PHYSICA L RE VIEW C VOLUME 11, NUMB ER 3 MARCH 1975

Pre-equilibrium alpha emission induced by different incident channels:

Evidence for alpha preformation in nuclei

A. Chevarier, N. Chevarier, A. Demeyer, G. Hollinger, P. Pertosa, and Tran Minh DucInstitut de Physique Nucleaire, Universite Claude Be~nard Lyon-I and IN2P3,

43 Bd du 11 novembre 1918, 69621 Villeurbanne, France(Received 23 July 1974)

A study of n emission induced by different incident channels has been undertaken. Mea-surements of energy spectra and angular distributions of cv particles emitted in proton-,deuteron-, 3He-, and e-induced reactions were performed. An analysis in the frame of thepre-equilibrium model succeeds in giving an over-all description of all particle spectra. Thee particle being in this approach considered as an exciton, a preformation factor around 0.2for four nucleons to be correlated as an e particle has been obtained. The n preformationprobability deduced from this analysis is independent of the proton, deuteron, He incidentchannel, incident energy, and mass of target nuclei.

NUCLEAR REACTIONS ~Fe, 5 Co, 66Zn, 118Sn, 9Bi(p, e); ~6Fe(d, n); Mn,5~Fe, ~Pb(3He, ~) Fe, 6~Cu, 11'In Pb(n, n') measured o{E„,0) deduced

reaction mechanism.

I. INTRODUCTION

Pre-equilibrium models account for the emis-sion from different intermediate states leadingthrough two body interactions to the compound nu-cleus. Recently, an evaluation of the intermediatestate lifetime has been proposed' ' allowing thecalculation of absolute cross sections. Moreover,the hybrid model' takes into account the reactiongeometry dependence and nuclear matter distribu-tion. Pre-equilibrium models have been proposedfor nucleon emission; however, the inclusion ofn emission in these formalisms is possible undersome assumptions.

Up to now the e pre-equilibrium emission hasbeen mostly studied in the case of neutron- ' andproton-induced' reactions on heavy mas s tar getnuclei. In such analyses, the first step of the re-action has been characterized by an initial con-figuration of three excitons corresponding to aknock-out mechanism. Such conditions imply aprobability for four nucleons to be correlated in

an a-like structure considered as an exciton. Thea preformation probability deduced in such ananalysis varies from 0, 1 to 0.8 in the mass rangeinvolved (140&A& 200).

In order to get more accurate information con-cerning n preformation probability, we have un-dertaken a study of the n pre-equilibrium emissioncorresponding to proton, deuteron, and 'He inci-dent channels leading to the same composite sys-

(58co60Ni 67Gn1 19Sb210po)

II. EXPERIMENTAL METHOD AND RESULTS

n particle energy spectra and angular distribu-tions have been measured for proton-, deuteron-,'He-, and n-induced reactions. The compound nu-clei and the excitation energies involved are givenin Table I.

The measurements have been performed on thesynchrocyclotron of the Institut de Physique Nu-cleaire de Lyon in the case of n- and deuteron-in-duced reactions and on the cyclotron of the Institut

TABLE I. Studied reactions.

Compositesystems

"CoE*=39 MeV E*=57.2 MeV

GaE*=55.5 MeV

119Sb

E*=55.5 MeV

210po

E*=48.2 Me V

Reactionsinvolved

"Fe(P, o.)Ep =32 MeV

Fe(d, e)E& =27.5 MeV

"Mn('He, ~)E3 ——22 MeV

He

"Co(p, 0.)E& =48 MeV

56Fe(e, 0. ')E~ = 54.8 Me V

"Fe('He, e)E3 =41.4 MeV

He

66Zn(p, e)Ep = 50.5 MeV

63Cu(e, cv')E~=54.8 MeV

'"Sn(p, n)Ep =50.5 Mev

"'In(0. , e')E„=54.8 MeV

209B.(pEp =43 MeV

206pb(cv, G. ')E~=54.8 MeV

207 Pb (3IIe ~)E&

——41.4 MeV'He

886

I

(a)

PRE F ~BR~UMM ALPHA MrSS D ByON INDUCE

59Co (p, a) 12 Mey'

