Alpha-cluster break-up and reaction mechanism in (p, α) reactions on light nuclei

Nuclear 0

Physics

A398 (1983) 189-202

North-Holland

Publishing

Company

ALPHA-CLUSTER BREAK-UP AND REACTION MECHANISM IN (p,a) REACTIONS ON LIGHT NUCLEI W. BUCK’,

F. HOYLER,

A. STABLER’+

and G. STAUDT

Physikalisches Institut der Universitiit Tiibingen, D-7400 Tiibingen, Germany

H. V. KLAPDOR

and H. OESCHLERttt

Max-Planck-Institut fir Kernphysik, D-6900 Heidelberg, Germany Received

29 October

1982

Abstract: The differential cross sections for the “B(p, a)*Be and 23Na(p , a)*“Ne reactions were measured at bombarding energies between 6 and 24 MeV. The observed angular distributions can be divided into two domains: at low energies the shapes vary rapidly with incident energy indicating a compound nucleus reaction ; at higher energies rather stable diffraction patterns are seen exhibiting a direct reaction mechanism and DWBA calculations are able to describe the shapes. The change from one region to the other is rather abrupt and this behaviour seems typical for reactions having an a-like compound nucleus. The energy at which this change occurs corresponds to an excitation energy in the compound nucleus of about 20 MeV above the a-threshold.

E

NUCLEAR

REACTIONS “B, “Na(p,a), change in reaction mechanism.

E = 6-24 MeV ; measured o(E; 0); deduced DWBA analyses. Enriched targets.

1. Introduction

Several studies of (p, CI)and (a, p) reactions on light nuclei have been reported during the last few years [see, for example, refs. ’ - “)I. Since at suffkiently high bombarding energies these reactions can be described by a direct three-nucleon transfer, they present attractive features for nuclear spectroscopy. In addition, great interest has been shown in the study of the dynamics of these processes. Most of these experiments have been carried out at incident energies greater than 30 MeV since compound-nucleus formation can be neglected. In some cases, however, a clear behaviour of a direct reaction mechanism has been found at + Present address : Institut Berlin, Physikalisch-Technische Bundesanstalt Braunschweig D-1000 Berlin 10, Germany. ++ Present address : Max-Planck-Institut fiir Plasmaphysik, D-8046 Garching, Germany. +++ Present address: Institut fiir Kernphysik, Technische Hochschule Darmstadt, D-6100 Germany. I89 April 1983

und Berlin,

Darmstadt,

190

W. Buck et al. / Alpha-cluster break-up

distinctly lower energies. predominance of a direct energies

between

angular

distributions

In a previous paper13) we have demonstrated the triton transfer in the reaction ‘9F(p,a)160 for proton

12 and 45 MeV. At E, = 12 MeV a change is observed,

indicating

that

in the shape

for proton

energies

of the

below

12

MeV more complicated reaction mechanisms are involved. Some hints for similar irregularities in the same region of excitation energy in the intermediate system (E, = 25 MeV) have been found 14,15) in the reactions 6Li(p, 3He)4He and “B(P, cc)‘Be. In the present experiment, which is part of a systematic study of (p, SI) reactions on light nuclei, we measured the differential cross sections of the reactions ’ 'B(p, cr)‘Be and ‘jNa(p cr)20Ne in the energy range between 6 and 24 MeV. We look explicitly for a change in the reaction mechanism in this energy region by investigating the shape of the angular distributions, by taking into account results of fluctuation analyses and by comparing the cross sections with their predicted spectroscopic strengths. The main point of this paper is to outline some general information concerning the predominance of the direct (p, CC)reactions on light nuclei at lower energies.

2. Experimental

reaction

mechanism

of

procedure

The experiments have been performed using the proton beam of the MP tandem accelerator of the MPI Heidelberg. At proton energies below 20 MeV outgoing particles were detected with 300 pm thick silicon surface barrier detectors installed in a scattering chamber. The depth of the sensitive region was chosen appropriately to discriminate against lighter particles. At proton energies of 20, 22.5 and 24 MeV the reaction products were detected with the multigap magnetic spectrograph using nuclear track plates. The boron targets consisted of self-supporting highly enriched boron foils with a thickness between 40 and 180 pg/cm’ while the sodium targets were prepared by evaporating either metallic sodium or sodium-fluoride onto 20 pg/cm’ carbon foils. The sodium target thickness was between 100 and 250 pg/cm2. Absolute cross sections were determined by a comparison with data of ref. 16) in the boron case and for the sodium experiment with the 19F(p, cr)160 reaction given by Stabler et al. 13) and data of Holmgren and Fulmer “). The values obtained are in good agreement with the values deduced from target-thickness measurements

