ALPHA-PARTICLE PRODUCTION IN HEAVY-ION REACTIONS

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ALPHA-PARTICLE PRODUCTION IN HEAVY-ION REACTIONS

R. Middleton, J. Garrett, H. Fortune, R. Betts

To cite this version:

R. Middleton, J. Garrett, H. Fortune, R. Betts. ALPHA-PARTICLE PRODUCTION IN HEAVY-ION REACTIONS. Journal de Physique Colloques, 1971, 32 (C6), pp.C6-39-C6-50.

�10.1051/jphyscol:1971606�. �jpa-00214824�

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JOURNAL DE PHYSIQUI:. Colloque C6, supplkment au no 11-12, Tome 32, Novembre-DPcembre 1971, page C6-39

AI-PHA-PARTICLE PRODUCTION IN HEAVY-ION REACTIONS (*)

R. MIDDLETON, J. D. G A R R E T T , H. T. F O R T U N E , a n d R. R. BETTS Physics Department, University of Pennsylvania, U. S. A.

R&umB. - Certaines caracteristiques des distributions angulaires et des fonctions d'cxcitation de la reaction 12C(12C7 r)zoNe suggerent une configuration en quartet du type [220] pour les etats suivants du ZoNe : 0 ' a 7,20 MeV ; 2' B 7,83 MeV ; 4.' 9,03 MeV. Des caracteristiques remar- quablement similaires de la reaction 12C(I3C, z)2lNe suggbrent pour les etats 312- A 3,66 MeV et 512-

a

3,89 MeV une structure dans laquelle un neutron 1 p1/2 est couple B la configuration en quartet [220]2+. Le mecanisme des reactions qui pcuplent les etats mentionnts ci-dessus semble etre de type direct ou semi-direct.

Abstract. -- Evidence from angular distributions and excitation functions of the 12C(12C, a)2ONe reaction suggests that the 7.20 MeV 0-, 7.83 MeV 2+ and 9.03 MeV 47 states of 2oNe have the quartet configuration [220]. Remarkably sin~ilar evidence from the I2C(13C, a)zINe reaction suggests that the 3.66 MeV 312- and the 3.89 MeV 51'2- states may have thc configuration of a 1 p l , ~ ncutron weakly coilpled to the [220]~+ quartet configuration. It appears likely that, in both reactions, the states mentioned are populated by a direct or semi-direct reaction mechanism.

1. A method of energy averaging.

-

It is well- known that reactions which proceed via compound nucleus formation and decay are subject to fluctuations a n d that it is dangerous to draw conclusions from measurements made a t a single energy. Ideally measurements should be made over a n energy range corresponding t o several fluctuation widths and then averaged. This is usually accomplished either by using a very thick target, in which case the energy resolution is very bad, o r by using a relatively thin target and laboriously taking data a t several discrete energies. It occurred to us that, with a broad range magnetic spectrograph, it might be possible to vary the incident energy over quite a large range and still preserve good energy resolution.

Figure 1 shows a portion of an energy spectrum from the 12C(160, a)24Mg reaction which was made while the beam energy was gradually increased from 30 t o 32 MeV. This spectrum was recorded by making 21 discrete exposures, the beam energy being successi- vely increased in increments of 100 keV. After each increment the spectrograph field was increased the appropriate amount to maintain the group a t 7.35 MeV in precisely the same position o n the nuclear emulsion detector plate. It will be noticed that the resolution remains quite good for several MeV on either side of this group and deteriorates only towards the ends of the spectrum, particularly the high energy end where the dispersion is greatest.

(*) Work supported by the National Science Foundation.

EXCITATION ENERGY (MeV;

8 / 6 . -

- -

" ,'

^I

E I2c ( "0. a ) 2 4 ~ 9 -:

E Icool-

i

I1

^E⁽1 6 0 = 3 0 - 3 2 ~ e v

FIG. 1. -- A n example of an energy averaged spectrum.

Gratifyingly this technique works almost equally well simultaneously for all angles in the range 00 to 900. Thus, with a multi-angle spectrograph it is possible to produce in a single exposure angular distributions of many states averaged over a 2 MeV range in bombarding energy while still preserving good energy resolution.

2. Reaction studies. - Some of the earliest experiments performed on Tandem accelerators were studies of heavy-ion reactions of the type (12C, a) and (160, a).

Particularly thorough and detailed investigations were made of the 12C(12C, oc)20Ne reaction by Almqvist et al. [ I ] (analysis by Vogt et al. [2]) and by Borggreen et al. [3] (analysis by Bondorf and Leachman [4]) and of the l 2 C ( I 6 0 , reaction

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971606

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C6-40 R. MIDDLETON, J. D . GARRETT, H. T . F O R T U N E A N D R . R. BETTS

by Halbert et al. [5]. The results of these studies were overwhelmingly in agreement with a compound reaction mechanism and were in accord with the predictions of the statistical model. Possibly because of the strength of the seconclusions, reactions of this type received little further attention until compa- ratively recently. However, it is notable that although these early experiments were extremely detailed, they were in the main directed at the ground and first few excited states and the possibility that higher excited states of unusual character might have direct components could not be precluded.

24Mg STUDIES. - It was against this background and with the belief that (12C, a) and ('('0, a) reactions were largely compound that, a little over a yea1 ago, we undertook a high resolution study [6] of the 160('2C, ~ 1 ) ' ~ M g reaction. The motivation was to look for high spin states and in particular for the 10' member of the ground state rotational band which had recently been predicted to lic near 17 MeV excitation by Akiyama et al. [7]. These we expected to be strongly excited due to an approximate (2 J

+

1) enhancement and to be narrow because of the centrifugal barrier.

As can be seen from the spectrum shown in figure 2 four intense narrow groups were observed corresponding to states in 24Mg at 14.14, 16.30. 16.56 and 16.84 MeV. The widths of these were all

<

20 keV with the exception of the 16.56 MeV level and here

EXCITATION E N E R G Y I MeV1

2 2 - _ 2 , . 23 85 ID 17 Ib

. ^, ⁵ + ' >

1 ;

Er4.360MeV

e,,,

.

