fission and emission of h and he in the reactions of 215 mev 16 o with 181 ta, 208 pb and 238 u

Z. Phys. A - Atoms and Nuclei 315, 169-182 (1984) Zeitschrift Atoms for Physik A

and Nuclei �9 Springer-Verlag 1984

Fission and Emission of H and He in the Reactions of 215MeV 160 with lSlTa, 2~ and 238U

Louis C. Vaz a, D. Logan b, E. Duek a, John M. Alexander a, M.F. Rivet *a, M.S. Zisman c, Morton Kaplan b, and J.W. Ball b

Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York, USA b Department of Chemistry, Carnegie Mellon University, Pittsburgh, Pennsylvania, USA c Lawrence Berkeley Laboratory, Berkeley, California, USA

Received September 2, 1983

The reactions of 215 MeV 160 with 12C, lSlTa, 2~ and 238U have been studied. Inclusive measurements for 4He emission are given from each target, and for fission and 1"2'3H from Ta, Pb and U. For H/He a high-energy, forward-peaked component is observed with characteristics similar to those reported by others. At backward angles a low-energy, nearly-isotropic component is also observed for 4He that cannot be accounted for by emission from fully accelerated fission products. The spectral shapes for this evaporative component are compared with statistical model calculations, and information is obtained concerning the effective barriers to emission. For the reactions of 16.O with 12C, complete fusion seems to be overwhelmed by incomplete fusion. Fission angular distributions and cross sections are also presented and discussed.

I. Introduction

In recent years observations of H/He emission have become increasingly popular for the study of mechanisms of heavy ion reactions [1]. For energies well above the entrance-channel Coulomb barrier, the cross sections are substantial and increase rapidly with increasing projectile energy. Typically in the forward hemisphere (forward here means in the direction of the lighter collision partner), the energy spectra show a broad, high-energy component [2- 54], and in the backward hemisphere there is a more narrow, nearly isotropic lower-energy component [2, 4, 5, 8, 17, 19, 20, 38, 55-66]. The forward-peaked component has been shown to include some sequential evaporation from the target and/or projectile-like fragments [7, 16, 24, 30, 33, 37, 44, 52, 54, 67-79] and also some direct (or prethermalization) emission that occurs during the initial impact [13, 15, 19, 25, 26, 29, 33-35, 37, 38, 40, 45, 52, 54, 74, 77, 80-94]. The spectra in the backward hemisphere include some evaporation from fission-like fragments [-95, 96], but often contain a significant amount of emission from the composite system prior to the accele-

* Permanent address: Institut de Physique Nucleaire, B.P. No. 1, F-91406 Orsay, France

ration of fission-like fragments [38, 46, 63-65, 95- 97]. The nearly isotropic component is particularly interesting for heavy nuclei as it offers a possible probe of the time evolution of the composite nucleus in its course toward fission-like breakup [64, 96-98]. Most available information on this evaporative component from targets of A>150 derives from 4~ induced reactions [38, 46, 63-65, 96, 98]. In this work we have used 215 MeV laO beams in order to gain information concerning the dependence of the reaction mechanisms on projectile. The comparison of Ta, Pb and U targets has been used to test the role of fissility of the composite nucleus and its relation to spin. Many studies have already been published on H/He emission in lac, 14N, 160 and 2~ induced reactions, but the emphasis has been on properties of the higher energy particles, es- pecially at forward angles [1-54, 67-94]. We also give some information on the forward-peaked emission, but our emphasis is on the H/He of lower energies primarily at backward angles. In addition, we have measured cross sections and angular distributions for fission fragments. We find many similarities between 160 and ~~

170 L.C. Vaz et al.: Fission and Emission of H and He

reactions. The forward-peaked, high-energy component for H/He decreases rapidly with increasing angle and is replaced by a nearly isotropic evaporation-like component at angles greater than

100 deg. This evaporation-like component for 4He cannot be accounted for by emission from fully accelerated fission fragments. By use of the statistical- model framework [-64, 99] we have obtained information concerning effective potential barriers of the emitting composite nuclei. The results imply that these emitters become quite extended compared to similar nuclei as observed in the fusion process ElO0, 101].

II. Experimental Techniques

Experiments were performed in a 36-inch reaction chamber of the 88-inch Cyclotron at the Lawrence Berkeley Laboratory. The ~60+~ beam was stripped to + 8 then steered and focused to a spot of ~0.25 inch diameter at the target. The targets were self supporting and consisted of ~8~Ta (366gg/cm2), 2~ (enriched, 445 gg/cm2), 238U (natural, 1,272 gg/cm 2) and l z c (179 gg/cm2). Beam intensity was monitored by a Faraday cup and by a monitor detector at ~10 degrees. Target thicknesses were obtained by measurements of energy loss for alpha particles from radioactive sources, and relative thicknesses were verified by Rutherford scattering measurements made during the experimental run. Four, three-member Si detector telescopes (45 gm, 500~tm, and 5 mm) were used for measurements of the H and He particles. The two forward-angle telescopes (25 deg. apart) were covered with beam-stop- ping Pb cover foils, and the two backward-angle telescopes (20 deg. apart) were covered with Au foils of 1.4 mg/cm 2. (The effective energy thresholds are given in footnotes to the tables later.) These four telescopes were mounted on a movable table that was rotated to cover the laboratory angular range from 5-165deg. A gas ionization telescope [102], mounted on a separately movable arm, was used for measurements of fission fragments and ~2C recoils. Data were recorded event by event on magnetic tape with a Modcomp IV/25 computer. The tapes were subsequently analyzed off-line. Details concerning the detection techniques have been given in earlier papers [-65 and references therein]. Measurements of inclusive H/He production are subject to two important sources of contamination: (a) reactions in the target support frame induced by beam halo and, (b) reactions of the beam with light element impurities in the targets. At the Berkeley

215 MeV teO +te"Ta (a) 104 4He ~ e ~ % o , ~ "

Tgrgel plus _ _ t ~ a Olab=5, carbon impur i ty ' ~ ' ~ e ,

lO 3 ~ ~ ~

> Target minus impur i ty � 9 a ~a 1~ (x 10 -1 ) rr. lO 2 �9 ~ % �9 zx LLJ �9 �9

U3 o o ~ ~o �9 �9 �9 o . . 0 % o ~ 1 7 6 �9

~ Carbon impur i ty only ,o cv % ,o 3 - - ~"%, \ (x,o-2) o % o~ / "- , \ OoOo

~ l o 2 \ , , , , , ,

� 9 o o % (b) %

�9 9 I I

o ,o 2'0 ~'o , o ~'o 6'0 ;o ' 80 90 100

(Ea) lab (MeV)

Fig. 1. Observed energy spectra that illustrate the subtraction for carbon impurities on the targets. Open circles show the contri- butions from carbon impurities; triangles show the measured sum for target plus impurities; closed circles show the net amount from the target

88-inch Cyclotron we were able to reduce the former source significantly by using a "cleanup" collimator of 1.9 cm diameter located _~40 cm from the target. The primary beam spot size was controlled by qua- drupole focusing, but a weak halo remained, presumably due to charge exchange and scattering with residual gas in the beam line. The collimator reduced the halo so that only a small blank correction was required. It is well known that in accelerator environments a carbon deposit builds up on target layers, presumably due to backstreaming of pump oil and sub- sequent cracking in the beam spot. Even though we used a liquid nitrogen trap for each pump down, this impurity buildup could not be eliminated. Therefore we devised a method of monitoring the extent of the C impurity and a quantitative means of subtracting its effects from our measurements. For each angle of interest we measured the production of H/He from a standard C target as well as from the Ta, Pb and U targets of primary interest. Then we measured the C impurity contents on each target via the elastic (and inelastic) scattering of C recoils into our gas telescope, positioned at 77 deg. These measurements were made relative to the standard C target which provided a very clear locus for C recoils on the AE, E display. The C recoils from this standard target exhibited a clear separation

L.C. Vaz et al.: Fission and Emission of H and He 171

from very small quantities of B, N and O recoils. Therefore, in principle one might be able to determine the contents of both C and O impurities by this technique. However, for our conditions, the heavy recoil nuclei from Ta, Pb and U targets pre- vented us from obtaining a quantitative estimate of the oxygen contents. For the Ta target both our recoil analysis and the chemistry of Ta indicated that oxygen impurities were small compared to the C layer we observed (_~10gg/cm2). Therefore, we are quite confident in the reliability of the impurity subtraction for this case. Figure 1 shows an example of the magnitude of the subtraction for 4He from the Ta target at 5 and 165 degrees. As one expects from the reaction kinematics, the correction is essentially negligible at 165 degrees, [Fig. 1, (b)] as well as for the other backward angles. This result holds for Pb and U targets as well. At 5 degrees [-Fig. 1, (a)] the correction for Ta was -~30%, but it decreased rapidly with increasing angle. Comparable corrections were applied for the Pb and U targets; for these targets, however, we cannot be sure that we have completely removed the effect of oxygen impurities. The trends of the spectra with angle convinced us that this systematic uncertainty is probably negligible for angles greater than -~20 deg. Many of the inclusive measurements reported in the literature could include significant amounts of contamination from light element impurities.