3. Differential and integrated cross sections 3.1. THE

REACTION

In the present

“B(p, @Be

experiment

we measured

the differential

cross

sections

of the

W. Buck et al. / Alpha-cluster break-up

191

reactions “B(p, cr)*Be(O+) and “B(p, c08Be(2+) at 40 energies in the range between 6 and 18 MeV. Some results of this experiment have been reported already in ref. 16). A typical spectrum at E, = 8.5 MeV is shown in fig. 1. Because of the high positive Q-value there are no peaks from competing reactions on l”B or other target contamination nuclei in the region of interest. The analysis of the transition to the first excited state of ‘Be turned out to be more difficult due to a large uparticle background originating from the 2~ break-up of 8Be. As background estimate a 4th order polynomial was fitted to the spectrum regions lying outside twice the width (FWHM) of both the ground state and the first excited state peaks. The fitting areas are indicated in fig. 1. The integration area was fixed to be twice the experimentally known width of 1.56 MeV for the 2.94 MeV level, thus encompassing 95% of the area of the assumed gaussian peak shape. In figs. 2 and 3 the differential cross sections of the transition to the ground state and first excited state of ‘Be are given; for each case the results of 14 energies have been selected. The error bars contain the statistical errors only. For the transition to the 2.94 MeV level systematic errors cannot be excluded but are likely to be the same for all spectra treated with the same procedure described above. The resulting angle-integrated cross sections a(O”- 180’) and o(O”-90”) for the two transitions are shown in fig. 4 as a function of the incident energy together with the average cross sections. The data of energies higher than 18 MeV are taken from refs. “2 18-22). At the higher energies the integrated average cross sections show an energy dependence of CJCCEP _ 2.5. This experimental law is well known

6

Fig. 1. Energy spectrum

of the reaction

7

6

9

10

11

12

at E, = 8.5 MeV. Solid lines represent tit to the background.

1‘B(p, a)%

the polynomial

W. Buck et al. 1 Alpha-cluster break-up

192

0 c.m. Fig. 2. Angular

distributions

from some transfer DWBA calculations understood

3.2. THE

@cm.

“B(p,a)sBe(g.s.) at E, between for the reaction Solid lines are Legendre polynomial fits.

6 MeV and

17 MeV.

reactions at various light nucleiz3). It is interesting to note that yield a flatter fall-off in general. This disagreement is not yet

24).

REACTIONS

23Na(p, a)“Ne

Up to now few data exist for the reaction 23Na(p, a)*‘Ne: angular distributions have been given by Nakamura et al. 25) at E,, = ,6.9, 7.1 and 7.3 MeV, by Warsh et al. 26) at Ep = 10 MeV and by Kost et al. *‘) at 41.3 MeV. In this experiment we measured differential cross sections at 15 energies between 6 and 24 MeV. Fig. 5 shows an energy spectrum at Ep = 18 MeV. Up to an excitation energy of about 8 MeV all states in the residual nucleus are excited strongly independent of their parity with the exception of the O+ state at 6.72 MeV. In the following analysis we discuss only the transitions to the first three positive-parity states. The differential cross sections at energies between 10 and 24 MeV are shown in fig. 6. Fig. 7 shows the integrated cross sections a(O”-90°) for the three transitions in

193

W. Buck et al. / Alpha-cluster break-up

8 cm.

6c.m.

Fig. 3. Same as for fig. 2 but for the excited state at 2.95 MeV.

Fig. 4. Integrated cross sections for the reaction O”-180” as circles, O-90” as crosses,

’ ‘B(p, a)‘Be(g.s.) average

and

cross sections

2.94 MeV. Integration as dashed

lines.

limits

194

W. Buck et al.

I Alpha-cluster

hwak-up

[~I E,=18.0

BLab=30Q

MeV

g 200h

3 t!

v) 150.

z 8

100, b YI

m

so-

’ ‘y

1

~Vy_J~~1

I

I

10

12

Fig. 5. Energy

spectrum

-i-i

-

14

of the reaction

16

23Na(p,a)ZoNe

E, He: t at E, = 18 MeV.

10'

Qcm.

Qc.m.

