Download - Dissipative phenomena and alpha-particle emission in reactions induced by 16O on 27Al between 46 and 85 MeV

Nuclear Physics A472 (1987) 358-380 North-Holland, Amsterdam

DISSIPATIVE PHENOMENA AND a-PARTICLE EMISSION

IN REACTIONS INDUCED BY

160 ON “Al BETWEEN 46 AND 85 MeV

SHEN Wenqing, ZHU Yongtai, ZHAN Wealong, GUO Zhongyan, YIN Shuzhi, QIAO Weimin

and YIN Xu

Institute of Modern Physics, Academia Sinica, Lanzhou, People’s Republic of China

Received 21 April 1987

Abstract: The various exit channels of reactions induced by I60 on 27AI with ejectiies ranging from cy

to Na have been studied at 84.5 MeV, 80.6 MeV, 75.5 MeV, 62 MeV and 46 MeV incident energy.

Three-fold differential cross sections d3c/(dR. dE_ dZ) of the reaction products have been

measured with a large-area position-sensitive ionization chamber. In addition, the nuclide distribu-

tions of the reaction products and the correlation between cu-particles and projectile-like fragments

were measured at 80.6 MeV. At Elab = 70 MeV the deep-inelastic collision starts to compete with

other reaction mechanisms like quasi-elastic reactions or complete fusion. The division of the

reaction cross section among the different channels and its dependence on the incident energy are

discussed. The relaxation process of the reaction is studied, the effect of the potential energy surface on the charge distribution and the nuclide distribution are discussed. The coincidence measurement

shows that some a-particles are possibly produced in incomplete deep inelastic processes.

NUCLEAR REACTION 27A1(‘60, X), E = 84.5,80.6,75.5,62,46 MeV; measured fragment E a(& A, E), inclusive o-spectra, (E,, 0,) o(C) coincidences; deduced potential energy sur-

face reaction time, reaction mechanism.

1. Introduction

Since the seventies when the so called deep inelastic collisions (DIG) had been

discovered in heavy ion induced reactions I-‘) the investigation of this mechanism

became one of the most important fields in nuclear reaction research. Such a reaction

is placed intermediate between the direct reactions and the compound nucleus

formation. A great deal of the relative kinetic energy is dissipated and part of the

relative angular momentum is relaxed into the internal angular momentum; the

N/Z degree of freedom, the deformation degree of freedom and the mass asymmetry

are also relaxed gradually. The reaction is strongly inff uenced by the potential energy

surface and is in competition with the quasi-elastic reactions (QE), the complete

fusion (CF), incomplete fusion and other reaction mechanisms, the relative import-

ance of which depend on the bombarding energy. Besides the mean field of the

nuclear interaction the average characteristics of the outgoing products are influen-

ced by nuclear structure effects. Deep-inelastic reactions have become a powerful

0375-9474/87/%03.50 @ Elsevier Science Publishers B.V.

(North-Holland Physics Publishing Division)

W. Shen et al. / Dissipative phe~ome~a 359

tool for studying the non-equilibrium statistics, the dynamics of the nuclear reaction

and the nuclear structure influence on the nuclear reaction.

Up to now, most of the research is still concentrated on the medium and heavy

projectile-target systems. For lighter systems a lot of very interesting problems

remain to be investigated, e.g. whether there are DIC at all, at which energy they

appear, how DIC compete with the other mechanisms and, in general, what are the

difference and similarity between the lighter and the medium heavy systems.

In the meanwhile, the light charged-particle emission (p or cu-particles) in heavy

ion reactions is also a very important subject of studies, it has become one probe

in heavy ion reaction research 637). In addition to the evaporation from the compound

nucleus, there are light particles produced by other interaction mechanisms. Besides

inclusive measurements of the emitted particles, coincidence measurements between

the emitted particles and the projectile-like fragments 8-‘0f are extremely important.

For the investigation of DIC the light systems are not typical because the total

number of the nucleons involved is small from a statistical point of view. Furthermore

the cross section of DIC is only a small part of the total reaction cross section and

is difficult to discriminate from the other reaction mechanisms. In lighter systems

the dissipative process in addition is strongly affected by the nuclear structure. On

the other hand some new characteristics of DIC and some new reaction processes

are expected to show up. With increasing bombarding energy the contribution of

DIC will increase gradually. Therefore, one can investigate the evolution of DIC

and its competition with the other reaction mechanisms in detail. For example,

using projectiles with an a-cluster structure in the ground state and low excitation

states such as 12C, 160, “Ne, it is easy to produce projectile break-up. In addition

to the elastic and inelastic break-up of the projectile ‘I), processes such as incomplete

fusion 12*13), in which the residue of the projectile fuses with the target or the

sequential fragmentation of the projectile-like fragment after the dissipative col-

lision 14,15) have been found in investigations of such systems. The possibility of an

incomplete deep-inelastic collision has been suggested theoretically 16) and used in

the analysis of reactions induced by 20Ne on several targets I’).

In order to investigate the characteristics of dissipative collisions in lighter systems

and their dependence on the bombarding energy, the characteristics of particle

emission and the correlation between the emitted particles and heavier fragments,

the I60 + *‘Al reaction has been chosen for systematic studies. Measurements of the

projectile-like fragments have been performed at 84.5 MeV, 80.6 MeV, 75.5 MeV,

62 MeV and 46 MeV. Inclusive measurements of the emitted cY-particles were carried

out at 84.5 MeV and 62 MeV. The coincidence measurements between the projectile-

like products and a-particles were performed at the bombarding energy of 82.7 MeV.

