ANGULAR MOMENTUM EFFECTS IN FUSION-FISSION AND FUSION-EVAPORATION REACTIONS

(1)

HAL Id: jpa-00220639

https://hal.archives-ouvertes.fr/jpa-00220639

Submitted on 1 Jan 1980

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of

sci-entific research documents, whether they are

pub-lished or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destinée au dépôt et à la diffusion de documents

scientifiques de niveau recherche, publiés ou non,

émanant des établissements d’enseignement et de

recherche français ou étrangers, des laboratoires

publics ou privés.

ANGULAR MOMENTUM EFFECTS IN

FUSION-FISSION AND FUSION-EVAPORATION

REACTIONS

F. Plasil

To cite this version:

(2)

JOURNAL DE PHYSIQUE CoZZoque C1 0, suppZ6ment au nOl 2, Tome 41, ddcembre 1980, Page

C10-

183

\NGULAR..MOMENTUM EFFECTS

I N

FUSIONrFISSION_.AND

FUSION-EVAPORATION. REACTIONS

F. Plasil.

Oak Ridge National Laboratory, Oak Ridge, Tennessee 3 7930, U. S. A.

1. INTRODUCTION

I was asked by the conference organizers to present the experimental status of fusion-fission and fusion-evaporation phenomena, with special emphasis on the role of angular moment-. This scope is obviously too vast to be covered in full, and I have therefore found it necessary to concentrate on only a few topics of current interest. Consequently, this is not intended to be a compre- hensive review of this field of research, and much material that would naturally fall under the title of this talk has not been included. Furthermore, some of the points that I make are illustrated with examples with which I am most familiar: when often other cases would have served equally well.

Heavy-ion-induced reactions increased greatly in popularity about ten years ago. At that time efforts were concentrated on the elucidation of deeply inelastic collisions, and our understanding of fusion reactions was not questioned. It was assumed that for any given system the fusion cross section could be obtained by measuring the sum of the fission cross section, of, and the cross section for evaporation residues, eR. It was also taken for granted that both evaporation residues, ER, and fission fragments result from the deexcitation of compound nuclei and that the compound nuclei are formed in collisions that involve the lowest partial waves (Fig. 1.a). One of the first modifications of this point of view came when it was realized that fission cross sections for several heavy systems indicate the contribution of partial waves, that exceed the liquid-dr~p limit at which the fission'barrier, Bf, is predicted to vanish.' This raised the'possibility that some of the fission yield in such caseLs.may not be due to the fission of compound

heavy-ion-induced fission. Of these, only one mechanism is compound nucleus fission, C N F , ~ ' ~ and while the other may also be regarded as fusion- fission, FF, its nature is not as yet fully understood (see Fig. 1.b). Second, there is a large amount of evidence that many ER do not result from the deexcitation of compound nuclei, but rather from the deexcitation of products of partial fusion4" (Fig. 1.c). In view of these complica- tions, a large part of this paper deals with questions regarding the identity of fusion reactions. Following this intfoductory section, the various types of heavy-ion-induced fission will be discussed in Section 2. In Section 3 compound nucleus fission will be considered, with reference to fission barriers deduced from heavy-ion-induced fission. In Section

4

we will concentrate on problems associated with measured values of oER and on

F U ~ I O N DEEPLY INELASTIC OTHER FISSION OUASI- ELASTIC \ U---, FUSION DEEPLY QUASI - ELASTIC L

-FUSION INCOMPLETE FUSION (MASSIVE TRANSFER)

Today our view of heavy-ion fusion react:$ons

is even more complex bekause of several develop- Fig. 1. Schematic illustration of cross secti.on as a function of angular momentum for various

.merits. First, as was pointed out above, two dif- _{kypes'of heavy-ion reactions. For description,}

ferent mechanisms may contribute to observed see text:

(3)

c10-184 JOURNAL DE PHYSIQUE

the angular momentum dependence of incomplete fusion. Finally, in Section

5

we will once again consider the deexcitation of compound nuclei, this time with reference to the greatly enhanced a emission predicted by ~ l a n n ~ , ~ on the basis of the rotating liquid-drop, RLD, model. 1

2 . CHARACTERIZATION OF HEAVY-ION-INDUCED FISSION PHENOMENA

Until fairly recently, the characterization of heavy-ion-induced fission did not pose a problem. Early studies were carried out with relatively light heavy ions, such as C and Ne, and the fission products formed well-defined peaks in the .

'.,

ouserved mass and kinetic energy distributions of reaction products. It was concluded from all indi- cations that fission followed compound nucleus formation. It was pointed out in Ref. 2 that there are four observable conditions that may be used to characterize heavy-ion-induced fission. These are: (i) a distinct peak in the mass (or charge) yield distribution of prodhcts that is centered at symmetric mass divisions; (ii) an angular distribution that follows a l/sine functional form; (iii) fragment kinetic energies that can be understood in terms of Coulomb repulsion between elongated fragments at the scission point; and

(iv) full momentum transfer from the projectile to the fissioning system.

An example.of a system which involves fission of compound nuclei produced in heavy-ion reactions is shown in Fig. 2. In this case fission fragments

Fig. 2. E vs. AE array of various products from reactions of\175-MeV 20Ne with lS0Nd. Fission events are well-separated from other products. From Ref.

8.

