Inelastic scattering of 30 Mev polarized protons from 112Cd

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Submitted on 1 Jan 1976

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Inelastic scattering of 30 Mev polarized protons from

112Cd

R. de Swiniarski, G. Bagieu, Dinh-Lien Pham, M. Massaad, J.-Y. Grossiord,

A. Guichard

To cite this version:

INELASTIC SCATTERING

OF

30 MeV POLARIZED

PROTONS

FROM

112Cd

R. DE

SWINIARSKI,

G.

BAGIEU,

DINH-LIEN

PHAM,

M. MASSAAD

Institut des Sciences

_Nucléaires,

B.P.

_257,

38044 Grenoble

_Cedex,

France

J. Y. GROSSIORD and A. GUICHARD

Institut de

_Physique

_Nucléaire,

Université Claude-Bernard de

_Lyon,

69621

_{Villeurbanne,}

France

(Reçu

le 23 mars

_1976,

révisé le 13 mai

_1976,

_accepte

le 21 mai

_{1976 )}

Résumé. - Les sections efficaces différentielles et

pouvoirs d’analyse des diffusions élastique et

inélastiques de _{protons polarisés} de 30 MeV sur 112Cd ont été mesurés. _{L’interprétation} des excita-tions des états à deux _phonons a été faite dans le cadre du formalisme des _{équations couplées.} Un

bon accord avec les sections efficaces et _{pouvoirs d’analyse} mesurés des _premiers niveaux excités

2+1

(0,617 MeV) et

₂₊₂

_{(1,31 MeV)} a été obtenu en _supposant que les

développements

choisis sur la base un _phonon et deux _phonons pour leurs fonctions d’onde sont

_orthogonaux

et un _mélange d’état à deux _phonons pour le premier

2+1.

Abstract. - Differential cross-sections and

analysing powers for elastic and inelastic scattering

of 30 MeV _{polarized protons from 112Cd} have been measured. The _{coupled-channel} formalism is used to _interpret the excitation of the _two-phonon states. A _good fit to the observed cross-sections and _analysing powers for the excitation of the first

2+1

(0.617 MeV) and the second

2+2

(1.31 MeV)

states is obtained if the expansions of their wave functions in terms of the _one-phonon and

two-phonon basis functions are assumed to be orthogonal and if some admixture of the _two-phonon

component is assumed in the

₂₊₁

state wave function.

Classification

Physics Abstracts

4.370

1. Introduction. - We have measured the diffe-rential cross-sections and

_analysing

_powers for the elastic and inelastic

_scattering

of 30 MeV

_polarized

protons

from

112Cd.

The elastic

_scattering

was

analysed by

an

_{optical-model potential,}

and the

excitations of the first collective 2+ and 3- states were

compared

to the

_predictions

of the

_{coupled-channel}

formalism. With

_analysing

_powers data in

_addition,

our interest was therefore to

_study

and

_interpret

conveniently

the excitations of the two collective

qua-drupole

states

_2i

and

_2’.

In the

_analysis

of 13 MeV ine-lastic

_scattering

cross-sections the

21+

state

_{(0.617 MeV)}

has been assumed to be a _pure

_one-phonon

_state,

while the

_2’

state

_{(1.31 MeV)}

has been assumed to

have a small admixture of the

one-phonon

state

[1].

These authors have obtained a rather

_good

_agreement

between

cross-sections data and calculated curves.

In our

_{analysis using}

the CC

calculations,

two

assump-tions have been made for the two states

_2-;-

and

_{2’ :}

the

orthogonality

of the

_expansions

of their wave

func-tions in terms of the

_one-phonon

and

_two-phonon

basis functions and the

_strong

admixture of the

two-phonon

component in the

_2i

state wave function.

2.

_Experimental

method. - The data were obtained

at an _energy of 30 MeV with the

_polarized

_proton

beam of the Grenoble

cyclotron.

Since the new

ana-lysing

magnet

[2] recently

installed was

_used,

an overall resolution of 80 to 100 keV

_(FWHM)

was obtained

for most of the data.