Fig. 6. Angular distributions for the reaction 23Na(p,a)20Ne at E, between 10 and 24 MeV for the ground-state transition and between 10 and 22.5 MeV for the 1.63 and 4.25 MeV level. Solid lines are Legendre polynomial fits to the data.

W. Buck et al.

i Alpha-cluster break-up

195

1.63 MeV L.25MeV

L-4, ’ 10

’

1

”

15

“1”“fi1’11

20

I

25 Ep (MeV)

ground-state transitions are Fig. 7. Partially integrated cross sections for the reaction 23Na(p, a)“Ne; indicated as circles, transitions to the 1.63 MeV level as squares and to the 4.25 MeV level as triangles.

the same manner as fig. 4. For the ground-state dependence is given by r~ K E, -4.0.

transition

the mean

energy

4. The reaction mechanism of (~,a) reactions 4.1. ANGULAR

DISTRIBUTIONS

In the energy range between 20 and 4.5 MeV, the predominance of a direct mechanism has been shown for the reaction ‘lB(p, cr)8Be reaction [refs. 15, ‘*-“)I. As can be seen in fig. 8 the angular distributions exhibit a diffraction-like pattern in this energy region. A comparison with the results of the present experiment (see fig. 2) shows that this behaviour can be observed for proton energies even down to about 13 MeV. In remarkable contrast strong irregularities in the shape of the angular distributions appear for energies below 13 MeV. In order to describe this change numerically, we determine the crosscorrelation coefficients, Y, as a function of the bombarding energy in energy steps of 0.25 MeV in the energy range from 6 to 13 MeV and of 1 MeV in the range from 13 to 18 MeV, where Y is given as Y(E) =

([cr,(ei)-(a,(ei)>][a,‘(ei)-(bE’(ei)>l) [((a,(ei)-(a,(ei)>)2)(((TE’(~i)-(~.E’(ei)))2)l~ ’

W. Buck et al.I Alpha-clusterbreak-up

196

I’SNIP.CL,)“C Ep (MeV)

30°600900

30' 60' 9~120°1500

120°150a

@c.m. Fig. 8. Survey

of the angular

distributions

L

I

3 8

0

0c.m

Qc.m. of the ground-state “B, “N and 19F. 6

E,,lMeV) 14 16

12

10

8

transitions

of the (p. a) reactions

on

1

.6-

A. .2 -

O_-___

-2-.L . -.6-

I” 18

Fig.

9. ‘The cross-correlation

20

22

2L

26

28

30 E,(MeW

coefficient, Y, as defined in text exhibiting excitation energy of about 25 MeV.

a stabilization

above

an

W. Buck et al. / Alpha-cluster

The result stabilization

of this calculation of the cross-correlation

is shown

break-up

in fig. 9. For both

coefficient

197

transitions

takes place in the range of incident

energies between E, = 10 and 13 MeV corresponding compound system between E, = 25 and 28 MeV.

to excitation energies of the In this region of excitation

energy the compound resonances are wide and overlapping channels are open. Therefore, it can be assumed that fluctuations the angular distribution will be damped gradually with increasing

4.2. x-CLUSTER

a sudden

and many exit in the shape of energy.

BREAK-UP

In order to understand the observed sudden stabilization one has to look for decay channels with thresholds near E, = 27 MeV which strongly reduce the rparticle emission of the compound nucleus 12C. As can be seen in fig. 9, in this region of excitation energy the d-, 3He- and t-decay channels open. In the cc-like compound nucleus 12C these decay channels are correlated with the disintegration of an cc-cluster and therefore are found at an excitation energy of about 20 MeV above the a-threshold. In this region of energy the decay probability of the compound nucleus 12C into the a-channels will decrease rapidly with increasing energy. This is because many new exit channels, correlated with the break-up of the outgoing a-particles, open up in a small interval of only a few MeV. Therefore in the reaction ’ ‘B (p, a)‘Be the direct reaction mechanism is expected to predominate for incident

energies

greater

than about

13 MeV.

A similar distinct change in the reaction mechanism might be expected in all (p, E) reactions leading to cc-like compound nuclei. Indeed, as mentioned above, the effect of sudden stabilization of the shape of the angular distribution was found originally in the reaction 19F(p, c()160 [ref. ‘“)I. In table I we have summarized the relevant

values

of the threshold

energies TABLE

Critical

excitation

energies

Ethr(~), the excitation

analyses

‘for various

pi, Deaction R

-%,(a)

nucl.