'

-

LIGHT DEEPLY

Elob (arbitrary scole)

Fig.

3.

Kinetic energy vs. mass contour diagram of products from the system 197Au+201-MeV

*OAr. Principal reaction-product groupings are labeled. From Ref. 9.

from reactions between 175-MeV 2 0 ~ e ions and lS0~d nuclei stand out well-isolated from other products in the raw E-AE array.8 The four conditions for heavy-ion-induced fission listed above are all satisfied for fissioning systems of this type. In Fig.

3

the mass-energy distribution is shown for reaction products from 248-M~v 6 5 ~ u bombard- ments of A U . ~ The fissioning system and the projectile are considerably heavier in this case than in the previous one. Once again, a well-separated, distinct fission peak can be seen, and the four conditions for fission are presumably also satisfied. There are, however, some significant differ- ences between this fission distribution and that shown in Fig. 2. First, it is possible that the tail of the distribution of deeply inelastic products contributes to the fission peak in the Cu+Au case. (We shall examine possible consequences of such ~ontam~nation in the following section.) Second, the integrated fission cross section from the Cu+Au ,reaction is such that partid waves with

1

(4)

It has been pointed out that in cases such as the above Cu+Au reaction, it is necessary to distinguish between fusion-fission (FF) and compound nucleus fission (cNF).~'~ Thus, while it may be reasonable to attribute all of the observed fission yield to the fission of fused systems, it is very likely that only those impact parameters which are below the Bf = 0 limit can result in the formation of true compound nuclei in which all degrees of freedom are equilibrated prior to fission. This view of CNF as a special case of FF is an appealing concept. Unfortunately, experimentally it is difficult to distinguish between CNF and other FF processes, since in both cases the faur empirical conditions for fission discussed above are satisfied. Recently, several investigations have focused on the nature of FF when Bf = 0. These studies have concentrated on the width of fragment mass distributions as a pos-

11-19 sible signature of a new reaction mechanism, and we shall examine some of the pertinent results below.

One of the first cases investigated was the 132~e+56~e reaction at 5.73 I4ev/u.l1 The charge distribution of reaction products is shown in Fig.

4.

The hatched area indicates the contribution from quasi-elastic events, and the remainder of

Fig.

4.

Element distribution of quasi-elastic reaction products (hatched area) and of fully relaxed fragments (open area) from reactions between and 56Fe at

5.73

M~V/U. From Ref. ll.

the yield is attributed to an energy-relaxed mass- equilibrated component. It was pointed out in Ref. 11 that this component cannot be understood on the basis of diffusion models and that it does not include a contribution from deeply inelastic events. In fact, the peak in Fig.

4

is consistent with FF on the basis of the empirical criteria discussed above. The two noteworthy features of the 132~e+56~e data are that from cross section considerations, as in the Cu+Au case, partial waves with Bf = 0 contribute to the fission yield and that the width of the charge distribution (22 charge units FWHM) is much larger than the 11 charge units FWHM predicted from liquid-drop-model calculations. l0 Similar results (very broad mass distribution and large fission cross section) were also reported by Olmi et al.'' for the case of 238~+48~a.

A systematic investigation of widths of fission mass distributions as a function of angular momentum was undertaken by Lebrun et a1.13 for the composite system 205~t obtained in the reactions 20~e+nat~e and 40~r+165~o. The bombarding energies were 124 and 206 MeV in the Ne case and 192 and 297 MeV in the Ar case. One of the mass distributions is shown in Fig. 5. It is clear that there is no difficulty in separating the fission component from other reaction products. The measured widths of the mass distributions were cor- rected for excitation energy effects; and it was concluded that the widths increase considerably with increasing angular momentum of the fissioning system.

(5)

c10- 186 JOURNAL DE PHYSIQUE

Fig. 5 . Mass distribution of the products detected at 30' for the 297-MeV 40Ar+165Ho system. Two peaks are observed, one corresponding to elastic and deeply inelastic products and the other one corresponding to fission following complete fusion. The dashed line indicates the separation between the two components. From Ref. 13.

dramatic change is seen near the angular momentum at which Bf is predicted to vanish. The curve through the data points is a curve to guide (or seduce) the eye. The data of Fig. 7 have been used by GrCgoire et al. l6?l9 for comparison with simple statistical model calculations. Their calculated curve is shown in Fig. 8. It can be seen that it is consistent with the available data, although the discontinuity at Bf = 0 is in marked contrast with the curve of Fig.

7.

Based on the experimental evidence reviewed above, several groups have invoked the existence of a newtype of interaction mechanism for fission which involves partial waves beyond the calculated Bf = 0 limit.11'15-19 There has not been a lack of proposed names for this "new" mechanism. These include fission without barrier, fast fission,16'19 and quasi,-f~sion.~* It is my opinion that the existing experimental evidence is not

sufficiently strong to warrant the inroduction of new terminology, although I find the terms fast fission and quasi-fusion fairly appealing for reasons that will be indicated below. In any case, it seems reasonable to infer that for the heavy systems discussed above, processes other than CNF contribute to the observed fission distributions..

The possible nature of heavy-ion-induced fission beyond the Bf = 0 limit is discussed below with reference to two schematic figures (Figs. 9 and 10) taken from Ref. 18. The second of these (Fig. 10) is based on considerations of

~wiatecki.~' In Fig.

