Experimental study of the E2 strength distribution in the 12 C and 16O nuclei

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Experimental study of the E2 strength distribution in

the 12 C and 16O nuclei

M. Buenerd, C.K. Gelbke, D.L. Hendrie, J. Mahoney, C. Olmer, D.K. Scott

To cite this version:

EXPERIMENTAL STUDY

OF THE E2

STRENGTH DISTRIBUTION

IN THE

12C

AND

16O

NUCLEI

M. BUENERD

Institut des Sciences

Nucléaires,

B.P.

257,

38044 Grenoble

Cedex,

France

and Lawrence

_{Berkeley Laboratory, University}

of

_California,

_Berkeley,

Cal.

94720,

U.S.A. and

C. K.

_GELBKE,

D. L.

HENDRIE,

J.

MAHONEY,

C. OLMER and D. K. SCOTT

Lawrence

_{Berkeley Laboratory, University}

of

California,

Berkeley,

Cal.

_94720,

U.S.A.

(Re~u

le 25 novembre

_1976,

_accepte

le 21 decembre

₁₉₇₆₎

Résumé. 2014 La distribution des transitions

quadrupolaires dans les

_noyaux

12C et 16O est étudiée par diffusion inélastique de 3He. La résonance

_{quadrupolaire}

_{géante présente} une structure fine distribuée sur _plusieurs niveaux individuels dans les deux noyaux, elle

_épuise

31

%

et 37

_%

de la

_règle

de somme E2 _(EWSR) dans 12C et 16O _{respectivement.}

Abstract. 2014 The distribution of the E2

strength

in 12C and 16O nuclei is

_{investigated by}

inelastic

scattering of 3He. The

_{giant quadrupole}

resonance is found to be

_splitted

into several states in both nuclei and exhausts 31 _% and 37 _% of the

_quadrupole

_{energy weighted} sum rule (EWSR) in 12C and 16O

_{respectively.}

Classification

Physics Abstracts 4.110

The

_{giant quadrupole}

resonance

_(GQR)

in nuclei

with mass A > 28 lies around

63 A -l/3

(MeV)

excitation _energy and exhausts most

_(~

60

_%)

of the

energy

weighted

sum rule

(EWSR).

In

lighter

_systems,

the 160

nucleus has been

_investigated

via the reaction

~ ~N(p,

y)

(ref.

[1])

and more

_recently

_by

inelastic hadron

scattering experiments [2,

3].

All these measurements

concur as to the existence of a noticeable E2

strength

between 15 and 30 MeV excitation _{energy. It} is

_clearly

shown in ref.

_[2]

that the

_GQR

does not _appear as a

single

broad

_{(4-5 MeV) bump,}

as in medium mass and

heavy

nuclei,

but is

_spread

over several individual states. This trend is

_{quite analogous}

to that of the isovector

_giant

_dipole

resonance

(GDR)

(ref.

[4])

which also appears as a

single

broad state in nuclei with A > 40 and show

_spreading

over several fine

structure states in

_lighter

_systems. It is of interest to

pursue the

study

of the

GQR

in

lighter

nuclei

tracking

the E2

_strength

and its

_spreading

into the continuum.

In this letter, we _report measurements of the distribu-tion of E2 states in

12 C

and

160

nuclei

_by

inelastic

scattering

of 130

MeV 3He

_particles.

The

160

data have been used for

_comparison

with the results from the

_160(a,

_a’)

_{study [2]}

in order to check that the weak

3 He-nucleus

isovector effective interaction

[5]

does not

_produce

a noticeable excitation of the

isovec-tor states

_(especially

the

_GDR)

in the 20-30 MeV excitation _energy

_region.

The

_experiments

have been

_performed

at the 88"

cyclotron

of the Lawrence

_{Berkeley Laboratory.}

The scattered

_particles

were identified with two AE - E

_(2.5

mm-5

_mm)

silicon detector

_telescopes.

The 12C

_target had a thickness of 650

gg/CM2 -

The _gas

cell for the

160

_experiment

consisted of a

_cylinder

of 60 mm diameter with a 3

mg/cm2

Havar

window;

the _pressure in the cell was between 8 and 13 PSI.

Spectra

were recorded between 12.5 and _40~ with an

overall resolution of about 300 to 400 keV for both

targets.

The measured spectra have been

_separated

into

background

and

_peaks.

The

_background

was

appro-ximated

_{by fitting by}

_computer, a set of five

_points

of the _spectrum with a

_polynomial.

The

_points

were

chosen so that the

_{background joined}

the

_high-lying

continuum

_smoothly

down to the

_(x-particle

threshold

region, passing by

the minima between the

peaks

in the 10 to 20 MeV excitation _energy

_region.

The results obtained are illustrated on

figure

1. After subtraction

of the

_background,

the difference _spectra have been unfolded into

_{single peaks using}

a _computer code

performing

a X2

search in each

_region

of the _spectrum and

_fitting

at most 4

_{three-parameters}

gaussian-shaped peaks.

The

_{160 spectra}

_(Fig.

