Nuclear Interactions: Conference held in Canberra, 28 August–1 September 1978

497 Pages·1976·31.876 MB·English

by  H. J. Specht (auth.), B. A. Robson (eds.)

FISSION PHENOMENA IN DEEP INELASTIC COLLISIONS
H°J. Specht
Physikalisches Institut, Philosophenweg 12
Universit~t Heidelberg, Germany
Abstract
Kinematically complete experi~eDts have been performed on fission occur-
ring in reactions of 7.5 MeV/amu ~U°Pb and 238U with 58Ni and 9Ozr. The frag-
ment Q-value distributions as well as their angular correlations suggest an
interpretation for the bulk of the events as sequential fission following
deep inelastic collisions, with no indications for any fast ternary compo-
nents at present. Referred to the rest frame of the fissioning nuclei, the
fragments are heavily concentrated in the plane of the first reaction step,
but distributed isotropically to~10% within that plane, pointing to a rather
strong alignment of the angularmomenttun transfer. The quantitative analysis
of these distributions and of the fission probabilities yield average spin
values of 30-45 %~ for the heavy fragment. The detailed dependence of the spin
on energy loss and nucleon transfer is also discussed. Following an initial
rise, a nearly constant oriented spin is observed even for the largest ener-
gY losses. This is interpreted as evidence for considerable fluctuations in
the correlation between energy loss and angular momentum.
.I Introduction
The mechanism of nuclear reactions between very heavy ions is of great
current interest. Besides studying kinetic energy loss, nucleon transfer and
angular distributions of the reaction products, more recent experiments have
also focussed on the transfer of angular momentum from orbital to intrinsic
rotation. Classically, the magnitude of the spin transfer measures the
strength of the tangential component of the friction force, but microscopi-
cally, the spin distribution function, the spatial orientation and the de-
tailed dependence on the other observables might give insight both into the
mechanism of the nucleon transfers during the interaction, and also into the
importance of collective degrees of freedom, thus providing more crucial
tests for the different theoretical reaction models.
Several quantities sensitive to angular momentum have been exploited in
previous investigations - average gamma ray multiplicities and their higher
moments, gamma ray angular distributions, circular polarization of gamma
rays, B-decay anisotropies, and angular distributions of light (preferen-
tially~-) particles emitted during or after the collision. If one of the
reaction products is sufficiently heavy, the signatures of its subsequent
fission (probability and fragment angular correlations) represent a unique
Probe for the spin transfer processes. Two inclusive experiments of this
type have been reported before, detecting two particles in coincidence and
covering selected cuts within the total angular distribution 1,2). A quan-
ta-mechanical formulation of the angular correlation problem has also re-
cently been presented 3).
At the UNILAC in Darmstadt, we have performed the first exclusive (count-
i t-) experiments in this field, simultaneousl~ninves~gati~@ the ~ an~, a
~ee particle exit channels in the systems zUOPb -~J°Ni, >uZr, , Nd, ''°Hf,
u~Pb, 238U and 238U-~58Ni, 9Ozr, 23BU at beam energies of 7.5/MeV/amu. By
Use of the heavy particle beams and suitable detectors, the measurements are
made in a manner to be complete both kinematically and in the total phase
space distribution of the events, including all correlations between the ob-
servables. Our aim has been severalfold -
)1( to verify that fission occurring in collisions between very
heavy ions is dominated by a sequential process as assumed thus
far,
(il) to study the angular momentum transfer in detail once the se-
quential picture and its possible limits are established,
(ill)to search for any deviations, i.e. "instantaneous" fission
influenced by the Coulomb or nuclear field of the light reac-
tion partner, or even true ternary fission following fusion,
(iv) to accurately follow the fission pattern of the heaviest ele-
ments produced in these reactions because of the relevance for
synthesizing nuclei with ~ Z 100 by multl-nucleon transfer.
In the following, we will concentrate on the first two points and restrict
the number of systems to a comparison of 208pb, 238U -~58Ni, 9Ozr for which
the analysis has been completed.
.2 Experimental Set-up
The kinematics of a typical sequential fission event in a specific co-
planar situation is illustrated in Fig. .I The numbers indicated correspond
approximately to the average values found in this reaction. The recoiling
target-like fragment, from the first reaction step is anal~zed in a ~E-E gas
ionization chamber J~ with a sensitive area of 40 x 12 cm , measuring both
coordinates x and y.