Some of the presented results have been reported elsewhere 2’-23).

A few investigations of the ‘60+27A1 reaction are already described in the

literature. Deep-inelastic results are reported ‘*) at the higher bombarding energies

of 90 MeV and 100 MeV, the dependence of the multi-nucleon transfer probability

360 W. Shen et al. / Dissipative phenomena

on the Q-value of the exit channels has been measured at 88 MeV “). Multi-nucleon

transfer has been studied 20) at 88 MeV, 70 MeV and 60 MeV.

The experimental set-up and the method of data analyses is described in sect. 2.

The experimental results are reported in sect. 3. The evolution of the general

characteristics of DIC with incident energy is presented in sect. 4. The effect of the

potential energy surface on the charge distribution is discussed in sect. 5. The

possible reaction mechanism of an incomplete DIC process will be discussed in

sect. 6. The decomposition of the reaction cross section and its dependence on the

incident energy are given in sect. 7. Finally, a brief conclusion will be presented in

sect. 8.

2. The experimental set-up and the method of data analysis

The experiment has been performed at the 1.5 m cyclotron of the IMP at Lanzhou.

87.3 MeV 160f5 ions of about 50 nA impinged on the target, the diameter of the

beam spot was about 3 mm. The thickness of the self-supported Al targets ranged

from 400 pg/cm* to 1.6 mg/cm2. In order to reduce the build up of light elements

on the target a Ni foil of 2 pm thickness was used to separate the vacuum system

of the accelerator from the target chamber; in addition, a liquid nitrogen trap was

surrounding the target. In order to reduce A1203 and other contaminations on the

surface of the target all targets were cleaned before mounting and analysed by the

electron sputtering method. During the experiment the target was changed every 10

hours. As an estimation, the contamination of light elements was less than 10 pg/cm’.

The projectile-like fragments have been measured by a large area position sensitive

ionization chamber (IC) 24,25) which determines the x, y coordinates of the products,

their total energy E and by means of a segmented anode four different bins of

energy losses AEi. By means of three sets of the semi-conductor Si(Au) AE -E

telescopes, the inclusive measurement of a-particles and the coincidences between

them and projectile-like fragments have been performed at the same time. The

thickness of the AE detectors were 17, 12 and 9 pm, respectively. In order to test

and compare the experimental results, a small telescope consisting of an ionization

chamber and a Si-detector was used also. To shield the detectors from. the high

count rate of the elastic scattering products, a 17.5 mg/cm2 thick Al foil was set in

front of the most forward placed a-particle telescope when used at angles below 20”.

The off-line data analysis has been performed on a WANG 2200 vs computer.

AE - E plots from the ionization chamber or the semiconductor telescopes which

yield the atomic charge number of the products have been linearized by a lineariz-

ation package. The energy loss in the entrance window, the target and the Al foil

for stopping the elastic products in front of the a-particle telescope at small angles

has been corrected for according to Northcliffe and Shilling energy loss tables. The

final quantities from the ionization chamber are the atomic charge number, the

energy of outgoing products (Et) and the outgoing direction (0, 4). The mass of

W. Shen et ai. / ~~ss~p~i~~~ ~he~orn~~a 361

the products can be obtained from the atomic charge number Z assuming the mass value of the most abundant isotope. These event parameters have been converted into the c.m. system under the assumption of two-body kinematics. Finally the correlated spectra are obtained which include the centre-of-mass quantities, the total kinetic energy E,,. = Ed.,. + E%,. and the angle S:,,..

The tu-particle energy spectrum in coincidence with the different outgoing fragments in the laboratory system, the contour plots of the Galilei-invariant coincident cross section d3a/(CP, d&r dfiR, dE,) for different fragment energies and the angular correlation between the outgoing fragments and the a-particles were derived. The relative normalization of the data is performed by the monitor counts of elastically scattered r60, the absolute normalization is obtained by the integrated beam current measured by the Faraday cup. In the experiment, the absolute error of the cross section is about 150/o, the typical 2 resolution Z/AZ of the IC is about 27, the total energy resolution of the a-detector is about 500 keV. The half-width of the coincidence time spectrum between the projectile-like fragments and the tu-particle is about 8 I-IS. The width of the coincidence time window has been chosen to 27 ns because the flight times vary from 20 ns to 2 ns depending on the different energies of cY-particles and projectile-like fragments. From the time spectrum, the random coincidence rate is estimated less than 15%.

3. The experimental results

3.1. HEAVY FRAGMENT DISTRIBUTIONS

The energy spectra and the angular distributions of the projectile-like fragments were measured at 84.5 MeV, 80.6 MeV, 75.5 MeV and 62 MeV, yielding the contour plots d3a/(dR dE dZ). The case of 80.6 MeV was investigated in detail; in addition here the nuclide distribution in the N - 2 plane and the energy spectra of different isotopes were measured in the vicinity of the grazing angle and at a few special angles by using the time of flight setup with the AE - E telescope. Since only C, N and 0 appeared in the experiment at 46 MeV bombarding energy, the experiment has been carried out only at a few angles by using the small AE -E telescope.

The derived cross sections are listed in table I. Because of the count rate divider and the Al foil which was used to shield a-detector at small angles the full elastic scattering angular distributions were obtained only at 80.6 MeV bombarding energy. The elastic scattering data were fitted using the Frahn formalism 27) and the derived results are as follows: grazing angular momentum t,, = 33Sh, diffusion parameter il = 2.2h and reaction cross section cR= 1425 mb. The results coincide within IO% with those in ref. 26) which were derived by using the optical model. In order to

discuss and analyse the problem on the same basis the optical model reaction cross sections in ref. 2”) as shown in table 1 were used in the following discussion.