^{7 t r}

!

PLATE POSITION I C m I

FIG. 2. - An cnergy spectrum from the 160('2C, a)24Mg rcac- tion showing the three intense and narrow states at around 16.5 MeV excitation which have recently been established~l

to be states of large angular momentum.

there was some indication that this may be a doublet.

Since the 14.14 MeV state had very recently been shown to be 8' by Wright and collaborators [8]

i t seemed extremely likely that the three higher states were also of high spin and one probably the 10' member of the ground state rotational band.

However, there remained the intriguing possibility that these states may owe their narrow widths, not to the centrifugal barrier but rather, to them having unusual configurations. For example, if they were

of a 12C

+

12C molecular nature, their decay would be strongly inhibited. Alternatively they may be quartet states [9] having little or no overlap with the ground state of 20Ne.

Clearly it was important to measure the spins of these states and work to this end was initiated both at the University of Pennsylvania and by Professor Bromley's group at Yale - the latter using the inverse reaction at the same center-of-mass energy. Both groups used the same technique, namely, to measure the angular correlation of the a-particle decaying to the ground state of 'ONe in coincidence with the reaction a-particle emitted by 00. The angular correlation is then of the form

P,(@)'

and uniquely determines the spin. At Penn all three states were observed to havc significant a-decay branches to the 2+ and 4' states of 'ONe but no ground state branch was observed. Thus, no spin assignments could be made. At Yale similar results were obtained with the exception that they observed a weak ground state branch from the center state. They were able to make a 6' assignment to this state. This discrepancy was finally resolved when the excitation energy of the 6' state was precisely measured. It turned out to be 16.59 MeV and was not the 16.55 MeV state strongly populated by the inverse reaction. The existence of two levels of about this excitation energy as since been directly confirmed by Siemssen [10] from high resolution studies of the 12C(160, E ) ' ~ M ~ reaction.

Recently, Balamuth and collaborators [I I] at Penn have, by making angular correlation measurements on the a-decay branch to the 2' state of "Ne, succeeded in placing limits on the spins of the three states strongly populated by the ' 6 0 ( L 2 C , a)'ONe reaction. All havc spin 8, 9 or 10 with the 16.30 MeV level possibly being the best candidate for the 10' member of the ground state rotational band. It is commentable that the assignment of high spin does not preclude the possibility that any of these three states might have unusual structure. To investigate this possibility further we undertook the study of a different heavy-ion reaction that also leads to 2 4 ~ g , namely, l 4 N ( I 4 ~ , ~ t ) ' ~ M g .

The first measurements were made at an energy chosen to correspond to the same compound nucleus excitation (37.3 MeV) as used in the 160('2C, 0oz4Mg study. This turns out to be rather low, being only 20.2 MeV. An energy spectrum, measured at 7.5O, is shown in figure 3.

The most surprising features of this spectrum are the extremely low cross sections and the complete absence of any discernable states above 10.5 MeV excitation. The cross section of the strongest state (10.35 MeV) is 17 pb/sr and that of the ground state is < 1 pb/sr. These cross sections, surprisingly, are almost three orders of magnitude less than those of the ^'"(I 'C, L Y ) ~ ~ M ~ reaction.

Since 20.2 MeV is not much above the Coulomb barrier a second exposure was made at an incident

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ALPHA-PARTICLE PRODUCTION I N HEAVY-ION REACTIONS C6-4 1

'41 ' ' ~ . ~ a 12'h8p E ,,". 2 0 2 MeV

- ⁷F

FIG. 3. - Energy spectrum from the l4N(14N, a)24Mg reaction measured at an incident energy corresponding to the compound nucleus excitation (37.3 MeV) as used in the

1 6 0 ( 1 2 C , x)?4Mg study (Fig. 2).

energy of 28.0 MeV. An energy spectrum covering the excitation range 9.5 to 24 MeV is shown in figure 4. The features are more or less the same as in the lower energy spectrum - no discernable groups above the continuum starting around 10 MeV excitation. An optimistic upper limit can be placed on the cross sections of groups around 16.5 MeV excitation of about 40 pb/sr. This is over two orders of magnitude less than the cross sections observed in the

160('2C,01)24Mg reaction.

EXClTATlON ENERGY l M e V l

, ,

, 7 . . ^2; y :' '0 ' '""6 " ^8" '? . ." " 2 , , ,

E,,, ~ 2 8 0 MeV

qo,

.

⁷5-

DISTANCE ALONG PLATE f c m )

FIG. 4. ^-Energy spectrum from the ^14N(I4N,%)24Mg reaction measured at a n incident energy of 28.0 MeV.

A possible explanation of the low cross sections is that the nitrogen projectile dissociates in either the Coulomb or the nuclear field of the targct and much of the reaction cross section goes into a continuum.

This does not appear to be the case since relatively intense groups have been observed in other (I4N, a) studies. For example, in a study of the I2C(I4N, a)22Na reaction, performcd at 30 MeV, many groups were observed to have differential cross sections in the range 0.2 to 2 mblsr. An energy spectrum from this reaction, measured at 7.50, is shown in figure 5.

An alternate ex~lanation of thc extremely small

EXCITATION ENERGY ( M e V )

DISTANCE ALONG PLATE l c m l

FIG. 5.

-

^Atypical energy spectrum from the lzC(14N, z)zzNa reaction measured at a n incident energy of 30 MeV. Many of the states have differential cross sections in the range 0.2 to

2 mblsr.

In this respect the 14N

+

14N system is very poor since both target and projectile have two nucleons oi~tside a-particle cores. The low probability of these four nucleons forming an a-particle may be responsible for the observed low cross sections. To explore this further another study was undertaken of reactions that have different entrance channels but a common exit channel.