₁₎

are identical to those obtained from the

_{(a, a’)}

reaction

_[2].

Furthermore

no El contribution was detected in the

_analysis

of the

L-54 JOURNAL DE _{PHYSIQUE -} LETTRES

FIG. 1. -

Examples of measured _spectra. Excitation energies of the E2 states above 10 MeV are indicated. The dashed _bump is the expected cross-section for _{giant octupole} resonance _{(see text).}

angular

distributions of the individual levels.

More-over, in

the 12C

_spectrum we have found no evidence

for the _strong El state at

_{E., ;:t~}

22-23 MeV

_{(ref. [4]).}

This confirms that the

_strength

observed in the _present

experiments

is

_mostly

isoscalar. and that the

cross-section for the excitation of the GDR can be

_neglected.

For both _nuclei, the

_peak

structure of the _spectrum between 15 MeV and 30 MeV excitation _energy. exhibit the same overall

_shape

across the

_angular

_range

investigated ;

we see this feature as an indication that

the continuum is dominated

_by

one excited

_multipole

with

_negligible

inclusion of other L values. Indeed,

assuming

that two states with different

_{multipolarities}

and

_comparable

cross-section are

_excited,

the calcula-tions

_(see

_below)

_predict

that the extrema of their relative cross-sections would be different

_by

a

_large

factor

_(~3)

between 15° and 30° c.m., and this was

not observed above

_{~ ~}

15 MeV. The

_experimental

angular

distributions

_displayed

on

_figure

2 exhibit

shapes

with

_quite

similar structure,

_{slightly changing}

with the excitation _energy.

DWBA calculations have been

_performed

with the code DWUCK

_(version

DWUCK

_{4). Optical}

model _parameters have been obtained

_by

_fitting

the inelastic

_scattering

data.

_they

are for

12C :

F=83.6MeV,~= 1.2,~=0.77mf.~= 13.45MeV,

rW = 1.83, aw = 0.59

fm;

and for

l60 : V

= 89.7, ry = 1.2, ay = 0.84

fm,

_W = 15.51

MeV, rw

=

1.73,

FIG. 2. -

Angular distributions of the E2 transitions. The error

bars are ± 5 % for the first 2+ state, + 10 % for states below

Ex = 15 MeV and _{:t 15 % above ; larger} error bars are indicated. The points are fitted with DWBA calculations for L = 2

transi-tions (solid line). The dashed line is an _example of L = ₃

cal-culation.

aw = 0.58 fm. The

experimental angular

distributions have been

_compared

to extended collective model calculations

_{[6]. Multipolarities}

and deformation

parameters

#L

have been deduced from this

compari-son, the latter

expressed

in terms of

_percentage

of the EWSR limit

_{given by}

the formula

_{[6] :}

where R is the radius of the real part of the

_optical

potential,

all other notations

_being

the same as in

ref.

_[6].

The

_{multipole-moments}

of the nuclear matter distribution have been calculated

_using

_parameters

taken from ref.

_{[7]. assuming}

a Saxon-Wood

_shape.

For the two nuclei, the DWBA calculations

_using

complex

form factor fit very well the first 2+

(Fig. 2)

and 3 - levels,

_providing

a sound basis for

L-assign-ments to

_high

excitation _energy states. However the deduced

_(~L

_{R )}

values are much smaller than those

obtained from other reactions due to _very different real and

_imaginary

radii of the

3He

_optical

_potential.

using

real form factor calculations as

_they

fit

_correctly

the forward

_angles

cross-sections and

_provide

_(#L

_R)

values in _agreement with other

_experimental

values

for the first 2+ and 3- states of both

12C

_{(ref. [8])}

and

l60

_(ref.

_[9]).

The

_angular

distributions of the

assigned

E2 transitions are shown on

_figure

_2, fitted

with L = 2 DWBA calculations, _one L = 3

calculat-ed

_shape

is also indicated for

comparison.

For the

16 0

nucleus

_they

confirm the results of ref.

_[2].

How-ever the

angular

distribution of the 23.5 MeV state exhibits a

slight

bump

in the 25°-30°

_region,

rather

than a

_rapid

fall off observed for the other

_angular

distributions. This _may be due either to a contamina-tion

_by

another

_{multipolarity}

or to the

_microscopic

wave function of this state

_[16].

In ref.

_[10]

evidence has been obtained for a

large

E3

_{strength (~}

70

_%

EWSR)

centered around

_{Ex N}

35

MeV.

We have calculated the

_expected

cross-section in our data and

found that for 50

_%

EWSR and

_assuming

a 5 MeV FWHM this

_giant

_octupole

resonance should _appear as shown on

_figure

1. Its non observation raises some

questions

about the

_assumptions

made in ref.

_[10].

For the 12 C nucleus

_(l)

E2

_assignments

have

pre-viously

been made for the 15.2 MeV

_(ref.

_[11])

and the 18.4 MeV

_(ref.