362 W. Shen et al. / Dissipariue phenomena

TABLE 1

The reaction parameter and various deduced cross sections

E lab Km “) OQE “1

(MeV) (MeV) Ecm-/vc (eL)1/4 zb) (mb) -it-E (mb)

FQE/% OblC ~CF ‘)

(mb) WI

84.5 53.1 3.24 13 1585 145 265 + 50 0.09 + 0.02 120+40 1320 80.6 50.6 3.09 14 1560 157 257 + 50 0.10+0.02 100-t-30 1303 75.5 47.4 2.89 15 1520 175 225 + 50 0.12+0.02 50+15 1295 62.0 38.9 2.31 20 1385 205 205 + 70 0.15+0.03 1180 46.0 28.9 1.76 30 1120 170 170+70 0.15+0.03 956

“) From optical model fits of elastic scattering.

Y uQE = (TINE- oDIC.

‘) (TCF.=LTR-rQE-r~,C.

Fig. 1 shows the d2a/(d0 dE) contour plots of the outgoing products from Be

to Ne in the E,,.- 8,.,. plane at 84.5 MeV, 80.6 MeV, 75.5 MeV and 62 MeV

bombarding energy. At the lowest energy of 62 MeV, the yield of a given element

decreases with increasing c.m. angle but the mean value of the energy spectrum

remains nearly unchanged, which is typical of QE reactions. There are two peaks

in the N contour plot. The higher energy component corresponds to the ground

state of 15N whereas the lower energy component corresponds to the QE components

which is a mixture of several excitation states of the N isotopes. With increasing

number of transferred nucleons, the corresponding excitation energy gets higher,

but the peak position of the energy spectrum is still independent of the c.m. angle.

In the case of the measurement at 46 MeV (not shown in the figure) there are only

C, N and 0 observed as outgoing products. The energy spectra and the angular

distribution which consist of only few experimental points show also the QE

characteristics. In the case of 75.5 MeV and the higher bombarding energies the

mean value of the energy spectrum shifts towards smaller energies with increasing

outgoing angle, finally reaching the full relaxation energies at large angles. This

tendency increases with the bombarding energy. For the case of a few transferred

nucleons, the slope of the ridge in the contour plot is steeper at small angles than

in the large angle region, for the case of the fragments far away from the projectile,

it becomes flatter in the total angle region. Such an energy relaxation behaviour is

a typical phenomenon in DIC.

The angular distributions integrated over the total energy spectra from Be to Ne

at the different bombarding energies are shown in fig. 2. Apart from the case of the

62 MeV measurement, there are two components in the angular dist~butions. The

flatter part in the large angle region is attributed to the DIC component. The steeper

one in the small angle region is mainly due to the QE contribution. The variation

of these angular distributions indicates the variation of the reaction mechanism with

the bombarding energy. Fitting the large-angle parts of the angular distributions

W. Shen et al. / Dissipative phenomena 363

160+ 27AL

62MeV 755MeV 80.6MeV 84.5MeV

30” 60’ 60” 90” 300 60” 90” 3o” 60’ 90’

ecm Fig. 1. Contour plots of the double-differential cross section d*c/(dE dR) (pb/MeV. ST) for the

projectile-like products from Be to Ne of the ‘60+27A1 reaction at four incident energies.

and extrapolating towards 0” and 180” (dashed lines in fig. 2), the cross section (T,,,~

can be estimated. Extrapolating the total angular distributions to 0” and 180”, the

total inelastic cross section u ,NE can be obtained also. The QE cross section can

then be roughly derived by uoE = uINE - u,,,c. All these cross sections are given in

table 1.

The evolution from QE to DIC can be also seen in the product energy spectrum

when the bombarding energy is larger than 70 MeV. At given angle, the product


UIL t 0

( fib/W

t 102

t lo=

lo* [

10 :

0 ‘60 +27AL

‘1 + \,O ~ 84.5 MeV

‘\

.\ \ *

x \ \* 755MeV

$ \+ ‘-t x

1: +-Y x

*

x

t xx 62MeV

t

Fig. 2. Energy integrated angular distributions of the products summed from Be to Ne at 84.5 MeV,

80.6 MeV, 75.5 MeV and 62 MeV.

energy spectra indicate mean values drifting towards lower energies (corresponding

to larger TKEL), the drift increases with increasing number of transferred nucleons.

As an example, fig. 3 shows the results measured at 0,_ = 25” and 80.6 MeV bombard-

ing energy, the peak position of the energy spectrum drifts towards lower energies,

when the number of the transferred nucleons increases. Full relaxation is reached

at larger outgoing angles. When the atomic charge number of the outgoing products

are far from the projectile, the full relaxation energy may even be reached already

in the small angle region.

The Z-distributions for different bins in TKEL integrated over the angle region

30”~ 8~ 90” at 80.6 MeV show that the width of Z-distribution increases with

increasing TKEL, the increase becoming even stronger at large TKEL values. Fig.

4 shows at 84.5 MeV, 62 MeV and 46 MeV the Z-distributions integrated over the

total energy spectrum of the outgoing products. Two angles were measured at each

energy which were chosen to 20” and 30” beyond the respective quarter-point angle.