III. Results and Discuss ion

A. Observation of H/He from Ta, Pb and U

For this experiment we used three heavy target ele- ments in order to study the influence of fissility on the production of H and He. As the results for each

10C

,o " T

i!i:~ ?oo [ ~ ~

~ oo%

b 1194 ~ �9 :....oO:=

F . .

6e ~ % i

%

( ) j , , -~

o 1o 20 3O 0 (cp)c.rn (MeV)

2|5 Me'V "O'+'S'To t

I.} '~176176 o " ,Z':':',', '. | ' . , ".'.',.., .'... -

33~ o~~176176176176 " "" " " - i o oQ,, �9

o ~

~176 2! 4 , . ::::,-..,. :~ �9 �9 o

� 9 o o . o o

"".....2 1 96o o~(~ o o o

,% ~ o o ,~7o" "" :~~

�9 % % o o

:- . . . e

, o

L i I . ~ i e lo 10 2 0 5 0 4 0 5 0

((~O)c.m. (Mev} 7 0 8 0

Fig. 2. Sample c.m. spectra at various angles for ~H and 4H from Ta after correction for carbon impurities on the target

target are quite similar, we give only a few sample figures of the raw data and then tabu la te the integrated cross sections, average energies, etc. Fig- ure 2 shows energy spectra at several angles for 1H and 4He from 215MeV 160+181Ta. The major point here is the marked difference between the spectra observed in forward and backward hemispheres. At backward angles the c.m. spectra assume an evaporation-like shape while at forward angles they exhibit a large amount of very high-energy emission. Proton energies were not recorded for energies >30 MeV due to the 5.5 mm thicknesses of the Si telescopes, but the integrated cross sections do include the protons of higher energies. A more global view of the 4He production pattern is given in Figs. 3 and 4 via contour plots of invariant

2C

1E

"G 12

o x

~ B

4

i , , , i . . . . i , i i , , , , , ,

215 MeV 160+181To~ 4He (inclusive)

. . . . . . ; o . r . . . . ~,, . . . ~ , . . . .

-12 -8 -4 0 4 8 12 16 20 24 2

(vitx 10/c)

Fig.3. Contour map of the invariant cross sections (d 2 a/df2 de) p-1 c-1 in the velocity plane for 4He from the reaction 160+181Ta; vii and v• denote components of the laboratory velocity parallel and perpendicular, respectively, to the beam direction. Each symbol corresponds to a value of the cross section as indicated in units of mb/sr MeV2/c. The heavy circles center on v . . . . ; light circles center on v~; the projectile velocity is indicated by vp. Straight lines are drawn along the laboratory angles for each measurement; they are terminated at the detector threshold

172

Fig. 4. Same as Fig. 3 but from the reaction 160+23~ U

20

~6

0

> 8

q

0

L.C. Vaz et al.: Fission and Emission of H and He

. . . . . ~ l s M~V' '~0'+ ~ U - - "H'e /i,~to~;~) . . . . .

32 x ~ I / / " 7 / / ... \

Ve,m. Vf vp 3'2xt0-~

-12 -8 -4 0 4 8 12 16 20 24

(v.x 102/c)

cross sections vs. velocity. These plots have been used to great advantage to categorize kinematic patterns by emission sources assumed to be essentially isotropic [see for example 34, 51, 67]. Such sources are indicated by the centers of circular contours that follow the data points, In Figs. 3 and 4 we show that the data at backward angles are well described by a set of heavy circles centered on the c.m. velocity, The data at very forward angles (01a b <37 deg.) are rather well described by a set of light circles centered on a velocity of ~-0.10 c (indicated by @. If these 4He particles do indeed arise from two isotropic emission sources, then both sources will contribute significantly at the side angles to distort the circular patterns. The obvious interpretation of the heavy circles centered on v .... is that one is observing evaporated particles in reactions involving essentially full momentum transfer to the composite nucleus. (The fact that the circles center on v .... does not in itself distinguish between emission before and after fission of the composite system.) For reactions of 3t5 MeV 160 and 340MeV 4~ with 238U, similar observations have been made via measurements of 4He production in coincidence with fission fragments of known fold angle [34, 38, 96 and references therein]. Production of #He in the backward hemisphere was found to be predominantly associated with essentially full momentum transfer to the fissile nucleus, The reaction 265MeV 2~ has also been studied by Rivet et al. [46] who arrive at similar conclusions. Several studies of similar reactions have reported that forward-angle inclusive spectra can be param- eterized by an isotropic emission source moving at one-half to two-thirds of the projectile velocity vp. [See for example 18 and 34.] The lighter circles that we show in Figs. 3 and 4 are centered on v j - 0 . 1 0 c or 59 ~ of the value of vp. These circles describe the

data rather well for angles up to _~37deg. in the laboratory or _~ 70 deg. in the frame moving with v~ =0.10c. Our results are consistent with the para- meterizations suggested by earlier work. If the moving source parameterization also describes the contribution of this mechanism at backward angles, then we can infer the degree to which it interferes with the evaporative component. The extension of the light circles to backward angles indicates a very small contamination of the evaporative process that dominates at backward angles. It is clear from Figs. 3 and 4 that the experimental energy thresholds did not allow us to examine the possible validity of the light circles as extended into the backward hemisphere. Measurements of the differential cross sections for low energy ~t-Ie could be very interesting as they would provide quite a de- manding test of the moving source hypothesis. Ob- viously one way to accomplish this would be to use detectors of very low threshold (e.g. gas ionization telescopes). A second way would be to utilize re- versed kinematics i.e. to bombard a light target with a beam of very heavy projectiles; such beams are now available at several accelerators. The effect of this reversal of target and projectile is to move the origir~ for zero laboratory velocity over to the point of the arrow marked vp in Fig. 3. Then the angles near zero degrees in the laboratory correspond to the backward angles and would be populated by 4He with quite large laboratory velocities. In a forth- coming paper [103] we will present some results from a study of this type. The patterns of Figs. 3 and 4 suggest the presence of two separable components in light particle production. Characterization and integration of these components have been accomplished by the conven- tional approach. We assume that there is a nearly isotropic source in the c.m. as observed at backward angles, and then subtract its contribution from the


I 0 ~" i , ~ i (o) qH

~ 10 2

"

10 o " ~ { xlO-2}

i I I I I 1 O- 20 4 0 0 80 1 O0

i i

215 MeV 160+X

\? ~o �9

i I A I I 0 20 4 0 60 80

(b)

100

ec.m.(deg)

Fig. 5. Angular distributions for the forward-peaked components for aH and 4He. These values are lower limits as they only include the particles that clear each detector threshold

Table 1. Integrated cross sections (mb) and cumulative decay fractions"

lSlTa 20Spb 238 U

Forward peaked component

IH 692_+173 2H 211_+ 63 3H 113_+ 37 4He 941 _+226

Symmetric Component

605-+151 308+ 77 188_+ 56 123+_ 37 97-+ 32 90_+ 30

844 -+203 658 -+ 160

~H 744-+ 67 281_+ 25 218_+ 20 2H 119_+ 67 59-+ 11 57-+ 10 3H 70_+ 13 38_+ 9 48-+ 9 CHe 704-+ 56 313_+ 25 290_+ 23 Fission 1,529 _+ 138 1,916 -+ 172 2,375 _+214 Fusion (1,832) b 1,916 2,375 /crit 89" 92 e 103 r 1ER (35) 0 0

