138 Nuclear Instruments and Methods in Physics Research B42 (1989) 138-142 North-Holland, Amsterdam

SOLID STAW NUCLEAR TRACK DETECTORS IN SCATTERING EXPERIMENTS

T.K. DE

B.&f. ~ahauidyulay~ ~id~a~ore, West Bengai, India

R.N. MUKHERJEE and B.B. BALIGA

Saha Institute of Nuclear Physics, Calcutta-700 009, India

Received 29 June 1988 and in revised form 2 December 1988

A method of detecting and analyzing the elastically and inelastically scattered alpha particles from “C by solid state nuclear track detectors (SSNTD) has been presented. Optical model analysis for elastic scattering and distorted wave Born approximation (DWBA) analysis for inelastic scattering data have been done. The obtained experimental data are compared with the data taken by surface barrier detectors in the same scattering chamber.

1. Introduction

During the last two decades solid state nuclear track detectors (SSNTD) are being used in many diverse branches of science such as fission studies, geochronol- ogy, space physics, to name a few. The technique pro- vides a very simple and inexpensive means of detecting fast particles. These detectors take advantage of the fact that a charged particle penetrating any nonconducting solid leaves a submicroscopic trail that can be chem- ically amplified. The increased chemical reactivity of the trails of radiation damaged materials is the basis for the so called etched-track process by which one can make the particle tracks large enough to measure in an optical microscope. These detectors are capable of re- cording all ions from protons to transuranium elements. The events can be stored by a track recorded for an almost infinite time. There are a few good review articles on how the tracks are formed and the method of their subsequent analysis [1,2].

Elastic and inelastic scattering experiments of charged particles on various nuclei have been done for many years using surface barrier detectors where the data is registered and processed very quickly and these days on-line computers are employed too. Recently some of the authors had the opportunity of observing the advantages of SSNTDs, particularly CR-39 (dioc- tylphthalate) in registering cosmic ray particles in space [3] and noting their sensitivity in detecting charged particles from alphas to heavy ions. It prompted us to use these detectors in scattering experiments. For this purpose we have taken up a very standard experiment of elastic and inelastic scattering of alpha particles on ‘*C as a test case. The CR-39 detectors we have used

0168-583X/89/$03.50 0 Elsevier Science Publishers B.V. ~orth-Ho~~d Physics Publishing Division)

have been manufactured by Pershore Moulding Ltd., UK. The results have been analysed with usual optical model and distorted wave Born approximation (DWBA).

2. Experimental procedure

The scattering experiment of alpha particles on ‘*C was done in our scattering chamber [4] situated in the zero degree channel of the Variable Energy Cyclotron Centre, Calcutta. A 33.8 MeV alpha particle beam was made to fall on a t*C target (- 100 ug,/cm’). The beam spot measured on an alumina beam viewer was found to be 3 mm. CR-39 (DOP) solid state nuclear track detec- tors in the form of a set of adjoined strips spanning the angular range 2O-30’ were fixed on a ring and the beam was allowed to fall on the target for 2 min. Typical beam current was of the order of 20 nA. These strips were then taken out and another set of CR-39 (DOP) strips covering the range 3S”-178’ were at- tached to the ring. Beam was allowed to fall on the target for about an hour. In both the cases the total charge carried by the alpha particles incident on the target was measured by a Faraday cup fixed at the rear end of the chamber. Considering the large negative Q-values for the various other reaction channels with protons, deuterons, tritons etc. one would expect the majority of the recorded events would correspond to the elastic and inelastic scattering of the alpha particles rHe). As the target used was a natural carbon which contained a very small percentage of t3C, the majority of the events would correspond only to the scattering from i2C and the fraction from l3 C would be negligible.

T. K. De et al. / Nuclear track detectors in scattering experiments 139

ALPHA SPECTRA

2000 - SE MONITOR DETECTOR

GLAG =30”

“C TARGET(rOOpS/cm2)

1500 -

ii 5 a

6 [L l$ lOOO-

c 5 is

500-

O- I I I 0 500 1000 1500

CHANNEL NUMBER Fig. 1. Experimental spectrum of scattered alpha particles

obtained with surface barrier detector at 30 ‘.

The data was also monitored by a surface barrier detec- tor fixed on the wall of the chamber at an angle of 30 O. The spectrum obtained by this detector is shown in fig. 1.

3. Data analysis

The exposed CR-39 detectors were etched in our laboratory following the technique given in the Appen- dix. The cleaned detectors were placed under a Leitz Optical Microscope fitted with filar micrometer having X 450 magnification for observation. Numerous tracks created by (different) scattered particles from “C (mainly scattered alpha particles) could be observed. The diameter of each track in a particular field of view was measured in arbitrary units and the scanning was done for as many fields of view as possible. The angular resolution was found to be f lo. Histograms were drawn with the number of tracks against the corre- sponding diameters. Typical histograms are shown in fig. 2.