2oepb-.-g°Zr at ?.5MeV/amu
NOISSIF FRAGMENTS
(Of =+150 )VeM
\
TARGET- LIKE
PARALLEL PLATE ~ ~ / -----~ LIGHT FRAGMENT
E H C N A L A V A R O T C E T E D {'~, \'I ,~ I 55'MCQ( ,= 10 = -150 ~VeM A )01-M
,,x( ),EA,it,,y
IONIZATION R E B M A H C
(x,y, E, AEI t)
Fig. 1 Kinematics of a specific eoplanar 3-body event and
schematic illustration of the detector arrangement
An acceptance angle of ®L,b~30 ° in the lab frame together with the kinematic
concentration at forward ~M) scattering angles and the focussing property of
the deep inelastic reaction for nearly all systems investigated allows one to
cover the major part of the quasi-elastic and deep inelastic distributions
with just one center angle setting, properly chosen for each system.
t The Pb- or U-like surviving fragment or its fission products are de-
ected in coincidence in a parallel plate avalanche counter ; with a sensi-
tiv e area of O.91 x O.91 2, m capable to simultaneously analyze two particles
according to time-of-fllght t , position i x and Yi and energy loss ~E .i Rou-
tine performance values for t~e overall time resolution achieved An connec-
tion with the bunched beam from the UNILAC are At ~ 500 ps, those for the
spatial resolutlon Zx = ~y ~ 0.5 mm. Since the lab velocity of the beam-like
fragment (~3 cm/ns) is large compared to the velocity of fission fragments in
its rest frame (NI.1 cm/ns), the lab frame directions of the two coincident
fission fragments are compressed into a narrow cone with a total opening
angle of 45 °- 50 ° around the direction of the fissioning nucleus. Thus,
again one suitably chosen (system-dependent) angle setting of the parallel
plate detector is sufficient to cover the entire cone, yielding an effective
solid angle of 4~ for the investigation of the various fission observables.
The detector acceptance angle is, in fact, made larger than the cone angle to
search for deviations from the sequential pattern. For a certain fraction of
the events, only one fragment is detected because of absorption losses which
occur both in the support structure of the counter window and a movable beam
stop and shield against small angle (~5 )° Rutherford scattering located in
front of the detector.
The data are fed into a PDP 11/55 on-line computer, stored event-by-event
on magnetic tape and finally analyzed off-llne.
Exploiting the conservation of linear momentum, energ~ and mass number,
the measurement of 4(n-I) independent quantities is required for a complete
kinematic analysis of a reaction with n particles in the exit channel. For
n=3, the determination of the velocity vectors alone (time-of-flight t ,i co-
ordinates xi , y~ ) yields 9 quantities, i.e. a one-fold redundancy. Alterna-
tively, the analysis can also proceed step-wlse on the basis of the ioniza-
tion chamber data, yielding the charge I Z (and via suitable assumptions the
mass MI) of the target-like fragment, the Q-value and CM scattering angle of
the first step of the reaction, and finally the reconstructed velocity and
lab angle of the beam-llke fragment. The fission direction in the frame of
the fissioning nucleus (see Fig. )I can then unambiguously be evaluated even
in the case where only one fragment has been observed. If both are detected,
the full information including the fission Q-value and fragment mass ratio is
obtained.
.3 Results
An example of a two-dimensional position spectrum from the parallel plate
detector for Pb-~ Zr, gated on 3-particle events, is shown in Fig. .2 Even
Such raw data on the fragment distribution immediately demonstrate the strong
concentration into the region expected for a sequential process, with a
strong decrease of the event density towards the detector edges. The vertical
and horizontal bars are due to the shadowing by the window support of the de-
tector, the circular region to that by the beam stop.
In Fig. 3, the observed lab velocity distribution of the fission frag-
ments from the same reaction Pb-~Zr has been projected into the plane de-
fined by the direction of the target-like fragment and that of the beam. The
overall pattern appears to be consistent with the sphere expected from kine-
matics for sequential fission. The tails of the event density inside the cir-
cular cut of the sphere with the plane are due (see below) to events ocurring
above and below the plane. Nevertheless, a strong thlnning-out of the density
in the middle is obvious, indicating a considerable degree of coplsnsrity
for the 3-body reaction.