Cumulative decay fractions, CDF

IH 0.41 +0.06 0.15 _+0.02 0.09 _+0.01 2H 0.06 _+0.02 0.03 -+0.01 0.02 _+0.01 3H 0.04 -+0.01 0.02 _+0.01 0.02 _+0.01 4He 0.38 -+0.05 0.16 _+0.02 0.12 _+0.02

a Cross sections for 1H, 2H, 3H and 4H have been integrated for the forward peak and the symmetric component as described in the text. Estimates of uncertainties include the various types discussed in [65] and those due to uncertainties in the amount of the C impurities on the Ta, Pb and U targets. Lower energy limits for integration of the forward peaked components are 9, 9, 12, and 29 (MeV in lab) for 1H, 2H, 3H and 4He respectively; for the symmetric components they are 8, 8, 9, and 14 (MeV in c.m.), respectively b Includes an estimated cross section of 303 mb for evaporation residues [65, 105] c Taken from (1) and the fusion cross section above

data at forward angles. In Fig. 5 we show c.m. angular distributions for the forward peaked components after this subtraction. They are all nearly exponential with half angles of ~20 deg. for IH and

10 deg. for 4He. These curves have been numerically integrated, and the results are given in Table 1. Complete cross sections for this forward-peaked component are certainly larger than we report due to loss below the detector thresholds (see Fig. 2). Angular distributions for the backward hemisphere are shown in the lower part of Fig. 6. They were fitted to an equation from the statistical model (as discussed below), and the integrated cross sections are given in Table 1. The near isotropy of the curves in Fig. 6d, e and f implies rather low spins for the emitters (as indicated in Table 2 later). A few measurements of differential cross section for 4He emission and fission (see Sect. B) were also made with a beam of l l 9 M e V 160. The isotropic component for 4He was _~ 80 and 25 mb for Ta and Pb, respectively. The angular coverage was not extensive, hence we do not consider these measurements to be definitive.

B. Observations of the Fission Cross Sections

By means of the gas ionization detector, we measured the angular distributions of fission fragments over the laboratory angle range from 76-165 degrees. These cross sections were transformed into the c.m. system by use of the approximation of purely symmetric fission with total kinetic energy from the Viola systematics [104]. The resulting angular distributions are shown in the upper part of Fig. 6, and the integrated cross sections are given in Table 1.

i i i i

Ta $oo (a) ~.,"

200 ,~ fission j "

-~ f r agmen ts~ . - I00

.= O J J I

(d) 4 -o o Heo .o .J0-c-*- 60 o~..~- -o

40 ..... .A.~___.~ __,_q~_.,., _ _

t H [ x t / 2 )

0 I I ~ I 90 I10 130 I 0 170

2t MeV t 6 0 + X

Pb y - : "(b)

/ .... ".--y/i

1 [ [ I

(e)

i t t i I

I U It%

T (c) ..."

Jl /

(f)

o o.o---~.o--o-# ~--o-~ .e- --o-O--o~ -e--~

I , (x1/Z, l ixl-/2.~"-- - '~" -'~-'~I "'A - ~ " ' - II0 130 150 170 110 130 150 170

<O)c.m.(deg)

Fig. 6a-e. Angular distributions for the fission fragments. The dashed curves are fits of an equation from Ref. [105] (similar to (3)) to the data for fission fragments. ( I f Angular distributions for IH and 4He; energy cutoffs are given in footnotes to Table 1. Dashed curves are fits of (3) to the data

174

Table 2. Quantities related to emission barriers

L.C. Vaz et al.: Fission and Emission of H and He

Target Observed Spheres a Fusion b

( ( ~ ) ) e 0 . . . . f12 d J rms T ~s B E o (MeV) (deg.) (h) (MeV) (MeV) (MeV) (MeV)

4 H

Ta 22.2 167 0.2 27 2.8 0.4 16.5 19.8 Pb 23.3 167 0.1 24 2.5 0.2 18.4 21.5 U 24.4 167 0.1 21 2.4 0.1 19.7 23.3

1 H

Ta 12.7 166 0 0 2.8 0 7.2 10.2 Pb 13.3 166 0 0 2.5 0 8.5 10.9 U 14.0 166 0 0 2.4 0 9.3 11,8

a From (3-5). The analysis is described in detail in [99] and [106], but with the difference that in this work we use the average energies from the most backward angle to emphasize emission from composite nucleus b From [101]. Typical uncertainties are ~ 3 c Typical uncertainties are g0 .5 MeV a Typical uncertainties are ~0.1

A summary of the various cross sections measured with the 215 MeV 160 beam is given in Table 1. For the Pb target the fission cross section can be approx- imately identified with the complete fusion cross section o-of. For Ta an additional contribution to acf has been estimated from the expected evaporation residue production 1-105]. For U, the evaporation residues are expected to be negligible, but the fission cross section surely gives an overestimate of a~f due to fission after transfer reactions. (We will discuss this point further in Sect. D below.) The magnitude of lcrit in Table 1 is obtained from the equation

aof = ~2(lCrit + 1) 2. (1)

Table 1 also gives cumulative decay fractions CDF, from the equation

CDF i = a]cr0f (2)

for evaporative H/He (symmetric component only). The fission cross sections measured with 119 MeV 160 are ~710, 1,170, and 1,330mb for Ta, Pb and U, respectively.

C. Properties of 1H and 4He Emission at Backward Angles

It is important to classify the sources of emission for these light particles if one is to use them as a probe of the reaction mechanism. For the forward-peaked particles this classification will require much more study as the energy and angular distributions must be determined for the projectile-like fragments that are potential sources of evaporated particles. For the nearly isotropic component, however, this problem is much more tractable as our major potential emission sources are the fully accelerated fission fragments or the composite system prior to acceleration

of these fragments. It is not possible for emission from projectile-like fragments to populate the backward angles, and although target-like fragments could be possible sources, their contribution is not expected to be prominent on account of their relatively low excitation energies (compared to those for the composite nuclei). As discussed in our earlier papers [65 and references therein], one expects a considerable broadening of the evaporation spectra for 1H and 4He if they are emitted from fully accelerated fission fragments. Fig- ure 7 shows a comparison of observed spectra to Monte Carlo simulations for such emission. The ex- tremely large width of the simulated 4He spectrum, relative to that observed, means that emission from fully accelerated fragments must be limited to only a minor portion of the actual emission processes. This argument does not distinguish near-scission emission

'215 M'eV (o) t0~ 4H

~176 'io.'n. ' ~176

=e c rj10

, o - ; ,o ~o ;o (Ep)c m.(MeV)

( b )

4He

=t67

o ~ o

o o o

o o o o o ~

tO 20 30 40 5 0

(~,'~)c.m. (MeV)

Fig. 7. Observed energy spectra (open circles) compared to a Monte Carlo reaction simulation (solid curve) for evaporation from fully accelerated fission fragments

L.C. Vaz et al.: F iss ion and Emis s ion of H and He 175

from that of a near-spherical compound nucleus. It simply rules out the large kinematic shifts that char- acterize the motion of fully accelerated fission fragments. For 1H this kinematic constraint is much weaker, and one cannot rule out a substantial amount of evaporation from the fission fragments. If we assume that 1H and 4He are evaporated from a spherical composite nucleus, then we can estimate its effective evaporation barrier B by use of equations from the statistical model as presented earlier [64, 99, 106]. First one must determine the anisotropy parameter fi2 by a fit of the measured angular distribution to the equation,

W j o , j T ( O ) OC exp [ - 1 f i 2 sin 2 O] I o [�89 sin201' (3)

Next one must estimate the effective temperature T and the inertial factor [ - J / ( J+#R2) ] for use in the following equations for the measured average channel energy

{{e(0))) = B + T + TEJ/(J + #R2)] + G(0) (4)

where G(0) denotes the spinoff energy as given by [106].

