Energy dependence of heavy ion reactions: Systematics

Nucl. Tracks Radiat. Meas., Vol. 19, Nos I-4, pp. 647-650, 1991 Int. J. Radiat. Appl. Instrum., Part D Printed in Great Britain

0735-245X/91 $3.00 + .00 Pergamon Press plc

ENERGY DEPENDENCE OF HEAVY ION REACTIONS: SYSTEMATICS

I.E.

QURESHI 1 AND H . A . KHAN2

INPD, PINSTECH P.O. Nilore, Islamabad, PAKISTAN 2SSNTD-Laboratory

(NED) PINSTECH, P.O. Nilore, Islamabad, PAKISTAN

ABSTRACT

With increasing projectile energy the heavy ion reactions exhibit systematic changes. The total cross section increases almost linearly with energy, the elastic events diminish and the probability for multlprong events is enhanced. The energy and angular distribution of reaction

products

is also affected

with

narrow energy region around I0 MeV/u, number of heavy

ion reacticns

the change

in the

injection

energy.

Within

a

these changes are not so marked. However, a large

performed

in this

features which are described here as the

range and studied with SSNTD

systematics

indicate

of energy

dependence

in heavy

have

studied

a very

ion

reactions.

INTRODUCTION

Over

the

last

two d e c a d e s ,

energy region;

GeV/u range [i]. The data relevant

for

the

heavy

ion

reactions

been

in

broad

starting from sub-coulomb energies to highly relativistic energies in the

specific

interpretation

energy

domains

has been

and/or

sought

specific

in terms of models which

mass

usually the following three energy regions are distinguished

regions.

For

this

by mean

purpose,

i) low energy region ( ~,~ 20

MeV/u), ll) medium energy region (20-200 MeV/u), ill) high energy region ( ~ The low energy region is characterized

are

field effects,

one body

200 MeV/u).

dissipation

and

long mean free-path. Within this region, a subdivision of qualitatively different reaction modes

is

made.

These

modes

depend

on

the

parameter. Thus one distinguishes the processes

projectile-target llke fusion,

combination

fast-fisslon,

and

impact

deep-lnelastic

and quasl-elastlc etc. During the last few years, the efficacy of SSNTDs in heavy ion reaction studies has been successfully

demonstrated

understanding

of

the

[2,3,4].

properties

This

and

success

behavior

of

largely

draws

materials

used

on as

the

increasing

track

detectors.

However, there does not seem to be a systematic effort towards understanding the physical aspects of nuclear reactions

at different energies,

using this detection

system.

In the

present paper we have put together the patch-work of SSNTD based heavy ion reaction within

the

energy

range

specific projectile-target is discussed. different

8-18

MeV/u.

combination,

The

effects

of

increasing

is given.

The

energy

data for

on the total and partial reaction cross-sections

In the next section a brief explainatlon

publications

projectile

discussion

of

of the data sets collected

the

results

is given

in

the

from last

section. DATA SETS

The SSNTDs are best suited for the study of reactions with a few heavy fragments in the exit channel.

Since

each

interaction

is

individually

registered

and

all

the

reaction

products ensuing from it are recorded as tracks under favourable conditions, it is easy to 647

I.E. QURESHI and H. A. KHAN

648

distinguish

and count

specific multiplicity target

thickness

the events

of different

is then calculated

and exposed

area of

multiplicities.

The

from the known values

the

target

[5].

The

data

of

cross-section projectile

discussed

in

for

a

fluence, the

next

section has been taken from references [2-21]. In most of the cases, mica has been used as detector which has a mass threshold of detection A

30. Moreover usually a 2 ~

set up is

used where only the reaction products moving in the forward hemisphere are registered. this situation

it is inevitable

that some of the correlated tracks do not represent

In the

true multiplicity of the event. Such events are called indirect [5] and are recognized by their obvious violation of momentum conservation. by summing the contribution

The total cross-sections

of partial cross-sections

are calculated

from 3-,4-,5-, ..... -pronged

events

(two prong inelastic events are also included in those case where they can be identified). The

binary

events

satisfying

the

criterion

of

expected

elastic

scattering

angular

correlation are separated from the total set of binary data. Apart from cross-sections,

a complete determination

of kinematical

quantities

i.e. masses

and energies of the reaction products is also possible [2] provided one measures the track parameters (lengths and scattering angles) of a sufficiently given multiplicity.

Such studies have been undertaken

[2,33.

for

large number of events of a

(Kr + U) and

(U+U)

reactions

respect

to input

DISCUSSION To t al C r o s s - S e c t i o n In order to see the systematics

of total

reaction

cross-sections

with

energy, there is enough data available only in the case of U÷U and U+Au reactions. These data are plotted in figure 1 & 2 as a function of inverse centre-of-mass energy.

t~-'-J--

"

" ~

. T.~o..,o.-

"r.. ~----RST~FIT

..o~.o.

1-

4

4 ""-.

'3 2

. i g . l . T~e ~+. t o t a l r e a o t i o n cross-sections for projectile energy range 7.5-16.7 MeV/u (see Ref. 12 for data sources). Solid llne is based on eq. (I) and (2). The broken line is the best representation of mica based data.

!

I

6

~Z~l

THEORETICAL PREDICTION

+

0.1 ~

-t

I,.1

8.7 -

reaction cross-sections energy range 16.7

v ~

4

BIll A"

~ II~ [7

,Q]

for MeV/u.