_Up

to 1 nA of energy

analysed

polarized

protons

were delivered on the _target, with a

polarization

close to 70

_%

which was measured with a

carbon

_polarimeter.

The carbon

_polarimeter

consists of a thin foil of

_graphite,

introduced into the incident

beam

_during

one minute for every twenty minutes

interval,

and of two

_Si(Li)

detectors of 5 mm thickness

located at 600 on each side of the beam L

(left)

and R

(right).

The

_analysing

_power for elastic

_scattering

of 30 MeV

_protons

_{by 12 C}

at this

_angle

is

_Ao=O.57

_{± 0.01.} The

_sign

of the

_polarization

was reversed _every 0.2 s.

We measured the

_polarization

of the beam for the two

spin orientations T (up) and I (down) using

the

follow-ing

relation :

If the

_polarized

source was well

_adjusted,

we would

find

_pi

= -

pt.

(This

_was

generally

the

case.)

Enriched _target of 1

_mg/cm2

thickness obtained from

1126

ORNL was used. The measurements were made

_using

two

_{telescopes comprising}

AE surface barrier detectors of

_{700 g}

thickness and E

_Si(Li)

detectors 5 mm thick all cooled to - 25 °C

_by

a thermoelectric device. The treatment of

_signals

_coming

from the two detectors of each

_telescope

was realized so that

_only

coincidence

events were

registered.

We eliminated therefore the

alpha-particle

groups of 33 MeV maximum energy, which were

_completely

_stopped

in the first detector AE.

The value of the

_analysing

power A for the studied reaction is

_given

_by

To obtain absolute values of differential

cross-sections,

we used a beam monitor

consisting

of two

Si(Li)

detectors

_placed

at 300 on each side of the beam

and

_slightly

above the reaction

_plane.

The beam monitor _gave a

_counting

rate which is

_proportional

to

_C/cos

_Otarget,

where C is the

_charge

obtained from the

_integration

of the

_Faraday

cup current and

_target

is the

_angle

between the normal to the _target and the incident beam direction. The

_good

resolution achieved

permitted analysing

powers for several

low-lying

states such as the

2 1+ , 2’

and 3 - to be extracted.

3.

_{Optical-model analysis.}

- The

optical-model

potential

used in this

_analysis

is local and has the usual form :

where

to which is added the Coulomb

_potential

from a

uniformly charged sphere

of radius

1. 17 A 1/3

F. The

optical-model

parameters

were determined from an

analysis

of the elastic cross-section and

_analysing

power

together,

data taken

_concurrently

with the ine-lastic data. The

_optimum

_parameters

were determined

by

use of automatic search routines MAGALI

_[3]

which minimized the

_quantity

_xf

which is the sum

of Z’

and x)

where

_O"exp((oi)

is the

_measured,

and

_6th(oi)

the calculated differential cross-section at

_angle

_Oi,

while

_ACep

is the

error associated with _(Texp;

_Pexp(oi

is the

_measured,

and

_Pth(oi)

the calculated

_polarization

at

_angle

_Oi,

while

_DPeXp

is the error associated with

_Pe.p*

Errors on the cross-sections were

_uniformly

set at ± 5

_%,

the errors on the

_polarization

were

sta-tistical. The best results of the

_analysis

are

_given

in table I. The value of

_x¡12

N is smaller than 7. The fits with the data

_using

the

_potentials

of table I are shown

on

_figure

1. No volume

_absorption

was needed to

reproduce

the data.

FIG. 1. - Elastic

scattering cross-section and _analysing power and

optical-model predictions with the parameters of table I.

4.

_{Coupled-channel}

calculations. - It has been

known _{that the pure} harmonic vibrational model does

not

_{explain completely}

the _proton inelastic

_scattering

cross-sections from several states in

112Cd

like the second

_2’

at 1.31 MeV in this nucleus

_[1].