THE "B(I4N, a)21Ne, ' ~ e ( ' ~ 0 , U ) ~ ' N ~ ^{A N D} I2C(' 3C, ~ ) ~ l N e REACTIONS.

-

The interesting featurc of these three reactions is that they have different entrance channels but the same exit channel.

A comparison of spectra from the three reactions is shown in figure 6.

As can be seen from the figure the "B(14N, L Y ) ~ ' N ~ and 'Be(160, a)21Ne spectra are very similar with the exception that the latter has about 10 times the cross section of the former. It might have been expected that these reactions would have slightly different cross sections due to the targets and projectiles having different spins, but, it seems unlikely that this would account for a factor of 10. An alternate ex~lanation i\ that the 9Be('60, a)21Ne reaction is the stronger since the projectile can be regarded as bcing composed of alpha-particle clusters.

The similarity between spectra also extends to that from the I2C(l3C, ~ ( ) ~ l N e reaction with one very obvious exception. This is the extremely strong excitation of the 3.89 MeV state by the ('",a)reaction.

(This state will be discussed more fully later.) It will be noted that the 'Be(160, ~ ) ~ l N e and j2C(I3C, U ) ~ ' N ~ reactions have comparable cross sections presumably since both have In the entrance channel an a-particle nucleus and an a-particle nucleus

+

neutron.

cross sections observed in the 14N(14N, COMPARISON ^01: ^THE 12C(12C, U ) ~ O N ~ , 12c(13c, reaction is that it reflects the importance of having ~ ) ~ l N e ^AN11 '3C('3C, a)22Ne REACTIONS. - Energy a-particle clusters in either the target or projectile. spectra from these three reactions measured at an

4

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C6-42 R . MIDDLETON, J. D. GARRETT, H . T. FORTUNE A N D R. R. BETTS

- ...-. _{- i}

"B("N. a ) 2 1 ~ e E14,,= 22.73 MeV 8Lob = 3%

a ( 8 ) 0 ,,= 0 0 2 3 mb/sr

i ^,7 ? = 30 3 MeV

1\24bs

i'

I .

;

B L O b Z 3 $

I

m ( 8 ) E , . 0 2 4 m b / s r -

*)

I

El,c = 3 0 0 MeV

!

1

^@Lob⁼^{3 7}^3'

I

EXCITATION ENERGY ( M e V )

FIG. 6. - A comparison of three reactions which have a com- mon exit channel but different cntrance channels.

incident energy of 30 MeV are shown in figure 7.

The interesting feature here is the dramatic decrease in cross section as the complexity of the target- projectile system increases. To a first approximation the addition of a neutron to either the target or projectile causes the cross section to fall by about a factor of ten. This fall is much greater than would be expected from considering the statistical factors and we believe is further evidence of the importance of a-particle- clustering.

3. Search for quartet states in 'ONe. - Although the

''c('~c,

a)20Ne reaction has been the subject of several previous investigations [I], [3] a number of recent developments prompted us to restudy this reaction :

(i) Shell model calculations [7], [I 21, employing the full sd basis, are unable to account for both of the 0' states, occurring at 6.72 and 7.20 MeV excitation in 2 0 ~ e . The results of some of these calculations along with the experimental data is shown in figure 8.

Since the 19F(3He, d)'ONe reaction [I31 strongly populates the lower Of state and only weakly excitcs the higher one, it is very likely that the 6.72 MeV state is the state predicted by the shell model. This conclusion is also supported by the results of studies of the 2 2 ~ e ( p , t)20Ne reaction [14]. Tablc I lists the

EXCITATION ENERGY ( MeV1

,3,CC0 I- 13 11-:m 13. 9 n.. 7 -6 5 4 3 - 2 { . ?-

m f . .

I2C (I2C, a 1 'ONe

8000 El,, = 3 0 . 0 MeV !

BLOb = 7 t 0

0 0

I

^r( ~ 3 1 % ~ ~ ~ = 7 5 0 m b / s r -1

'*c ( I J c , a ) "Ne E,,, = 3 0 . 0 MeV

= 1 1

ff (el,,,, = 0.27 mb/sr

1

1%. ! 5 14 13 12 I! - I0 9 8 7-_-6 . 2 4

lf

ll

^.⁷

"C c " ~ . a ) ~ ~ N e A

Else ⁼3 0 . 0 MeV

. e,,,.~~f'

r (8),,,, = O . O I 7 m b h r .

DISTANCE ALONG PLATE (cm l

FIG. 7. - A comparison of energy spectra from the 12C(12C, r ) ZQNe, 12C(I 3C, a)ZlNe and 13C(13C, a)22Ne reactions illus- trating the dramatic fall in cross section as the complexity of

the entrance channel increases.

spectroscopic factors determined from the (3He, d) and (p, t) reaction studies.

It will be noticed from figure 8 that the shell model calculations also fail to reproduce a 2' and a 4' state observed in 'ONe. These we believe to be respectively the states at 7.83 and 9.03 MeV excitation. Thus, it seems very likely that the 7.20, 7.83 and 9.03 MeV states are part of a rotational band and have the same basic cc anomalous >> configuration. (The 7.20 and 7.83 MeV states had previously been suggested to belong to the same rotational band by Litherland et al. [15].)

(ii) Arima et al. [9] have suggested that the 0 + state at 7.20 MeV might have quartet structure of the form [220] (i. e. two sd-shell a-particles outside a ''C core).

(iii) If the states at 7.20, 7.83 and 9.03 MeV have the configuration [220], they would be expccted to be

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ALPHA-PARTICLE PRODUCTION I N HEAVY-ION REACTIONS

Excitation Energy

r,

S(3He, d) g e x p ( ~ , t ) / 6 ~ ~ ~ ~

J" EXP Th (b) (key) Exp (‘') Th (b) 35.1 MeV (') 42.4 MeV (")

(") SIEMSSEN (R.), LEE (L). L. and CLINE (D.), Phys. Rev. (1,965), 140B, 1258.