9

the calculated potential energy is shown as a function of the separation distance for the case of Ar+Ho at several values of angular momentum, a . It can be seen that pockets in the potential energy curves exist up to

L % 90. However, because of tangential friction, the orbital angular momentum in the exit channel

Fig. 6. Reduced full width at half maximum,

rM/~tot,

versus the difference between the critical angular momentum for fission events, fi

crit

'

and the angular momentum at which the fission barrier is predicted to vanish,

&B*

(6)

Fig.

7.

FWHM of the mass distribution of fission products as a function of L

.

Experimental points from Refs. 13, 15, 20, an$*i6. The curve is drawn through the data to guide (or seduce) the eye.

is less than that in the entrance channel. For illustration purposes, a loss of 2/7 of the initial orbital angular momentum, corresponding to the case of rolling, is indicated in Fig.

9.

It is possible that a sufficient condition for fission to be observed is that there be a pocket in the two-body potential in the exit channel. This situa- tion may involve sufficiently long trapping times to lead to l/sin8 angular dist~ibutions and to equilibrate the mass degree of freedom, thus leading to symmetric mass distributions. This point of view is similar to that of Birkelund et al. ,23 who have used it for the purpose of an operational definition of fusion in the case of heavy fissioning systems.

Perhaps a more graphic, but less quantita- tive, description is given schematically in Fig. 10.18 Here potential energy contours are indicated as a function of both the separation distance and of the neck radius of the dinuclear system for cases involving L waves both below and above the Bf = 0 limit. The collision approach, as well as the various reaction paths, is indicated. As the two colliding nuclei approach each other, they will encounter a ridge in the potential energy surface. If the partial wave involved is such that the fission barrier of the composite system is finite (Bf > 0), then there exists a minimum desig- nated by CN (compound nucleus) which can be

reached via the fusion path. The resulting compound nucleus may subsequently undergo fission via the fission saddle. If, on the other hand, L is such that B _f

5

0, then there is no minimum in the

Fig. 8. Same data as in Fig.

7.

In addition, a calculated curve of Grggoire et al. (Refs. 16,191 is shown. From Ref. 16.

Fig. 9. Potential energy V(r) versus separation distance for the system *'Ar+l6'~o. The nuclear potentials were calculated with the energy- density method. Centrifugal potentials were calculated at several L values with the assumption of rigid body moments of inertia for two spheres. The drop of 2/7 in the region of close contact is expected for orbital angular momentum dissipa- tion in rolling conditions. The limiting L value corresponds to the disappearance of a pocket in the exit channel curve (dZv/dr2 = 0). This is a

modified version of a figure from Ref. 18.

potential energy surface. However, it is conceiv- able that in this case the system still proceeds to the same regions of the separation distance vs., neck radius space, along the shallow potential energy contours, as indicated. In such an eventu- ality, the time involved may once again be long enough to allow both the rotational and the mass _.

(7)

c10-188 JOURNAL DE PHYSIQUE

sepamtion distance

Fig. 10. A two-dimensional plot of potential energy in which possible entrance and exit trajec- tories are indicated. The abscissa is the separation distance, and the ordinates correspond to the neck radius. For a description of the reaction paths, see the text. From Ref. 18.

degrees of freedom to equilibrate. In both cases,. the deeply inelastic collision path is indicated by a bouncing-off from the initial potential energy ridge.

If the conjectures discussed above are correct, then it is reasonable for the noncompound fission to be subject to the following conditions.18 First, there should be a pocket in the sudden interaction potential as a function of the separation distance (see Fig. 9). This condition defines a limiting value of the orbital angular momentum in the entrance channel. Second, it is necessary that there should be a range of !L values between the

a

at which Bf = 0 and the critical ,.?

value calculated with the sudden approximation. These conditions define a region in the target mass vs. projectile mass diagram where noncompound nucleus. fission may be expected. This region is indicated in Fig. ' 1 1 , which is taken from Ref. 18.

Experimental points are also shown in the figure and can be seen to be consistent with predictions.

TARGET MASS

Fig. 11. Combinations of projectile and target masses at which noncompound nucleus fission can be expected (hatched area). Below the hatched area, compound nucleus fission is predicted. Above the hatched area it is expected that no fission- like events will be observed. Experimental cases are indicated by closed squares for compound nucleus fission, open circles for noncompound nucleus fission, and closed triangles for cases where essentially no fission is observed. From Ref. 18.

It can also be seen that for projectiles with A

( 20 only CNF is expected. In this context it is worth pointing out, however, that Viola et al.24 have observed FF cross sections that exceed the Bf = 0 limit in the case of 20~e+

235~.

(8)

FREE

ENERGY

U,

I

=30h,

T

=l.GMeV

U

I

=120h,

T=1.6 MeV

U

I=30h,

T=4.5 MeV

0 Q 0

'0.4 1.0 1.6 "0.4 1.0 1.6 O 0 . 4 1.0 l . 6 MASS ASYHHETRY RASS ASYRHETRY flASS ASYflHEfRY

Fig. 12. Free-energy surface of '''At is shown along the liquid-drop valley as a function of the neck thickness related to the size of the sphere and of the mass asymmetry ZM,/(M,+M, ). Three different combinations of angular momentum (I) and tem- perature (T) are shown. The free energy is related directly to the potential energy (Ref. 25). From Ref. 25.

