E2 contributions to backward (e,e′) cross sections in heavy deformed nuclei

hog.

Parr. Nucl. Phys., Vol. 34, pp. 319-320, 1995 Copyright 0 1995 Elsevier Science Ltd tinted in Great Britain. All rights reserved 0146-6410/95

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0146-6410(95)00027-5

E2 Contributions to Backward (e,e’) Cross Sections in Heavy Deformed Nuclei* M. DINGFELDER,

and A. FAESSLER

R. NOJAROV

Inslirutfiir Theoretische Physik Universitd’t Tiibingen, Auf der Morgenstelle 14, D-72076 Tiibingen, Germany

ABSTRACT It is shown that E2 transitions to the rotational band of low lying Ml excitations in heavy deformed nuclei contribute to the Ml (e,e’) cross section at backward angles even at low incident energies of 50 MeV. The agreement after taking

with experiment

is improved

the E2 contributions

considerably,

especially

for intermediate

transferred

momenta,

into account.

KEYWORDS Ml and E2 excitations,

deformed

nuclei,

backward

inelastic

electron

scattering,

cross sections,

DWBA,

QRPA Low lying magnetic interest (Bohle

dipole

since their discovery et. al., 1984).

(Ml)

excitations

in deformed

in 1984 in Darmstadt

They are described

test for this models than the Ml

and interpreted

strength

distribution

sensitive to details of the nuclear structure. angles (usually

8 =

while the electric scattering.

165”)

favouring

inelastic

by various theoretical alone are the (e,e’)

and theoretical

electron

models.

scattering

A more stringent

cross sections,

which

The (e,e’) cross sections are measured at backward

transverse

ones are dominated

nuclei are of both experimental

by high precision backward

Magnetic

transitions.

by their longitudinal

On the other hand, their large longitudinal

transitions

part and therefore

often

are purely neglected

part could give rise to appreciable

are very scattering

transverse in backward

contributions

to

the cross sections. Another

fact is the observation

sections of heavy deformed

of systematic

nuclei.

deviations

There the theoretical

decrease faster at larger momentum

transfer

p as found experimentally.

in lighter

nuclei suggests to take possible contributions

transition

to the Z”Z< = 2+1

Z”Zi

=

1+1.

transition,

The

state

E2-excitation

of the rotational

energy

because of the large moment

between theory

is only of inertia.

30-50

built

with the energy resolution

keV larger than

= l+ states, we use a quasipartice mean field

tial. * van

The

It includes pairing correlations supported Hadronen

by the

und

Deutsche

part

consists

random-phase

of an axially

symmetric

in the BCS approximation.

Forschungsgemeinschaft

that

(DFG)

Kernen”

319

and

experimentally

E2 with

Ml

(Bohle

This energy separation

(e,e’) experiments. approximation deformed

The separable the

an accompanying

of the corresponding

Ml transition.

of the present high precision

et. a/.,

1994b).

arising from

up on top of the Ml excitation

Such a 2+ state was identified

To describe these Zi”

l+ excitations

The absence of these discrepancies

into account, band,

et. a/., 1985) in lsfiGd It lies only 21 keV higher than the strongest is comparable

in the Ml cross

and experiment

Ml form factors of low lying orbital

Graduiertenkolleg

(QRPA)

Woods-Saxon

residual interaction “Struktur

und

(Nojarov potenincludes

Wechselwirkung

M. Dingfelder et al.

320 1o-4 BI’I’

1'1'

I’I’I’I’I’ -Ml

+ E2

1o-5

1o-6

10.’

1o+

d

1

I

’

10

’

’

20

30

’

’

’

40

’

60

incident energy Fig. 1.

Total

DWBA

cross sections

versus the incident an compared quadrupole

and spin parts.

and isovector

channels.

of rotational

The relative

/CR remains a free parameter.

The Ml

resonance

w

(IVGQR),

&K=I(r)

and Blok,

h’IC h

IS

and ,17&,~=r (r),

(longitudinal)

The transition

densities are reduced matrix

are calculated

microscopically

1. It is seen that

the E2 cross section

in distorted

isoscalar

by the deformaby the condition

and its coupling

position

constant

of the isovector

(Nojarov

of the multipole

giant

Ml strength.

wave Born approximation (r) and the E2 transition

~~I,K=I

(transversal)

violated

microscopically invariant

the high lying orbital

density

for the strongest

Ml

(DWBA) densities

et. al., 1994a)

charge and current

excitation

is two orders of magnitude

the Ml cross section

with

shifts the theoretical

cross sections to higher transferred

and theoretical

in 156Gd

type and contains

symmetry

is rotational

with

becomes comparable experimental

transitions

excitation

operators.

They

using the QRPA wave functions.

Ml and E2 cross sections

The calculated

elements

Ml

is of Pyatov

by the experimental

separately

J&,Ii=l(~)

’

100

E2 and Ml+E2

Its is determined

1983) using the Ml transition

90

et. a/.,1984)

interaction

connected

are calculated

for Ml,

interaction

constant

isovector

’ ’

’

60

for the strongest

restores the rotational

It can be determined

and E2 cross sections

(Heisenberg

(Bohle

The quadrupole-quadrupole

The isoscalar coupling

invariance.

quadrupole

to experiment

’

’

70

[MeV]

165’)

energy, calculated

The isoscalar interaction

tion of the mean field.

(6 =

’

I ’

’

50

Ml cross sections

cross section and a very good agreement

already

at &ncidenr momenta.

are removed

with experiment

in 156Gd are shown

smaller

at low incident

= 50 MeV.

in figure

energies,

In this way the discrepancies

after adding

but

The higher multipolarity

the E2 contribution

between

to the Ml

is achieved.

REFERENCES Bohle

D., A. Richter, Phys.

Lett.

W. Steffen,

B, 137,

Bohle D., A. Richter,

A.E.L.

Dieperink,

N. Lo ludice,

F. Palumbo

and 0. Scholten

K. Heyde,

and A. Sevrin (1985).

P. Van Isacker, J. Moreau

Phys.

Rev. Lett., 55,

1661. Heisenberg

(1984).

27.

J. and H.P. Blok (1983).

Ann. Rev. Nucl. Part.

Nojarov

R., A. Faessler and M. Dingfelder

(1994a).

J. Phys.

Nojarov

R., A. Faessler and M. Dingfelder

(1994b).

Phys.

Sci., 33, 569. G: NucI.

Part. Phys., 20, Llll.

Rev. C, submitted.