( b ) HALBERT (E. C . ) , MCGRORY (J. B.), WILDENTHAL (B. H.), and PANDYA (S. P.), Advances in Nuclear

Physics, 197 1.

(? FALK (W. R.), KULISIC (P.) and MCDONALD (A.), NucZ. P l ~ y s . (1971) A 167, 157.

POSITIVE PARITY STATES IN ^'ONP

s e v e r o ! '\,

levels \-.L ----L---* *- a

-..-L

, levels

,

.

^--⁴ ^_-4L17_.z:--&

2 ,=.-3- , 4

.-

-~ -

² ^----2,,'

.-

01 0

"

^! ^. ⁰^--⁰

G o u s s K - B K+"O K+12 FP

Akiyarna, A r ~ m o EXPT H a l b e r t , et 01.

and Sebe

FIG. 8. -The results of some shell model calculations, employing the full sd basis, for 2oNe compared with the experimental data.

The calculations are unable to reproduce the 0 ' state at 7.20 MeV, the 2+ state at 7.83 MeV and the 4' state at 9.03 MeV.

weakly populated in alpha transfer to ^{1 6 0 ,}which has the configuration [300] in its ground state. This appears to be the case as can be seen from figure 9 which shows a portion of a spectrum from the 160('Li, t)'ONe reaction [I61 measured at an incident energy of 20 MeV. Unfortunately, in this spectrum, the 7.20 MeV 0' state is not completely resolvcd from the intense group at 7.17 MeV. Howevcr, careful analysis does show it to be vcry weak and certainly less intense than thc 6.72 MeV O f state. Also it will be noticed that the 7.83 MeV 2' statc is considerably more weakly excited than thc 2' state at 7.42 MeV.

EXG:T.\TIOEI ENERGY It.l.leV1

- -

'

^{! . - ,}

1

^7:6 ¹⁶⁰⁽^{' ~ i ,}^t ^{ON^}

EL, = 2 0 0 M e V

5 7 8

FIG. 9. - A portion of an energy spectrum from the 160(7Li,t) 2oNe reaction measured at an incident energy of 20 MeV.

That the 7.83 MeV 2+ state is more weakly excited than the 7.42 MeV 2+ state is apparent.

(iv) Furthermore, it would be expected that the alpha decay widths of the 7.20, 7.83 and 9.03 MeV states would be smaller than those of other states of the same J" at comparable excitation energies. Such indeed is the case as can be seen Table I [17]. The 7.20 MeV state has a width of 4 keV compared with a width of 19 keV for the 6.72 MeV state (which lies at a lower excitation energy and would be expected to have a smaller width if the widths were governed solely by penetrabilities). Likewise the 7.83 MeV state has a width of 2 keV compared with 8 keV for the 7.42 MeV state. It will also bc noticed that the 9.03 MeV 4' state has a width of only 3 keV compared with the 120 keV width of the 4' state at 9.99 MeV -

however, this difference might be accounted for by pcnetrability factors.

Since the [220] quartet configuration corresponds to two alpha particles outside a I2C core, states having

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C6-44 R. MIDDLETON, J. D. GARRETT, H. T. F O R T U N E AND R. R. BETTS

this configuration should be strongly populated by a reaction that adds 2 alphas to a I2C targct. Such a possiblc reaction is the 12C(12C, a)20Ne reaction.

Our multi-angle spectrograph and tandem accelerator have been used to measure excitation functions and angular distributions for the I2C(l2C, N ) ~ O N ~ reaction. These were made in the incident energy range 22 to 35 MeV in steps of 0.5 MeV.

The targets were self-supporting foils of natural carbon, ranging in thickness from 3 to 15 pgm/cm2.

A portion of a typical alpha particle spectrum measured at 25 MeV with a 3 pgm/cm2 target is shown in figure 10. It is evident from this figure that the (( anomalous ^)> 0' and 2' states at 7.20 and 7.83 MeV, respectively, are much more, strongly excited than the normal 0 + and 2' states at 6.72 and 7.42 MeV.

EXCITATION ENERGY (MeV)

FIG. 10. - Portion of a n alpha-particlc cnergy spectrum measured at a laboratory angle of 3.75<'for the reaction 12C(12C, a)2oNe at a bombarding energy of 25 MeV. The experimental energy

resolution is approximately 20 keV F W H M .

Excitation functions, measured at a laboratory angle of 3 3/40, for the two 0' and the two 2+ states are shown in figure 11. It is evident that the 7.20 MeV O + state is consistently stronger than the O f state at 6.72 MeV, the average differential cross section of the formcr being about twice that of the latter. The difference in strength of the two 2 + states is even more

striking, the 7.83 MeV state being on average about 5 times that of the 7.42 MeV state. These differences in strength -though single angle data - are inconsistent with the statistical model which predicts that the avcrage cross sections for the two Of states should be comparable as should the average cross sections for the two 2+ states.

INCIDENT ENERGY (MeV)

FIG. 11. - 1ZC(L2C, 3)ZONe yicld curvcs for the 6.72 and 7.20 MeV 0' states and the 7.42 and 7.83 MeV 2.'- states measured a t a laboratory angle of 3.75O. The average of the yield over

the range of measurements is indicated for each state.

Angular distributions for the 7.42 and 7.83 MeV 2 + states are shown in figure 12. These were measured at bombarding energies of 25 and 27 MeV. It can be observed that the angular distributions, at both energies, for the two states are strikingly different, both in magnitude and shape. The 7.42 MeV state has a highly oscillatory angular distribution which closely resembles that of the 1.63 MeV 2' state of 20Ne as measured by Borggreen et al. [3]. On the other hand, the angular distribution for the 7.83 MeV state is barely oscillatory and is strongly forward peaked - reminiscent of a direct process. It is notable that the forward peaking for the 7.83 MeV state is present both at 27 MeV (a peak in the excitation function) and at 25 MeV (ncar a minimum).