_Although

good

fits to the data were obtained

_by

_adding

to the

basically

two-phonon

state

₂₊

some admixture of a

one-phonon

state, several

problems

in this nucleus still remain to be

_{investigated.}

In

_{particular, recently,}

it has been

_suggested

₍₁₎

that a _strong

_two-phonon

admixture should be added also to the

_one-phonon

wave function of the first

21+

at 0.617 MeV

in 112 Cd

to describe

_successfully

this state. The data taken at

the Grenoble

_cyclotron

were

_analysed

with the

program ECIS 74

[4]

by

coupling

the

_{0 +,}

_{2’, 2’}

and 3-

_(EX

= 1.97

_MeV)

states

_using

the vibrational model. The two states

_2i

and

_2’

of which the expan-sions of the wave functions in terms of the

_one-phonon

and

_two-phonon

basis functions are assumed to be

orthogonal,

may be

represented by,

following

the notation of

_Raynal

_[5]

TABLE I

Optical-model

parameters

TABLE 11

Optical-model

and

_deformation

_parameters used in the

_{coupled-channel}

calculations

In view of the determination of the value for the admixture of

_one-phonon

and

_two-phonon

compo-nents for each state, and therefore the deformation

parameters

flj,

we have

_{analysed simultaneously}

the

differential cross-sections and

analysing

powers

using

the CC calculations. The

_{optical-model}

_parameters

used as initial values for the

optical-model

search

procedure

were taken from table I. The interaction

potential

arises from the deformation of the Coulomb

potential,

the

_complex

central

_potential

and the

spin-orbit potential.

The

deformed

_spin-orbit

poten-tial was of the full Thomas form

[7].

The best results

obtained from the search

_procedure

over the

optical-model _parameters as well as the admixture

compo-nents, and therefore the deformation

_parameters,

show that we have to consider an

equal

admixture

(50

%),

i.e. _T = -

450,

for each _component. These

results are

_presented

in

_figure

2 and the

_{corresponding}

parameters listed in table II. As can be seen in this

figure,

good

agreement is obtained for the measured cross-sections and

_analysing

_{powers. The}

_X2

values vary

rapidly

with T, calculations indicate that

x2

increases at the rate of about

_{2 %}

per

degree

for

(p ~- - _450.

5. Conclusions. - The

_experimental

cross-sections and

_analysing

_powers

_reported

here for the

0+,

2i ,

2’

and 3 - levels were

_analysed

simultaneously

in the

coupled-channel

formalism

_by

_coupling

them

_together

and

_using

the vibrational model. The best _agreement between

_experimental

data and theoretical curves has shown

_firstly

that the data could be

_analysed

_correctly

assuming

the

_{orthogonality}

of the

_expansions

of the

wave functions for the two states

_2i

_(EX

= 0.617

MeV)

and

_2’

_(E.

= 1.31

_MeV),

in terms of the

_one-phonon

and

_two-phonon

basis

_functions,

and

_secondly

a

strong

two-phonon

admixture

_{(50 %)}

for the

₂₁

state

which has been considered _up to now as a _pure

one-phonon

state

_[1].

This

_proposed

_strong

_two-phonon

admixture in the first

_21+i

in

112 Cd

is however in _agreement with a theoretical

_suggestion

made

recently

(1).

Acknowledgments.

- We would like to thank Dr. J.

_Raynal

for

_using

his

_{coupled-channel}

code ECIS 74 and for his constant interest in this work.

FIG. 2. -

Coupled-channel predictions for the 0+, 2-;-, 21 and

1128

References

[1] STELSON, P. H. et al., Nucl. _Phys. A 119 ₍₁₉₆₈₎ 14.

[2] LEROUX, J. B., Thesis, University of Grenoble _(1973), unpu-blished.

[3] RAYNAL, J., « _{Magali »} D. _{Ph/T/69-42 (Saclay).}

[4] RAYNAL, J., « ECIS 74 » (Saclay), unpublished.

[5] LOMBARD, R. M. and RAYNAL, J., Phys. Rev. Lett. 31 ₍₁₉₇₃₎

1015.

[6] TAMURA, T., Progr. Theor. _{Phys. Suppl.} 37-38 (1966) 383.