0.1

(b) 209' (P, e)

~ ~~ ~

4

0 ~4

0.1

001 o 20+ 3go

6goggo

~ 150

~ A

A

AQ

~ 2 +4) o+~~ + ++0

+4A

+ Qo

4++ 0

+0~ A

0+ o

oo

0001~ 300p 6go~ 750A ggo

12go

150O

~ 0

001

A g~ pp

~0

AA ~ 0

~ 4A ~A

A pA P

Cg

Q +

+++

+++

+Ag

+

++ AgA

+oo

I

10

I

20I

40~ (Mey)

I

30I

30 9g 150

8 (g«)

(a)

4

I

40

30I

'

(

50 30 90 15gI

~IG. y

8 (deg)20

~ partic]e sp t

40 50

ec ra and an~1gu ar di

e (Mey)

I

a ' Co(p' ns from (a) &9 0

I

»(P, e

I

reactions

I

E1 ~

U

U Q"a

0.1

001

57Fe( He, ~)

h4 ~

4~4

~4+

QA +

+ +

+.~ y ++

00~~+ a0 0 8 +++++ ~

+ +

20.1

U

M QU

001

(b)

4 ~~44 444 ~

~44 4 44 ~ ~

~ 4h4

44

~ 44

+

~ + + ++ +

++

++

+ ~++

~g JgS+ ++

+ ++

0 sgkp

0 0 8

eAoo

Ao

Ap

QQ ~4~5

8 0

000

A 0

4

I

10

~ 300+ 60O

8 900P 12Qo

16g 0

I

20I

30

ag ~AQA

0 ~0 g0 A

g

0 ~A

Nl.

40e (Mey)

pec tra

4o

~ 80 g

~ 450+ 60o

9oo 140o

16go

I

20I I

a

30 90 1508 (deg)

istribution fs rom

0AAA A

0.00100

0

2Q7

0

p3

COQ

b(H, ~) kk0

I

o

10I I

30 4gI

30 90 15g

(a) ~7q

e (Mep)

) and (b) 207 Pb 3

8 (Beg}

('He, ~) react;

11

ferred to a ca computer in orde opn corrections leadin

e usual

e center-of-ue

case of heav y mass tar e-mass system In

contaminatiogets, the light 1

f 11y i a . t

e spectra diRVO1

y elastic scatterio ead

Typical spectra d gura and an 1'

on

ombardments leadinea ing to "Nigo,'-d f...e,

t e

umming in 1 M

ener-

e eads to the totegra-

~ ~ ~

e spectra show an'

Re

qui lbrium contribut'an important pre-

fereri ution. The corn p

'nfl hes e shape of the fA

e

nucleae-integrated spe- spectra.

e omi-

ear react'ons 'd

, the main corn onenge nuclei near

t d rium onesd pre-equilib 'y the evapora-

ngle-integrated s, are visible in th

tar etout.

ra ive part is practicallic y washed

888 HE VAR1E R

3des clences Nuclc eaires de Gr( He, &) reactt

G«noble for (p'lo~. Self,u

and

Fe, "Co e~C «- PPorting targets (55M

tng mg/

eavier mass l . P 'f mg/cm' fs nuclei PRrtlcl

or the

range of emis '. c es over the wh 1

ssion ener w

oe

three silico d' '

on etector t 1

gy were detected 'thWl R

o e esco e.our detector t

cessary; the last delescope was

etector waspulses arising fro

used to cancel

in orrom elasticl s

cR ion

The particle id ' ' asi entification wase c '

u lng methodsing

tion of which h1CR

bod, a detailed d

een iv

~ ~

'on was acc tura e enough to eg'ven. This id tien

lnction between 'H eand no ensure a clea d'r is-

por tant in th e ca.se of the ('Heparticles which

'1S im-

calculation of th e detec 'e He, o. ) reaction. Th

inte r

e

g~ion solid an

oferi ied throu h

r scattering on old

sg

'"(leved usin "'

e as i and inelastic sc

Energy sspectra were measured '

e experimental dataa were trans-

56Fe (a, a')