365

Channel

Fig. 3, Energy spectra at 80.6 MeV and 0, = 25” for the different masses of the reaction products.

The widths of these total Z-distribution are getting larger with increasing bombarding

energy: As mentioned earlier, at 46 MeV only C, N and 0 are observed. At 62 MeV

most of the yield comes from the products of C, N and 0, there are only few other

products. At 84.5 MeV the width of Z-distribution becomes larger obviously. With

increasing angle the width of Z-distribution at 46 MeV and 62 MeV is nearly constant,

but at 84.5 MeV it becomes larger and the most probable element drifts towards

smaller element numbers. All these observations are in accordance with the assump-

tion that the reactions at 46 MeV and 62 MeV are mainly of QE nature and DIC

processes occur only at the higher bombarding energies.


k’rl

ZZZ 46MeV

2 4 6 8103 5 7 91

Fig. 4. Z-distributions integrated over total spectrum at 84.5 MeV, 62 MeV, 46 MeV; the left distribution

was measured at 20”, the right one behind the respective quarter-point angle.

3.2. a-PARTICLE MEASUREMENTS

Fig. 5 shows the d’u/(dR dE) contour plots in the EC.,. - 8_,. plane for the

inclusive cz-particles emitted at 84.5 MeV and 62 MeV. At the higher bombarding

energy, the peak position of the kinetic energy decreases from 10.5 MeV at small

angles to about 8.5 MeV at larger angle. At 62 MeV, it decreases from 9.5 MeV to

8.5 MeV. The mean value of the kinetic energy of the cw-particles is compatible with

the Coulomb energy calculated with a parameter r. = 1.4 fm. The yield in the

backward angle region is larger than that at 90”. This tendency is stronger at the

higher bombarding energy and the angular distribution approaches l/sin 8 at

84.5 MeV, which is interpreted as an angular momentum effect. The angular distribu-

tion is not symmetrical to 90”, the yield is higher in the small angle region, this

effect is stronger at the higher bombarding energy. It is assumed that this increase

is caused by a direct reaction mechanism. Assuming that the angular distribution

of cu-particles evaporated from the compound nucleus is symmetrical to 90” and

supposing that in the 6,.,. >90” region cu-particles are mainly coming from the


62MeV

2!5 5

5 1

60" 90- 120" 150' 18(P @cm

Fig. 5. Contour plots of the differential cross sections d’u/(dE dR) (pb/MeV . ST) for ru-particles emitted in “0 t 27A1 reaction at 84.5 MeV and 62 MeV.

evaporation process, the evaporation and direct cu-particles can be separated in the

angular distribution. This leads to cross sections of evaporation cu-particles of

1460 rnb. and 980 mb at 84.5 MeV and 62 MeV, respectively, and thase of direct

o-particles of 140 mb and 68 mb. The last values are compatible with the systematics

of ref. “) which was obtained with a lighter projectile on medium and heavy targets

and was expressed as a ratio oa/o- or of the cross section of the direct cu-particles

to the complete fusion cross section. There are, perhaps, two components in the

angular distribution of the direct o-particles itself. One is the forward peaked

component from the break-up of the projectile, pre-equilibrium emission and other

similar mechanisms. The other is the QE component, peaked around the grazing

angle.

Fig. 6 shows the contour plot of ~alilei-invariant cross section

d3u/(CP, dam dan, dE,) of cw-particles coincident with carbon ejectiles at

82.7 MeV. V,, and Vi are the parallel and perpendicular components of the a-particle

velocity with respect to the beam direction; V,.,, is the velocity of the centre of

mass, V,, is the beam velocity, VP, and VT, are the most probable velocity of the

projectile-like and target-like fragment, respectively. The shadowed arcs in the figure

show the detector threshold of the a-telescope and the energy spectrum cut-off

caused by the absorber foil. The solid circles which centre at V,, and VI-, are the

velocities corresponding to Coulomb energies of a-particles emitted from the corre-

sponding fragments (PL and TL) respectively. The dashed curves are an extrapola-

tion into the region not covered by the experiment. There are three peaks in fig. 6,

which are interpreted as follows: the peak in the large negative-angle region (the


82.7 MeV

Fig. 6. Contour plot of the Gaiilei-inhalant cross section (d3FjCP, da,,, dS& dE,) of rr-particles in

coincidence with carbon at 83.7 MeV; and the insert demonstrates the possible incomplete deep inelastic

collision mechanism.

side of the measured projectile-like fragment is called positive) corresponds to

cu-particles emitted from TL, the peak in the large positive-angle region corresponds

to a-particles emitted from PL and the maximum peak in forward angle region is

contributed by the break-up process. The C-cr angular correlation integrated over

the total cu-particle energy spectrum is shown in fig. 7 in which the coordinate on

the right side d2cr/(d& d~~~)/(d~/d~~,) is differential multiplicity, from which

the total multiplicity of the C-cu coincidences can be derived by integration over

dti,. From calculations based on a simple model, the cont~butions of a-particles

emitted sequentially from PL and TL can be estimated and marked in fig. 7 by the

dotted lines. Subtracting them from the total C-cu angular correlation, there is still

a considerable part left in the forward direction, its velocity is close to the beam

velocity and the corresponding C energy spectrum is similar to that of the dissipative

collision induced by “C on 27Al. As reaction mechanism for this part, the following

picture can be suggested: in the first stage 160 breaks up into an a-particle and “C,

then in the second stage ‘*C (the projectile residue) undergoes a dissipative collision

with the target, a so called incomplete DIC ‘6**7). In lower insert of fig. 6 the

demonstration of the possible reaction process is shown.

