Compound nucleus formation in the 14N + 16O system

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Compound nucleus formation in the 14N + 16O system

C. Volant, M. Conjeaud, S. Harar, E.F. da Silveira

To cite this version:

C. Volant, M. Conjeaud, S. Harar, E.F. da Silveira. Compound nucleus formation in the 14N + 16O system. Journal de Physique, 1977, 38 (10), pp.1179-1183. �10.1051/jphys:0197700380100117900�.

�jpa-00208685�

COMPOUND NUCLEUS FORMATION IN THE 14N + 16O SYSTEM

C.

VOLANT,

^M.

CONJEAUD,

^{S. HARAR and E. F.} DA SILVEIRA

(*) Département

^de

Physique Nucléaire,

^CEN

Saclay,

^BP

^2,

⁹¹¹⁹⁰

Gif-sur-Yvette,

^France

(Reçu

^le

17 juin 1977, accepté

^le

30 juin 1977)

Résumé. ^- La formation du noyau

composé

^30P par la voie d’entrée 14N + 16O a été étudiée pour des énergies incidentes de

E(14N)

^{= 20 à} 60 MeV. On compare la

population

des états indivi- duels observés dans les voies de sortie d + 28Si et 6Li +

24Mg

^aux prévisions ^{du modèle} statistique

Hauser-Feshbach. Pour des énergies incidentes supérieures ^{à 30 MeV, on} constate que les valeurs des moments angulaires maximaux contribuant au processus de fusion ^sont inférieures à celles des moments angulaires ^à l’effleurement

disponibles

dans la voie d’entrée.

Abstract. ^- The formation of the 30P

compound

^nucleus by ^{the 14N} + 16O incident channel has been studied from

E(14N)

^{= 20 to 60 MeV lab. The} population ^of individual states observed in the d + 28Si and 6Li +

24Mg

outgoing ^{channels are} compared ^to predictions of the Hauser-Feshbach statistical model. For incident energies higher ^{than 30 MeV the maximum} angular ^{momenta contribut-} ing ^{to the} fusion process ^are found smaller than the grazing angular ^momenta available in the incom-

ing ^channel.

LE JOURNAL DE PHYSIQUE

Classification

Physics ^Abstracts

12.30

1. Introduction. ^- The

study

^{of the formation}

and

particle

de-excitation of s-d shell

compound

nuclei has been the

subject recently

^{of a}

large

^amount

of interest.

Particularly, by

^the

analysis

^{in the frame-}

work of the statistical

theory

of well-chosen

decay channels,

^{it has} been shown

(ref. ^[1]

and references

therein) ^that,

for incident

energies larger

^{than a}

certain

.value,

all available

angular

^{momenta in the}

entrance channel do not contribute to the

compound

nucleus formation. More

precisely,

^for

^{the 14N} + 12C

system ^{over a}

large

^incident range, it has been

possible, by

the Hauser-Feshbach

(HF) analysis

^{of the}

12C(14N’ 6Li)2 ONe

^reaction

producing

discrete levels of

2oNe,

^to determine the maximum values of

angular

momenta

(so-called

^critical

angular

^momenta

Jcr)

which contribute to the

compound

^{nucleus formation.}

In the present paper ^we shall use the same method for the 14N

+ 160

_system.

2.

Experimental procedure. - The 14N 5 +,6 +

beams from the FN Tandem Van de Graaff of

Saclay

^have

been used with incident

energies ranging

^{from 20}

to 60 MeV.

The 160

_targets have been made of silicon oxides of natural

isotopic composition, typically

^the

repartition

was 30

gg/CM2

of silicon and 20

gg/CM2

^of oxygen ;

they

^{had also a thin}

deposit

^of

gold (about

¹

gg/cm 2 )

for

monitoring

purposes. The elastic

scattering

^{at small}

angles

^of

low-energy alpha particles

^{on these} targets has been used to evaluate their

thicknesses,

^{the beam}

current has been

integrated

^{in a}

Faraday

cup and Rutherford

scattering

has been assumed. The uncer-

tainties in the absolute

cross-sections, mainly

^{due to}

errors in these

thicknesses,

^are estimated ^at about

40 %.