'L .:.. •
+40 ". . . . : " . ".'.
.. . . . . • .::..,..."', ~. . . •
Fig.2 • .. , . .",:".:'.,, ';..: • ?: ',~' ... .:.
Raw data of the fission • . i ..,,", ,,..' .,.' ',~.'- ..~" "L'~ ",~,. .'.
fragment spatial distrib- A E 02+ :-:.::'; , :.:-: :.: .; '~." ;.i':~ :.. ~.": :.:-..-",'~'..':. .,;~:j..'.,.~ • ":'. • .
ution in the parallel tJ ,j~;.~,,~'..:i-..,: : ~. ~ :;~:.~: ~-- .~.~,:,;~., ~: -_', ... ..... .
plate detector, gated on • '., ....IF, ...~.1.~ " .-t;;. ~ ~ r. 'll~ " T'., .. ~ ... "-' "~,~,.. 1 "J : '~'r ' ' ~'." ~ ~ .~, ..'.r,.* :..,,-
3-particle events from
• "='" . ~"-~ ' , - , ~-~' : ! ~ ~ "" ~:'.'":":'~'I,R ~;-,.~ I." ~,%;',:,~.'L*.".; :-
Pb-~Zr
Z 0 • :- ... ,~.:-,. ~ :-...~..... , ,~;~;~.-. ;., i~,~-:,,j.~=: ~ ~ -.~. ',~1;~ ,~:..,...~.
.... ,
t'~ " ~ -~,,ir,~-~. ,.~r~ ,~ ,~-,~_..~ .; .,. :
n- • . ,~. ~ -~ .,.~',~ ,, .~ ,. ~,.' ....
O O • -.,:.~:.'.:;,/_ ' '.;.~~,.~,..~..~?,+;.-.. - ;;r . . . ~.: -~:~;~. ;,~i' ~,, -$.- .÷ ~. ] -~: ~.",'.~;~ ,.,..:~..~:.~.+~ ~ 7."~ ~. ~l., " .; .:.. .... ,,.:'., '" "-~'- " ~ .. . '
(J -20 • ".. ~-~ ..~,~ • • : . ; ~'..-~.'~7..,~ .t~..:... ;,...,,, ~ .. ~. ?..... ,
.~ .'.?.,;.." .~..",.~,.~.:~". :';...'~ q~.5:, -;:," ~.: . . •
I
> .:,.~ .;" .~, -.= ..., :. ...~ -:"):.,.~",.~.,• .......... -'.. ..,.
• . ".'" :,,...." . ..~. '.:' : ':," . ": :
-40
I ] '' .I I I
-/,0 -20 0 +20 +/,O
X COORDINATE (cm)
2°8pb-~ 9°Zr at ?.SMeV/amu
FISSION FRAGMENTS
(PROJECTION INTO
PLANE)
,,t---'--,--
TARGET-LIKE
LIGHT FRAGMENT
BEAM DIRECTION
Fig. 3 Lab velocity distribution of the fission fragments from
Pb~Zr (coincident with target-like fragments) projected
into the plane of the first reaction step
A more quantitative test for sequentiality, contained in Fig. 4, is based
on the intensity distribution of the vector difference lR~VJ =;{i-~21 of the
fission fragment lab velocities. The quantity I~RI (compare again Figs. 1,3)
c?rresponds to the diameZer of the sphere and essentially determines the fis-
slon Q-value Qf = I/2 ~v~, /~ being the reduced mass of the two fragments. The
~rag~values Q~145 MeVZand 172 MeV deduced for the two systems 2OSpb and
s~U~=~Zr are consistent with data on both low and high energy induced fis-
ion in this region 6,7). The variances ~16 and 19 MeV, respectively, are
i , i i ~ l I I I I
~.bp802 rZ09
238 u .~. 90Zr
80
-~ 06
z
UL 15x(
~Z - 40
20
, . .... _ J
I I I I I
~.o o.8 1.2 ~.6 o.~ 0.8 ~.2 1.6
(~'1-~2
NOISSIF TNEMGARF CM VELOCITY ½ ) (cm/ns)
Fig. 4 Distribution of the vector difference J Vl-Vgl of the
fragment lab velocities, integrated over all fission
directions. It demonstrates the existence of an inter-
mediate fissioning system as a "resonance"
definitely larger than those usually observed in light-particle induced fis-
Slon at low excitation energies ; and much closer to the values found in_,
fUSion-flssio' n reactions with heavy ions at excitation energies y100 MeV Y).