G(O)=fi2T (-j +J-~R2 )

. {cos20 + �89 [14 Ii(}fl2sinZO)] 10(�89 sin20) 1 (5)

~r is the moment of inertia of the residual nucleus,/~ is the reduced mass in the exit channel, I i is the i'th order modified Bessel function and R is the sum of radius of light particle (1.44fro for XH and 2.53 fm for 4He) and the interaction radius of the residual nucleus [64, 1071. Table 2 presents values of the emission barriers and the other quantities characteristic of hot nuclei obtained from (3-5). The last column gives values of the fusion barriers inferred from empirical systematics of cold nuclei [1011. As the emission barriers are significantly smaller than the fusion barriers, we

conclude that the hot emitters, observed in this work, must be quite different from the cold nuclei observed in the fusion process. In Ref. [99] it was shown that such differences could be attributed to rather extended forms for the hot nuclei. Reference 99 also gives a survey of other similar measurements. In this paper we want to put more constraints on the argument by using the shape of the energy spectrum as opposed to the mean energy alone. To this end we have written a computer program, ATHENA [108] to calculate the shape and intensity of evaporative spectra as a function of spin and the height and width of the effective emission barrier. We explore the role of barrier penetrability by vary- ing the width of the barrier, and we estimate the temperature by comparison to the spectral shape at high energies. We then study the effect of the lower- ing of the effective barrier expected for a hot nucleus 1-109], Finally, we get a rough idea of the width of the spectrum of emission barriers that characterizes the evaporative alpha particles. Equations (3-5) have been derived with the assumption of sharp cutoff transmission coefficients and a constant temperature form for the level density as described earlier [64]. This approximation was nec- essary to obtain the simple and convenient analyti- cal relationships. By numerical integration (via the program ATHENA) we relax this approximation and evaluate the shape of the evaporative energy spectrum at any angle. For this purpose semiclassical equations (from Ericson's review article [-110]) have been used for the deexcitation of a compound nucleus. The energy and angular distribution of a particle b emitted from a compound nucleus with channel energy e b is given by (5-26) Ref. [110]. The spins of projectile, target and emitted particle are neglected. Therefore the spin r of the compound nucleus is set equal to the entrance channel orbital angular momentum. The expression is then

d2a(eb, O) ~ 2dTjdY co [ df2bd G rcPt2! G(J) P(Ub'O)~o 2IbTl~(G)exp - - - -

pJlb 2a 2 ] j~ ] Wj' dlb

where

G ( J ) = Z ~ p(Ub',O) dUb' 21b, Tl~,(G,)exp b' 0 0

J2+12 [iJlb,]d l 2a2, ]Jo \ a~ , ] b'

and

~(-)k(4k+1) L(2kk!)2j J2~ P2k(cosO) \ O- b ] Wjzb = ] - k

4-~

(6)

(7)

(8)


I b is the orb i ta l angular m o m e n t u m of the exit par- a is the spin cut-off p a r a m e t e r defined as ticle, crb

~ =JT/h ~ (9)

Jb is the m o m e n t of inert ia, Tj or T t is the t ransmiss ion coefficient, p(Ub,O ) is the level densi ty of a res idual nucleus of spin zero and exci ta t ion energy U b. The symbol Jzk s tands for a spher ica l Bessel funct ion and P2k for a Legendre po lynomia l . A computer code, A T H E N A , was wr i t ten to evaluate (6)- (8) numer ica l ly [-108]. Transmiss ion coefficients were ca lcu la ted by using the Hi l l -Whee le r express ion [111].

TI (0= l + e x p h c o ( V z - e ) . (10)

The cons t an t - t empera tu re level densi ty fo rmula was used for the daugh te r nucleus with t empera tu re values for first s tep emission. In Eq. (10), the curvature of the pa rabo l i c ba r r i e r is deno ted by ha) and the l- dependen t ba r r i e r height, V~, is given by

g~ = B + h( l + 1/2)2/2# R 2. (11)

In Tab le 3 and in Fig. 8 our analysis of the evap- o ra t ion spec t ra is summar ized . W e have ma tched the observed mean energies with three sets of assump- t ions. Line (a) in Tab le 3 s imply carries over the results from Table 2 for sharp cutoff t ransmiss ion coefficients (i.e. ha)=0) . Line (b) shows the effect of bar r ie r pene t rab i l i ty as reflected by set t ing ha) = 4 M e V in the Hi l l -Whee le r pene t rab i l i ty formula.

i l , i

15 MeV teO+X (b)

4 U ~

0 0

0 (

I

. . . . 0 t 0 20 50 0 10 20 30 4 0 50

(~p)cm.(MeV) (E a )c.m.(MeV)

Fig. 8a and h. Energy spectra of evaporated 1H (a) and 4He (b) from each target at the angles indicated. Curves were calculated with the parameter sets given in Table 3; dashed and solid lines for parameter sets (b) and (c), respectively

(The value of 4 M e V for ha) has been found to provide a good a p p r o x i m a t i o n to the cor respond ing bar r ie r curva ture of several theore t ica l potent ia l s

Table 3. Effective barriers to evaporative emission obtained with various assumptions

4 H e 1H

J~m~ T ho) B A J,m~ T ho~ B A (h) (MeV) (MeV) (MeV) (MeV) (h) (MeV) (MeV) (MeV) (MeV)

215 MeV 160+ 181Ta

a 27 2.8 0 16.5 0 0 2.8 0 7.2 0 b 27 2.8 4 17.4 0 0 2.8 4 8.1 0 c 27 2.8 4 19.3 4_0 0 2.8 4 9.9 4.1

215 MeV a60+z~

a 24 2.5 0 18.4 0 0 2.5 0 8.5 0 b 24 2.5 4 19.3 0 0 2.5 4 9.4 0 c 24 2.5 4 21.1 4.0 0 2.5 4 10.7 3.3

215 MeV 160+2asU

a 21 2.4 0 19.7 0 0 2.4 0 9.3 0 b 21 2.4 4 20.6 0 0 2.4 4 10.2 0 c 21 2.4 4 22.9 4_5 0 2.4 4 11.6 3.3

a Obtained from (3-5) as described in [-106]. (Parameter B adjusted to fit ((e))) b Corrected for barrier penetrability with he)=4 MeV. (Parameter B readjusted to fit ((e)). See Fig. 8)

Empirical barrier taken from systematics of complete fusion, [101], and corrected for thermal expansion as in [1091. (Parameter A, half width of B spectrum, adjusted to fit ((e)). See Fig. 8)

L.C , V a z et al . : F i s s i o n a n d E m i s s i o n o f H a n d H e 177

[101].) Inclusion of barrier penetrability requires the addition of 0.6-0.9 MeV (4-5 % for 4He) to the effective mean emission barriers (compare line b to line a). As the fusion barriers in Table 1 are still sub- stantially larger (11-13 %) than the emission barriers on line b of Table 3, one still concludes that the emitters must be rather extended. The calculated spectral shapes are shown for this assumption by dashed lines in Fig. 8. The calculated spectra are significantly narrower than those observed, and suggest that the evaporated particles have experienced a spectrum of barriers due to nuclear distortions. We have tried to obtain a rough parameterization of this spectrum of barriers by assuming a uniform distribution of B values of half-width A. For these estimates of the transmission coefficients, the quantity T z from (11), has been averaged over a uniform spectrum of barriers.

1 B+A

=hq ;_ (12)

For these calculation we started with the average barrier for cold nuclei ( T = 0 ) from systematics of barriers for complete fusion [101]. Then we used the procedure suggested by Tomasi et al. [109] to calculate the reduction in this effective s-wave barrier due to thermal expansion. For the nuclear temperatures encountered in our reactions this reduction amounts to about 0.5 MeV and 0.2MeV for 4He and 1H fusion barriers, respectively. Finally we varied the parameter A until the observed mean energies (@(0)}} where reproduced; results are listed on line c in Table 3. This procedure leads to a reasonably good fit to the spectra as shown by solid lines in Fig. 8. The challenge implied by these results is to construct a reaction model that can account for a very broad spectrum ( F W H M ~ 9 - 1 0 M e V ) of emission barriers. Recent T D H F calculations do indeed indicate the possibility of large shape oscillations of the composite nucleus just after impact [112].

