Investigation of the quadrupole deformation of 11B by means of 30 Mev polarized proton inelastic scattering

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Investigation of the quadrupole deformation of 11B by

means of 30 Mev polarized proton inelastic scattering

Dinh-Lien Pham

To cite this version:

L-67

INVESTIGATION OF

THE

_QUADRUPOLE

DEFORMATION

OF

11B

BY

MEANS OF

30

MeV

POLARIZED PROTON

INELASTIC SCATTERING

DINH-LIEN PHAM

Institut des Sciences

Nucléaires,

BP

_257,

38044 Grenoble

_Cedex,

France

(Re~u

le

_{6 fevrier}

_1976,

_accepte

le

_{16 fevrier}

₁₉₇₆₎

Résumé. 2014 Les sections efficaces et

pouvoirs d’analyse de la diffusion _inélastique

_11B(p,

_p’) à

Ep

= 30,3 MeV _ont été

analysés

dans le formalisme des

équations

couplées.

Ces calculs _suggèrent la valeur _positive de la déformation _{quadrupolaire 03B22} du 11B _(prolate) et donnent le résultat suivant

03B22 = ₊ 0,52.

Abstract. 2014 The cross-sections and _{resolving powers of the}

_11B(p,

_p’) inelastic _scattering at

Ep

= 30.3 MeV _are

_analyzed

in the

_{coupled-channels}

_{formalism. These calculations suggest a} posi-tive value for the

_quadrupole

deformation

_03B22

of 11B

_(prolate)

and

_give

the result

_03B22

= ₊ 0.52.

LE JOURNAL DE _PHYSIQUE - LETTRES Classification Physics Abstracts 4.370 TOME _37, AVRIL _1976,

In the

_{understanding}

of

_lp

shell

nuclei,

the

investi-gation

of their deformation

_plays

an

_important

role.

For

the 11B

_nucleus,

Hartree-Fock calculations

_[1]

do not

_give

a

_prolate

lower minimum

_compatible

with the

_positive

electric

_quadrupole

moment obtained from

_experiments.

For this nucleus a

_{strong-coupling}

rotational model

_[2]

has

_given

a better result

_although

a

quantitative disagreement

with the

experimen-tally

determined electric

_quadrupole

moment still remains

_[3].

The above

_{discrepancies}

have

_suggested

that we need much more

_{investigations}

about the

_quadruple

deformation of

the 11B

nucleus

_by

means of inelastic

scattering.

In

_particular

a recent

_{investigation}

of the

quadrupole

deformation of

11B

_by

inelastic helion

(3He)

scattering

at

_E3He

= 74 MeV

[4]

has

shown,

with

_{analysis using}

the

_{coupled-channels}

_{(CC) method,}

the

_possible

existence of

_{oblate-prolate}

effects

of 11 B

in this reaction. It would therefore _{appear necessary}

to determine the

_quadrupole

deformation of

11B

by

means of

_polarized

_proton

inelastic

scattering.

In view of the determination of the

sign

and the value for the

_{quadrupole deformation ~i2}

of 11B,

we have

_analyzed,

in the

_{coupled-channels (CC)}

forma-lism with the rotational model

_using

the code ECIS 75

[5],

the

_experimental

data for the cross-sections and

resolving

powers in the

11B(p,

p)

and

11B(p,

p’)

scattering

to the lower two members of the K1t =

~-band

_{of 11B,}

i.e. the

_{1 -}

_ground

state and

_the

second-excited state

_(Ex

= 4.46

MeV)

_at

Ep

= 30.3 MeV

[6].

The

_optical

_parameters used as initial values for the

optical

model search

_procedure

were taken from the

analysis performed by

Karban et al.

_[6]

and are listed

in table I. In the CC

_formalism,

the nuclear radius

is defined

_by

where the

_#’s

are the deformation _parameters deter-mined

_by

the

_experiment,

the Y’s are

_spherical

har-monics

_{and Ri corresponds}

to the various

_optical

potential

radii. The interaction

_potential

arises from the deformation of the Coulomb

_potential,

the

complex

central

_potential

and the

_{spin-orbit potential.}

The deformed

_{spin-orbit potential}

was of the full Thomas form

_[7].

In the CC

_{calculations,}

the states ,

explicitly coupled

are the lower two members of a

TABLE I

Optical model parameters

used in the

_{analysis of}

_{the 11B(p, p)1’B}

_scattering

L-68 JOURNAL DE PHYSIQUE - LETTRES

K

_{= ~-}

rotational band in

"B.

The results are

presented

in

_figure

1 and the

_{corresponding}

para-meters listed in table II.

The two values

_P2

= ₊ 0.43 and

P2

= - 0.50

obtained from reference

_[4]

_{by analyzing only}

the cross-sections of the

_"B(3He,

_3He’)

inelastic

scat-tering

at

_E3He

= 74 MeV with the CC method

give

equally

low X2

values. But it should be mentioned

[4]

that

_P2

= + 0.43 _agrees

_quite

well with the

experi-mental value of + 0.0372 b

_[3]

for the electric

qua-drupole

moment. The results we have obtained

_by

analyzing simultaneously

the cross-sections and

resolv-ing

powers of the

"B(p,

p’)

inelastic

scattering

at

Ep

= 30.3 MeV

using

the CC calculations

suggest

also a

positive

value for the

quadrupole

deformation

~32

of 11B

_(prolate)

and

_give

the

_{result ~2}

= + 0.52.

We are

_grateful

to Dr. R. de Swiniarski for valuable discussions and his interest in this work.

v·~~r

FIG. 1. -

Experimental results of the

_11B(p,

_{p’) 11 B* scattering}

compared to the results of the _{coupled-channels} calculations

cor-responding to the two _parameter sets of table II.

TABLE II

Coupled-channel

parameters used in the

_{analysis of}

_{the 1 iB(p,}

_{p’) 11}

B * _inelastic

scattering

References

[1] RIPKA, G., Advances in Nuclear Physics, vol. 1, ed. M. Baranger

and E. _{Vogt (Plenum Press,} New _{York), 1968,} p. 183.

[2] EL-BATANONI, F. and KRESNIN, A. A., Nucl. Phys. 89 (1966)

577.

[3] STOVALL, T., GOLDEMBERG, J. and ISABELLE, D. B., Nucl. Phys.

86 (1966) 225.

[4] ASPELUND, O., INGHAM, D., DJALOEIS, A., KELLETER, H. and

MAYER-BÖRICKE, C., Nucl. Phys. A 231 ₍₁₉₇₄₎ 115.

[5] RAYNAL, J., ECIS 75, Saclay, France, unpublished.

[6] KARBAN, O., LowE, J., GREAVES, P. D. and HNIZDO, V., Nucl.

Phys. A 133 (1969) 255.