The detection and identification of the reaction

products

have been achieved

by

conventional AE x E solid-state counter

telescopes

^and

light particles

^{up to}

lithium were discriminated. A monitor recorded the elastic

scattering

^of

nitrogen projectiles

^{at forward}

angles,

^the

scattering

^on

gold being

^{used for norma-}

lization of the different runs for the excitation function measurements.

It has been

possible

to extract the contributions of reactions

occurring

^on target

contaminants, mainly

on

carbon,

because for each measured _energy the same

reactions were recorded on a pure

12C

_target; the results of this

study

^have

already

^{been described}

elsewhere

(ref. [1]).

^We have also checked that the silicon made no contribution ^to the studied processes.

The energy resolution was

typically

^{200 keV}

(FWHM)

or better. In the

following, only

the first low

lying

residual levels will be considered _up to around 9 MeV in

24Mg

^{and 7 MeV in}

^28Si

^{which are}

regions

^where

the level schemes are well known.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0197700380100117900

1180

3.

Comparison

between HF calculations and

experi-

mental data. ^- The

(14N, ’Li)

^{reaction on}

^12C

^has

been shown

[1]

^to

proceed essentially through

^a

compound

nucleus formation in the same incident energy range and we can expect ^{the same mechanism} for this reaction induced

on 160.

Indeed

experimental

features such as the

symmetry

^{about 900} observed for the

angular

distributions

(Fig. 1)

favour this inter-

pretation.

^{For the}

(14N, d)

reaction such a mechanism is also

highly probable.

^The

following analysis

ⁱⁿ

terms of statistical treatment of the

compound

^nucleus

decay

will prove

also, a posteriori,

that such an

assumption

^{is valid.}

FIG. 1. ^- Angular distributions of the 16o(14N, 6Li)24Mg ^reaction

at 45 MeV, ^the 24Mg ^{levels are labelled} by their excitation _energy,

spin ^and parity. The effects of various cut-off in the HF summa-

tion (1) is illustrated for the first 2+ state ; the dashed ^curve is the HF result when the sum is made _up to negligible contributions, the dotted curves are for Ycr ^{= 16 and 14 h} (upper ^{and lower} respec-

tively), the solid curves are the best fit obtained over all states

(J,, ^{= 15} h).

The method of the

present

^HF

analysis

^has

already

been described

extensively [1]

^and

here, only

^{a few}

points

^{will be}

pointed

^out.

The HF average cross-section for a

given outgoing

channel can be

expanded

^{in terms of}

partial

^cross-

sections :

where

Q(J)

^{are the} contributions from different

angular

momenta of the

compound

^nucleus.

This behaviour was observed in reference

[1],

^the

main contributions to the cross-sections of states

populated through

^the

(14N, ’Li)

^{reaction come from}

higher compound

^nucleus

angular

^{momenta than for}

the

(14N, d)

^channels.

Hence,

^{if a maximum}

angular

momentum

Jcr

^{has to} be assumed in

expression (1),

^the

(14N, ’Li)

channels will be more sensitive to this

limit ; furthermore,

^if another channel such ^as the

(14N, d)

^{one is not affected}

by

^this

cut-off,

^an agree-

ment between deuteron

experimental

cross-sections and theoretical

predictions

^will

give

confidence in the parameters used in the HF

analysis

^{and the value}

of

Jcr

will be the main free

parameter

^{to fit the cross-} sections of the

(14N, ’Li)

^channels.

In

figure 2,

^the

experimental

excitation functions of

a few

28Si

^states are

compared

^{to HF}

predictions

obtained when the summation

(1)

^is

computed

up ^to J values for which the contributions of

higher

^{J’s are}

negligible.

^A

satisfactory

agreement in both relative and absolute values is obtained. The restriction of the

FIG. 2. ^- Excitation functions of the 160e4N, d)28Si ^{reaction at}

150, ^the curves are the results of HF calculations without _any normalization.

measurements to one

angle

^with energy

steps

^{of 5 MeV} in the

laboratory

system ^{is not too}

important

^{since the}

behaviour of

angular

distributions and excitation functions for such systems ^{are known to be rather} smooth

(ref. [1]).

^{Moreover the}

^agreement

^{with the HF}

predictions

indicates that this

assumption

is reasonable and that

experimental

conditions ensured

adequate averaging

of fluctuations.