D. Angular Anisotropies of the Fission Fragments

F r o m Fig. 6 it is apparent that the fission fragments have rather large anisotropies that decrease slowly from Ta to Pb to U. The values of lcrit in Table 1 can be used along with the rotating liquid drop model (RLDM) [113] to estimate these anisotropies if only fusion fission has occurred. This standard theory [105, 114] leads one to expect a weaker anisotropy than that observed for the reaction 160 +23sU, and a stronger anisotropy than that observed for 1 6 0 + i S l T a . A number of similar studies

5 0 0 0 .... ,

I 0 0 0

500

~ 0 0

b 5 0

t 0 0

5 0

~60+~Z,8 u

t 6 0 + a ~ - �9 Sikkeland

I . . . . . f 0 Viola ,oo +oooo t

rcr i l =0 .95 fm

1 10 I I I I I 1

70 90 110 1~0 150 t70 190 2,o Ec.m (MeV)

Fig. 9. Fission excitation functions for 160+2~ and 160 +~3sU. The smooth curve for Bi is a fit obtained with r c r i t = 0 . 9 5

and a fusion barrier from [101]. The solid curve for U was calculated in the same way (rorit=0.95). The dashed curve was obtained by reducing the barrier by 2 MeV. Data points are as follows: �9 Ref. 116; o Ref. 117; v this work

have been reported, and the pattern of results has been discussed in detail elsewhere [105, 115]. In this paper we want to explore the possible effects of transfer reactions on the anisotropy parameters K02 and ~r From the work of Viola and Sikkeland [116] it is clear that for 166MeV 160+23sU there is a substantial amount ( ~ 30 %) of sequential fission after transfer reactions. By contrast, for the reaction J60+2~ one observes essentially complete momentum transfer [116] and therefore presumably a much smaller role for sequential fission. This result suggests that the reaction 160+2~ provides a desirable reference for compound-nucleus behavior [117]. Figure 9 shows the fission excitation functions for 160+2~ Following the critical radius method of Galin et al. [119] we can parametrize the high energy data (fiof>800mb) for i 60+2~ (refit =0.95 fm) and identify the curve with fusion fission. Using the same value of rorlt one can estimate the fusion-fission contribution (fia) for 1 6 0 + T a / P b / U . Even small uncertainties in the barrier could, of course, lead to substantial errors in O-cf(E ) at low incident energies, but this is not of primary concern here. The excess of the fusion cross sections (Ta- ble 1) over the predicted values of fief(E) provides a reasonable estimate for sequential fission after transfer reactions. Further, one may infer that these transfer reactions deposit spins in the target nucleus that are much less than lcrit [120]. In this spirit we

i78 L.C. Vaz et al.: Fission and Emission of H and He

can estimate a corrected value for this quant i ty that

we denote Fcrit.

lcrit = lcrit FOcf/(of is -}- 0"ER)] 1/2. (13)

Measured fission fragment anisotropies can be char- acterized by a parameter p, which is related, in tu rn to the m a x i m u m spin I,, of the fissile nuclei [114].

2 2 (14) p = I,,/4 Ko.

Table 4. Analysis of the fission anisotropies

Target p" E*b Tb I,. * K2 ~sph/~e ff (MeV) (MeV) (h)

exptd. ~ RLDM~, f

g 181Ta 7.00 173 2.4 89 283 0.81 1.30 h ~SlTa 7.00 173 2.4 78 217 1.08 1.49 i aS~Ta 7.75 173 2.4 78 196 1.19 1.49

g 2~ 4.67 154 2.1 92 453 0.57 0.62 h z~ 4.67 154 2.2 82 359 0.73 0.75 i z~ 8.50 154 2.2 82 197 1.33 0.75

g 238U 2.94 163 2.1 104 911 0.34 h 23au 2.94 163 2.2 82 566 0.57 0.15 i aasu 6.65 163 2.2 82 250 1.28 0.15

The value of p was obtained by use of the semiclassical theory as described in [105]

Excitation energy and temperature for first-step fission as described in [105] ~ For each target the first entry is for Im=lcrlt ; the second for I m = l'crlt (13); and the third for Ira= l',,i, with an additional correction for the anisotropy parameter p a Values deduced fiom (14)

~ph is for a rigid sphere with radius parameter of 1.22 fm f From the rotating liquid drop model of [113] g Value of p taken directly from the data and Im from Table 1 h Value of p taken directly from the data but I m set to l',~ t from (13)

Value of p corrected for sequential fission taken as isotropic and 1~ set to l'crlt from (i3)

The anisotropy parameter K 2 (or J~feT/h 2) is the variance of the K dis t r ibut ion for the t ransi t ion-state nuclei. In Table 4 we give parameters related to fission fragment anisotropies measured in this study, along with values of K 2 and Jefe from three separate

assumptions: (line g) Im=Ierit; (line h) Im=/~rit; and (line i) Im=l~ri, with a correction for sequential fission. This correction (line i) was made for the limit- ing case of isotropy for the sequential fission. This reasoning suggests that the best values for K~ and J e f f lie between those given on lines h and i. The results show that the effect of transfer reactions on Ko 2 is substant ia l for 1 6 0 + z 3 8 U / 2 ~ but is not as

severe for the relatively non fissionable 18aTa target. Rossner et al. [122] have made more detailed es- t imates of K~ for several specific assumptions about prefission particle emission and incomplete fusion. The results from our work as well as theirs dem- onstrate that it is difficult to assign precise values

to K~ from such data. Fur ther discussion of the informat ion content for the values of Ko z is given elseqhere [105, 115, 121, 122]. Suffice it to say here that the value of Ko 2 for ~ 6 0 + 2 3 8 U is much smaller than expected from the s tandard fission theory.

E: Properties o f 4He Emission in the Reaction 215 M e V 1 6 0 + 1 2 C

In this study we were pr imari ly concerned with reactions involving heavy target nuclei. In order to correct for carbon con tamina t ion , we found it nec- essary also to study the reactions with a carbon target. This latter study shows an interesting contrast to the results for heavy targets that can be seen in the con tour maps of invar ian t cross section. Fig- ure 10 shows this map for 215 MeV t 6 0 + 12C. The dark circles for backward labora tory angles are

Fig. 10. Contour map of the invariant cross sections for 4He fiom the reaction 215 MeV ~60+ ~zC. Notation is the same as Fig. 3 except that the heavy circles center on v b and the dot-dashed circle centers on v ....

20

16

"~ 12 o x ~8

4

C

' ~m/~eV' "0 '+"& ~ "fie /i~cL~i,,~l' '

\ \.o., ,.. / / /," . , /

(v,,• IO~c)


centered on the arrow marked v b. Similarly the light circles for forward labora tory angles are centered on the arrow marked vy. In contrast to Figs. 3 and 4 neither vy nor v b can be identified with Vo.m.. By reference to the dot -dashed curve, centered on v . . . . . one can see the significant differences of these patterns (both forward and backward) from that expected for isotropic emission from a source moving with velocity v . . . . . Fo r this reaction the angular distribution is backward peaked in the c.m., (or along the direction of 12C) ' This should not surprise us as 12C is indeed the light collision partner and therefore has the greater velocity relative to the center of mass. One normal ly expects to see the major part of the direct componen t in the direction of the light reactant nucleus. Of greater interest, however, is the implication of this figure with respect to complete vs incomplete fusion. If one accepts the not ion of moving isotropic sources, he must conclude that incomplete fusion dominates the pattern. The circles centered on v b can be accounted for by a source formed by breakup of the 160 followed by partial fusion and a light fragment(s) continuing along the beam direction. The circles centered at vz can be accounted for by a source formed by breakup of the ~2C followed by partial fusion and a light fragment(s) continuing along the direction of ~2C in the c.m. system. These two sources seem to be of such impor tance relative to truly complete fusion that the latter cannot even be identified. To us the implicat ion of this result is that at tempts to measure the complete fusion cross section, via heavy evaporat ion residues, will be greatly confused by the presence of incomplete fusion. Indeed such findings have been recently reported [25, 123, 124]. In the light of these observations it would seem that theoretical models for complete fusion at high energies must directly address the occurence of incomplete fusion and its role in any practical detection system. To date theoretical models have emphasized compet i t ion between complete fusion and deeply inelastic reactions.

IV. Summary

We have measured inclusive energy and angular dis- tr ibutions for H / H e and fission fragments produced by reactions of 215 MeV 160 with 181Ta, 2~ and 238U. The forward peaked componen t of H / H e emission can be accounted for by isotropic emission from a source moving with ~ 6 0 ~o of the projectile velocity. The evaporat ive componen t at backward

angles can be accounted for by emission from the composi te nuclei before full fission fragment acceleration. Estimates are given for the effective emission barriers; which are significantly smaller than those for fusion even after correct ion for the effect of finite temperature. For the reaction 2 1 5 M e V 1 6 0 + 1 2 C we infer that there must be a substantial amount of incomplete fusion reactions. This incomplete fusion adds complexity to the interpretat ion of so called "comple te fusion" cross section studies at rather high energies for such systems. The fission fragment angular distributions have rather strong anisotropies and cannot be explained by the s tandard theory. For 215 MeV 160-[-238U we infer that there must be a substantial amount of fission after transfer reactions and therefore a concommitan t reduct ion in the fission fragment anisotropy.