Interesting fission mass distributions have been obtained recently by Oeschler et for 32~-induced fission of relatively light systems. Scatter plots of fragment lab kinetic energy vs. fragment mass are shown in Fig. 1 3 for four of the systems that have been investigated. In the case of 3 2 ~ + 8 9 ~ a fission peak appears well-isolated from other reaction products. In this case the observed fission is certainly FF, and possibly CNF. In the other cases shown in Fig. 13 the fission peak is less distinct and merges with other reaction products. Mass distributions from Ref. 26 are shown in Fig. 14. The mass distribution from the 3 2 ~ + 8 9 ~ reactions forms a sharp peak centered at symmetric mass divisions. The remarkable feature of this distribution is that it is much narrower than predicted on the basis of the liquid- drop-model calculations.1° It is seen in Fig. 14 that as the fissioning systems become lighter, the mass distributions broaden, and finally they no longer peak at symmetric mass divisions. This is qualitatively what is expected for systems that r,ange from one side of the Businaro-Gallone liquid- drip point to the other. However, Oeschler et have, concluded on the basis of indepen- dence-hypothesis'arguments that the proximity.of the Businaro-Gallone lilhit is not likely to be the correct explanation. While'arguments are also presented in Ref. 26 against the possibility of increasing contamination of the fission distr'ibu-

tions by deeply inelastic products, this appears to me to be the most likely explanation in view of the data presented in Fig. 13.

Oeschler and ~reiesleben~ have combined the above findings with other measurements of widths of fission mass distributions and have concluded that the trend of the measured widths as a function of the fissility parameter is essentially orthogonal to the liquid-drop-model predictions of Nix.'' In concluding this section, it is fair

i

to say that, in view of the many open questions, the general area of FF and of associated fission mass distributions constitutes a potentiall$ fruit- ful field for futuye investigations.

3.

FISSION OF THE COMPOUND NUCLEUS 1 5 3 ~ b In this section angular momentum effects 5n CNF will be illustrated with reference to the deexcitation of 1 5 3 ~ b compound nuclei produced in the 20~e+133~s and 1 2 ~ + 1 4 1 ~ r reactions.28 The purpose of this study was to deduce the fission barrier for l S 3 ~ b and to check the predictions of the rotating liquid-drop model1 with respectr to the $tudy of angular momentum dependence by Beckerman

(9)

JOURNAL DE PHYSIQUE

A,,, Elab:153neV

I

""

"'

A s y m m e t r y ( A ~ / A ~ + A T I

Fig. 13. Scatter plots of laboratory energy vs. mass for four reactions demonstrating a change in the mass distributions of the relaxed frag- ments. From 'Ref. 26. '

Fig.

14.

Mass distributions of the relaxed reaction products vs. asymmetry for six "S-

(10)

Our system was chosen with some care, since it is necessary that all observed fission events can be attributed to CNF. Thus the fission peak must be well-separated from other reaction products. Furthermore, the system must not involve partial waves that approach the Bf = 0 limit. These two cpnstraints both point to fissioning systems in the medium-mass region (A % 150-180) formed with relatively light heavy ions.

Fission barriers can be extracted from heavy- ion-induced fission data by means of statistical model calculations. In order to do so reliably, '

it is necessary to measure excitation functions for both fission and the production of evaporation residues (ER). In addition, the calculations have to include the following : ( l ) spinLdependent level densities; (2) the possibility of multiple particle emission prior to fission; and (3) the variation of the fission barrier with angular momentum. All of these conditions have been met, and our systems constitute the only case in which both fission and ER cross sections, of and oER have been measured as a function of excitation energy for two different reactions that produce the same compound nucleus.

The statistical model analysis of the measured of and uER excitation functions was performed by means of the computer program ORNL ALICE, 30y31 which includes all the features listed above. Only those partial waves were considered that contribute to the sum of of and aEE, i.e., to the measured compound nucleus cross section. The yrast line and angular momentum dependence of the fission barrier were given by the RLD model.' Fits were made with two variable parameters. The first, af/av, is the ratio of the level density parameter for fission to that for particle emission, The second parameter, k, is a scaling factor defined by Bf = k~~~~ ( J = 0) where BfLD (J = 0) is the fission barrier from the RLD model at zero angular momentum. Effective J-dependent f issioi barriers

LD used in tbe pro,gram are given by B _f(J) = kBf (J). It was found that the slopes of calculated excitation functions are sensitive primarily to changes in k and relatively insensitive to changes in af/>. The effect of varying k is shown in Fig. 15 for fits to the lowest of point from the 12c+ 14'pr reaction. It is clear that here the curve with k = 0.8 is the best fit to the measured excitation function, implying that Bf in this case is equAl 'tb

80%

of liquid-dro,p value. A similar

sensitivity of the calculated slope to Bf was found in the 20~e+133~s case. In Fig. 16 both fission excitation functions are shown, together with the best fit to both sets of data. The parameter values for the fit are af/av = 1.08 and k = 0.83. Since the value of BfLD(~ = 0) used in the calculation was 34.3 MeV, we have concluded that the fission barrier of lS3~b is 28.5

*

1.7

MeV.