W Shen et al. / Dissipative phenomena

Fig. 7. Angular distribution d*cr/(d& da,,,) of cu.particles emitted in coincidence with carbon as

projectile-like fragment, the angle of which is denoted by the arrow HI (TL being the corresponding

binary recoil). The ordinate scale on the right gives the differential multiplicity. The dotted lines are explained in the text.

4. Evolution of the general DIG characteristics with incident energy

The energy relaxation is one of the main characteristics of DIC. The difference

between this system and medium-heavy systems is that the full relaxation energy

of different exit channels can not be explained by Coulomb energy alone, the

centrifugal energy and the residual nuclear interaction of the dinuclear system affect

strongly the full relaxation energy. As the mean angular momentum increases with

increasing bombarding energy, the centrifugal energy will increase also; the full

relaxation energy of different exit channels therefore increases a little bit with

increasing bombarding energy. If this full relaxation energy was fitted by only

considering the Coulomb energy Z,Z,e’/ ( ro(A_i’3 + AA13)), a value r, = 0.98 fm would

be obtained, which roughly coincides with 1.04 fm given in ref. 28), this is already

close to the critical radius of complete fusion, and is too small for DIC obviously.

In order to describe the observed full relaxation energy, the following formulae will

be used:

‘IKE = &ou, + Ko, + -6, ,

E,=-50ER3RJ(R,+R,)1exp((-Rf+(R3+R,))/a),

Ri = 1~233A:‘~ - 0.978/Af’3(fm) ; a=0.63fm,

E,,,=20.9L(L+l)/(li~.R~/I,))


where 1i and 1, are the rotational moments of inertia of entrance and exit channels

calculated under sticking condition of rigid bodies. Rf is the separation radius in

the outgoing channel calculated according to Rf= F,,(A:‘~+ Ai’3); the extracted r,

is 1.32 fm. The calculated and experimental results are shown in table 2. We can

see that r,, is between the critical radius of complete fusion rcrit = 1.04 fm and

interaction radius riot = 1.65 fm, inside which the nuclear potential is active. This

proves that the radius of DIC is in the region which is less than the interaction

radius of QE but larger than the radius for complete fusion, which seems to be

reasonable.

TABLET

Experimental and calculated full relaxation energies E,, (MeV) at 80.6 MeV

incident energy for products from Li to Ne

Products Li Be B C N 0 F Ne

(&denp 16 19 22 25 27 28 29 30

(&A,, 15.9 19.4 22.3 24.8 26.9 27.9 28.7 29.3

The calculated E,, is the sum of Coulomb energy I&,“, , rotation energy

E,,, and interaction I&,; for details see text.

In order to describe the evolution process from QE to DTC in detail, we assumed,

according to the semi-classical theory of DIC, that the dinuclear system rotating

with an angular velocity w has a mean lifetime r. The angular distributions were

fitted by the following formula:

da/da = const (l/sin B)[exp (-pe)+exp (-~(27r- I!)))],

where lu. = l/w7 is the angular decay parameter and ed is the decay angle ( ed = wr)

[ref. “)I. In case of p s l/277 we have:

dcr/df2 = A(l/sin 0) exp (-~0) .

For different outgoing channels, as a function of TKEL or at given TKEL bin as a

function of the charge of outgoing products the parameter p has been deduced by

fitting the angular distributions with the above expression; the results are shown in

fig. 8. With increasing TKEL or increasing number. of transferred nucleons, the

parameter ,u decreases smoothly and it makes the angular distribution gradually

approach l/sin 6, characteristic of complete fusion. The error in p is within kO.3 rad.

The tendency of these values is similar to that indicated in refs. ‘9720). There are,

however, no structures in p as a function of the number of transferred charges. The

reason is that the isotopes of a given element were not identified in our experiment,

which will smear out the structures, These characteristics of the angular distribution

are in agreement with the earlier conclusion about the evolution from QE to DIG

processes.


TKELIM eVf z

Fig. 8. Dependence of the parameter or, on TKEL (left) and Z (right) of the reaction products at

80.6 MeV. p is determined by a fit of the corresponding angular distributions with the given formula.

The angular decay parameters ,u and the corresponding reaction time r deduced

from the summed angular distributions of products from Li to Na, are listed in

table 3. In the calculation of the reaction time, the angular velocity w of the dinuclear

system was deduced as follows:

W =I 2(J??i - V&)1’2/( ?TlRi)q

where Ei is the incident energy, V&, mi and Ri are Coulomb energy, the reduced

mass and the interaction radius of the incident channel, respectively. A radius

parameter of r, = 1.4 fm was used. The deduced reaction times range from 0.8 to

10 . 1O-22 sec. The time increases with increasing TKEL and increasing number of

transferred nucleons and demonstrates again that the reaction process evolves

gradually from QE to DIC. For example, when TKEL increases from 10 MeV to

40 MeV, the reaction time increases from 2 1 1O-22 see to 9 . 1O-22 sec. By fitting the

TABLE 3

The angular decay parameter TV and the mean lifetime 7 as a function of TKEL at 80.6 MeV incident energy*

TKEL (MeV) <5 5-10 10-15 IS-20 20-25 25-30 30-3s 35-40 DIC

p(rad-‘l 4.2 2.8 1.6 1.3 0.95 0.75 0.55 0.32 0.8

7(10-= s) 0.75 1.10 1.95 2.40 3.40 4.50 5.70 9.80 3.9

* These values were obtained from angular distributions summed over the products from Li to Na; the last column gives the results for the integrated DIC component.