_[12])

states. However E2

_strength

at

higher

energy has not been observed hitherto. A state found at 21.3 MeV from inelastic

_scattering

of 155 MeV _protons was

assigned

E3 on a solid basis

_[12]

and some other E3

_strength

has been located around 21.6 MeV

_(ref.

_[13]).

The _present results _suggest that the latter could be isovector, but there is some

unclear-ed

_ambiguity

about the _presence of E2 and E3

_strength

in the

21-22

MeV excitation _energy

_region

of

l2C.

The _present results also

_suggest

that the El

_strength

reported

in ref.

_[14]

could have been overestimated because of some undetected E2 cross-section in the

spectra.

For the two nuclei

studied,

the

_percentages

of the EWSR limit exhausted in the observed E2 transitions

are listed in table I

together

with the excitation

energies,

widths and deformation

_lengths.

The total

E2

_strength

exhausted _up to 30 MeV excitation _energy

is around 46

_%

in

12C

and 55

_%

in

~0,

the latter value in reasonable

_agreement

with

_previous

measu-e) In a _{just published paper} [15], similar results are _reported on

12C but the deduced values for the E2 strengths are _markedly smaller.

TABLE I

Excitation

_energies

_{Ex, full}

width at

_half

maximum

(FWHM)

corrected

_from

_experimental

resolution r,

deformation

length

(~2

R) and percentage

of

the EWSR

for

the measured

_quadrupole

transitions. Associated

uncertainties are indicated

_for

the

_first

two

_quantities.

(a)

doublet

_(19.95

MeV - 20.6

_MeV)

resolved at

Blab

= 17° 5.

rement

_[2].

In both nuclei, the

_giant

_quadrupole

resonance is

splitted

into several states and its

_strength

is

_spread

over a

_larger

excitation _{energy range}

(-

13

_MeV)

for

12C

than for

l60

(-

8

_MeV).

The centroid of the

_GQR

_(assumed

to include states at

Ex

> 15

_MeV)

lies around 21.5 MeV in both nuclei and the

_{strength corresponds}

to 31

_%

and 37

_%

of the

EWSR

for 12C and 160

_{respectively.}

Thus, in conclu-sion. it is clear that in

_light

nuclei the

_GQR

exhausts

a

_markedly

smaller _part of the sum rule limit and lies at a smaller excitation _energy

(~

50 to 53 A - il3

_MeV)

than in heavier

_nuclei,

_exhibiting

trends similar to those observed for the isovector

_giant

_dipole

reso-nance.

References

[1] HANNA, S. S. et _{al., Phys.} Rev. Lett. 32 (1974) 114. [2] KNÖPFLE, K. T. et al., Phys. Rev. Lett. 35 (1975) 779.

[3] BUENERD, M., MARTIN, P., DE SAINTIGNON, P. and LOISEAUX,

J. M., Phys. Rev. C 14 (1976) 1316.

[4] BERMANN, B. _L., Nuclear Data Tables 15 (1975) 319.

[5] MOALEM, A., BENENSON, W. and CRAWLEY, G. M., Nucl.

Phys. A 236 ₍₁₉₇₄₎ 307.

[6] SATCHLER, G. R., Nucl. Phys. A 195 (1972) 1.

[7] HOFSTADTER, R., Nuclear and Nucleon Structure (Benjamin)

1963.

[8] SATCHLER, G. R., Nucl. Phys. A 100 (1967) 97 ; WALECKA, J. D., Phys. Rev. 126 (1962) 663.

[9] AJZENBERG-SELOVE, F., Nucl. _Phys. A 188 (1971) 1 and to

L-56 JOURNAL DE _{PHYSIQUE -} LETTRES

[10] LEBRUN, D. et al., Nucl. _Phys. A 265 ₍₁₉₇₆₎ 291.

[11] BUENERD, M. et al., La _Physique Nucléaire autour des

Cyclo-trons et des Tandems, Louvain-la-Neuve, Belgium (1974).

J. _{Physique Colloq.} 35 ₍₁₉₇₄₎ C5-4.

[12] BUENERD, M., Thesis, Université de Grenoble _(1975).

BUENERD, M., MARTIN, P., DE _{SAINTIGNON, P. and}

LOI-SEAUX, J. M., in preparation.

[13] YAMAGUSHI, A., TERASAWA, T., NAKAHARA, K. and YORI-ZUKA, Y., Phys. Rev. C 3 (1971) 1750.

BUENERD, M., MARTIN, P., DE SAINTIGNON, P. and

LOI-SEAUX, J. M., Int. Conf. on Nuclear Structure and Spec-troscopy, Amsterdam, vol. II _{(1974), p.} 286.

[14] BUENERD, M., MARTIN, P., DE SAINTIGNON, P. and LOI-SEAUX, J. M., Phys. Rev. Lett. 33 (1974) 1233.

[15] KNÖPFLE, K. T. et al., Phys. Lett. 64B ₍₁₉₇₆₎ 263.

[16] For _{(p, p’)} reactions, DWBA calculations _{using microscopic}

wave functions show that for a _{given multipolarity,}

different wave functions give angular distribution with