References

1. Proceedings of the International Symposium on Continuum Spectra of Heavy Ion Reactions, San Antonio, 1979. Tamura, T., Natowitz, J.B., Youngblood, D.H. (eds.). New York: Har- wood Academic Publishers 1979; Proceedings of the Inter- national Conference on Selected Aspects of Heavy Ion Re- actions, Saclay, 1982. Martmot, M., Ngo, C., Gugenberger, P. (eds.) Amsterdam: North Holland Publishing Co. 1982

2. Britt, H.C., Quinton, A.R.: Phys. Rev. 124, 877 (1961) 3. Reames, D.V.: Phys. Rev. 137, B332 (1965) 4. Kapuszik, A., Perelygin, V.P., Tret'yakova, S.P., Ukraintseva,

L.V.: Yad. Fiz. 6, 1142 (1967) [Soy. J. Nucl. Phys. 6, 829 (1968)] 5. Brun, C., Gatty, B., Lefort, M., Tarrago, X.: Nucl. Phys. All6,

177 (1968) 6. Galin, J., Gatty, B., Guerreau, D., Rousset, C., Schlotthauer-

Voss, U.C., Tarrago, X.: Phys. Rev. C9, 1126 (1974) 7. Slater, D.C., Hall, J.R., Calarco, J.R., Watson, B.A., Becker, J.A.:

Phys. Rev. Lett. 33, 784 (1974) 8. Chevarier, A., Chevarier, N., Demeyer, A.: Nucl. Phys. A274,

223 (1976) 9. Ost, R., Sanderson, N.E., Mordechai, S., England, J.B.A.,

Fulton, B.R., Nelson, J.M., Morrison, C.J.: Nucl. Phys. A265, i42, (1976)

10. Gelbke, C.K., Bini, M., Olmer, C., Hendrie, D.L., Laville, J.L., Mahoney, J., Mermaz, M.K., Scott, D.K., Weiman, H.H.: Phys. Lett. 71B, 83 (1977)

11. Ball, J.B., Fulmer, C.B., Mallory, M.L., Robinson, R.L.: Phys. Rev. Lett. 40, 1698 (1978)

12. Gamp, A., Jacmart, J.C., Poffe, N., Doubre, H., Roynette, J.C., Wilczynski, J.: Phys. Lett. 74B, 215 (1978)

13. Bhowmik, R.K., Pollacco, E.C., Sanderson, N.E., England, J.B.A., Morrison, G.C.: Phys. Lett. 80B, 41 (1978)

14. Gamp, A., Harney, H.L., Roynette, J.C., Plagnol, E., Fuchs, H., Doubre, H., Jacmart, J.C., Poffe, N.: Z. Phys. A - Atoms and Nuclei 291, 347 (1979)

15. Bhowmik, R.K., Pollacco, E.C., Sanderson, N.E., England, J.B.A., Morrison, G.C.: Phys. Rev. Lett. 43, 619 (1979)

16. Billerey, R., Cerruti, C., Chevarier, A., Chevarier, N., Cheynis, B., Demeyer, A.: Z. Phys. A - Atoms and Nuclei 292, 293 (1979)


17. Delagrange, H, Logan, D,, Rivet, M.F., Rajagopalan, M., Alexander, J.M., Zisman, .M.S., Kaplan, M., Ball, J.W.: Phys. Rev. Lett. 43, 1490 (1979)

18. Symons, T.J.M., Doll, P., Bini, M., Hendrie, D.L., Mahoney, J., Mantzouranis, G., Scott, D.K., Bibber, K. Van, Viyogi, Y.P., Wiemann, H.H., Gelbke, C.K.: Phys. Lett. 94B, 131 (1980)

19. Utsunomiya, H., Nomura, T., Inamura, T., Sugitate, T., Moto- bayashi, T.: Nucl. Phys. A334, 127 (1980)

20. Logan, D., Delagrange~ H., Rivet, M.F., Rajagopalan, M., AIexander, J.M., Kaplan, M., Zisman, M.S., Duek, E.: Phys. Rev. C22, 1080 (1980)

21. Castaneda, C.M., Smith, H.A., Jr., Singh, P.P., Karwowski, H.: Phys. Rev. C21, 179 (1980)

22. Gierlik, E., Kalinin, A.M., Kalpakchieva, R., Oganessian, Yu.Ts., Penionzhkevich, Yu.E., Kharitonov, Yu.P.: Z. Phys. A - Atoms and Nuclei 295, 295 (1980)

23. Gierlik, E., Kalinin, A.M., Kalpakchieva, R., Oganesyan, Yu.Ts., Penionzhkevich, Yu.E., Vakatov, V.I., Salamatina, T.S.: Yad. Fiz. 32, 45 (1979) [Sov. J. Nucl. Phys. 32, 23 (I980)]

24. Novotny, R., Winkler, U., Pelte, D., Sann, H., Lynen, U.: Nucl. Phys. A341, 301 (1980)

25. Gonthier, P., Ho, H., Namboordiri, M.N., Adler, L., Natowitz, J.B., Simon, S., Haget, K., Terry, R., Khodai, A.: Phys. Rev. Lett. 44, 1387 (1980)

26. Back, B.B., Wolf, K i . , Mignerey, A.C., Gelbke, C.K., Awes, T.C., Breuer, H., Viola, V.E., Jr., Dyer, P.: Phys. Rev. C22, 1927 (1980)

27. Roynette, J.C., Frascaria, N., Blemenfeld, Y., Jacmart, J.C., Plagnol, E., Garron, J.P., Gamp, A., Fuchs, H.: Z. Phys. A - Atoms and Nuclei 299, 73 (1981)

28. Awes, T.C., Gelbke, C.K., Poggi, G., Back, B.B., Glagola, B., Breuer, H., Viola, V.E., Jr., Symons, T.J.M.: Phys. Rev. Lett. 45, 513 (1980)

29. Ho, H., Gonthier, P., Namboordiri, M.N., Natowitz, J.B., Adler, L., Simon, S., Hagel, K, Terry, R., Khodai, A.: Phys. Lett. 96B, 51 (1980)

30. Schmitt, R.P., Wozniak, G.J., Rattazzi, G.U., Mathews, G.J., Regimbart, R., Moretto, L.G.: Phys. Rev. Lett. 46, 522 (1981)

31. Borcea, C., Gierlik, E., Kalpakchieva, R., Oganessian, Yu.Ts., Penionzhkevich, Yu.E.: Nucl. Phys. A351, 312 (1981)

32. Futmer, C.B., Ball, J.B., Ferguson, R.L., Robinson, R.L., Wu, J.R.: Phys. Lett. 100B, 305 (1981)

33. Namboordiri, M.N., Gonthier, P., Ho, H., Natowitz, J.B., Eggers, R., Adler, L., Kasiraj, P., Cerruti, C., Chevarier, A., Chevarier, N., Demeyer, A.: Nucl. Phys. A367, 313 (1981)

34. Awes, T.C., Poggi, G., Gelbke, C.K., Back, B.B., Glagola, B.G., Breuer, H., Viola, V.E., Jr.: Phys. Rev. C24, 89 (1981)

35. Bhowmik, R.K., Pollacco, E.C., England, J.B.A., Morrison, G.C., Sanderson, N.E.: Nucl. Phys. A363, 516 (1981)

36. Awes, T.C., Poggi, G., Saini, S., Gelbke, C.K., Legrain, R., Westfall, G.D.: Phys. Lett. 103B, 417 (1981)

37. Fukuda, T., Ishihara, M., Tanaka, M., Miura, I., Ogata, H., Kamitsubo, H.: Phys. Rev. C25, 2464 (1982)

38. Kildir, M., Logan, D., Kaplan, M, Zisman, M.S., Guerreau, D., Alexander, J.M., Vaz, L.C.: Z. Phys. A - Atoms and Nuclei 306, 323 (1982)

39. Kasagi, J., Saini, S., Awes, T.C., Galonsky, A., Gelbke, C.K., Poggi, G., Scott, D.K., Wolf, K.L., Legrain, R.L.: Phys. Lett. 104B, 434 (1981)

40. Rae, W.D., Cole, A.J., Dacal, A., Legrain, R., Harvey, B.G., Mahoney, J., Murphy, M.J., Stokstad, R.G., Tserruya, I.: Phys. Lett. 105B, 417 (1981)

41. Robinson, R.L., Auble, R.L., Lee, I.Y., Martin, M.J., Young, G.R., Gomez del Campo, J., Ball, J.B, Bertrand, F.E, Ferguson, R.L., Fulmer, C.B., Wu, J.R, Wells, J.C., Yamada, H.: Phys. Rev. C24, 2084 (198i)

42. Auble, R.L., Ball, J.B., Bertrand, F.E., Ferguson, R.L., Fulmer, C.B., Lee, I.Y., Robinson, R.L., Young, G.R., Wu, J.R., Wells, J.C., Yamada, H.: Phys. Rev. C25, 2504 (1982)