EXCITATION ENERGY ( M e V )

Fig. 15. Effect of fission barrier variati* on statistical model fits to the fission excitation function from the 12C+141Pr reaction. The labels on the curves indicate values of k in the relationship Bf = k (J ~= 0). The corresponding ~ ~ ~ values of af/ay range from 0.985 for k =

0.7

to

(11)

A very important aspect of our results is the fact that the measured fission excitation func-

10-2

60

70

80

90

100 EXCITATION

ENERGY (MeV)

Fig. 16. Excitation functions for the fission of the Is3,Tb compound nucleus produced in reactions of 12C with 141Pr and "Ne with "3Cs. The' circles indicate expercmental results. The curves 'are statisticaf model f.its to both sets of data -with:tlf/au = 1.08 and

Bf =

28.5 MeV. From Ref. 28.

tions from the l2C+l4'pr and the 20~e+133~s systems both lead to the same values of the parameters, a /a and Bf. Since the difference,in fis-,

f v

sility between the two systems is due to the larger angular momenta involved in the Ne+Cs case, we can conclude that the variation of Bf with angular momentum is adequately described by the RLD model. This supports the view that the RLD model description of nuclear deformatbns as a function of angular momentum is also reasonable.

Our Bf value of 28.5 HeV for lS3Tb (83% of the liquid-drop value) is in marked contrast to Bf = 16.4 MeV (57% of the liquid-drop value) deduced in Ref. 29 for the neighboring nucleus l5'~o. Several factors contribute to the discrep- ancy between our results and those obtained,by Beckerman and ~ l a n n . ~ ~ First, in at least three cases considered in Ref. 29 (35~1+62~i., 20~e+ lo7~g, and 40~r+109~g), there is no doubt that deeply inelastic events contribute to the apparent fission cross sections. For example, our 20~e+ lo7Ag data32 quoted in Ref. 29 were difficult to decompose, as can be seen from Fig. 17, which shows the charge distributions obtained for this system by Babinet et Second, the value of Bf extracted from the excitation functions depends primarily on the slope of these functions at the lowest energies. In this work the lowest of values are in the region of 0.03 mb, while the lowest

a results for 55~l+i16Sn and 35~1+141~r are' only f

about 20 In addition, we cover a range of 30 MeV in excitation energy, in contrast to a range of only 15 MeV in the 3 5 ~ 1 cases above.

The Bf value of 28.5 f 1.7 MeV obtained for l S 3 ~ b can be compared with the recent calculation

of-nuclear masses performed by Moller and ~ i x . ~ ~ The calculated Bf value for lS32b of 26.0 MeV is

(12)

4.

CHARACTERIZATION OF EVAPORATION RESIDUES In the previous two sections we have concentrated on fusion-fission phenomena. In this section and in the following one we shall consider angular momentum aspects of fusion reactions that lead to evaporation residues. As in the fission case, our view of reactions leading to ER has been undergoing changes recently. Thus, it has become apparent that in many experiments products which at first appeared to be ER resulting from the deexcitation of compound nuclei turned out to be residues from incomplete fusion. This appeared to be one of the main themes at the recent Bad Honnef workshop on heavy-ion fusion reactions.' We will illustrate this point with references to the 160+40~a reaction. 38'39

Interest in the 160+40~a reaction has been considerable for two reasons. First, it was found that as the bombarding energy was increased from 63 to 214 MeV, the cross section of ER appeared to remain near 1200 mb.38 At the highest energy of 214 MeV, the measured uER was in apparent dis-

100 175 MeV

+

107sT79~g

-

L 9 n

.!5

l0 5

-

G

F

b I 9 0.1 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32

Fig.

17.

Production cross sections vs. Z at various laboratory angles for the system Ag+ZoNe. From Ref. 33.

agreement with predictions of the rotating liquid- drop model,' based on the consideration that fission should compete when the fission barrier becomes similar to the particle binding energy

_-

(about 10 MeV). This is illustrated in Fig. 18, which is taken from Ref. 38. It is clear thatiif uER were to rkmain at 1200 mb at an even higher bombarding energy, then the RLD model limit given by Bf = 0 would be exceeded. The second reason for interest in this system was provided by TDHF calculations which predict that at fairly high energies, the lowest partial waves do not lead to fusion. Consequently, an attempt was made to measure oER for 16~+40~a at 312 M ~ v . ~ ~

Fig. 18. Measured evaporation residue cross sections as a function of 1 / ~ _c.m.for 'the system 160+40Ca (closed circles). The dashed lines indicate estimated upper limits on the total fusion

(trius) and evaporation residue (o ) cross sec- ER

(13)

C10-

194

The method used for the above measurement was similar to that of Ref. 38. ER were measured at several angles by means of E-AE telescopes. Unfortunately, it was found that there was not a clean separation between ER and other reactions products, such as the heavy partners of deeply inelastic collisions. This was also the case in the 214-MeV case of Ref. 38, although to a lesser extent. In addition, the angular distribution of apparent ER at 312 MeV was found to be very broad and inconsistent with evaporation theories. In Ref. 38 a similar problem can again be found in the 214-MeV case. This is shown in Fig. 19. It can be seen that at 214 MeV the angular distribution extends to very backward angles and that it even exhibits a shoulder which may be the result of the presence of two distinct processes. We were forced to conclude that the operational definition of Ref. 38 for observed ER has broken down, at least at 312 and 214 MeV, and that the extracted values for uER had little meaning. This conclusion was corroborated recently by Gonthier et

who studied the similar reaction of 160+~i at 310 MeV. Since in this case a coincidence experiment was performed, it was possible to conclude that a considerable fraction of the ER were accompanied by the prompt emission of energetic light particles and thus did not originate from the deexcitation of a true compound nucleus.