(b)206

Ph (a, a') e,eeee~e

21

~bU

0.1

001

~gtyp ~+I ~e

4 ~ eee

0

+ app4 00+4 00 0

0

+ 4

ee

21

M Q

L

e000 00 0

0 000

+ ~$+&~ «a 0

ay +4~ o4 0

+ 4 0

+pp

+ +000pp

044

4

+ aa

4

0 pOp 0

00 0.1 ~

g+L ~

+ 4 a

L++ +

+

L++++

04+

L0.01

~ 3040

0 600~ 90+ 1200

1500e 30L 500 754 90

120+ 140

L+ +

I

40I

10

I

30I

20 30 90 150

8 (Jeg)10

I

++

I

40 50 30 90 150I

FIG. 3. n ar '

e(MeV) e (d eg)

20 30 50I u I

particle spectra and an I.ra and angul. ar distributi f

e (MeV )

a and an I.' ' ions from (a) 56FeFe(e, a') and (b) 20 Pb 0' &'Pb(0., e') reactions.

PRE-EQUILIBRIUM ALPHA EMISSION INDUCED BY.. . 889

III. ANALYSIS

A. Formalism

The initial formulation of the pre-equilibriummodel proposed by Griffin' has been improved by

many authors. Different approaches were devel-oped in order to obtain an absolute cross sectionevaluation. ' 4 In the hybrid model, ' the decayprobability for a particle of type x and energy be-tween c and a+de can be written as

p. , (I7) ~.( )(E) 1() 1 ()

06n =+g

0.1

&x

~ Mn ( He, u)56

x Fe (d, ajh.xg 57

QXO Fe(p, n j~x+~x~ E= 39 MeVx~ x ~~y ~X ~ ~

~ "xb,~ XX

x exxX

X

X

x

10He, 1x)

x (I -P„, ,),—n' =n0

where nP, is the number of excited particles ofthe type x which are in an n particle-hole state.

~ ~

10

0g~a ~ 00 oo~ 0

0 0 0~ o 0OO OOO 10—

~ e ~ ~ ~ ~

57~ Fe ( He, n)

59co(p, u)01 56

o Fe (n, a')57.2MeV

10E= 48.2 MeV

00

0~ ~

0~

o

( )0

~ ~ 0~ ~ ~ ~

h ~

0.1

10

0.1

&07 3~ Pb ( He, u)

2060 Pb (a, n')

2098i (p, n)

0.1II

I

I

10

1

20I

40I

50

E~ (MeV)

I

10

I

20I

30E„(meV)

FIG. 4. Comparison of integrated over angI. es spectrain the case of (a) Co, (b) Ni, and (c) Po compositesystems.

FIG. 5. The angle-integrated energy distribution of eparticI. es emitted from 58Co composite systems comparedwith hybrid model calculations.

890 A. CHEVABIEB et al.

TABLE II. Slope analysis.

Reactions Slope

Initialexcitonsnumber

Initial possibleconfiguration

Predominantreaction

mechanis m

(P, ~)(d, e)('I-Ie, ~)(e, e')

1 & S(1.4S= 0.8

0.3 & S(0.6S —0.2

1proton, le, 1hole1', 2 holesln, 1 hole1e, 1 degree

of freedom

KnockoutDouble pickup

PickupInelastic

scattering

p„,(U) represents the state density in the residualnucleus at the excitation energy U, p„,(E) the in-termediate state density, and g the single particlestate density. A. ,(e) and A. „(e) a.re the transitionrates for emission into continuum and for internaltransitions, respectively. Finally, the third set ofbrackets in Eq. (1) gives the fraction of the initialcross section remaining after particle emissionfrom preceding intermediate states. The transi-tion rates for emission into continuum are de-duced from the detailed balance principle and theintranuclear transition rates are evaluated usingthe optical model.