43. Awes, T.C., Saini, S., Poggi, G., Gelbke, C.K, Cha, D., Legrain, R., Westfall, G.D.: Phys. Rev. C25, 2361 (1982)

44. Homeyer, H., Burgel, M., Clover, M., Egelhaaf, Ch., Fuchs, H., Gamp, A., Kovar, D., Rauch, W.: Phys. Rev. C26, 1335 (1982)

45. Tricoire, H., Gerschel, C., Perrin, N., Sergolle, H., Valentin, L., Bachelier, D, Doubre, H., Gizon, J.: Z. Phys. A - Atoms and Nuclei 306, 127 (1982)

46. Rivet, M.F., Gatty, B., Guillemot, H., Borderie, B., Bimbot, R., Forest, I., Galin, J., GaMes, D., Guerreau, D, Lefort, M., Tar- rago, X., Tamain, B., Novicki, L.: Z. Phys. A - Atoms and Nuclei 307, 365 (1982)

47. Duek, E., Kowalski, L., Rajagopalan, M., Alexander, J.M., Logan, D., Zisman, M.S., Kaplan, M.: Z. Phys. A - Atoms and Nuclei 307, 221 (1982)

48. Glasow, R., Gaul, G., Ludewigt, B., Santo, R., Ho, H., Kuhn, W, Lynen, U., Muller, W.F.J.: Phys. Lett. 120B, 71 (1983)

49. Gelbke, C.K.: Nucl. Phys. A387, 79c (1982) 50. Gerschel, C.: Nucl. Phys. A387, 297c (1982) 51. Natowitz, LB.: Nucl. Phys. A387, 65c (1982) 52. Bhowmik, R.K, Driel, J. Van, Siemssen, R.H., Balster, G.J.,

Goldhoorn, P.B, Gonggrijp, S., Iwasaki, Y., Janssens, R.V.F., Sakai, H., Siwek-Wilczynska, K., Sterrenburg, W.A., Wilczynski, J.: Nucl. Phys. A390, 117 (1982)

53. Borcea, C., Gierlik, E, Kalinin, A.M., Kalpakchieva, R, Oga- nessian, Yu.Ts., Pawlat, T., Penionzhkevich, Yu.E., Rykhlyuk, A.V.: Nuel. Phys. A391, 520 (1982)

54. Fukuda, T., Ishihara, M., Tanaka, M., Ogata, H., Miura, I., Inoue, M., Shimoda, T., Katori, K., Nakayam, S.: Phys. Rev. C27, 2029 (1983)

55. Knox, W.J., Quinton, A.R., Anderson, C.E.: Phys. Rev. 120, 2120 (1960)

56. Hunting, C.E.: Phys. Rev. 123, 606 (1961) 57. Durham, F.E., Halbert, M.L.: Phys. Rev. 137, B 850 (1965) 58. D'Auria, J.M., Fluss, M.J., Herzog, G., Kowalski, L., Miller,

J.M., Reedy, R.C.: Phys. Rev. 174, 1409 (1968) 59. Reedy, R.C., Fluss, M.J., Herzog, G.F., Kowalski, L., Miller,

J.M.: Phys. Rev. 188, 1771 (1969) 60. Avdeichikov, V.V., Lozhkin, O.V., Perfilov, N.A.: Izv. Akad.

Nauk SSSR 37, No. 1, 143 (1973) 61. Galin, J., Garry, B., Guerreau, D., Rousset, C., Schlotthauer-

Voos, U.C., Tarrago, X.: Phys. Rev. C9, 1113 (1974) 62. Miller, J.M., Logan, D., Catchen, G.L., Rajagopalan, M., Ale-

xander, J.M., Kaplan, M., Ball, J.W., Zisman, M.S., Kowalski, L.: Phys. Rev. Lett. 40, 1074 (1978)

63. Logan, D., Rajagopalan, M., Zisman, M.S., Alexander, J.M., Kaplan, M., Kowalski, L.: Phys. Rev. C22, 104 (I980)

64. Rivet, M.F., Logan, D., Alexander, J.M., Guerreau, D., Duek, E., Zisman, M.S., Kaplan, M.: Phys. Rev. C25, 2430 (1982)

65. Rajagopalan, M., Logan, D., Ball, J.W., Kaplan, M., Delag- range, H., Rivet, M.F., Alexander, J.M., Vaz, L.C., Zisman, M.S.: Phys. Rev. C25, 2417 (1982)

66. Dilmanian, F.A., Sarantites, D.G., Jaaskelainen, M., Puchta, H., Woodward, R., Beene, J.R., Hensley, D.C., Halbert, M.L., Novotny, R., Adler, L., Choudhury, R.K., Namboodiri, M.N., Schmitt, R.P., Natowitz, J.B.: Phys. Rev. Lett, 49, 1909 (1982)

67. Babinet; R., Cauvin, B., Girard, J., Alexander, J.M., Chiang, T.H, Galin, J., Gatty, B., Guerreau, D., Tarrago, X.: Z. Phys. A - Atoms and Nuclei 295, 153 (1980)

68. Young, G.R., Ferguson, R.L., Gavron, A., Hensley, D.C., Obenshain, F.E., Plasil, F., Snell, A.H., Webb, M.P., Maguire, C.F., Petit, G.A.: Plays. Rev. Lett. 45, 1389 (1980)

69. Bini, M., Gelbke, C.K., Scott, D.K., Symons, T.J.M., Doll,


P., Hendrie, D.L., Laville, J.L., Mahoney, J., Mermaz, M.C., Olmer, C., VanBibber, K., Wieman, H.H.: Phys. Rev. C22, 1945 (1980)

70. Sobotka, L.G., Hsu, C.C., Worniak, G.J., Rattazzi, G.U., McDonald, R.J., Pacheco, A.J., Moretto, L.G.: Phys. Rev. Lett. 46, 887 (1981)

71. Kuhn, W., Albrecht, R., Damjantschitsch, H., Ho, H., Ron- ningen, R.M., Slemmer, J., Wurm, J.P., Rode, I., Scheibling, F.: Z. Phys. A - Atoms and Nuclei 298, 95 (1980)

72. Sobotka, L.G., Hsu, C.C., Wozniak, G.J., Morrissey, D.J., Moretto, L.G.: Nucl. Phys. A371, 510 (1981)

73. Tsang, M.B., Lynch, W.G., Puigh, R.J., Vandenbosch, R., Seamster, A.G.: Phys. Rev. C23, 1560 (1981)

74. Driel, J. van, Gonggrijp, S., Janssens, R.V.F., Siemssen, R.H., Wilczynska, K.S., Wilczynski, J.: Phys. Lett. 98B, 351 (1981)

75. Ho, H., Albrecht, R., Damjantschitsch, H., Demond, F.-J., Kuhn, W., Slemmer, J., Wurm, J.P., Disdier, D., Rauch, V., Scheibling, F., Dossing, T.: Z. Phys. A - Atoms and Nuclei 300, 205 (1981)

76. Gamp, A., Burgel, M., Clover, M.R., Egelhaaf, C., Fuchs, H., Gebauer, B., Homeyer, H., Jacmart, J.C.: Z. Phys. A - Atoms and Nuclei 300, 63 (1981)

77. Robinson, R.L., Auble, R.L., Ball, J.B., Bertrand, F.E., Ferguson, R.L., Fulmer, C.B., Gomez del Campo, J., Lee, I.Y., Novotny, R.W., Young, G.R., Wells, J.C., Maguire, C.F., Yamada, H.: Phys. Rev. C27, 3006 (1983)

78. Fan, G.Y., Ho, H., Gonthier, P.L., Kuhn, W., Pfoh, A., Schad, L., Wolski, R., Wurm, J.P., Adloff, J.C., Disdier, D., Rauch, V., Scheibling, F.: Z. Phys. A - Atoms and Nuclei 310, 269 (1983)

79. Sobotka, L.G., McDonald, R.J., Wozniak, G.J., Morrissey, D.J., Pacheco, A.J., Moretto, L.G.: Phys. Rev. C28, 219 (1983)

80. Bimbot, R., Gardes, D., Rivet, M.F.: Nucl. Phys. A189, 193 (1972)

81. Inamura, T., Ishihara, M., Fukuda, T., Shimoda, T.: Phys. Lett. 68B, 51 (1977)

82. Harris, J.W., Cormier, T.M., Geesaman, D.F., Lee, Jr., L.L., McGrath, R.L., Wurm, J.P.: Phys. Rev. Lett. 38, 1460 (1977)