Incomplete-fusion reactions, which played a role in the above example, provide an interesting field of study in themselves, particularly since there appears to be a correlation between the nature of the incomplete fusion and the angular momentum transfer involved. Siwek-Wilczynska et have proposed a generalized concept of critical angular momentum to describe incomplete fusion. In this picture, complete fusion takes place.for the lowest partial waves involved in the reaction. For incomplete fusion, lower !t waves are associated with heavier captured mass, and higher !t waves are associated with lighter captured mass. Thus in the case of + 160 bombardment, for-example, the region of partial waves associated wi,th the'capture of 12c lies just ibove the critical !t value for complete fusion. The next highest region of partial waves is associated.with the capture of 8 ~ e , and so on.

The most conclusive evidence for the above point of view has been provided by Geoffroy et

in an experiment in which charged-particle

Fig. 19. Laboratory angular distributions of evaporation residues at a number of bombarding energies for the system 160+'"Ca. From Ref. 38.

energies were measured at several angles, together with ER and with associated Y multiplicities. Strongly forward-peaked a particles have been observed in coincidence with final products, which were identified by means of their y spectra. Some of the results are shown in Fig. 20. From the higher moments of the Y-multiplicity distributions, distributions of J the angular momentum

Y'

prior to y.decay, were constructed for the final products l6'Er, 157~y, and lS4Gd. These are shown in Fig. 20.a. In Fig. 20:c the average value of J

(14)

together with <J >, the average angular momentum prior to neutron emission. From the <Jn> values and from the J distributions, distributions of J

Y n

were deduced. They are shown in Fig. 20.b. Since the average angular momentum transferred to the incompletely fused system increases linearly with the mass of the captured fragment (Fig. 20.c), it is possible to deduce the average entrance-channel orbital angular momentum, <P,>, on the assumption

that the angular momentum of the initial system is divided between the projectile fragments in propor- tion to their masses. The values of <Q> were found to be 52, 60, and

74

for reactions involving the

4

capture of "C, 8 ~ e and He, respectively. This ,

result is shown in Fig. 20.d, together with the predictions of Siwek-Wilczynska et alS4 It cah be seen that the agreement between experiment and theory is excellent.

yrast

162n,C

/

line

J

Acaptured

Fig. 20. (a) Entry-state J distributions in

'

6 0 ~ r (dashed curve), Y

lJ7Dy (dotted curve), and "'Gd (dash-dotted curve) associated with energetic forward-emitted fragments, The vertical arrows give gy>. (b) Jn distributions prior to neutron emission leading to the same products. The vertical arrows indicate the U > values. The base-line ordinate for each

n

J distribution represents the excitation energy of the product after emis- _n sion of the appropraite projectile fragment(s) with the beam velocity. The yrast line is for a rigid sphere of A = 162 and r , = 1.2 fm. (c) Plot of

d >and U n > vs. captured mass, assumed to be twice the captured charge.

Y

(d) Regions of incomplete fusion based on the model of Ref.

4.

The vertical lines 1, 2, 3, and

4

give the critical Q values for the onset of "C,

(15)

C10-196 JOURNAL DE PHYSIQUE

5.

ANGULAR MOMENTUM EFFECTS IN THE DECAY OF DEFORMED AND SUPERDEFORMED NUCLEI

In this secti,on we turn to problems of angular momentum effects associated with the decay of equilibrated compound nuclei. We shall restrict our attention to the case of possible a-decay amplification in superdeformed nuclei. 6'7 The roots of this work lie in the rotating liquid-drop model,' which predicts the existence of superdeformed shapes at high angular momenta. In Ref. l shapes of rotating ground-state configurations

Figr 21. Quilibrium ground and saddle-point shapes for several values of angular momentum for a nuclkus near "'Tb. The axis of rotation is indicated, as well as the shape for the Itground statesv1 (H gr BK). The higher deformation in each case represents the saddle-point shape (PP). Rotational parameter y and fissility parameter X

are defined in the text. The superdeformed

Itground-state" shape is indicated by BK. From Ref.

1.

were calculated, as well as those of rotating nuclei at the saddle point. These are illustrated in Fig. 21 for several values of the rotational parameter y and for X = 0.6, where X is the fissil-

ity parameter. (y is defined as the ratio of the rotational energy of a sphere'to its surface energy, and X is defined as the ratio of the Cou- lomb energy of a sphere to twice its surface energy. The value of X = 0.6 corresponds approxi- mately to the region of rare-earth nuclei.) For a nonrotating nucleus (y = O), the liquid-drop ground state is spherical. As the angular momentum is increased, the nucleus is predicted to rotate about its axis of symmetry and to take on an oblate shape (see Fig. 21). With further increase in angular momentum, a critical angular momentum, yIJ is reached beyond which the rotating nucleus is predicted to assume a superdeformed prolate shape and to rotate about an axis which is perpen- dicular to its axis of symmetry. Such a superdeformed shape is illustrated for y = 0.09 in Fig. 21. If the angular momentum is increased still

Fig. 22. Regions of stability in the RLD model X-y space. X is the fissility parameter

(16)

further, rotating ground and saddle-point shapes become identical at a second critical value of angular momentum yII. This is the point at which B is predicted to vanish. Values of yI and yII

f

are shown as a function of the fissility parameter in Fig. 22. It can be seen that for X values below

X %

0.6

there is a considerable range of y values for which superdeformed nuclei are predicted (the region between the yI And yII curves).