Geometrical considerations have been includedin the case of emission from the initial excitedstate. The contribution of each zone of the nucleusdetermined by the impact parameter of the incidentparticle is taken into account. The expression forthe particle spectrum is then:

50

10

e (u, u'j

0r ~

~ ~

50

//

/l

I

10

excited nucleus, a probability P for four nucleonsto be correlated in an n-like structure. This eparticle is considered as an exciton correspondingto a state density g„=4g; moreover, intranuclear

l=o

T, is the transmission coefficient correspondingto the partial wave l of the incident particle.P„(e, l) is defined in Eq. (1) where A. +(e, 1) andA.,(e) are expressed as

0 ~ 0 ~

W(B) and o;„„(e)are the imaginary optical potentialand the inverse cross section corresponding to theemitted particle. Transmission coefficients andinverse cross sections for nucleons are takenfrom tables. ' In the case of deuterons, 'He, andu particles the values are calculated using theMagali code" with optical parameters taken fromRefs. 11-14. The single particle level density istaken as g= 6A/8w' (neutron and proton state den-sities being g„=g~ =;g), the evaporative part beingcalculated with the same parameter.

In order to use the above presented formalismin the analysis of precompound n emission, wemake the following hypothesis: There is, in the

10

10 20 40F~ fMeVJ

FIG. 6. The angle-integrated energy distribution of eparticles emitted from 6 Ni composite systems comparedwith hybrid model calculations.

PRE-EQUILIBRIUM ALPHA EMISSION INDUCED BY. . . 891

10

10

u ((», (»')

transition rate and transmission coefficients havebeen obtained with the same optical parameters.

B. Integrated spectra analysis

The pre-equilibrium calculations are performedby taking initial exciton numbers deduced from theslope method. " Such analysis is performed on 30'spectra and results obtained are summarized inTable II. The uncertainties pointed for (P, n) and

('He, a) reactions correspond to a slight increa, sefor the calculated slopes from the heavier to light-er targets. The initial exciton nu~ber so deter-mined corresponds to the dominant mechanism in-volved. As shown in Table II, a knock-out mecha-nism dominates in the first step of the pre-equilib-rium emission in the case of the (P, o.) reactionwhile (d, o.) and ('He, ot) reactions go preferably

10 20 30 40E„(me@)

FIG. 7. The angle-integrated energy distribution of nparticles emitted from 67Ga composite systems comparedwith hybrid model calculations.

E10

)E

104I~~

'rm/n ((», (»')

0~g «V

0.1

~ ~ ~ ~r

7 3Pb ( He, (»)

0.1

o~ ~ ~

0.1 0.1

I

10

I

20I

30I

40I

50E (meV)

10

I

20 30 40 50(me@)

FIG. 8. The angle-integrated energy distribution of o.'

particl. es emitted from 9Sb composite systems com-pared with hybrid model calculations.

FIG. 9. The angle-integrated energy distribution of eparticl. es emitted from OPo composite systems com-pared with hybrid model calculations.

11

TABLE III. Values of the I'~ factor deduced from a pre-equilibrium analysis.

ReactionsReactions

(P, 0.)

Reactions(p, ~)Ref. 16

Reactions(e, e')

"Fe(d, e) 0.12

"Mn('He, ~) 0.125~Fe(3He, n) 0.1

Pb(3He, n) 0.25

59go66Zn

"'Sn20 9I3i

0.13

0.180.14

0.160.22

54 [39 MeV(62 MeV

89m 62 MeVPSn 62 MeV

»~ $39 MeV162 MeV

0.160.120.150.160.250.2

631.uii5I

"'Pb

0.4

0 40.6

0.8

through a double and simple pickup mechanism.fn the case of the (n, o. ') reaction, the degree offreedom left stands for a collective excitation.

In this analysis, the probability I' of findingfour correlated nucleons in an a-like structure inthe excited nuclei is left as a free parameter. Thefits obtained are shown in Figs. 5-9, on which thecalculated spectra are drawn in full lines whilepre-equilibrium contributions are represented indashed lines. The values of I'~ corresponding tothe fits obtained are given in Table III.

The agreement of theoretical calculations andexperimental data is good, the hybrid model givinga correct description of the shape of particle spec-tra as well as of their amplitude. In the case of(P, n), (d, o.'), and ('He, n) reactions the value ofthe probability P deduced from this analysisstands between 0.1 and 0.2. This factor is similarfor proton-, deuteron-, and 'He-induced reactionsand is slightly more important, for heavy masstargets. In the case of (n, n') reactions the inci-dent n particle seems to keep its integrity parti-cularly for heavy mass targets. We extended such

analysis to the Bertrand and Peelle" measure-ments on (P, n) reactions for ' ie, "Y, ' 'Sn, and

Bi targets at 39 and 62 MeV incident energies.As shown in Table III the deduced values of I'are similar for the two incident energies involvedwith our own data.