83. Ho, H., Albrecht, R., Dunnweber, W., Graw, G., Steadman, S.G., Wurm, J.P., Disdier, D., Rauch, V., Scheibling, F.: Z. Phys. A - Atoms and Nuclei 283, 235 (1977)

84. Nomura, T., Utsunomiya, H., Motobayashi, T., Inamura, T., Yanokura, M.: Phys. Rev. Lett. 40, 694 (1978)

85. Zolnowski, D.R., Yamada, H., Cala, S.E., Kahler, A.C., Sugi- hara, T.T.: Phys. Rev. Lett. 41, 92 (1978)

86. Nomura, T., Utsunomiya, H., Inamura, T., Motobayashi, T., Sugitate, T.: J. Phys. Soc. Jpn. 46, 335 (1979)

87. Siwek-Wilczynska, K., Marchie yon Voorthuysen, E.H. du, Popta, J. van, Siemssen, R.H., Wilczynski, J.: Phys. Rev. Lett. 42, 1599 (1979)

88. Inamura, T., Kojima, T., Nomura, T., Sugitate, T., Utsunomiya, H.: Phys. Lett. 84B, 71 (1979)

89. Yamada, H., Zolnowski, D.R., Cala, S.E., Kahler, A.C., Pierce, J., Sugihara, T.T.: Phys. Rev. Lett. 43, 605 (1979)

90. Awes, T.C., Gelbke, C.K., Back, B.B., Mignerey, A.C., Wolf, K.L., Dyer, P., Breuer, H., Viola, V.E. Jr.: Phys. Lett. 87B, 43 (1979)

91. Geoffroy, K.A., Sarantites, D.G., Halbert, M.L., Hensley, D.C., Dayras, RA., Barker, J.H.: Phys. Rev. Lett. 43, 1303 (1979)

92. Wilczynski, J., Kamermans, R., Popta, J. van, Siemssen, R.H., Siwek-Wilczynska, K., Werf, S.Y. van der: Phys. Lett. 88B, 65 (1979)

93. Barker, J.H., Beene, J.R., Halbert , M.L., Hensley, D.C., Jaaskelainen, M., Sarantites, D.G., Woodward, R.: Phys. Rev. Lett. 45, 424 (1980)

94. Ho, H., Gonthier, P.L., Fan, G.Y., Kuhn, W., Pfoh, A., Schad,

L., Wolski, R., Wurm, J.P., Adloff, J.C., Disdier, D., Kamili, A., Rauch, V., Rudolf, G., Schiebling, F., Strazzeri, A.: Phys. Rev. C27, 584 (1983)

95. Wilcke, W.W., Kosky, J.P., Birkelund, J.R., Butler, M.A., Dougan, A.D., Huizenga, J.R., Schroder, W.U., Wollersheim, H.J., Hilscher, D.: Phys. Rev. Lett. 51, 99 (1983) Kaplan, M., Kildir, M., Ajitanand, N.N., Alexander, J.M., Duek, E.: Phys. Rev. Lett. 51, 1492 (1983)

96. Duek, E., Ajitanand, N.N., Alexander, J.M., Logan, D., Kildir, M., Kowalski, L., Vaz, L.C., Guerreau, D., Zisman, M.S., Kaplan, M.: Phys. Lett. (in press) Kildir, M., Logan, D., Eriksen, D.O., Moses, D.J., Kaplan, M., Duek, E., Vaz, L.C., Ajitanand, N.N., Alexander, J.M., Zis- man, M.S.: Preprint (1983)

97. Miller, J.M., Catchen, G.L., Logan, D., Rajagopalan, M., Alexander, J.M., Kaplan, M., Zisman, M.S.: Phys. Rev. Lett. 40, 100 (1978)

98. Alexander, J.M., Delagrange, H., Rajagopalan, M., Rivet, M.F., Vaz, L.C.: Z. Phys. A - Atoms and Nuclei 307, 149 (1982)

99. Alexander, J.M., Guerreau, D., Vaz, L.C.: Z. Phys. A - Atoms and Nuclei 305, 313 (1982)

100. McMahan, M.A., Alexander, J.M.: Phys. Rev. C21, 1261 (1980)

101. Vaz, L.C., Alexander, J.M., Satchler, G.R.: Phys. Rep. C69, 375 (1981)

102. Fowler, M.M., Jared, R.C.: Nucl. Instrum. Methods 124, 341 (1975)

103. Kaplan, M.: Report COO3246-22 Annual Progress Report to the U.S. Dept. of Energy, November, 1982 (unpublished), and unpublished data from the Carnegie-Mellon Stony Brook group

104. Viola, V.E. Jr.: Nucl. Data 1, 39 (1966) 105. Vaz, L.C., Alexander, J.M.: Phys. Rep. C 97, 1 (1983) 106. Vaz, L.C., Logan, D., Alexander, J.M., Duek, E., Guerreau,

D., Kowalski, L., Rivet, M.F., Zisman, M.S.: Z. Phys. A - Atoms and Nuclei 311, 89 (1983)

107. Vaz, L.C., Alexander, J.M.: Phys. Rev. C10, 464 (1974) 108. Vaz, L.C.: Computer code ATHENA, for calculating energy

and angular distributions of particles evaporated from a compound nucleus

109. Tomasi, E., Chert, X.S., Leray, S., Ngo, C., Barranco, M., Vinas, X., Ngo, H.: Nucl. Phys. A389, 69 (1982) Chen, X.S., Ngo, C., Tomasi, E., Barranco, M., Vinas, X., Ngo, H.: Preprint Saclay 1982

110. Ericson, T.: Adv. Phys. 9, 423 (1960) 111. Hill, D.L., Wheeler, J.A.: Phys. Rev. 89, 1102 (1953) 112. Dhar, A.K., Nilsson, B.S., Davies, K.T.R., Koonin, S.E.:

Nucl. Phys. A364, 105 (1981) 113. Cohen, S., Plasil, F., Swiatecki, W.J.: Ann. Phys. (NY) 82,

557 (1974) 114. Halpern, I., Strutinski, V.M.: Proceedings of the Inter-

national Conf. on the Peaceful Uses of Atomic Energy, Ge- neva, 1955, 2, 131 NY: United Nations (1956)

115. Vaz, L.C., Alexander, J.M.: Z. Phys. A - Atoms and Nuclei 312, 1 (1983)

116. Sikkeland, T., Viola, V.E. Jr.: Proceedings of the Third Con- ference on Reactions Between Complex Nuclei, Asilomar. Vol. 232 Berkeley and Los Angeles: University of California Press 1963

117. Sikkeland, T.: Phys. Rev. 128, 767 (1962); lbid 135, B669 (1964)

118. Viola, V.E., Sikkeland, T.: Phys. Rev. 128, 767 (1962) 119. Galin, J., Guerreau, D., Lefort, M., Tarrago, X.: Phys. Rev.

C9, 1018 (1974) 120. Lefort, M., Ngo, C.: Riv. Nuovo Cimento 2, 1 (1979) 121. Back, B.B., Betts, R.R., Cassidy, K., Glagola, G.G., Gindler,

182 L.C, Vaz et ak: Fission and Emission of H and He

J.E., Glendenin, L.E., Wilkins, B.D.: Phys. Rev. Lett. 50, 818 (1983)

122. Rossner, H., Hilscher, D., Holub, E., Ingold, G., Jahnke, V., Orf, H., Huizenga, J.R., Birkelund, J.R., Schroder, W.U., Wilcke, W.W.: Phys. Rev. C (1983)

123. Morgenstern, H., Bohne, W., Grabisch, K., Kovar, D.G., Lehr, H.: Phys. Lett. 113B, 463 (1982)

124. Chart, Y., Murphy, M., Stokstad, R.G., Tserruya, I., Wald, S.: Phys. Rev. C27, 447 (1983)

Department of Chemistry State University of New York and Stony Brook Stony Brook, NY 11794 USA

D. Logan Morton Kaplan J.W. Ball Department of Chemistry Carnegie Mellon University Pittsburgh, PA 15213 USA

Louis C. Vaz E. Duek John M. Alexander M.F. Rivet

M.S. Zisman Lawrence Berkeley Laboratory Berkeley, CA 94720 USA

fission and emission of h and he in the reactions of 215 mev 16 o with 181 ta, 208 pb and 238 u

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