372 U! Shen et al. / Dissipative phenomena

DIC component of the angular distribution after integration over the total energy

spectrum and the elements from Li to Na, the corresponding time is about

3.9 . 1O-22 set (last column in table 3). It is larger than the QE time (about 1O-23 to

1O-22 set) and less than the complete fusion time (about 1O-2o set). Using the same

method we find a mean DIC reaction time of 3.8 . lo-** set at 84.5 MeV and of

4.1 . 1O-22 set at 75.5 MeV, respectively.

The Z-distributions deviate from gaussian distributions obviously. In order to

determine the average behaviour, the mean value (2) and the variance a: of the

distribution have been calculated explicitly instead by gaussian fitting.

Fig. 9 shows the curve of the mean values (2) and the variances a$ (the first and

second moments) of Z-distributions at 80.6 MeV as a function of TKEL. As men-

tioned above, the reaction time T can be related with TKEL, so it can also be related

to the first and second moment of the Z-distribution. In ref. 30) it was pointed out

that in the dissipative collision the reaction system will undergo a process from the

local equilibration to the diffusion process. By solving the Langevin equation, the

TKEL ' ' (Me'4 ‘60 t"AL

40- 80.6MeV P

4 ,.-* -w

30- I

P'

i d'

20- b

‘b

B

1 y ” I 1’0

lo- k t 7

/I

6- I T

4- b b !

t /

0

0 23

2

i

P t G 15~10sec

P u O.n5~ld'Chu % r/ D Om5d'c~

Fig. 9. Mean values (2) and variances u: of Z-distributions as a function of TKEL or the reaction time

7 at 80.6 MeV. The dashed lines are to guide the eye, the solid line is a calculation; see text for details.


dependence of the variance of the charge distribution a; on the interaction time 1

can be deduced by the following equation:

where V, is the charge drift coefficient at the moment t = 0. r, is the local equilibration

time constant, D is the diffusion coefficient. The diffusion stage can be described

by (T; = 2Dt, when 1 is getting larger. Fitting the experimental results with this

equation, we deduced V, = 0.115 . 1O23 charge units/set, T, = 1.5 * lo-** set and

D = 0.0255 . 1O23 charge units*/sec. The interaction time of the QE reaction deduced

from the experimental angular distribution is about 1.3 * lo-** set and is consistent

with the local equilibration time. The diffusion coefficient calculated by the Noren-

berg theory ‘) is 0.03 . 1O23 charge units2/sec, which is compatible with the above

result. The charge drift coefficient V,, on the other hand, is a very small negative

number in that theory, which is in variance with the present result. This difference

may be caused by the effect of the nuclear structure which is not considered in the

calculation. In addition, V,, is the charge drift coefficient at t = 0 in this approach

and has a different meaning than that in the Norenberg theory. As mentioned in

sect. 3 the general characteristics of the charge distribution in the lighter system is

similar to those of DIC for the medium and heavy system and can be fitted by the

same theory. But in such a light system as 160 + “Al there are only a few nucleons

which can be exchanged and the nuclear structure effect is strong (there is a valley

between 5 > Z > 9 in the potential energy surface by which the nucleon exchange

is limited), so that us is much smaller than in medium and heavy systems. When

plotting a$ as function of TKEL/&, in semi-logarithmic coordinates as proposed

in ref. ‘) our results deviate strongly from the general trend and the a; values at

large TKEL are much smaller than those in heavier systems.

5. Effect of the potential energy surface on charge distribution

Z-distributions integrated over the total energy and angles from 30” to 90” at

several bombarding energies are shown in fig. 10. As mentioned earlier the Z-

distribution at 46 MeV shows only C, N and 0 as outgoing elements, among which

the yield of 0 is dominant. At 62 MeV the Z-distribution is still very narrow, the

main products are C, N and 0 with a maximum at 0. These characteristics support

the conclusion that at these two bombarding energies most of the products come

from QE reactions. The probability of a stripping reaction is much larger than that

of a pick-up reaction and the transfer of one cY-particle is enhanced compared to

the transfer of one or two nucleons. At the higher bombarding energies the width

of the Z-distribution increases and C becomes the most probable product. These

observations again tell us that the contributions of the DIC processes increase with

increasing bombarding energy and that the mean value of the Z-distributions drifts

towards lighter elements with increasing TKEL. These results are not in agreement

374 W, Shen et at. / Dissipative phenomena

Fig. 10. Z-distributions of the reaction products integrated over the total energy spectra and all c.m. angles larger than 30” for four incident energies.

with those predicted by the potcntia~-energy surface 31) if calculated with liquid-drop Q-values without shell correction, which is not valid for such light systems. The potential energy surfaces for I = O#i, 2011, 30h and 35h for ‘60-k27A1 are shown in fig. 11. They are calculated by using the experimental nuclide masses for QBg instead

of the liquid drop model value. The figure shows that there is a potential valley

with a depth of about 6 MeV in the region of 2 = 5-9, and the injection point is at the right side of the valley. Therefore, the potential energy surface prefers the system to evolve towards smaller element numbers, whereas the evolution to Z < 5 and 2~9 out of the valley is strongly hindered. The experimental mean value of Z

$5 El2

i

3% > 1

‘?) + 27AL

30% 20fl oh -

8

4

0 T li

-4-

i

I

Fig. 11. Calculated minimum potential energy at given element nuclei in the ‘%f2’AI system for the angular momenta L = 35, 30, 20, Oh.


indeed evolves towards smaller element number with increasing TKEL. The drift,

however, is smaller than expected the maximum drift being about 1.2 charge units.