The angular distributions for the 7.42 MeV state are entirely consistent with it being populated via a compound nucleus reaction mechanism ; whereas the

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ALPHA-PARTICLE PRODUCTION I N HEAVY-ION REACTIONS C6-45

-. : '1' ¹ 1 7 1 _

:

^E ⁼^{M e}

^I.,

E l ' ~ i = 270 MeV

!

1. . : _, ^{A !} I

I ! . L . .. l . l...

0 3 0 6 0 9 0 0 3 0 6 0 9 0

@c.m.

FIG. 12. - 12C(12C, a)zoNc angular distributions for the 2'- states at 7.42 MeV (broken linc curve) and at 7.83 MeV (full linc curve) measured at incident energies of 25 and 27 MeV.

7.83 MeV state, though undo~~btedly possessing a compound contribution, appcars to have a large direct-like component. It will be noticed that between about 60° and 900 the angular distributions to the two states show some similarity. For example, at 25 MeV both exhibit a minimum at 900 while at 27 MeV both have a maximum.

If, indeed, the 7.83 MeV state has a large direct component, it is difficult to understand the pro- nounced structure in the excitation function.

Remarkably similar structure, together with per- sistently forward peaked angular distributions, have recently been observed in (7Li, t) and ('Li, a) reactions by Carlson and Johnson [18]. They suggest that the peaks in the excitation function may correspond to

(( doorway ⁾⁾states, the latter being of the ⁽⁽extended ⁾⁾ structure target

+

t

+

cr. Also that such a process has a large cross section only if the final state (residual nucleus

+

outgoing particle) has a large overlap with the ^ctdoorway ⁾⁾ state. These authors further point out that similar processes may occur in other heavy-ion reactions whenever the target or projectile consists of loosely bound clusters.

Since the binding energy of 12C with respect to break-up into 3 alpha-particles is only 7.27 MeV, it seems not unlikely that such a process could occur in the ' 2 C ( ' 2 ~ , cr)''Ne reaction. This would explain the direct-like angular distributions and the structure of the excitation function observed for the 7.83 MeV 2' state. It would also explain the preferential excitation of the 7.20 and 7.83 MeV states, if they are of the proposed [220] quartet configuration. Extended doorway structures of the form [221] and [230] are expected to be readily formed in a "C

+

"C encounter and have good overlap with the [220]

configuration.

If this picture is correct it might be expected that the peaks in the 7.20 and 7.83 MeV excitation functions should occur at the same energies. This does not

appear to be the case. There are several possible explanations of this, one being that the peaks are the results of interferences between two competing reaction processes. To explore this possibility further we extended our investigation to include the 4+ state at 9.03 MeV excitation.

Figure 13 shows a comparison of the excitation functions of the 7.20, 7.83 and 9.03 MeV states.

Two points are apparent from inspection of these.

Firstly, all three have the same type of structure but with no obvious correlation in peak positions.

Secondly, the apparent centroid of the structure seems to move towards higher energy with increasing final-state spin. This second point is highly suggestive of a direct reaction mechanism and could easily arise as a result of satisfying angular momentum matching conditions.

INCIDENT ENERGY (c.rn.1 IN MeV

10 Ex = 7 . 2 0 MeV

J". o+

-

A

Ex = 7.83 MeV

-

J " = 2 + ^I

15: ^-

\

E x = 9.03 MeV

30 J"

-

^4'

INCIDENT ENERGY ( l a b ) IN MeV

FIG. 13. - Comparison of 12C(12C, a)zUNe yield curves to the 7.20 MeV 0'- state, the 7.83 McV 21. state and the 9.03 McV 4'-

state, all measured at a laboratory angle of 3.75".

To investigate this further, optical-model transmission coefficients have been calculated for the entrance and exit channels. The ''C

+

l Z C optical model parameters were taken from the analysis of

(9)

C6-46 R. MIDDLETON, J. D. GARRETT, H. T. FORTUNE A N D K. R. BETTS carbon-carbon elastic scattering data [19]. The

potential used in the a

+

2 0 ~ e channel [20] is one that has proven successful in a variety of studies involving a-particles and nuclei in the lower half of the sd shell. The parameters are : for the 12C f 12C channel, V = 14 MeV, W = 0.4

+

^{0.1 E}

,.,.

(MeV),a ⁼0.35F,

R R

= 6.18F and R, = 6.41 F ; and for the a

+

20Ne channel, V = 180 MeV, W = 15 MeV, r , ⁼r; ⁼r, ⁼1.42 F, a = a' = 0.56 F.

The results of the calculations are shown in figure 14.

The calculation performed for an incident energy of 22 MeV corresponds specifically to the 7.20 MeV O + state, that at 27 MeV to the 7.83 MeV 2' state and that at 33 MeV to the 9.03 MeV 4+ state. If it is

Additional evidence that the reaction mechanism is at least in part direct - may be inferred from the angular distributions - particularly those corresponding to the 2' and 4+ states. Figure 15 shows the angular distributions of the Of, 2' and 4 + states measured at energies corresponding to peaks in the excitation functions. The 2' and 4 + distributions look remarkably reminiscent of a direct process, both are smooth, are strongly forward peaked with the 4' distribution being just a little broader than the 2 + and even exhibiting a hint of a slight forward minimum. The 0' angular distribution is consistent with what is expected from either a direct or compound process.

Fro. 14. - zoNe

+

^{a and}^'LC

+

transmission coefficients calculated for the bombarding and excitation energies shown

in the figure.

assumed that the dominant L-value is that corresponding to T, = 0.5, then at 22 MeV the most probable angular momentum transfer to a state at 7.20 MeV excitation is about 1 unit. At 27 MeV it is 2 units of angular momentum for a state at 7.83 MeV excitation and at 33 MeV it has increased to 4 units for a state at 9.03 Mevexcitation. Thus, we see that at low bombarding energies (actually < 22 MeV) a n g ~ ~ l a r momentum matching favors the excitation of the 7.20 MeV O + state, at around 27 MeV it favors the 7.83 MeV 2 + and at 33 MeV the 9.03 MeV 4 + state. This is more or less in agreement with the experimental observations.