It should be especially emphasized that, with the present limits of accuracy,
the gross velocity distributions of neither the Pb-like nor the more fission-
able U-like nuclei exhibit any significant dependence on the fission direc-
tion or the Q-value QI of the first reaction step, as would have been expect-
ed in a fast non-sequential process. Thus, the bulk of the data clearly de-
monstrates the existence of an intermediate fissioning system, appearing as
a "resonance" in Fig. 4. The weak (<1%) low velocity tails may possibly be of
instrumental origin, but have not yet been investigated in detail.
The overall fragment mass distributions (not shown here) of all systems
investigated are symmetrical as @~ected for the high excitation energies in-
Volved. A specific selection of z~ U data for a cut-Q I< 50 MeV, however,
shows the usual 1.4:1 mass split with a peak to valley ratio of about 5 and
a mass dispersion ~A~8 amu in each of the two groups, demonstrating the high
quality of the kinematic analysis.
The probability distribution of the fission directions in the rest frame
of the beam-like fissioning nuclei from again Pb ~Zr is shown in Fig. .5 Po-
lar coordinates together with a Mercator projection are used. The equator
(GEM = O) corresponds to the reaction plane of the first step, defined by the
target-like fragment and the beam; "Greenwich" (~M = O) has been a~bitrarily
chosen as the recoil direction of the target-like ~ragment, where ~6M O > is
counted anti-clock wise. The events are strongly concentrated along the
eouator, but do not show any recognizable dependence on the azimuth angle
~M, quite different from the 2:1 in-plane enhancement at ~ = 0 found be-
fore in the nearly identical system 85Kr+209Bi )I (see beloW5 .~
+60
Fig. 5 z
,.z,.i r..)
Probability distribution 'Q) +30
of the fission direc-
IJJ
tions from Pb-~Zr in Mer- ._1
cator projection, refer-
red to the frame of the Z 0
fissioning nuclei (see
text) Lt, i
Z
,,,( -30
._J
O...
I
IJ.
0 -60
0-
0
-30 0 30 60 90 120 150
AZIMUTH ANGLE M~(@ (deg)
The overall fission fragment angular correlation data for the four sys-
tems, integrated over the energy loss-Q I and the charge distribution of the
first reaction step, are quantitatively su/mnarized in Fig. 6. The out-of-
plane distributions shown in the upper part are, in addition, inSegrated over
all azimuth angles ~M" They will be discussed first. For the 2OSpb reactions,
the ceplsnarity of the fission direction and the scattering plane of the
first reaction step is very pronounced. The o 0 to 90 ° ratio is found to be
~5, nearly independent from the target; a preliminary analysis of 2OSpb ~-
zU°Pb still yields about the same va~e. T~s va~ is also in-quantitative
agreement with th~8observed before "J in ~ Kr-~U~Bi for the specific cut
~M = Oo For the ~ U reactions, on the other hand, the ratio is only ~3, but
again nearly independent of the collision partner.