The energy of the elastically and inelastically scattered alpha particles from ‘*C are obtained from kinematics. The corresponding diameters of the alpha particle tracks are obtained from a calibration curve of diameter of alpha particle tracks versus energy. Then from histograms the number of alpha particle tracks

corresponding to a particular diameter are obtained. The differential cross-section are then calculated from the following relation:

da AnM _= dQ SIN,p Ax’

where An = number of scattered particles per unit time

into the solid angle,

NA = Avogadro’s number, I = beam intensity

= number of particles per unit area per unit time,

PAX = thickness of the target.

3.1. Optical model analysis

The cross-sections of elastic, inelastic and nucleon transfer reactions may be calculated from a knowledge of the nucleon nucleus potential V(r) and properties of the interacting nuclei. In the present paper we discuss cross-section in the light of the so called optical model for elastic scattering and in the light of DWBA for inelastic scattering.

The model is referred to as optical model because of the analogy between the scattering and absorption of particles by a nucleus and the scattering and absorption of light by a cloudy crystal ball. The former may be treated mathematically using a complex potential just as the latter may be treated by using a complex refractive index. The model was first proposed by Serber [7] and Fembach et al. [8]. Later various articles have appeared in the literature [9].

Usually the scattering by a complex potential may be calculated quantum mechanically by allowing the potential V(r) in the appropriate Schrodinger equation to take the form

I/(r) = U(r) +iW(r),

where U(r) and W(r) are real and imaginary potentials respectively. It is easy to show that a complex potential absorbs particles as well as scattering them. A detailed description of this may be found in an excellent work of Hodgson [lo].

In the present paper the elastic scattering data were analysed using a phenomenological optical model pro- gram [ll] with an automatic search code at the IBIS-80 computer facility of the Variable Energy Cyclotron Centre, Calcutta. The spin-orbit part of the potential was not considered. The Coulomb potential was due to a uniformly charged sphere of radius R, A1/3. It was observed that the predicted cross-sections were not very sensitive to the value of R, and it was fixed at 1.25 fm. Six parameters are I$, R,, a,, W,, R,, aI where V,, R,, a,, are the depth, radius and diffuseness parameter of the real potential respectively and W,, R,, a, are

140

120 -

100 -

80-

60-

i? K. De et al. / Nuclear track detectors in scattering experiments

LO.

60

65’

I i t I 1

2.0 L.0 6.0 6.0 10.0

DIAMETER IN MICRONS

Fig. 2. Track diameter histograms at different angles.

the depth, radius and diffuseness parameter of the imaginary potential respectively.

These parameters were searched on repeatedly in a suitable order to minimize x2 per degree of freedom defined by

x2 = f ,t du~(8i)fd~-du,(Bi)ldS2 I 2 ,

1=I A(d~~~(~i)/d~)

where F is the total number of experimental points. We

Table 1 Optical model parameters used in the calculations

Set V0 (MeV) ;“,I$

1. 218.01 1.299 0.588 12.25 1.564 0.300 2. 65.10 1.596 0.633 11.35 1.525 0.514 3. 159.92 1.195 0.577 10.88 1.477 0.338

have observed that the data could be fitted fairly well by three sets of parameters one for a shallow rea.l depth (65.1 MeV), the other for a deeper real depth (218.01 MeV) and the third one for an intermediate real depth (159.92 MeV).

It is seen that out of the three sets, the one with the deepest real depth gives a better fit to the elastic scatter- ing data. In the same chamber later or-scattering experi- ment from 12C was done at an incident energy of E, = 40 MeV using surface barrier detectors. The set of parameters obtained from this data after analysis are found to be consistent with the third set of optical model parameters discussed above, obtained from SSNTD data. The set of optimum parameters is given in table 1. Fitting of the experimental data are shown in fig. 3 where 6’,, is the centre of mass angle in degrees. There is surprisingly good fit in the forward and back- ward angles. The errors indicated are essentially due to

T.K. De et al. / Nuclear track detectors in scattering experiments 141

ld,

10' _-

‘*c (a,uf 12 c

E, = 33.8 MeV

- set 1 ---- set 2 . . . set 3

e CH (DEGREES)

Fig. 3. Differential cross-section (ratio to Rutherford) data for elastic scattering of alphas from 12C. Three different lines give optical model fit with three sets of parameters as given in

table 1.

statistics. Other errors due to target thickness and solid angle measurement are negligible.