In

figure 3,

^we

present

the excitation functions for several states of

24Mg

^{recorded at}

9lab

^{= 15°. The}

curves are the HF results

using

^{the same}

parameters

as in

figure 2 ;

^{the dashed ones are} obtained when the summation

(1)

^is

performed

up ^to

negligible

^contri-

butions. At low incident

energies

^the relative and absolute cross-sections are

again

^well

reproduced;

however,

^for

energies greater

^{than 35}

MeV,

^the

predicted

^{values are too}

large.

^{The solid curves in}

figure

^{3 are HF results when}

limiting

^{the summa-}

tion

(1)

^{to a value}

Vcr

^{chosen at each} energy

(>,

³⁵

MeV)

to fit the

experimental

cross-sections

(see

^Table

I).

The same

aspect

is observed for the excitation func- tions of the

160(14 N , 6Li)24Mg

reaction measured at 22.5° between 40 and 60 MeV incident

energies

(Fig. 4) showing

that the restriction of the measure-

FIG. 3. ^- Excitation functions of the 160e4N, 6Li)24Mg ^reaction

at 15°, the curves are the results of HF calculations not normalized to the data. The dashed curves are obtained without limitation in the sum (1), ^{the solid ones are} the results when using ^the Jcr ^values

given ^{in table I.}

FIG. 4. ^- Excitation functions of the 160e4N, 6Li)24Mg ^reaction

at 22.50. The curves are HF results obtained in the same way ^as in

figure ^3.

ments to a few

angles

^{is not} crucial since the

angular

distributions are smooth and well

predicted by

^{the HF}

calculations

(see

^also

Fig. 1).

TABLE I

Comparison

between deduced critical

angular

^momenta

and

grazing angular

^momenta

On

figure 1,

^{for the case} of the first 2+ state of

24Mg,

is illustrated the

sensitivity

of the calculated differen- tial cross-sections to variations of the

Jcr

^values

by

± I h around ^the best fit value

(15 h) ;

^the

curve

obtained without limitation in _eq.

(1)

^{is also}

drawn;

similar effects are observed for the other residual states.

In table I the

Jcr

^{values are}

given

^and

compared

^to

the

Jg,

^values

^(taken

^{as the}

angular

^{momenta for which}

the transmission coefficients of the entrance channel

are

equal

^{to one}

half).

4. Discussion of the

parameters.

^- The crucial

point

^{of the HF} calculations is the determination of the denominator

G(J)

^which describes all the

possible decay

^modes open ^to the

compound

nucleus. The

parameters

used have been taken from the literature and are

given

^{in table II}

(the

^{notations are standard}

and the same as in reference

[1]).

It can be

pointed

^out that the level

density

para- meters

by

themselves are not of real

importance

^{in the}

determination

of lcr

values since the denominator

G(J)

is checked

experimentally,

^{as a}

whole, by comparison

of the HF calculations with

the 160(14N, d)28Si data;

the extension towards

larger

^J values needed to cal- culate the

16Q(14N, 6Li)24Mg

reaction cross-sections

assumes standard behaviours for

G(J)

^and may ^not introduce

large

^errors.

For

evaluating

the theoretical cross-sections of the

( 14N, d)

^and

( 14N, 6 Li)

^{reactions at low}

energies (20-25 MeV),

^the p ⁺

29 Si

channel is the most

impor-

tant one, but at

higher energies (35-40 MeV)

^both

p ⁺

29Si

and a +

26 Al

channels contribute

mainly

to the calculated cross-sections and the

agreement

^with

the

experimental

^data

gives

confidence in the choice of the parameters ^{used to describe}

G(J).

^{The trends}

of

G(J)

^and

6(J)

for the studied cases are shown in

figure

^{5 for}

E(14N)

^{= 35 MeV.}

At

energies higher

^{than 40 MeV the}

(14N, d)

^reac-

tion cross-sections for low

lying

^{states of}

^28Si

^are very small and have not been measured. In the case studied

1182

TABLE II

Level

density

parameters ^and

optical

model parameters

(’) Imaginary wells of surface type, ^{the other sets are of volume} type. Optical parameters ^{from :} (p) ^Ref. [2] ; (6) ^Ref. [3] ; (C) ^Ref. [4] ; (d) ^Ref. [5] ; (e) ^Ref. [6] ; (f) ^Ref. [7] ; (9) ^Ref. [8]. ^Level density parameters ^{from :} (‘) ^Ref. [9] ; (j) ^{Deduced from Ref.} [9] ; (k) ^Ref. [10].

