How does the elastic scattering of 12C + 20Ne compare with that of 16O + 16O ?

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Submitted on 1 Jan 1975

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Saintignon

To cite this version:

HOW DOES THE

ELASTIC SCATTERING OF

12C

+

20Ne

COMPARE WITH THAT OF

16O

+

16O ?

H.

_DOUBRE,

E. PLAGNOL

_(*),

J. C. ROYNETTE

Institut de

_Physique

Nucléaire,

BP

1,

91406

_Orsay,

France

and

J. M.

_LOISEAUX,

P.

_MARTIN,

P. de SAINTIGNON Institut des Sciences

_Nucléaires,

BP

_257,

38044

Grenoble,

France

Résumé. - Les fonctions d’excitation de

cinq voies de sortie du _système 12C + 20Ne entre

22 et 28 MeV _{(C.M.) présentent} une structure _importante à 90° et 130° _(C.M.). Cette structure, analogue à celle _qu’on observe

_pour

16O + 16O est _analysée en termes d’accord des moments

angulaires.

On _présente une distribution _angulaire à 24,7 MeV _(C.M.). Il est montré que

l’absorption

due aux voies directes est intermédiaire entre celle de 16O + 16O et 18O + 18O.

Abstract. - Excitation functions for 5 exit channels of the 12C + 20Ne

system are _given in the range 22-28 MeV centre of mass incident energy. An important structure is observed in the elastic scattering excitation functions taken at 90° and 130° (C.M.). This structure, which reminds one of the 16O + 16O case, is studied in terms of _angular momentum _matching. An _angular distribution taken at 24.7 MeV _(C.M.) is also _presented. The direct channel _absorption is shown to be inter-mediate between the 16O + 16O and 18O + 18O cases.

Since the observation

_[1]

of a _{strong gross} structure

in

the 160

+

16 0

elastic

_scattering

_functions,

_many other systems of identical or non identical

_light

nuclei have been studied

_[2].

It was soon

_recognized

that the observed structure is not a

_specific

feature

of identical

_{particles (i.e.}

not due to the lack of

odd-partial

waves in the

_{scattering amplitude)}

as the

180 + 180

_{system shows} a

strongly damped

struc-ture and a small _average cross-section.

_Upon

consi-derations on

_angular

momentum

_matching

between the entrance channel and the reaction

_channels,

it was

_{suggested [3]}

that the

_pronounced

structure and the

_large

cross-sections observed in the

160 + 160

elastic

_scattering

were related to the

_inability

for this system to _{carry away}

_through

the direct reaction channels the

_large

_angular

momentum

_brought

in

by

the

_grazing

waves of the entrance channel. In

terms of

_{optical-model}

_parameters, this

_implies

that

the

_magnitude

of the _average cross-section is

_roughly

determined

_by

the

_strength

of the

_imaginary

_potential,

whereas the

_{peak-to-valley}

ratio

_{critically depends}

on its transparency for the

_grazing

_partial

waves.

Such an

_{interpretation}

seems to be

_{strongly supported}

by

the

_{impressive improvements}

of the fits to the

(*) Now at S.P.N.B.E., C.E.N. Saclay, BP 2, 91190

Gif-sur-Yvette, France.

experimental

data,

obtained when an

_1-dependent

imaginary

potential

is used

_[4].

Potentials of this type are able to

_explain

_{the appearance} of

_shape

resonances. The

existence,

in the

_{160( 160,}

_12C)

2 ONe

reaction

_{[5, 6]}

of a similar structure has been

interpret-ed as evidence for such a mechanism. This

coupling

may,

however,

also be

explained

by

considerations

based on the

_I-space

localisation of the

_4-particle

transfer

_{[6], [11].}

From this

_viewpoint,

the

_comparison

of the

12C

+

2°Ne

_{system with} the

160

+ 160 system is of interest. In terms of

_angular

momentum

matching,

it has been shown

_by

_Vandenbosch,

Webb and Zisman

_[7]

that some differences should

exist between them and result in a more

_damped

structure and smaller cross-sections in

the 12C

+

2°Ne

system. This seems to be

_{supported by}

their

data,

which was however limited for

_experimental

reasons

to smaller

_(80°)

centre of mass

_(C.M.)

_angles.

In this

_letter,

we _{present excitation functions} of

the

12C

+

2°Ne

system for the elastic channel and the 4 reaction channels which are best matched with

the entrance channel. These measurements,

performed

at

_70°,

90° and 1300

_(C.M.)

show for the backward

angles

some

_interesting

differences with the conclu-sions of reference

_[7].

An elastic

_scattering

_angular

distribution at 24.7 MeV

_(C.M.)

incident _energy is also

_given.

I.S.N. Grenoble

_Cyclotron.

The beam _energy, as

measured

_by

_magnetic

_analysis,

is considered to be

known within an absolute _accuracy of 500 keV

_(lab.),

and the energy

dispersion

of the beam to be

approxi-mately

400 keV

_(lab.),

that is 150 keV

_(C.M.).