3.2. DWBA ana&sis

The simplest type of nonelastic interaction is inelas- tic scattering and the cross-section for this process may be calculated by the perturbation theory. In some cases, however, perturbation theory is not sufficiently accu- rate; this occurs for example when there is a strong coupling between the elastic and inelastic channels. It is then necessary to solve the coupled equations for the wave functions in all the reaction channels. The coupled channels theory of inelastic scattering provides, in principle, an exact way of calculating the cross-sections of inelastic reactions. The numerical solutions of cou- pled equations, even in their truncated form, is however a very laborious process and in many cases it is suffi- ciently accurate to use an expression for the scattering

matrix element that is exact in the limit of weak cou- pling between the elastic and inelastic channels.

To obtain this expression which is known as dis- torted wave Born approximation (DWBA), we consider the incoming particles in the incident channel and the scattered particles in the outgoing as well as the inci- dent channels. The detailed mathematical treatment for the matrix element may be found in ref. [lo].

The DWBA is the most widely used procedure for treating direct reactions and gives a rather unified view of them. In this method the initial state and the final state are described pi and Vr respectively, say, and the transition amplitude for inelastic scattering from state i to state f given by

and the cross-section is

Here xi+) and xl-) are the exact wave functions for the motion of the projectile with respect to the nucleus;

lx- 1% (d,oq) ‘2c (2+)

E,: 33.8 MeV

‘x- 8- ?- 6- 5-

4-

2- Q

toox- GO 60 80 100 120 160 160

B,, i DEGREES )

180

Fig. 4. Differential cross-section for scattering to 4.438 MeV, first excited 2+ state in “C. The solid curve is a DWBA calculation with a collective model form factor and set 2 OM

parameters.

142 T. K. De et al. / Nuclear track detectors in scattering experiments

they are eigen states of the optical model interaction between the projectile and target. Thus

where U is the optical interaction. The potential Y causes the transition but does not influence the dis- torted waves. For excitation of the surface, I’ is that part of the potential caused by the deformation of the nucleus from its equilibrium shape while U is the equi- librium part of the optical potential. A detailed descrip- tion of DWBA may be found in ref. [12]. In the present experiment the inelastic scattering data (Q = -4.439 MeV) was analysed using the code DWUCK - 4 [13] at IRIS-80 computer. We have used all the sets of optical model parameters obtained from the elastic scattering analysis. It is observed that the set of parameters with a shallow real depth gives a better fit in this case. By comparing the theoretical curve with experimental one, we have calculated the deformation parameter p which is a measure of the deviation of nucleus from its spheri- cal shape. The value of p is 0.47 which is nearly the same as obtained from other analysis. Fitting of the experimental data are shown in fig. 4.

4. Conclusions

The results obtained using SSNTDs in scattering experiments are satisfactory as they are comparable to the ones obtained by surface barrier detectors. A typical spectrum taken by the surface barrier detector at 30° has been shown in fig. 1. It gives confidence in the quality of the data obtained. The detectors are espe- cially handy in small forward angles and large back- ward angles. Even though we had exposed some foils at the most forward angles in this experiment, they were lost in transferring them to the etching laboratory. However, one can see the results at the backward angles upto 178”. The theoretical fits calculated in the labora- tory prompts us to take up some more anomalous back angle scattering experiments. Except that the long period for analysis is the discouraging factor, the SSNTDs can be used in sophisticated nuclear physics experiments. We feel that these detectors can be used with advantage for small forward angles and large backward angles.

We are thankful to several colleagues who assisted in performing the experiment and mentioned in our pre- liminary reporting. We thank the Director of VECC and the crew of the machine for their splendid cooper- ation and support. Special thanks are due to Sri P.K. Das who patiently etched all the SSNTD foils and

prepared them for scanning by microscope. He also assisted in scanning. Our thanks are due to the Director of Saha Institute for his interest in the work.

Appendix

Etching procedure

For etching the irradiated CR-39 (DOP) solid state nuclear track detector foils, we have adopted a very standard procedure. The etchant used was sodium hy- droxide solution of normality (6.25 f O.l)N. The etch- ing temperature was kept constant at (70 + 0.1) o C. The solution in the etching tank was constantly stirred by a stirrer (with plastic stirrer blade) at 100 rpm. All the detector foils were etched for 3 h.

As a stop bath, we have use 20% HCL for 20 min, followed by preliminary washing of the samples with hot ( - 50 o C) stirred water for about 30 minutes. Then the foils were washed in an untrasonic bath for 2 h. Finally, the samples were wiped and allowed to dry under room temperature, and then transferred to scan- ning laboratory.

References

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