FIG. 15. - Angular distributions from the 12C'(12C, a)ZoNe reaction corresponding to the 7.20 MeV 0'. state, the 7.83 MeV 2+

state and the 9.03 MeV 4+ state. The incident energies correspond to peaks in the yield curves.

The simple minded argument involving angular momentum matching suggests that there will be energy ^(<windows ⁾⁾in which a direct process favors the excitation of a specific state - assuming the state has a configuration amenable to excitation by a direct process. However, it does not tell us the width of the window. In an attempt to estimate the width of the window we undertook D W B A calculations for the 2' and 4 + states at 7.83 and 9.03 MeV respectively.

It should be stated at the outset that we did not anticipate reproducing the angular distributions nor have we attempted this, but, rather predicting the kinematic dependence of the zero degree differential cross sections. The calculations, which were made using the parameters mentioned earlier, were local, zero-range and assumed the reaction to proceed by adding 8 nucleons (M = 8, Z = 4) to the sd shell [2(N - 1)

+

L = 161. Investigation showed that the use of a cutoff near the nuclear surface gives results very similar to those obtained for no cutoff.

Since finite-range, non-local corrections usually servc merely to damp the interior contributions, it is felt that the present calculations are not entirely meaning- less.

The result of the calculations for the 2' state is shown in figure 16 together with the experimental data.

Allowance was made for the fact that there are identical particles in the entrance channel by adding the O0

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ALPHA-PARTICLE PRODUCTION IN HEAVY-ION REACTIONS C6-47

INCIDENT ENERGY (lab) IN MeV

FIG. 16. -Comparison of the 3.750 (laboratory) 12C(I2C, r)2oNe excitation function for the 7.83 MeV 2- state with the 00 DWBA

predictions.

and ,180° amplitudes and then squaring to get the cross section. As can be seen from the figure, the calculations reproduce quite well the gross features of the energy dependence. The results of the calculation for the 4 + state are shown in figure 17. I t will be observed that here the maximum occurs a t about 36 MeV

-

a little higher than the present measurements extend -

and that the ((window ⁾⁾is about 9 MeV wide. It is gratifying that the ratio of the maximum differential cross sections predicted by theory for the 4+ and 2' states is 2.7 which is in rough agreement with the experimental ratio of 2.1.

4 0 7 1 - 1 - . .... i -:- _b . _. _,. - .- . . ₁ _. _:

_---.

' 2 ~ ( ' Z ~ . a ) ON^ I' \ \ , - .

E x = 9.03 MeV

--

^on,,^a,,: ^5.8"

o r u r acm

.

⁰^.

22 24 26 28 30 32 34 36 38 40

INCIDENT ENERGY ( l a b ) IN MeV

FIG. 17. - Comparison of the 3.750 (laboratory) lZC(IZC,x)

2oNe excitation function for the 9.03 MeV 4- state with Ou DWBA predictions.

In summary, the previous information on the 7.20 MeV Of state, 7.83 MeV 2+ state and the 9.03 MeV 4' state is consistent with them belonging to the same rotational band and that the basic configuration is ⁽⁽unusual ^N.That these states are strongly populated by the "C("C, a)"Ne reaction by a direct or direct

+

semi-direct processes strongly suggests the ^ctunusual ^)> configuration consists of 2 alpha-particles in the sd-shell outside a 12C core.

In quartet terminology, the basic configuration of the 7.20, 7.83 and 9.03 MeV states of 'ONe is 12201.

4. Possible evidence for quartet states in "Ne.

-

In the study of the 12C(13C, a)"Ne reaction, made in collaboration with J. N. Hallock and H. A. Enge [21]

of M. I. T., it was observed that the 3.66 and 3.89 MeV states were selectively excited. Further, it was observed that the angular distributions were highly asymmetric, the 3.89 MeV state being strongly forward peaked and the 3.66 MeV state being strongly backward peaked. The shapes of the angular distributions were highly suggestive of a direct reaction mechanism but since the data was obtained at a single energy (14.4 MeV in the center-of-mass system) no firm conclusion could be drawn.

The experiment has since been repeated using the energy averaging technique described earlier.

Exposures were made for both the 1ZC(13C, a)*'Ne and its inverse reaction '3C(12C, a)"Ne. During these the center-of-mass energy was varied from 14.28 to 14.52 MeV. It was hoped that, by averaging over 240 keV in the compound system, the effects of fluctuations would be removed and that if the asymmetry persisted it could be concluded that the reaction mechanism was at least in part direct. However, subsequent events have shown that this assumption may be erroneous.

Figure 18 shows the energy averaged spectra from these two reactions measured at a laboratory angle of 3 3/40. It is evident from the figure that the asym- metry in the population of the 3.66 and 3.89 MeV states very definitely persists. In the (13C, a) reaction the 3.89 MeV level is by far the strongest in the entire spectrum - in the inverse reaction (corresponding to a laboratory angle of about 176O in the coordinate

DISTANCE ALONG P L A T E ( c m )

FIG. 18. - Energy averaged spectra from the 13C(J2C, a)2JNc and 3C, a)z'Ne reactions measured while the center-

of-mass energy was varied from 14.28 to 14.52 MeV.

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C6-48 R. MIDDLETON, J. D. GARRETT, H. T. FORTUNE A N D K. R. BETTS

system of the former reaction) it is one of the weakest states. The inverse is true for the 3.66 MeV level.

Energy averaged angular distributions of the 3.66 and 3.84 MeV states are shown in figure 19.

These are drawn as if all measurements had been made in the coordinate system of the (13C, a) reaction.

