the parity of the 8.92 MeV state in 11B agree that the parity is negative except for a single 1.°B(d, p)l i B measurement 16). 1he shape of the angular distributions measured by these workers at Ed = 7.78 MeV differ qualitatively from the (d, p) measurements at 3.5 MeV (ref. 20)) and 10.1 MeV (ref. 1.7)) for this level. A plane wave analysis at 10.1 MeV and a DWBA analysis at 3.5 MeV give L = 1 and thus predict a negative parity in agreement both with the 9Be(3He, p)l 1B data 6. ~) at 5.7 and 10,2 MeV and with the analysis of Olness et al. 19). The results presented here (figs. 7 and 13) for both plane wave and DWBA show an L = 0 transfer of angular momentum and hence agree with the negative parity assignment of the state. The authors would like to thank Dr. R. M. Drisko and Dr. R. H. Bassel for the elastic scattering fit with their search program, and also the assistance with the

0Be(3He, p)lIB REACTION

DWBA

calculations through

use o f t h e i r p r o g r a m

II1

JULIE.

A l s o w e w o u l d like t o

thank The Institute for Chemical Research, Kyoto University, Japan, for allowing us t o use t h e i r b o r o n e l a s t i c s c a t t e r i n g d a t a in o u r o p t i c a l = m o d e l s e a r c h . T w o o f t h e authors (M.M.D.

and W.R.C.) wish to acknowledge financial assistance which was

given under the ORAUS-contract

travel program.

References

1) 2) 3) 4) 5) 6) 7) 8) 9) I0)

I1) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21)

H. C. Newns, Proc. Phys. Soc. A76 (1960) 489 H. D. Holmgren, M. L. Bullock and W. E. Kunz, Phys. Rev. 104 (1956) 1446 E. Almqvist et al., Bull. Am. Phys. Soc. 1 (1956) 195 E. A. Wolicki, H. D. Holmgren, R. L. Johnston and E. G. Illsley, Phys. Rev. 116 (1959) 1585 D. R. Sweetman, Bull. Am. Phys. Soc. 3 (1958) 186 S. Hinds and R. Middleton, Proc. Phys. Soc. A74 (1959) 196 S. Hinds and R. Middleton, Proc. Phys. Soc. A75 (1960) 754 R. L. Johnston H. D. Holmgren, E. A. Wolicki and E. G. Illsley, Phys. Rev. 109 (1959) 884 P. E. Hodgson, Proc. Phys. Soc. 77 (1961) 997 M. R. Blieden and G. R. Temmer, Proc. Conf. on direct interactions and nuclear reaction mechanisms, 1962, ed. by E. Clementel and C. Villi (Gordon and Breach, New York, 1962) p. 155 J. Kokame and K. Fukunaga, Bull. Inst. for Chem Research, Kyoto University, (1965) G. Parry, H. D. Scott and S. Swierszczewski, Proc. Phys. Soc. 77 (1961) 230 R. H. Bassel and R. M. Drisko, private communication F. Ajzenberg-Selove and T. Lauritsen, Nuclear Physics 11 (1959) I B. Sjogren, Ark. Fys. 12 (1957) 537 O. M. Bilaniuk and J. C. Hensel, Phys. Rev. 120 (1960) 211 S. Hinds and R. Middleton, Nuclear Physics 38 (1962) 114 A. J. Ferguson et aL, Phys. Rev. Lett. 1 (1958) 414 J. W. Olness, E. K. Warburton, D. E. Alburger and J. A. Becker, Phys. Rev. 139 (1965) B512 D. J. Pullen and S. B. Whitehead, Proc. Int. Conf. on nuclear structure, 1960, ed. by D. A. Bromley and E. W. Vogt (University of Toronto Press, Toronto, 1960) p. 40 R. M. Drisko, R. H. Bassel and G. R. Satchler, O R N L Report 3240