FIG. 5. ^- Contributions of the _{main open} channels to the HF denominator G(J) ^{at an} excitation energy of 36.99 MeV in the 3op compound ^nucleus (left part), ^HF predictions ^{for the} 6(J) expansion

of some states of 24Mg ^{and 28Si at 35MeV incident} energy (right part).

in reference

[1],

^{the a}

outgoing

^channel

^remained,

whatever the incident _energy, the most

important

^one

in

determining

^the

(14N, ^6Li)

^reaction

cross-section ;

then it was reasonable to assume that the low _energy

. data had well defined the parameters ^{needed to com-} pute the denominator. In

the 14N + 160

^{case this is no}

more true since at

high

energy

(>

⁴⁰

MeV)

^the present ^HF calculations

predict large

contributions of the

’Li

+

25Mg outgoing

^{channel to the denomi-}

nator

G(J).

This channel becomes the most

important

one for

high angular

^{momenta of the}

compound

nucleus and

consequently

influences

strongly

^the

6Li

+

24Mg outgoing channel;

^{this is} illustrated at 60 MeV incident _energy in

figure

^{6 where are}

drawn

G(J)

^and

u(J)

^{for the two first}

24Mg

^states.

The

5 Li

ions

being

^{unstable it is not} easy ^to check

experimentally

^the

importance

^{of this}

^channel;

^thus

we describe it with the same rules as we treated other

FIG. 6. ^- The HF denominator G(J) ^{is drawn for the 3°P com-} pound ^{nucleus at an} excitation _energy of 50.32 MeV

(E(14N)

^{= 60} MeV);

the a(J) expansions ^are also shown for the two first 24Mg ^states (upper right corner).

channels. On the other

hand,

^as checked in similar situations

(ref. [1]),

the contribution of discrete levels in the

G(J)

denominator is not

important;

^{so we}

neglect

^{it in most} of the calculations.

Another

difficulty

of this method arises from the choice of

optical

^model

parameters

^{for the}

outgoing

channels. Both in this work and in reference

[1]

^the

parameters

^found

by Bethge et

^al.

[7]

for incident

energies

^{of 20 MeV} have been used

because,

^{for a}

large part

^{of the incident} energy range, the

6Li

ions cor-

responding

^{to the}

decays

^{towards the} studied discrete

residual levels have

energies

around these

values ;

^the

same arguments ^{are also}

valid,

^{to a lesser} extent, ^for the

description

^{of the}

^{5 Li}

⁺

25Mg

channel if one

makes the

assumption

^{that the 5Li}

scattering

^{can be}

described

by

^{the same}

optical

^model

parameters

^as the

’Li

ions. When

using typical heavy

^ion para- meters

[8, 11]

^the

(14N, 6Li)

cross-sections are under- estimated

by

^{about an order of}

magnitude

^{at low}

incident

energies ;

^{it can} be also noticed that these

parameters largely

^{fail to}

reproduce

^{the data of}

reference

[7].

Finally,

^{it can be}

pointed

^out that the results of the

present

^{method of}

determining

^critical

angular

momenta have been confirmed for the

14N

+

12C system by

^direct measurements of the fusion cross-

section

[12].

5. Discussion of the results. ^-

By studying

^a

parti-

cular

decay

^{mode of the 30p}

compound

^{nucleus we}

found that between 35 and 60 MeV the fusion of the

14N

+

160

_system is limited

by Jc,

values which

are lower than the

angular

^momenta available in the entrance channel. The

understanding

of this limitation in the fusion of

light

systems ^{is still a}

challenging problem :

^{the 30p}

compound

^nucleus itself could not be able to accept ^so

high angular

^{momenta as}

Jgr

between 37 and 50 MeV excitation _energy and our

deduced

Ycr

values would be a determination of the yrast

line;

^{on the other}

hand,

^entrance channel effects could be an alternative _way to

interprete

the limitation of the fusion of the

two 14 N and 160

ions

[13].