In the bombarding energy region at which DIC starts to be important the absolute

width of the Z-distribution in the lighter system is smaller than that in the medium

and heavy system. This can be explained at least partly by the potential energy

surface as well.

The picture is somewhat different at bombarding energies lower than that, at

which DIC starts to happen. For example, the potential energy surface has a

pronounced minimum at Z = 6, which will get even more pronounced with decreas-

ing angular momentum. The experimental data show that a decreasing yield from

C to 0 with decreasing bombarding energy. When the bombarding energy is larger

than that at which DIC just starts to happen, C becomes the most probable outgoing

product in agreement with the potential energy surface picture. This result seems

to indicate that the effect of the potential energy surface needs enough interaction

time to develop.

In order to understand quantitatively the nuclide distributions in terms of the

partial statistical equilibrium principle, the yield da( N, Z) have been calculated as

follows:

dv(N, Z) K exp (- V,,,(N Z)/ T)

where T is a constant parameter related to the nuclear temperature and V,,,( N, Z)

is the potential energy surface,

V,,,( N, Z) = V,,, - vi, = -Q,, + Vc,,, + V,,,

where Q,, is calculated by means of known nuclide masses. The experimental

rr I I I

i4- I60 + *?AL m -

80.6MeV 0

12. 0,=14' D 00 - 00. -

IO- 00 N - cl0

8- BOB&

ODO 6- cb

. 0 .

6 8 IO 12 Z

Fig. 12. Comparison of experimental nuclides (2, N) distribution measured at 14” and 80.6 MeV (left), and yields predicted on the basis of the potential energy surface of the ‘60+27A1 system (right).


nuclide yields, which were measured by using the time of flight set-up with a AE -E

telescope at 80.6 MeV and eL= 14”, are compared with the calculated ones in fig.

12. The area of the squares corresponds to the yield normalized to the yield of C,

the temperature parameter T is chosen as 3 MeV; the shadowed area is the entrance

channel. Except for few products the lifetimes of which are too short to be measured

and the experimental results are in quite good agreement with the calculated ones.

6. Incomplete deep inelastic collision

Various possible mechanisms of three-body reactions have been discussed in

which the projectile-like fragments are emitted together with a light particle *,‘). The

possibility of an incomplete deep inelastic collision has been suggested ‘) especially

in the case of projectiles with strong cluster structure such as 12C, I60 and *‘Ne.

Based on reactions of 20Ne+ “‘AU at 175 MeV, 20Ne+““‘Ca at 170 MeV [ref. 32)],

20Ne + 56Ni at 164 MeV [ref. “)I and *‘Ne +40Ca at 151 MeV [ref. ‘“)I a phenomeno-

logical two-stage model was suggested 17) which can explain successfully the results

in terms of an incomplete DIC process. Based on the contour plot of the Galilei-

invariant C-(Y coincidence cross section d3a/(CP, da, dL?n, dE,) and the energy

spectrum of correlated projectile-like fragments and a-particles, we found that in

the present experiment, at least part of the a-particles is due to incomplete DIC

(cf. sect. 3). In fact this kind of phenomena could be found also in ‘60+27A1 at

88 MeV [ref. lo)], but it was not analysed in detail.

Assuming that the angular correlation of cY-particles is isotropic in azimuthal

direction (b, the multiplicity (M),_, of C-cx coincidences is about 0.7. Considering

that an a-particle emitted from the target-like fragment does not influence the yield

of C in the inclusive measurement and after subtracting this component the remaining

part of the multiplicity is about 0.3. Among them more than one half comes from

incomplete DIC (fig. 7). So the contribution from the process, in which the excited

0 after DIC decays sequentially by emission of an a-particle, is not big enough to

account for the enhancement of C in the inclusive measurement. Besides the effect

of the potential energy surface, the C enhancement must be explained by the

accumulated effect of both the sequential decay of excited 160 and the incomplete

DIC process.

In fact, the interpretation of the Z-distributions in terms of the potential energy

surface in sect. 5 is a qualitative one. The experimental nuclide distributions depend

on the emitting angle and the bombarding energy, the yield ratio of C to 0 increases

with increasing bombarding energy and outgoing angle. All this can not be explained

by the potential energy surface alone. But from the point of view of incomplete

DIC these phenomena observed in the experiment can be understood at least

qualitatively. With increasing energy of relative motion between projectile and target

the I60 nucleons can break apart into 12C and an a-particle more easily after an

initial interaction.

W. Shen et at. / ~i~s~~a~~ve p~eno~ena 377

Due to the a-cluster structure in the projectile 160, the probability of the exit

channels *Be and ‘*C is enhanced. Since ‘Be splits into two Lu-particles, only the

enhanced yield of C can be seen. Experiments which we have performed with 14N

on light targets showed much smoother Z-distributions without a special enhance-

ment of one or two other elements. This supports our conclusion further and means

that it is difficult to produce incomplete DIC by using 14N as a projectile. In order

to establish the incomplete DIC process in greater detail, it is necessary to perform

further experiments as well as theoretical studies on this reaction mechanism.

7. ~eco~position of the reaction cross section and its dependence on the incident energy

Based on the variation of the Wilczynski plots (cf. fig. 1) the energy spectrum,

the angular distribution, Z-distribution and the interaction time as function of the

bombarding energy, the following conclusion can be made: DIC starts at a bombard-

ing energy of about ‘70 MeV. The evolution from QE to DIC proceeds gradually.