The forward angle data (circles) were indeed measured using this reaction but the backward angle data (crosses) were obtained from the inverse reaction. To avoid confusion all subsequent data will be presented as if it had been obtained solely in the coordinate system of the (13C, a) reaction.

FIG. 19. - Energy averaged angular distributions for the 3.66 and 3.89 MeV states presented in the coordinate system of

the 12C(13C, 1)2 1Ne reaction.

The angular distributions shown in figure 19 exhibit several interesting and unusual features.

Firstly, they are highly asymmetric, secondly, in the region of maximum cross section they are fairly smooth and reminiscent in shape of a direct process and thirdly, they are close to being mirror images of one another. This latter aspect is very evident from figure 20 which shows the 3.89 MeV angular distribution compared with the 3.66 MeV angular distribution drawn reversed.

To determine whether the asymmetry in the 3.66 and 3.89 MeV angular distributions persists over a larger energy range than 240 keV, excitation functions were measured for these states. The results of these measurements, which were made with a position- sensitive detector mounted in the focal plane of

FIG. 20. - Illustrating the similarity in shape of the 3.66 and 3.89 MeV angular distributions shown in Fig. 19. Here the

3.66 MeV angular distribution has been drawn rcversed.

the 3 3/40 gap of the multi-angle spectrograph, are shown in figure 21. The data for the 3.66 MeV state a t @ (cm) = 1750 was obtained using the '"(12C, a)

reaction at @ (cm) = 50 - no data for the 3.89 MeV state was obtained at this angle owing to experimental dificulties.

The excitation functions exhibit several unusual and interesting features : (i) Over the entire energy range (13.8 to 15.4 MeV) that back angle data was obtained for the 3.66 MeV state, the asymmetry persists -

the ratio of the backward to forward cross sections ranging from a minimum of about 3 to a maximum of 15, (ii) the remarkable similarity between the forward angle yield of the 3.89 MeV state and the back angle yield of the 3.66 MeV state, (iii) the large widths

(> 500 keV) of the strong resonances observed at

about 14.5 MeV for the 3.66 MeV state at backward angles and for the 3.89 MeV state at forward angles.

There is also a remarkable similarity between the excitation functions for the 3.89 MeV state and that of the 7.83 MeV 2' state in

ON^

observed in the study of the I2C(l2C, a)'ONe reaction. For example, both appear to exhibit the ⁽⁽ window effect )) that has previously been discussed. This similarity also extends to the angular distributions if the effects of identical particles in the entrance channel of the 12C(12C, a) reaction are taken into account. Indeed, if the angular distributions of the 3.66 and 3.89 MeV states are summed, they are very similar in shape to that of the 7.83 MeV 2' state of 'ONe as is evident from figure 22. (The 'ONe data was measured at a center-of- mass energy of 13.5 MeV corresponding to the strongest peak in the 12C(12C, a) excitation function.) The spin and parity of the 3.66 MeV state is known [22] to be 312- and although that of the

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ALPHA-PARTICLE PRODlJCTlON I N HEAVY-ION REACTIONS C(i-49

1 I - u-,

E x = 3.66 MeV

INCIDENT ENERGY (c.m.1 IN MeV FIG. 21. - lC(l('3C, x)ZINc cxcitation functions for thc 3.66 MeV state measured at Oc.,. = 5" and 1 7 9 . (The 175"

measurements wcrc madc a t 5 O using the invcrse reaction.) Also shown is the yield to the 3.89 MeV level measured at

0 c . m . = 5''.

3.89 MeV state is unknown limiting values of 312 and 512 have been placed [23], parity unknown.

However, comparison with the mirror nucleus " Na strongly favors a 512- assignment - a conclusion also supported by comparison with 23Na.

IT indeed the 3.66 and 3.89 MeV states have J R = 312- and 512- respectively, an interesting possibility is that they have the same [220] quartet configuration as the 7.83 MeV 2' state of 2 0 N ~ with a weakly coupled I p,,, neutron. Such configurations would explain not only their selective population by the I2C(l3C, a) reaction but also many of the unusual features exhibited by the excitation functions. Further it would also explain the similarity in shape between the summed angular distributions and that of the 7.82 MeV 2' state of 'ONe (see Fig. 22). Normally it is expected that the cross section of the parent state should equal the summed cross sections of the weakly

-+- IZC ⁽' Z C , a ) 2 0 ~ e (7.83 MeV)

--*--

( " ~ , a ) ~ ~ ~ e ( 3 6 6 + 3 . 8 9 M e V l

B,,,,

(Degrees)

FIG. 22. Illustrating the similarity in shape between the summed angular distributions of the 3.66 and 3.89 MeV states measured using the IzC(I'C, u)2INc reaction and the l-'C(f2C,z)2'JNe angular distribution to the 7.83 MeV 2 ' state.

coupled states. As is evident from figure 22, this is not the case. This may be in part due to the presence of identical particles in the entrance channel of one of the reactions, but, it is difficult to take this fully into account without making detailed assumptions. Howe- ver, it is commentable that the ratio of the integrated cross sections of the 3.89 and 3.66 MeV states is 1.46 which is very close to the (2 J

+

I ) ratio of 1.5 assuming the states to have spins of 512 and 312 respective1 y.

The plausibility of the suggestion that the 3.66 and 3.89 MeV states have the same [220] quartet configuration as the 7.83 MeV 2' state of ,ONe with a weakly coupled p,,, neutron is further heightened by figure 23.

Here is shown a comparison of the 8 particle-n hole 8p-nh levels in the weak coupling model of the sd shell nuclei with that of the 4p-nh levels. The identification of the 3.66 and 3.89 MeV levels of 21Ne as a neutron weakly coupled to the 8p-4h 2' state at 7.83 MeV in 'ONe is indicated. A state at 2.79 MeV in ,'Ne, which is known to be 112-, is tentatively identified as the 112- member of the 8p-3h configuration. Two or threc states between 6 and 8 McV excitation in ,'Ne were observed to be strongly excited by the 12C(13C,a) reaction and may possibly be the 712- and 912- 8p-3h states.