~ l a n n ~ ' ~ has investigated in detail the consequences of the existence of superdeformed nuclei on the nuclear deexcitation process. He has used deformations based ,on the RLD' model to generate transmission coefficients as a function of the compound nucleus angular momentum. These were then incorporated into a Hauser-Feshbach calculation in which fission competition was included. The results are illustrated below with reference to the 149~b compound nucleus. The radii and potentials appropriate to this case are shown as a function of angular momentum in Fig. 23. They are expressed as a ratio of the corresponding values for a spherical nucleus. It can be seen that there is little deviation in these quantities from spher-

Fig. 23. Ratios of radii and potentials to those of a sphere for lU9Tb nuclei as a function of angular momentum, a . Values of R and V were

; calculated as shown by, the small open and closed

points. The shapes of some of the nuclei are shown superimposed on-a spherical projection of a nucleus of the same volume. The oblate and prolate regions are indicated, as well as values of the angular momentum at which the RLD model predicts the fission barrier, Bf, to be zero and 8 MeV. .From Ref.

7.

2.2 2.0 1.8

-

L. P 1.6 % S 0 '2 1.4 K 1.2 1.0 0.8 0.6

ical values until an angular momentum of about 70 h is reached. Beyond this point Blann assumes that the superdeformed shape exists, and both quantities change rapidly with increasing angular momentum. The results of the Hauser-Feshbach calculations for this case are shown in Fig. 24 in terms of calculated branching ratios for the various deexcitation channels. It can be seen that while fission is expected to dominate the decay process for

a

> 70 if transmission coefficients for spherical nuclei are used, a emission dorni- nates in the case of transmission coefficients appropriate to the deformed nuclei. The effect is so large that the term "a-decay amplification" 6 may not be unreasonable.

Blann points out that his conclusions are consistent with a number of experimental results that were previously explained on the basis of nonequilibrium a e m i ~ s i o n . ~ It should be remem- bered, however, that the a-decay amplification is the result of emission from very elongated shapes. The shapes of the dinuclear system as it evolves from the collision configuration to the compound nucleus are also very elongated. Thus, it

- - -

Deformed '-Tb

-

_{- - -}

VIV, RIRo

-

Oblate Pmlate

-

:

-

-c-.-

-

.,

-4;

-

- U . - - , W - -

Cl

I

- 7 , B , = 8 p s * x , B f = o L

Fig. 24. Calculated branching ratios for the deexcitation of lQ9Tb at 120 MeV of excitation vs., initial angular momentum. The open circles near the abscissa represent the values of compound nucleus angular momenta for which results were calculated. Smooth curves were drawn through these points. Fission curves (f.) represent total .fission,' whereas n,p,a curves represent only first- chance emission. Results are' shown for spll;rical (solid lines) and deformed nuclei (dashed lines'). From Ref..

7.

1 I I I I I I

'.

.

(17)

C10- 198 JOURNAL DE PHYSIQUE

may be possible that a emission could take place Acknowledgments

prior'to the establishment of equilibrium and be This work was sponsored by the Division of enhanced by the same effects as those discussed by High Energy and Nuclear Physics, U.S. Department Blann. It is also possible that it may be diffi- of Energy, under contract W-7405-eng-26 with the cult to distinguish experimentally between the Union Carbide Corporation.

a-decay;'amplification from an equilibrated rotat- The help of R. L. Ferguson, of S. J. Ball, ing compound nucleus and nonequilibrium cx emission. and of F. Pougheon in the preparation of the final

manuscript is gratefully acknowledged.

REFERENCES 1. S. Cohen, F. Plasil, and W. J. Swiatecki, Ann.

P h ~ s .

82,

557 (1974).

2. F. Plasil and R. L. Ferguson, Proceedings of the IAEA Symposium on the Physics and Chemis- try of Fission (Julich, Federal Republic of Germany, October 1979).

3. H. Oeschler and H. Freiesleben, Proceedings of the Symposium on Deep Inelastic and Fusion Reactions with Heavy Ions (Berlin, October

1979).

4.

K. Siwek-Wilczynska, E. H. du Marchie von Voorthuysen, J. van Popta, R. H. Siemssen, and J. Wilczynski, Phys. Rev. Lett.

42,

1559 (1979).

5.

Proceedings of the International Symposium on Heavy-Ion Fusion Reactions (Bad Honnef, Federal Republic of Germany, March 1980). 6. M. Blann, Phys. Lett.

E,

5

(1979).

7.

M. Blann and T. T. Komoto, LLL Report UCRL- 83247 (August 1979), unpublished and M. Blann, Phys. Rev. C z , 1770 (1980).

8. M. L. ~albert, R. A. Dayras, R. L. Ferguson, F, Plasil, and D. G. Sarantites, Phys. Rev. C17,

-

155 (1978)-

'

9.

C. Ng6, J. Piter, B. Tamain, M. Berlanger, and F. Hanappe, Z. Phys.

a,

161 (1977). 10. J. R. Nix, Nucl. Phys.