The in angular ofbracket is number the reference data based on eq. (1) and (2) . O

'

, 4.0

L°"'"

in C R - 3 9 , A

I

,

i

~

i

5.0

6.0

7.0

8.0

z~'1¢,6'

i

i

i

9.0

I0.0

I1.0

.o q')

i 12.0

HEAVY ION REACTIONS

This is done because

in the sharp

cut-off

649

approximation,

the reaction

~R

cross-sectlon

is given in terms of Ecm by,

~R = where

Rint.

~R~nt.

(1-V(Rint.)/Ec.m.)

is the interaction

radius

and V (Rint.)

the interaction

the SSNTD based data for

radius.

~'R deviates

between

where Zp,

ZT a r e

partial

the

projectile

values

of

cross-sections

their

and

target

A~3

+

results.

interaction

radii.

It

charges

numbers.

This

do not exhaust

is not

clear

T h r e e and F o u r - p a r t i c l e The c r o s s - s e c t i o n s

respectively

whether

the

and

indicates

cross

data

Ap,

that

f o r t h r e e and f o u r - b o d y c h a n n e l s ,

•o

in the

low enegy

reaction

(fig.

2) produce

overestimates

~ 3 and

or

~4 a r e shown i n f i g .

,.o

,,

,,

.

,,

[

s (~,v/.)

,o n 7

a ]1 J

~ (u-*.)-J

.

._.._.~r (~,.m_! Col |

el

,..,

"1

''

1

[.]~"--~(x,,~

]

'" .,cA--

I I''cH"

,4

'

LsJ

i6' n

[I

3 & 4.

_ C.].,...~(..., t L,'tJ_.

[9]~ ~e"

,e

underestimates

' ' ' ' I e~m~ cmo.-ss~r,o, I I 4-esom e~ms I

,d ~ . .

,,

the

observed

section

t C,1.

z,

,,

AT a r e the

Channel

'04~ I[ |

•

In

(2)

result

the total

~[

,o,

Rint.

)

region. The total cross section studied in the case of (U + Au) conflicting

at

from Rint. of ref. [22].

mass

in mica

energy

~R

Rint. = 1.7445 - 0.04338 In (ZpZ T) (~l! 3

corresponding

is the Coulomb

and E-I . The slope of the straight cm. In the case of U+U reaction, as shown in fig. I,

this model there is a linear relationship line determines

(1)

9

~

II

13

15

/ 19

17

E (MeV/u) F i g . 3. The p a r t i a l c r o s s s e c t i o n s f o r t h e t h r e e - p r o n g e v e n t s i n t h e c a s e of different (projectile + t a r g e t ) combin a t i o n s . The d a t a a r e J o i n e d by l i n e s as g u i d e t o t h e e y e . The r e f . number of a data source brackets.

The physical

is

given

in

the

process envisaged

Flg. 4. The partial cross sections for the four-prong events in the case of different (projectile + target ) combinations. The data for a given combination are Joined by lines as guide to the eye. The ref. number of a data source is given in the angular brackets.

angular

for these channels

colliding nuclei give rise to two intermediate one or both of these masses

subsequently

is the sequential

masses as a result

undergo

fission.

For

fission mechanism. of nuclear

each

The

interaction;

interacting

pair

of

heavy ions we have used two energies

in order to note the effect of increasing energy. The

points

as

are

increasing different

joined ~3

with

with

combinations.

the interacting

solid

increasing

lines

energy,

a guide although

This trend is reasonable

nuclear complex

increases

to eye. the

There

rate

of

is a

since the additional

the probability

general

increase

pattern

is different

energy available

of fission in the fissile

of for to

650

I.E. QURESHI and H. A. KHAN

partner even in the peripheral collisions. possibly

causes

longer mass

asymmetry

In the case of Pb + Pb, the increasing energy

and consequently

heavier intermediate mass are increased.

the

It is worthwhile

chances

noting

experiment (e.g. 16.7 MeV/u ( U + Au)) performed at different

of

that

fission for an

in

the

identical

laboratories very different

results have been reported. This could be due to human errors or non-standardizatlon

of

procedures for identifying 3 prong events

in CR-39. The picture is more confusing in the

case of 4-prong events. Here the value of

~4 decreases with increasing energy for (Kr+U),

(U+U) and (U+Bi) reactions. On the other hand, for (Xe+U), (U+Au) and (Pb+Pb), slight increase in

there is a

~ 4 with increasing energy. In the case of U+Au, the data for

been reported at six different

energies.

However,

there

are

~ 4 has

large discrepancies

in the

results. In fig. 4. only those data values are shown which follow smooth variation.

It is

interesting to note that the (Pb+Pb) system behaves very similar to (U+Au) at 14 MeV/u, so far as this channel is concerned. These two systems have similar reduced masses.

CONCLUSIONS

We have

surveyed

the

reported

total

and partial

reaction

cross-sections

of heavy

ions

studied with SSNTDs. The total reaction cross-section is found to deviate at high energies in the case of mica approximation three particle

using

from the prediction interaction

systematics

nuclei. The situation for

the rate of incease ~4

is more complex;

model

of ref.

exit channel has a general behaviour

projectile energy. However,

decrease.

radius

of theoretical

i.e.

based

[22]. ~3

is dependent

on

sharp

cut

The cross-sections

off of

increases with increasing on the masses

of reacting

there is no general trend of increase or

The behaviour of 4-particle channel seems to strongly depend on the nature

of

reacting nuclei and their initial mass asymmetry. REFERENCES

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Physics

and