In the framework of a sequential process transferring angular momentum
from orbital motion to intrinsic nuclear rotation, the strong and rather iso-
tropic concentration of the events around the equator is immediately indica-
tive of a considerable spin in the heavy fissioning nucleus being predominant-
ly aligned perpendicular to the reaction plane. Defining this perpendicular
direction as a space-fixed quantlzatlon (z@axis , the fragment angular corre-
lation in the traditional Bohr picture can be rigorously formulated in terms
of D-functions (see also re f s 1,3) ) a s
I * ,~D
,M~e(W F)MC~ ~ = )xcP~zcP ~, KMD K ~I~
I I I I f I r i i i
I I
1 I 2os Pb i ..... 230 U
,° I ,0
L .," •
s.o~ i, I • 0
4o
,°
UL
2,0
W
>
-w -J
,,n • se Ni
5olf • g0 Zr
tt • 90 Zr
ALL e ALL >4
i i i i I I I I I I t I I I I I
0 20 40 60 80 0 20 40 60 80
OUT-OP-PLANE ANGLE 8~ (deg)
I I I I I i I I I I I I I I t I I 1 I |
i
(D I i
50- I i
I
LL i I
O I i
z I
20 l
~C
(n I 10
I l I l I t I I I I I I I I I I I ~ ~
n,
2
I I
, -I0 < e < +10 i ~I0 < 9 < +10
...I ILl I I
o'..* ,, .,, ° °, °
ILl +
> I
c-. I I
<[ (15- i I
U..I.J
n-
i i I I 8'0 ' t i ~ ' I ' I ' i ' ' ' )~C~ L
0 t.O 120 1 0 O 40 80 120 1
AZIMUTH ANGLE oFM (deg)
208
Fig. 6 Q~rall^fisslon fragment angular correlations for Pb,
z U-~NI, 90Zr. The out-of-plane distributions are integrated
over all azimuth angles ~M- The in-plane distributions in the
lowest part represent a specific selectlon -I0°<8~<+ 10 ° close
to the equator and are reflected around ~6M = 0 (the recoil di-
rection of the target-like fragment)
where I is the intrinsic spin of the fissioning nucleus and P(I) its distri-
bution function; K is the projection of I on the nuclear symmetry axis and
P(K) its distribution function, the orientation of this axis being taken as
the fission direction; M z = M is the projection of I on the z axis. The K
distribution depends only on the properties of the fissioning_nucleus and has
been investigated in detail in nume{o~@ previous experlmen ts 6J . I n the
framework of the statistical model v,~, it is a Gaussian
P(K)~ exp(-K2/2 K~) )2(
with a variance O K = (T.~eff) I12 /~ depending on the nuclear temperature T
and the effective moment o~-inertia ~e~ at the saddle point. Typical values
at an excitation ener~[ of 100 MeV are'~ O = 11 and 15 for Pb-like and U-like
nuclei, respectively ~/, the difference being due to a contraction of the
saddle point shape with increasing Z /A. The aim of the experiment then is to
deduce information about I and M.
In the case of complete alignmen~ I = M = Mz, the angular distribution is
independent from the azimuth angle ~CM as intui£ively expected. The out-of-
plane distribution W(e~M) for an average spin <I> has - apart from the polar
regions - an approxima£e Gaussian shape with a variance (rms-width) 0 6- gi-
ven by 8)
sinGe~(~l> 12 + K~ )112 )3(
~i> 2
where the agreement with exact (only numerically evaluable) quantum-mechani-
cal results ~; is within <1% for <I> /K o >3.
The considerable difference between the 2OSpb and 238U r~tions visible
in Fig. 6 can now be directly read-off from eq. (3). In the ~U case, the
width is larger due both to a larger average value for O K (see above) and a
smaller average spin <I> , caused by a much stronger contribution from fis-
sion at small energy losses (-QI) <100 MeV with lower angular momentum
transfer (compare discussion for Fig. 7). The remarkable degree of indepen-
dence from the target is also readily understood. The values for K_ are not
different, because similar average excitation energies (not Q1-val~es, comp.
Fig. )7 and nearly the same sample of fissioning nuclei (compare Fig. 8) are
involved. The average spin values <I> may not significantly differ either be-
cause of an approximate cancellation between the target mass dependences of
the orbital angular momentum brought in by the entrance channel, and that
fraction of it transferred to the heavy fissioning fragment in the limit of
rigid rotation of two spheres sticking together. Assuming - just for the
sake of the argument - the average entrance channel angular momentum contri-
buting to sequential fission to be ~0 = I/2 far, these sticking values are
4I> = 38, 42. 37 for lgr ~2OO, 300, in the @eactions 7.5 MeV/amu 208pb~
58Ni, 9Ozr, 208pb, respectively.