U ,

241 (1969). 11. B. Heusch, C, Volant, H. Freiesleben, R. P.

Chestnut, K. D. Hildenbrand, F. ~Eehlhof er, and W. F. W. Schneider, Z. Phys.

m,

391

(1978).

12. A. Olmi, H. S a w , U. Lynen, V. Metag, S. Bjiirn- h o G , D. Habs, H.J. Specht, R. Book, A.. Gobbi, H. Stelzer, Proceedings of the 15th Winter Meeting on Nuclear Physics (Bormio, Italy,

1978), P. 724.

13. C. Lebrun, F. Hanappe, J. F. Lecolley, F. Lefebvres, C. Ng6, J. Piter, and B. Tamain,

- Nucl. Phys.

a,

207 (1979).

14. F, Hanappe, M. Berlanger, C. Lebrun, C. Ng8, J. ~Qter, .and B. Tamain, Proceedings of the

.

' _IAEA_{Symposium on the Physics and Chemistry}

of Fission (Julich, ~ederal Republic of Ger- many, May 1979)

..

15. C. Gregoire, M. Berlanger,

R.

Borderie, D. Gardes, J. Girard, F. Hanappe, J. Matuszek, C.' Ngo, and B. Tamain, unpublished preprint, 1980.

16. C. Grigoire, R. Lucas, C.Ng6, B. Schiirmann, and H. Ng6, Report D P ~ - N / H F / ~ ~ / ~ , Saclay, France, unpublished preprint, 1979. 17. F. Hanappe and B. Borderie, Proceedings of

the 17th Winter School on Nuclear Physics (Bielsko-Biala, Poland, February 1980). 18. M; Lefort, Proceedings of the International

Symposium on Heavy-Ion Fusion Reactions (Bad Honnef, Federal Republic of Germany, March 1980).

19. C. Gregoire, R. Lucas, C. Ng6, H. Ngs, and B. ~chiirmann, proceedings of this conference, volume of contributed papers, p. 145.

20. F. Plasil, D. S. Burnett, H. C. Britt, and S. G. Thompson, Phys. Rev.

142,

696 (1966). 21. J. P. Unik, J. G. Cuninghame, and I. F.

Croall, Proceedings of the Second IAEA Sym- posium on the Physics and Chemistry of Fission (Vienna, July 1979), p. 717.

22. W. J. Swiatecki, Proceedings of the Interna- tional School of Nuclear Physics (Erice, Italy, March-April 1979).

23. J. R. Birkelund, L. E. Tubbs, J. R. Huizenga, J. N. De, and D. Sperber, Phys. Rep.

56,

107

(1979).

24. V. E. Viola, Jr., R. G. Clark, W. G. Meyer, A. M. Zebelman, and R. G. Sextro, Nucl. Phys.

e,

174 (1976).

25. M. E. Faber, AIAU Report 80203, Vienna, Aus- tria, unpublished preprint, 1980.

26. H. Oeschler, P. Wagner, J. P. Coffin, P. Engel- stein, and B. Heusch, Phys. Lett. Q, 191 , (1979).

27. U. L. Businaro and S. Gallone, Nuovo Cimento

-

1, 629 and 1277 (1955).

28. F. Plasil, R. L. Ferguson, R. L. Hahn, F. E. Obenshain, F. Pleasonton, and G. R. Young, to be published in Phys. Rev. Lett.

29. M. Beckerman and M. Blann, Phys. Lett.

E,

31 (1977).

30. F. Plasil, ORNL/TM-6054, unpublished report, 1977.

31. F. Plasil, Phys. Rev. C S , 832 (1978). 32. F. Plasil, Proceedings of the International

(18)

33. R. Babinet, L. G. Moretto, J. Galin, R. Jared, J. Moulton, and S. G. Thompson, Nucl. Phys. A258, 172 (1976).

34. P. ~:ller and 3 . R. Nix, Proceedings of the Workshop on Nuclear Dynamics (Granlibakken, California, March 19801, Report LBL-10688 (1980); P. kf&ller, J. R. Nix, and A. J. Sierk, private communication.

35. L. G. Moretto, S. G. Thompson, J. Routti, and R. C. Gatti, Phys. Lett.

S ,

471 (1972). 36. A. Gavron, Phys. Rev. C z , 230 (1980).

37.

C. Cabot, H. Gauvin, Y. Le Beyec, H. Dela-

grange, J. P. Dufour, A. Fleury, Y. Llabador, and J. Alexander, proceedings of this conference, volume of contributed papers, p. 137.

38. S.E. Vigdor, D.G. Kovar, P. Sperr, J. Mahoney, A. Menchaca-Rocha, C. Olmer, and M. Zisman, Phys. Rev. C S , 2147 (1979).

39.

H.

C. Britt, R. M. DeVries, E. R. Flynn, M. P. Webb, K. Van Bibber, M.S. Zisman, D.G. Kovar, F. Plasil, D. L. Hendrie, unpublished data. 40. P. Gonthier, H. Ho, M.N. Namboodiri, L. Mler,

J. B. Natowitz, S. Simon, K.,Hagel, R. Terry, and A. Khodai, ~hys.~ev.~ett.

a,

1387 (1980). 41. K. A. Geoffroy, D.G. Sarantites, M.L. Halbert,