Several values of beam _energy for the excitation functions

were obtained

by slowing

down the incident ions

through

carbon foils. It was checked that the beam

quality

suffered no

_significant

deterioration.

The

_experimental

_set-up

_comprised

two different

systems of detection. For centre of mass

angles

close to

90°,

particles

were identified

_by

the

associated-particle

method in two 200

mm2

solid-state surface-barrier detectors. One was

_kept

fixed at 45°

_(lab.)

while the

_position

of the other was

_adjusted

to obtain the maximum

_counting

rate. For the excitation function measurements, the solid

_angle

was as

large

as 2.4 msr. The

_presented

excitation functions are

averaged

over a _± 3°

_(C.M.)

horizontal

_angle.

For

the elastic

_{scattering angular}

distribution,

this value

was

_brought

down to _± 1°

_(C.M.).

With this _system, the _energy resolution was limited

_{mainly by}

the

target thickness

₍₁₀₀

_Jlgjcm2)

and

_by

the beam _energy

dispersion.

Special

care was taken to make sure of

the maximum

_efficiency

_{of the system, but} no

correc-tion has been

_applied

_(e.g.

for in

_flight

_gamma

_decay

of an excited nucleus or

_{multiple scattering).}

The other

_detecting

_system was a standard AE - E

telescope

(10 ~m)

for detection and identification of reaction

_products

emitted in a 0.2 msr. solid

angle

at a

_{laboratory angle}

~ 25°

(lab.),

(i.e.

70°

(C.M.)

if 2°Ne are detected or > 130°

(C.M.)

if

recoil 12C are

_detected).

_Energy

resolution in

FIG. 1. - Excitation functions of the 12C

+ 2°Ne elastic scattering thick full curve _guides the eye between experimental points thin full line = _{optical model predictions with the potential of} refe-rence _[8] dashed line = _optical model _predictions with the _potential

of reference [7] (see text).

cross-sections are

_given

within an _accuracy of 25

%.

The elastic

_scattering

excitation functions _appear

in

_figure

1. At 700

_(C.M.),

it is

_strongly

_decreasing,

without _{any strong} structure and in excellent

agree-ment with the results of

Vandenbosch,

Webb and

Zisman

_[7].

Excitation functions at 700 for the

12C

+ 2 °Ne and the 160

+ 160 _systems were

compar-ed in reference

_[7].

It was concluded that the different

behaviour of the excitation functions was due to a

larger absorption

for

_high

1-values in the

12C

+

2°Ne

case. In contrast with what is observed at

_700,

both the 900

_(C.M.)

and the 1300

_(C.M.)

elastic

_scattering

excitation functions

_clearly

show a structure. It is well-known

that,

at 900

_(C.M.)

the absence of

odd-partial

waves in the

_{scattering amplitude}

can

_give

more

_pronounced

structure to the

cross-section,

but this argument no

_longer

holds at 1300 where a similar

structure is observed. The 900 excitation function is

quite

comparable

to the 160 + 160 one at the same

angle.

The main differences are in the

peak-to-valley

ratio,

which is

_slightly

smaller

_(though

the limited _energy and

_angular

resolution of this

experi-ment can account for some reduction of this

_value),

and in the absolute values of the

_{cross-sections,}

one order of

_magnitude

smaller for

12C

+

_2°Ne,

even

if the

_identity

of

_particles

in the 160 +

160

_system

is taken into account.

FIG. 2. - Angular distribution of the 12C + 2°Ne elastic

scattering ,

at 24.7 MeV _(C.M.). Full line = _optical model _{predictions with the}

potential of reference [7]. Dashed line = _optical model predictions

As shown in the same

_figure,

the

_experimental

data lie between the

_predictions

of the

_{optical-model}

potential proposed

in reference

_[7]

for

12C

+

2°Ne

and of Gobbi’s

_potential

_[8]

_applied

to the same

system. The latter appears to be too _transparent

whereas the former allows for too much

_absorption.

It is

_interesting

to note that the

_disagreement

between the data and

_predictions

of the

_{optical-model}

poten-tial of reference

_[7]

increases with

_angle.

Such a

conclusion is also

_supported

_by

_figure

2 where the

angular

distribution at 24.7 MeV

_(C.M.)

incident

FIG. 3. - Excitation functions for the reaction channels _1606-7MeV corresponds to the 4 excited states of 160 at 6.05 MeV _(0+), 6.13 MeV (3-), 6.92 MeV (2+) and 7.12 MeV (1-), at _{~c.M. ~} 62~.

In

_figure

3 are

_presented

the excitation functions

for several reaction

channels,

namely

the inelastic

scattering

to the

2+,

(1.63 MeV)

and the

_4+,

_{(4.25 MeV)}

excited states of

2 °Ne,

and the

4-particle

transfers to the

_ground

state and to the 6-7 MeV excitation

energy doublets in 160. These channels were chosen

because of their

_ability

to carry away the

angular

momentum

_brought

in

_by

the entrance channel.