Turning next to the dependence of the fragment angular cqrrelations on
the azimuth angle ~M~ the center part of Fig. 6 demonstrates the variance
~8 of the out-of-plane distributions W(8~M) to be essentially constant for
all four systems investigated, any residual variations being ÷ ~ 10% (th E pre-
sent limit for possible systematic errors). SUch a plot of ~8-versus ~6M has
the obvious advantage of exploiting the full experimental information avail-
able from the 43 ~ geometry, within the framework of the parametrization con-
tained in eqv (I), a constant behaviour of 6~ is mathematically equivalent to
i~otropic azimuthal distributions W(~) at ~ny arbitrary polar angle
8~M = const. This is borne out in the Tower part of Fig. 6, where the "in-
p~ane" distributions - defined by the specific selection (-10 ° <O~M < +FIO o)
close to the equator and reflected around the target recoil direction ~cM = O
- again show at most weak variations, in clear disagreement with the 2:~'in -
plane enhanceme~ at ~ = O reported previously for the quite analogous re-
action 86Kr + z ~Bi I).
Angular correlations independent from the azimuth angle do not automati-
cally imply full alignment, i.e. ~I> = <Iz> = <Mz>. It is conceivable, on
the contrary, that the oriented part <Iz> of the intrinsic spin drawing from
the orbital motion only presents the main component, smaller additional ran-
dom components with different orientations being generated by the detailed
mechanism of the first reaction step I-3,9,10). To first order, components
alon~ the z-axls do nat influence the angular distribution, but those in the
reaction pla/le lead to an effective "depolarization" of the oriented a~ular
momentum with a corresponding weakening of the out, of-plane anlsotropy. De-
noting the directions ~ =Oi ~M = 900 and ° O as the x- and y-axls, re-
spectively, it is conve~ient to parametrize the distributions of the in-plane
components Mx and .~M in terms of Gaussians similar to eq. (2), centered at
<M~> = <M..> = O (beCause of the symmetries involved) with variances MOX and
MO ~ v 3 .)~ Because the reaction complex ha& no rotatlonal • symmetry around the
~ ~-Rxls Mo~ -- and M~ may, in principle, be different, causing azimuthal anise-
ropies ~ the angular --J -- distribution. Speciflcally, • the analysis / , ~ J of the
r~IU + z~3Bi data has lead to the conclusionFMox ~ Mov. Since from a simple
kinematical consideration the y,dlrection (~CM = )O cSincides with the sym-
metry axis connecting the two nuclei at the moment of contact on a grazing
trajectory I~ = i.~, this result has been interpreted to imply a prefersntial
depolarization in~ plane perpendicular to the internuclear axis. Possible
mechanisms .creating random spin 9o~ponents with this property include the
collective bending oscillations ]-~Jof two nuclei in contact as known from
nuclear fission 6~, but also the diffusion of particle~ dur/ng the interac-
tion time 9,10).
The present experiments, however, cannot support this notion. The quite
~niversally observed azimuthal isotropy rather points to
Mo ~ x Moy
We therefore conclude that the effects of a non-isotropic depolarlzatlonm~y
be essentially washed out by the considerable rotation of the internuclear
axis relative to the y-direction during the contact time for all trajectories
li< lg r. In a strictly focussed reaction, the very low partial waves i i~O
correJpond, in fact, to a rotation angle of 120 ° for a CM scattering angle of
600 in the first reec+tion step. One can, moreover, evoke a mechanism for cre-
atlng random spin components which is completely analogous to that responsi-
ble fQr the K-distributlon in Duclear fission. Rather th@n restricting this
mechanism to the y-axis alone 3), it can be generalized ~) to a thermodynami-
cal equilibrlu/n involving all rotational degrees of freedom of the collision
complex and the appropriate sharing of the angular momentum between the two
final products. For Pb~Zr ro( Kr~Bi) at a temperature of 1.7 MeV, average
Values Mo~14 ~ are obtained with only small differences between the compo-
nents Mox, Mm~, and Moz. This result is.s~memhmt related to that calculated
asymptotical[{ (at long interaction times) for the quantity ~M in the diffus-
ion model 9,1D). Similar conclusions about the magnitude and ~he ransom orx-
entation of the depolarizing spin components have also been obtained by a
closely related consideration of thermally excited bending and twisting os-
Cillations 2).