Tn conclusion, the asymmetries observed in the I2C(l3C, a) angular distributions for the 3.66 and 3.89 MeV levels of 21Ne persist over a wide range of incident energies. Furthermore, both the angular distributions and the excitation functions of these states are very similar to those of the 7.83 MeV 2' state of ,ONe observed in the 12C(12C, a) reaction.

These striking similarities suggest that the 3.66 and

(13)

C6-50 R. MIDDLETON, J. D. GARRETT, H. T. FORTUNE AND R. R. BETTS

FIG. 23. - A comparison of the 8p-nh levcls in the weak coupling model of the sd shell nuclei with that of the 4p-nh levels.

3.89 MeV states in "Ne may be the 312- a n d 512- states of a n 8p-3h configuration arising from coupling a 1 p,,, neutron t o the 2+ [220] quartet state a t 7.83 MeV in 2 0 ~ e . A t present, the question remains open as t o why, in the 12C('3C, a) reaction, thc angular distribution of the 3.89 MeV level is,forward peaked, whereas that of the 3.66 MeV level is backward peaked.

Acknowledgements.

-

The authors wish to thank Drs. R. D. Amado R. M. Dreizler a n d D. P. Bala- muth for several useful a n d interesting discussions, Mr. Charles T. Adams a n d his staff for the careful maintenance a n d operation of o u r tandem accelerator a n d Mr. Laszlo Csihas for preparing all of the targets a n d in particular the ultrathin carbon films used in this work.

References [I] ALMQVIST (E.), KUEHNER (J. A.), MCPHERSON (D.)

and VOGT (E. W.), Phys. Rev., 1964,136, B 84.

[2] VOGT (E. W.),

MCPHERSON

(D.), KUEHNER (J.) and ALMQVIST (E.), Phys. Rev., 1964, 136, 1399.

[3] BORCGREEN (J.). ELBECK (B.) and LEACHMAN (R. B.), Mat. Fys. Skr. Dan. Vid. Selsk., 1964, 34, 1.

[4] BONDORF (J. P.) and LEACHMAN (R. B.), Mat. Fys.

Skr. Dan. Vid. Selsk., 1965, 34, 10, 1.

[5] HALBERT (M. L.), DURHAM (F. E.) and VAN DER WOU-

DE (A.), Phys. Rev., 1967, 162, 889, and HAL-

BEKT (M. L.), DURHAM (F. E.), MOAK (C. D.) and

ZUCKER (A.), ibid. p. 919.

[6] MIDDLETON (R.), GARRETT (J. D.) and FORTUNE(H. T.), Phy.s. Rev. Letters, 1970, 24, 1436.

[7] AKIYAMA ( Y . ) , ARIMA (A.) and SEBE (T.), Nuc/. Phys., 1969, A 138, 273.

[8] BRANFORD (D.), GARDKER (N.) and WRIGHT (I. F.), in Proccedings of the lnternational Conference on Properties of Nuclear States, Montreal, Canada, 1969, edited by M. Harvey et al. (Les Presses de I'Universite de Montreal, Montreal, Canada, 1969), p. 112.

[9] ARIMA (A.), GILLET (V.) and GINOCCH~O (J.), Phys.

Rev. Letters, 1970, 25, 1043.

[lo] SIEMSSEK (R. H.), Private communication.

[ l l ] BALAMUTH (D. P.), HOLDEN (J. E.), NOE (J. W.) and ZURMUI-II,F (R. W.), Phys. Rev. Letters, 1971, 26,

1271.

1121 HALBERT (E. C.), MCGROKY (J. B.), WIL.DENTHAL (B. H.) and PANDYA (S. P.), in Advances in Nuclear Physics, edited by M. Baranger and

E. Vogt (Plenum Press, Inc., New York, 1970), vol. 4.

[13] SIEMSSEN (R. H.), LEE (L. L.), Jr., and CLINE (D.), Phys. Rev., 1965, 140, 12.58.

[14] FALK (W. R.), KULISIC (P.) and MCDONALD (A.), N~tcl. Phys., 197 1, A 167, 1 57.

[15] LITHERLAND (A. E.), KUEHNER (J. A.), COVE (H. E.), CLARK ( M . A.) and ALMQVIST (E.), Phys. Rev.

Letters, 1961, 7, 98.

[I61 MIDDLETON (R.), Proceedings of the International Conference on Nuclear Reactions Induced by Heavy-Ions, Heidelberg, Germany, edited by R. Bock and W. R. Hering (North-Holland Publishing Co., Amsterdam, The Netherlands, 1970), p. 263.

[I71 CAMERON (J. R.), Phys. Rev., 1953, 90, 839.

[18] CARLSON (R. R.) and JOHNSON (D. J.), Phys. Rev.

Letters. 1970. 25. 172.

[19] REILLY (w!), G O ~ B I (A.), WIEI-AND (R.), BHUA (L.), SHAPIRA (D.), SACHS (M.) and BKOMLEY (D. A.), Bull. A m . Phys. Soc., 1971, 16, 100.

1201 KATTENRORN (H.), MAYER-BOKICKE (C.) and MER-

TENS (B.), NucI. P / l y . ~ . , 1969, A 138, 657.

[21] HALLOCK (J. N.), ENGE (H. A.), GARRETT (J. D.), FORTUNE (H. T.) and MIDDLFI.ON (R.), Bull. Am.

Phys. Soc., 1971, 16, 645.

[22] PKONKO (J. G.), ROLFS (C.) and MAIER (H. J.), Phys.

Rev., 1969, 186, 1174.

[23] HOWARD (A. J.), ALLEN (J. P.), BROMLEY (D. A.), O L N ~ (J. W.) and WARBURTON (E. K.), Plzys.

Rev., 1967, 157, 1022.