A strong structure

_only

_{appears for the}

4-particle

transfer

_leading

to the

_ground

state

of 160,

for which

the results agree with those of the inverse reaction

studied in reference

_[5].

The lack of structure in the

inelastic

_scattering

excitation function should not

be too

_surprising.

This is

_strongly

reminiscent of

160+

160 inelastic

_scattering

where,

with a

compa-rable

_angular

momentum

_matching,

there is no

structure in the inelastic excitation function.

4-particle

energy is

compared

to the same

optical-model

pre-dictions.

Up

to 700 the _strong decrease of the cross-section with

_angle

_{may be}

_interpreted

as due to a _strong

absorption,

as

_proposed

in reference

_[7].

At more

backward

_angles,

the

_angular

distribution _{is very}

rapidly

oscillating,

with a

period

close to 1 ()ü

_(C.M.).

Even

_though

it does not extend to the utmost back-ward

_angles,

it shows no evidence for an elastic

transfer

contribution,

which would involve a _very

improbable 8-particle

transfer.

transfer to the 6-7 MeV doublets of

160

presents a more

_intriguing

behaviour. From

_1-matching

consi-derations,

the 3 - _{component of these doublets is} in a favorable

_position

and

_according

to the

_analysis

performed

by

Rossner et al.

_[6],

this should

_imply

a

_large

cross

_section,

whereas the

0+,

1- and 2+

levels should exhibit smaller cross sections. The data collected so far

indicate,

quite contrarily,

that the contributions of both

doublets

are of the same order

of

_magnitude.

To elucidate this

_unexpected

and

interesting

behaviour,

a more

_complete

_experimental

and theoretical

_analysis

_{is necessary.}

Finally,

it could be worthwile to mention a small but

_{persistent irregularity}

present on every excitation

function at about 25 MeV. However, such an

irregu-larity

does not _{appear in the}

2°Ne(12C, a)2gSi

data

160 + 16 0 and 180 + 180 systems with

_regard

to both the structure and the

_magnitude

of the cross-sections. This can be related to the fact

_that,

in this

case,

only

few direct reaction channels are able to

carry away the entrance

_angular

momentum, whereas

in the 180 +

180

case, a _very

_large

number of chan-nels exist. In the 160 + 160 case, there are none,

at _{least up} to 30 MeV

_(C.M.)

incident _{energy. As}

the energy

rises,

the still limited number of these

reactions channels

increases,

resulting

in a reduction

of the observed elastic cross-section with however a

persistent

structure

_[10].

In the

1.2C

+

2 °Ne

case,

the

_integrated

cross-sections of these channels

₍₂₊

and 4+ inelastic

_scattering)

were

_crudely

evaluated

and amount to about 100-150 mb. It can be noticed

the intermediate behaviour of the

12C

+ 2°Ne elastic

scattering.

Finally,

the

_study

of the

12c

+

2°Ne

system

confirms

_nicely

that

_angular

momentum

considera-tions

_[3]

can

_provide

a reliable tool for

_predicting

the

qualitative

differences for

_absorption

in

_heavy

ion reactions.

Acknowledgments.

- Three of

us

(H.

_D.,

E. P. and J. C.

_R.)

thank Professor J. Valentin for his kind

hospitality

and the

_cyclotron

crew for efficient

operation.

We thank Professor P. P.

_Singh

and Dr. A.

Weidin-ger for many

enlightening,

discussions.

References

[1] SIEMSSEN, R. H., MAHER, J. V., WEIDINGER, A. and BROMLEY,

D. A., Phys. Rev. Lett. 19 (1967) 369.

[2] See, for instance, SIEMSSEN, R. H. in _Heavy ion _scattering,

Argonne National _{Laboratory Report} ANL 7837 (1971)

unpublished.

[3] VANDENBOSCH, R., in Heavy ion scattering, Argonne National

Laboratory Report ANL 7837 (1971) unpublished.

[4] CHATVIN, R. A., ECK, J. S., ROBSON, D. and RICHTER, A.,

Phys. Rev. C 1 ₍₁₉₇₀₎ 795.

[5] SINGH, P..P. et al., Phys. Rev. Lett. 28 (1972) 1714.

[6] ROSSNER, H. H., HINDERER, G., WEIDINGER, A. and EBERHARD,

K. A., Nucl. Phys. A 218 (1974) 605.

[7] VANDENBOSCH, R., WEBB, M. P. and ZISMAN, M. S., Phys.

Rev. Lett. 33 (1974) 842.

[8] GOBBI, A. et al., Phys. Rev. C 7 ₍₁₉₇₃₎ 30.

[9] COSNAN, E. R. et al., Bull. Am. _Phys. Soc. 18 ₍₁₉₇₃₎ 565.

[10] HALBERT, M. L. et al., Phys. Lett. B 51 (1974) 345.