The probability for four nucleons to be corre-lated in an n-like structure at medium excitationenergy (40 MeV &E & 'lO MeV) seems to be a prop-erty of nuclear matter. Such correlation is pre-dominantly on the surface of the nucleus. Clearexperimental evidence for this is seen in Fig. 10on which it is shown that the probability for epre-equilibrium emission varies as the inverse ofthe cube root of the target mass number as ex-pected for peripheral collisions. This result fol-lows from analysis of the e spectra measured inproton-induced reactions either by Bertrand andPeelle" or in our experimental data. Moreover,

E

b100

10—

Qx

oPqt 5A

510

Pjp(x 70)

50I

100I

150I

200

0.5

l

0. 1

FIG. 10. Variation of the probability of pre-equili-brium e emission with A [0(z„p2p Mev) is the crosssection for pre-equilibrium e particle emission, o~ isthe total reaction cross sectionj . Bertrand and Peelleresults: e carbon; (3 oxygen; a aluminium; 0 iron;o yttrium; + tin; bismuth; t lead. Lyon group re-sul.ts: k cobalt; a zinc; a tin; z bismuth.

70 15

8 R (fm)

FIG. 11. Theoretical geometry dependence of totalreactions cross section ( ) and G.' particle emission(---) in the Co(P, e) case. In addition, the distributionof matter density (Ref. 19) for this nucleus is given.

PRE-EQUILIBRIUM ALPHA EMISSION INDUCED BY.. . 893

from a theoretical point of view it can be stressed(Fig. 11}that the largest part of calculated emis-sion arises from the diffuse edge of the nucleus.These observations agree very well with calcula-tions of Clark and Wang" which conclude that 20%clustering is possible when nuclear matter densityis less than 0.9 of the central density.

The so deduced P absolute values can be uncer-tain but the stability of such results is interestingin itself. As pre-equilibrium emission corre-sponds to a large part of the total cross section,such observation could reflect an average behaviorof correlation between nucleons in excited nuclei.Such results are confirmed by the backward angleanalysis.

C. Backward angle analysis

10

Because the concept of intermediate states sug-gests that their lifetime must be intermediate be-tween the transit time of the incident particle andthe relaxation time, then backward angles must bea good case to see whether they exist. The com-

10

10

bX

b~4g

xIIx

x4 &x

l

50

10E

44 ~e- 140'

10

10

10

4 g

P o0

0b, ~

0

o~ 4 o

000 0

I

10 20 30

4~4+4

~4 ~

y4

X» 4

50F (MeVJ

10

70

10

10

h ~45 ~ 4

a4 4

0o o

0o 0

o og ~ ~4

I I IW w

4

(~)

'Pgg

~~ o

4 o~

gohoo

I l~0

I

10 30 40Fz (MeV)

I

20

FIG. 12. e emission probability for 140' particlespectra in the case of (a) Co, (b) 6 Ni, and (c) Pocomposite systems. (o, is the total reaction crosssection. ) Symbols: (a): x 8Fe(d, e); 6 'Fe(p, n);~ Mn( He, G.). (b) o Fe(G., +'); o Fe( He, e);

~Co(p, ~). (c) 0 6pb(~, ~') ~ pb( He, ~);209Biy )

8= 140

10

10

10 20

X ~X ~

g4X ~

go%4

30I

40I

50E~ (Mev)

FIG. 13. Backward angle energy distribution com-pared with evaporation ( ) and pre-equilibriumcomponents ( ——) from a seven exciton state inthe case of (a) (P, &) reactions on 9Bi and (b) ~Co

target nuclei.