WeW

(Mh) = E,,,(a)

Petri’ =

1

and results of fluctuation

Comp.

energies

Energy

E”” (Mh)

+ 20 MeV “B(p,a)sBe ‘sN(p, a)“C

12C lb0

7.4 7.1

27.4 27.1

12.4 16.0

‘9F(p,a)‘60 23Na(p, a)“Ne “Al(p, a)Z4Mg

“‘Ne “+Mg “Si

4.8 9.3 10.0

24.8 29.3 30.0

12.5 18.4 19.2

(p, a) reactions range

Yu

%

(“A

WV)

WV)

85 95 90

7-12 12-15 7-12

23-27 27-29.5 19-24

;,

<50 70 75

11-13 13-15 IS-17

22-24 24-26 26-28

1 I 32)

90

17-19

28-30.5

EX

ref.

28

’ 3’)

W. Buck et al. / Alpha-cluster break-up

198 E&r)+

nuclei

20 MeV and “C,

160,

the corresponding

“Ne,

compared

with results

transitions

of “B(p,

24Mg

and

of angular a)‘Be,

“N(p,

proton

energies

28Si. These

distribution cc)“C

EPri’ for the compound

proton

measurements

and

19F(p, cc)“0

energies

.EFi’ can

be

for the ground-state given

in fig. 8. The

data are taken from refs. 13.“. 18m23,28-30). In all three reactions strong irregularities in the shape of the angular distributions are found at low proton energies, whereas at higher energies a smooth dependence is observed. The change between these two energy regions is found to take place in the vicinity of the critical bombarding energies E_cprit as given in table 1.

4.3. RESULTS

OF FLUCTUATION

ANALYSES

Some conclusions on the reaction mechanism can also be drawn from the study of fluctuations in the excitation functions. The results of some fluctuation analyses are also given in table 1. In the three reported cases 28,31*32) a direct yield of about 90 )!,,, was found at proton energies reaching the critical values. This is demonstrated in detail for the reaction 27Al(p, a)24Mg(g.s.) [ref. 32)] where by changing the energy interval from 15-17 MeV to 17~19 MeV the direct yield increases from about 75 % to 90 ‘I<,.These results support the conclusions drawn from the study of the shape of the angular distributions. Up to now there exists no fluctuation analysis for the reaction 23Na(p,cc)20Ne. From table 1 one expects the reaction to be predominantly direct at proton energies higher than 20 MeV. This result is consistent with the observed stabilization of the angular distribution of the ground-state transition.

4.4. DWBA

CALCULATIONS

We have shown

in our previous

papers i3, “),

that the angular

distributions

of

the reations ’ 'B(p, x)8Be(g.s.) and 19F(p, c()160(g.s.) can be reproduced by simple zero-range DWBA calculations for energies E, > EZ”‘. Now DWBA calculations in zero-range approximation using a cluster form factor were carried out for the reaction 23Na(p, a)“Ne. The optical and bound-state parameters used are given in table 2. For the entrance channel the global optical potential of Becchetti and Greenlees34) has been taken and the a-potential of Hansen et al. 35) was used as a starting point of a best fit search. In order to obtain acceptable fits the imaginary part of the LYoptical potential had to be decreased drastically. As already needed in the calculations for the (p, c() reactions on ’ 'B and “F a rather large radius parameter for the bound state was required. The excited states have been calculated with the same set of parameters as the ground-state transition. Due to to I = 0 states in the spin of I = 5 of the ground state in 23Na only transitions 20Ne have uniq ue angular momentum transfer j. In order to calculate the angular

W. Buck et al. / Alpha-cluster break-up

199

TABLE 2 Optical-model

and

bound-state

“0 (MeV)

parameters

(&

(:$I

1.17 1.54 2.0

0.65 0.45 0.6

23Na+p “‘Ne +a “Ne + t

- 52.2 - 205.2

distributions

for the excited

for the reaction [ref. “)I

W (MeV)

w, (MeV)

- 2.25 - 4.0

15.0

states

‘3Na(p,a)20Ne

as used

in DWUCK4

(f:)

(fZ)

(?I%)

($1

(Z)

1.32 1.52

0.6 0.54

- 24.2

1.01

0.75

of 2oNe, the individual

transitions

(f:) 1.2 1.3 1.2

have been

weighted by spectroscopic amplitudes Sj and summed up incoherently. These spectroscopic factors were calculated by Chung 36) in SU(3) approximation using shell-model wave functions of Chung and Wildenthal 37). The results of our DWBA calculations are shown in fig. 10. In fig. 11 the experimental cross sections, integrated from 0” to 90” (open bars are compared to the calculated cross sections ccalc = cj(2j+ 1))‘Sj$‘w4, multiplied with a common normalization factor N. Furthermore, neglecting all effects of reaction