Assuming then Mox~Mov~Mo z =Moa~ suggested by the present experiments, the
non-complete alignment f=o the total spin <i> is still associated with an ap-
Proximate Gausslan shape ofs~he cut-of-plane angular distribution, its vari-
ance ~8 now being given by
(4)
~iz>2
.... I
where <I~ _~ <M~> is the averaqe oriented part of the intrinsic spin
~I>~<~2>I/z = ~<iz>2 + 3 ~)172.
pUnfortunately, the measurement of the out-of-plane angular distribution
W(eCM) alone cannot uniquely determine the two unknowns <Iz> and O M at the
Same time. As should explicitly be stressed, an identical problem arises in
01
the case of azimuthal anisotroples, where then the three unknowns <Iz> , ~ox
and MO~ cannot independently be extracted from the two distributions W(eCM)
and W(~M) (the extraction of spins in refs 1,3) has only been possible via
the arbitrary assumption Mov = 0). This ambiguity can only b~ sQlvedby uti-
lizing additional experimen%al information, for example the fission probabi-
lity PF which is solely sensitive to the total angular momentum <I> (apart
from Z,A and excitation energy), but not to the alignment. This will be dis-
cussed in more detail below.
Independent from these uncertainties, however, certain limits can at
least be d~ived for the degree of alignment. Defining its magnitude by the
parameter ~;
3 <I~> I 3 <Iz>2 + M~ I
PZZ ~ - =-- )5(
2 ~I2> 2 2 <Iz>2 + 3~ 2
values of I ~Pzz>O.5 are obtained for the 208pb reactions and the unrealis-
tically large range O~M o< ~ , with PzZ~0.65 for M o~K O. We thus conclude,
in agreement with data on ~-emission 7T), that the alignment of the angular
momentum transfer in deep inelastic collisions for all systems investigated
is quite large, too large in fact to account for the generally observed weak
anisotropies of continuum ~-ray emission as suggested recently 2). This con-
sideration, on the other hand, also demonstrates the restricted usefulness of
the quantity PZZ, being so insensitive to wide (correlated) variations in
<Iz> and o. M
We will now discuss the more detailed information contained in the depen-
dences on total kinetic energy loss rQ4~and charge transfer. The energy loss
spectra coincident with fission and the fission probabilities PF' defined as
usual by the ratio of fission coincidences to the total, a{~ 8 shown in the up-
per part of Fig. .7 The differences between the 208pb and U reactions men-
tioned before are immediately recognized. For U-llke nuclei, the fission pro-
bability already approaches I at very small excitation energies and angular
momenta; the Q-value- and angular distrlbut/ons~are thus representative for
the true average. For Pb-llke nuclel, however, the coincidence spectra are
essentially cut-off at energy losses 4100 MeV. In this region of PF~I, fis-
sion mainly occurs via reduction of the fission barrier by rotation, leading
to a selection of only the largest spin values I which is not reRr~sentative
for the true average <I>. The apparent target difference of the ~u°Pb reac-
tions is of a rather trivial nature; it nearly disappears if the data are
plotted versus excitation energy E* in Pb rather than-Q~value, assuming a
sharing of the total available energy in proportion to the masses of the two
fragments 12,13).
In view of the azimuthal isotropies, the angular distribution data have
bee~ condensed again into the variances e ~ of the out-of-plane distributions
w(e6M), which contain - in the spirit of eq. )4( - the essential information.
The conversion into the oriented part ~Iz> of the angular momentum transfer
as shown on the bottom of Fig. 7 is. however, based on the exact formulation
of eq. )I( (significant only for 238U at -Q4<150 MeV). The angular distribu-
tion for a single average value <Iz> is taken to be equal to that obtained
from a correct averaging via P(I), justified by the nearly complete (unfor-
tunate) insensitivitv to the higher moments of the spin distribution. The pa-
rameter ~ o K E( ~ -EF)I/4 has been extrapolated from previous results 6), shaft
ing the energy as just mentioned and ignoring a possible dependence on <I> )3,6
Most important, o = O M has been assumed. Thus, the values extracted represent
a lower limit.
Since the ambiguity associated with O M mainly influences the absolute
scale rather than the relative variation of ~Iz> with energy loss (compare
Fig. 9), we will discuss the latter first. Apart from the great similarity
now between all four systems, two features are noteworthy - a gradual rise up
to -Q~150 MeV, and a nearly constant behavlour beyond. Experimentally, both
the initial rise - although possibly somewhat faster - and the adjacent pla-