C HE VARIE 8, e t &l.

parison between 140 e particle spectra corre-sponding to the deexcitation of MCo, 6 Ni, and' Po composite systems is shpwn on Fig. 12. For

the light target, as in the 56Fe(o., o.') reactioncase, the entrance channel seems still to be fa-vored at backward angles. For entrance channelsother than n particle, and for all of them in the'"Po case, the shape and magnitude of the spectrabecome similar. In the case of the "Co compositesystem corresponding to lower excitation energy(E =39 MeV) the emission at backward anglescorresponds mainly to compound nucleus evapora-tion. But the backward angle spectra correspond-j.ng tp ~ emissjpn from the eoNi and 2ioPp composite systems cannot be explained entirely by acompound nucleus emission even using an energydependent level density parameter as proposed forthe "'Po excited nucleus" (Fig. 13). Consequentlythe hard part of the spectra exhibits a reactionmechanism for which the emission is independentof the entrance channel while evaporation calcula-tions cannot account for it. They can be explainedby pre-equilibrium emission from seven or eightexciton states, implying at least three intranuclearcollisions.

The calculations are made assuming that theemission is isotropic. Such hypothesis is sup-ported by the experimental fact that the 140' and160' backward angle spectra have the same shapeand amplitude. A preformation o. probability equalto 0.2 has been assumed. An example is given inFig. 13 in the case of (P, a) reactions on "Co and

'"Bi for which the pre-equilibrium component isespecially important relative to the low evapora-tive part. Then, while pre-equilibrium analysisfor forward angle spectra shows the importanceof states of small exciton number correspondingto direct reaction mechanism, at backward angles,pre-equilibrium emission from complex interme-diate states is stressed, Such intermediate statesare characterized by lifetimes long enough to losethe memory of the entrance channel.

IV. CONCLUSION

In this work the hybrid model has been extendedto n particle emission. In this approach the eparticle is considered as an exciton, the proba-bility I' of four nucleons to be correlated in ane-like structure being left as a free parameter.A simultaneous analysis of n particle spectra in-duced by protons, deuterons, 'He, and n particleswas achieved. The probability I' deduced fromthis analysis stands between 0.1 and 0.2, indepen-dent of the proton, deuteron, and 'He incidentchannel as well as of the mass of the target in themedium excitation energy range.

The concept of intermediate states has been veryuseful in explaining numerous nuclear reactions.The existence of pre-equilibrium n particle emis-sion at backward angles independent of the en-trance channels has been observed. Such emis-sion confirms the existence of complex interme-diate states having a long lifetime.

~G. D. Harp and J. M. Miller, Phys. Rev, C 3, 1847(1971).

M. Blann, Phys. Rev. Lett. 27, 337 (1971).3E. Gadioli and E. Gadioli-Erba, Nucl. . Phys. A210, 590

(1973).M. Bl.ann, Nucl, Phys. A213, 570 (1973),L. Milazzo-Colli and G. M. Braga Marcazzan, Nucl.Phys. A210, 297 (1973).

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N. Chevarier, Ph. D. thesis, University of Lyon, France,1973 (unpublished) .J. J. Griffin, Phys. Rev. Lett. 17, 478 (1966).

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lished) and 2380, 1963 (unpublished).J. Raynal, Code Magali, Centre d'Etudes Nucl. eairesSaclay Report No. D.Ph. T-6942, 1969 (unpubl. ished).

~~ J. R. Huizenga and G. J. Igo, ANL Report No. ANL-

6773, 1961 (unpublished) ~

~2M. A. Melkanoff, Nucl. Data A2, 243 (1966) ~

E. F. Gibson, J. J. Kraushaar, B. W. Ridley, M. E.Rickey, and R, H. Bassel, Phys. Rev. 155, 1208 (1967).

~4S. G. Kadmenshii, V. E. Kal.echits, and V. I. Furman,Yad, Fix. 11, 1237 (1970) [transl. : Sov. J. Nucl. Phys.11, 688 (1970)].

~J. J. Griffin, Phys. Lett. 24B, 5 (1967).F. E. Bertrand and R. W. Peelle, Oak Ridge NationalLaboratory Reports Nos. ORNL-4450, 1969 (unpub-lished); ORNL-4460, 1969 (unpublished); ORNL-4469,1970 (unpublished); ORNL-4471, 1970 (unpublished);ORNL-4638, 1971 (unpublished); Phys. Rev. C 8, 1045(1973).

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