+*,+t++ +t -++Y x100

lo3

r

Ep=22.5MeV

r

_

d

-*-:++

n =

%

163

+ ++

102 : \

+++

W’“.,

A‘

1. 25 *- ,****+

1

i?i ++

- l+*** x.2

**+

E,(MeVl

.\\.,i

30°

60° 90° 120° 150”

0c.m. Fig. 10. Angular distributions for states in *‘Ne. The solid lines represent the results of zero-range DWBA calculations using cluster form factors.

Fig. 11. Comparison of the experimental integrated from 0’ to 90’ cross sections, (open bars), the calculated cross sections u,.,~ = NCj(2j+ I)-‘Sjb, uW4 (black bars) and the relative spectroscopic factors 6’ = Cc Sj (hatched bars) for the three lowest states in ZdNe. The data are normalized to the experimental cross section for the 2+ state at 1.63 MeV.

W. Buck et al.

200

kinematics, for each transition factors, (T’ = C~,S,, are added are normalized

for various

to the experimental

to the relative

transition

cross

indicates

break-up

section

for the 2’

that dynamical

intensities.

(p, E) and (CX,p) reactions

4.5. SPECTROSCOPIC

Alpha-cluster

the normalized sum of appertaining spectroscopic (hatched bars). Both quantities, crcalc and G’, which

agree very well. This agreement influence

/

A similar

state

at 1.63 MeV,

effects have no important conclusion

has been drawn

‘. 12,38.39).

INFORMATION

Turning now to a comparison of the spectroscopic factors with the experimental cross sections at various energies a further hint for the change in the reaction mechanism can be found. In fig. 12 the relative cross sections at four energies between 10 and 22.5 MeV are plotted together with the normalized spectroscopic factors (black bars) and the normalized values of 2Z+ 1, with I being the spin of the residual states. It can be seen that at higher energies the experimental cross sections are proportional to the spectroscopic factors, whereas at lower energies a proportionality to 2Zf 1 is found. We can interpret this result that at E, = 22.5 MeV the direct triton transfer process is the more appropriate description of the 23Na(p, cx)“Ne reaction and that at E, = 10 MeV the compound nucleus formation predominates. A similar result is found for the “B(p,a)‘Be reaction (see fig. 4). The ratio of the integrated cross sections of the ground and first excited state varies from a factor of 6 at low energies to a factor of about 2.5 at the high energies. The 21+ 1 rule4’) predicts a factor of 5 and the spectroscopic factors for the triton transfer as calculated by Kurath et ~1.~~) give a ratio of 2.23. The change from the low- to the high-energy region is observed in a range around E, = 12 MeV in agreement with the critical energies as given in table 1.

2’

ll-il II I63

Fig. 12. Comparison of measured relative cross sections, O(O”-90’). for states in “Ne at E, = 10, 15, 18 and 22.5 MeV with the 21+ 1 rule (open bars) and the relative spectroscopic factors (black bars). The data are normalized to the sum of the three transitions.

W. Buck et al. / Alpha-cluster break-up

201

5. Summary A systematic study of (p, tl) reactions on “B and 23Na, which have a-like nuclei as the compound system, have been carried out in the energy range between 6 and 24 MeV. Similarly to the ground-state transitions of the 15N(p,a)1ZC and the 19F(p, cc)“‘0 reaction we found for the reaction “B(p,a)*Be(O+) and l’B(p,~)~Be(2+) a sudden change in the reaction mechanism when increasing the beam energy. This change towards a direct reaction mechanism occurs at a critical energy which turns out to correspond for all reactions to an excitation energy in the compound nucleus of about 20 MeV above the a-threshold. At this energy new decay channels open up which are correlated with the break-up of an a-cluster in the a-like compound system. At proton energies higher than the critical energy the angular distributions for the ground state transitions can be described by DWBA calculations. The relative strengths of the discussed transitions agree well with shell-model predictions by Kurath in the boron case and by Chung in the sodium case. Thanks are due to the tandem group of the MPI fur Kernphysik, Heidelberg, for its help during the course of the experiment and to Dr. H. Oberhummer for helpful discussions. This work was sponsored by the Bundesministerium fur Forschung und Technologie.

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W. Buck et al. / Alpha-cluster break-up

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