^Unfor-

tunately,

up ^{to now,} the models to evaluate both effects are too crude to

distinguish

^{between the two}

possibilities. Experimentally

the studies of the same

decay

channels after the formation of the

compound

nucleus with another entrance channel could

help

^to

remove this

ambiguity.

Another

interesting point

^{is to} relate the

Jcr

^values

to the fusion cross-sections of the two

ions,

^{this is}

drawn in

figure

^{7 and}

compared

^to the reaction cross-

sections

predicted by

calculations

using

^{two different}

optical

^model

parameter

^sets for the elastic

scattering.

The errors on

Jrr

values have been taken to be ± I h

(see Fig. 1)

^to estimate the uncertainties in the fusion cross-sections. It can be seen on

figure

^{7 that}

depar-

tures from the reaction cross-sections are

significant.

A

tendency

^{for a structure in} this excitation function is also _seen;

independently

^{of the}

analysis

this effect could

already

be observed on

figures

^{3 and 4 where the}

excitation functions at

high

energy remain about constant whereas one could

expect

^a decrease of the cross-sections when

increasing

^{the incident} energy.

To check the existence of the structures observed in the excitation function of the

160(14N, 6Li)24Mg

reaction and to confirm the

presently

deduced critical

angular

momenta, it would be _very useful to measure

complete

fusion cross-sections of the 14N +

164

system

by detecting

^the

evaporation

^residues.

We wish to thank S. M. Lee and A.

Lepine

^for

fruitful discussions and

helps during experiments.

FIG. 7. ^- Fusion cross-sections deduced from the Jcr ^values given

in table I, ^the curves are the calculated reaction cross-sections using

two different sets of optical parameters : ^curve (1), parameters ^from reference [8] (see ^Table I) ; ^curve (2) ^set from reference [14]

(V ^{= 100}

/MeV,

^{W = 27 MeV), R = 5.87 fm, Rj = 6.21 fm,}

Rc ^{= 6.90} fm).

References

[1] VOLANT, C., CONJEAUD, M., HARAR, S., LEE, S. M., LÉPINE, ^A.

and DA SILVEIRA, ^E. F., ^Nucl. Phys. ^{A 238} (1975) ^120.

[2] BADAWY, I., ^Private communication.

[3] HODGSON, ^P. E., ^The optical ^model of ^elastic scattering (Cla- rendon Press, Oxford) ^1963.

[4] HÖHN, J., POSE, H., SEELIGER, ^{D. and} REIF, R., Nucl. Phys.

A 134 (1969) ^289.

[5] MERMAZ, ^M. C., WHITTEN, C. A. Jr and BROMLEY, ^D. A., Phys. ^{Rev. 187} (1969) ^1466.

[6] BARNARD, ^{R. W.} and JONES, ^G. D., ^Nucl. Phys. ^{A 108} (1968)

641.

[7] BETHGE, K., Fou, ^{C. M. and} ZURMÜHLE, ^R. W., Nucl. Phys.

A 123 (1969) ^521.

[8] ^{SIEMSSEN, R. H.,} Heavy ^ion scattering, Argonne ^{25-26 march} 1971, ^{ANL 7837} (1971) ^145.

[9] GILBERT, A. and CAMERON, ^{A. G.} W., ^{Can. J.} Phys. ⁴³ (1965) 1446.

[10] FACCHINI, ^{U. and} SAETTA-MENICHELLA, E., Energ. ^{Nucl. 15} (1968) 54.

[11] KLAPDOR, H. V., ROSNER, G., REISS, ^H. and SCHRADER, M., Nucl. Phys. ^{A 244} (1975) ^157.

[12] CONJEAUD, M., GARY, S., HARAR, ^{S. and} WIELECZKO, ^J. P., Proceedings ^{of the} European Conference on nuclear

physics ^with heavy ^ions (Caen September 1976) ^116.

WIELECZKO, ^J. P., ^Thesis Orsay (1977).

[13] GLAS, ^{D. and} MOSEL, U., ^Nucl. Phys. ^{A 237} (1975) ^429.

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