Close to 70 MeV it is therefore very difficult to separate the cross section of DIC

from that of QE. As discussed earlier one can use the angular distribution to

decompose the measured cross section into the cross sections of QE and DIG. The

energy, at which we have determined the DIC reaction to start, is rather close to

the Glas-Mosel prediction “5),

where rIB and V,, are the fusion radius parameter and the fusion barrier height,

respectively; r,, and V,, are the critical radius parameter and the barrier at the

critical distance. By fitting the measured complete fusion cross sections in the

160 + 27AI system ‘8,26*36-39), these parameters can be deduced, and the mentioned

bombarding energy limit is calculated to about 70 MeV in the lab system. Since our

experimental cross sections are only summed from Li to Ne, lighter products, e.g.

He, and the products heavier than Ne are not included and *Be is missing due to

its splitting into two a-particles. In fact, from the energy spectrum and the angular

distribution of the inclusive a-particle, we find that besides the evaporation (Y-

particles from the compound nucleus, there are direct cr-particles with a cross section

at 84.5 MeV of about 140 mb. A part of them should be accounted for by the DIC

cross section. So our DIC cross section represents a lower limit. Of course, according

to the definition:

(TfF = @R - uDIC - Oh'!?,

the deduced complete fusion cross section can therefore be larger.

The cross section of DIC increases with increasing bombarding energy and so

does the ratio of DIC to QE. The errors in the QE cross section are rather large,

but within these errors of *25% the ratio of QE cross section represents at all

incident energies the same percentage of the total reaction cross section, which is


taken from the optical model fits of the elastic angular distribution *‘j) (cf. table 1).

This observation is compatible with ref. 40). Since the grazing angle increases with

decreasing bombarding energy and, probably, the angular distribution of QE prod-

ucts will drop down at the very forward angles, the deduced QE cross section is

somewhat overestimated by extrapolation of the angular distribution at the lower

bombarding energy. Nevertheless, the conclusion of the independence of the ratio

of QE cross section to the total reaction cross section is helpful to predict the QE

cross section with a certain error.

Based on the cross sections given in table 1 and the sharp cut-off model, table 4

lists the grazing angular momentum Lgr, the critical angular momentum for the

complete fusion L,, and the angular momentum Lo, which divides the QE and

DIC. All these angular momenta increase with increasing bombarding energy; it

can be also seen that in the present light system the number of the partial waves

contributing to QE, (L,, - Lob), and DIC, (Loo - L,,), is rather small. For the DIC

component, it increases with increasing bombarding energy from only 0.6h at

75.5 MeV to 1.5h at 84.5 MeV.

TABLET

The various angular momenta obtained from the cross sections according to the sharp cut-off

model

Gab (MeV) L gr LQD L CT

84.5 34.9 33.2 31.7 80.6 33.8 32.0 30.8 75.5 32.2 30.2 29.6 62.0 27.7 25.5 46.0 21.2 19.5

8. Conclusion

The investigation of the reaction mechanism in the ‘60+27A1 system at various

bombarding energies shows that the DIC starts at about 70 MeV in laboratory. This

energy coincides with the energy at which the limiting factor of complete fusion

changes from the fusion barrier and radius to the critical barrier and radius, as

calculated from the Glas-Mosel model. The DIC cross section and the cross section

ratio of DIC to QE increase gradually with increasing bombarding energy. Neverthe-

less, the ratio of the QE cross section to the total reaction cross section keeps

constant. At bombarding energies higher than 70 MeV, the peak position of the

energy spectrum gradually decreases towards the full relaxation energy with increas-

ing outgoing angle; the angular dist~butions can be decomposed into two com-

ponents. With increasing TKEL and outgoing angle the width of the Z-distribution


is getting larger, the most probable yield of the outgoing element drift from 160

towards 12C and the interaction time is getting longer. All of these facts indicate

that there are QE and DIC components in the reaction. Based on the different

angular distributions of QE and DIC products a rough distribution between both

components seems feasible. But since the evolution of the reaction mechanism from

QE to DIC is continuous, an exact quantitative separation is very difficult.

The effect of the nuclear structure in the projectile influences strongly the projec-

tile-like fragment distribution; since the cluster structure of 160 leads to an enhance-

ment of ‘*C and makes the projectile break up easily. That is why a new process,

the incomplete DIC, becomes possible. It enhances the C yield and the correlated

cr-particles at smaller angles. The element distribution and nuclide distribution of

the DIC products can be qualitatively explained by the potential energy surface.

It is especially these nuclear structure effects and the incomplete deep inelastic

collision which make the study of such light systems interesting and further

investigations desirable.

The authors would like to thank the operating group of the 1.5 m cyclotron at

IMP for supplying the high quality I60 beam. They acknowledge the financial

support by the Alexander-von-Humboldt Foundation and the Academia Sinica for

the construction of the large-area position-sensitive ionization chamber. The authors

thank also the Gesellschaft fiir Schwerionenforschung (GSI), especially Prof. R.

Bock, A. Gobbi, H. Sann, K.D. Hildenbrand and G. Augustinski for their help and

advice.

The authors would like to express their gratitude to Prof. Yang Cheng-zhong for

his helpful interest. The help of Jiang Cheng-lie, Jin Gen-ming, Fan Guo-ying and

Li Song-lin who participated in the experiments at different stages is acknowledged.

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