Nonequilibrium effects in a-particle induced reactions on gallium isotopes

I. A. RIZVI, M. K. BHARDWAJ, M. AFZAL ANSARI, AND A. K. CHAUBEY Department of Physics, Aligarh Muslim University, Aligarh 202002, India

Received March 7 , 1989

The stacked foil activation technique and Ge(Li) y-ray spectroscopy have been employed for the determination of the excitation functions, up to 60 MeV, of six reactions, 69Ga(a,n), (a,2n), (a,3n), (a,p3n); 71Ga(a,n) and (a,4n). Since natural gallium used as the target has two odd-mass stable isotopes of abundance, 69Ga(60. 1%) and 71Ga(39.9%), their activation in some cases gives the same residual nucleus through different reaction channels, but with very different Q values. In such cases, the individual reaction cross sections are separated with the help of the ratio of their theoretical cross sections. A preliminary theoretical comparison with the preequilibrium geometry-dependent hybrid (GDH) model has been done using an initial exciton number no = 4 (2n + 2p + Oh), and general agreement was found for all reactions at high energies.

On a utilisC la technique d'activation de lames empilees et la spectroscopic Ge(Li) des rayons y pour la determination des fonctions d'excitation, jusqu'i 60 MeV, de six rkactions : 69Ga(a,n), (a,2n), (a,3n), (a,p3n); 71Ga(a,n) et (a,4n). Etant donne que le gallium nature1 utilisC cornme cible contient les deux isotopes stables de masse impaire 69Ga et 71Ga avec des abondances de 60,1% et 39,9% respectivement, I'activation de ces isotopes donne dans certains cas le m&me noyau residue1 par des voies diffkrentes, mais avec des valeurs Q trks differentes. Dans de tels cas, les sections efficaces des reactions individuelles sont separkes les unes des autres I'aide des rapports entre leurs valeurs thCoriques. Une comparaison thCorique prkliminaire avec le modele de prC-Cquilibre GDH (gComCtry-dipendent hybrid) a CtC effectuie en utilisant un nombre initial d'excitons no = 4 (2n + 2p + Oh), et un accord general a CtC constat6 pour toutes les rCactions haute Cnergie.

[Traduit par la revue]

Can. 1. Phys. 67, 870 (1989)

1. Introduction As far as a-particle interaction with a nucleus is concerned,

mechanism of the mode of reaction has been a point of interest for several years. Sufficient evidence is present to believe that the mode of reaction is not merely through compound nucleus formation. Hence, the emphasis on the nonequilibrium type of reaction mechanism that takes place in such a type of nuclear reaction has to be given due consideration. The experimental data on a-particle interactions show a high-energy tail in the excitation function, which is inexplicable in the framework of the equilibrium (compound) model. When the preequilibrium (PE) emission of particles prior to equilibrium formation is taken into consideration, the experimental data are somehow explained. Several semiclassical models (1-6) have been pro- posed that take care of the above considerations. Among these models, the hybrid and geometry-dependent hybrid (GDH) models (5, 6) have been reasonably successful in reproducing a broad range of experimental data. Efforts are also in progress to give a fully quantum-mechanical picture of the preequili- brium reactions in the framework of multistep theories (7- 10) but, due to the complexity of computation, the interaction of such a four-nucleonic complex system as a-induced reactions has not, so far, been explained. The purpose of the present work was to compare cross sections for gallium isotopes with Blann's geometry-dependent hybrid (GDH) model, which takes into account both compound and preequilibrium (PE) processes. To the best of our knowledge, excitation functions for the 69Ga(a,n), 69Ga(a,2n), 69Ga(a,3n), 69Ga(a,p3n), and 71Ga(a,4n) reactions are reported for the first time.

2. Experimental procedure The excitation functions for gallium were measured from

9.7 + 2.0 MeV to 59.5 4 0.6 MeV in an a-particle beam. The stacked-foil activation technique was employed for the present measurements. Targets for irradiation were prepared

by the vacuum evaporation technique from natural gallium oxide of spectroscopic purity better than 99.99% (natural abundance, 69Ga = 60.1% and 71Ga = 39.9%). Gallium oxide deposits of thickness 0.9 mg/cm2 were made on thin alurnin- ium backing of thickness 6.75 mg/cm2. The target foil was cut into pieces of size 1.5 cm X 1.5 cm and each of them was glued to an aluminium frame, having a circular hole of diam- eter 1.2 cm in its centre. The stack comprised 15 such foils. Energy-degrading aluminium foils of thickness 20.387 and 6.75 mg/cm2 were sandwiched between the target foils when- ever required, to get the desired a-particle energy incident on each foil. The stack was irradiated (1 1) with a 60-MeV dif- fused a beam of diameter 8 mrn, at the Variable Energy Cyclo- tron Centre (VECC), Calcutta (India). Beam energy was deter- mined from a curve that related the cyclotron RF with energy, constructed from experimental data on elastic scattering. The irradiation was performed with a beam current of about 100 nA. The irradiation period was about 45 min. The a-particle flux incident on the stack was monitored by the charge col- lection method. The target stock was clamped in a water-cooled target holder, and the a-particle beam intensity was measured in a Faraday cup close behind the target, connected to a charge integrator. A typical experimental setup for stack irradiation is shown in Fig. 1. Energy spread in the a-particle beam facing each foil was calculated by taking into account the thickness of the foil and the energyloss within it, using the stopping power table of Northcliffe and Schilling (12). This energy spread varies from 1 to 20% from the first to the last foil facing the a-particle beam.

After irradiation of the stack, the characteristic y activities induced in the individual foils were recorded with a high-res- olution 100 CC Ortec Ge(Li) detector (FWHM 2 keV at 1.33 MeV) coupled with a precalibrated 4096-channel Canberra-88 analyser. The dead time for counting was kept less than 10% by adjusting the target-detector separation in these measure- ments, and proper account of the dead time was taken in the

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Water

eut let (Faradays CUP)

a - b e

To current integrator Tantalum collirYtat0r

--Insulating screws

FIG. 1. Experimental set-up for stack foil irradiation with a-particle beam.

calculations. Several spectra were taken at suitable intervals to permit identification of the half-lives of various residual nuclei. Energy and efficiency calibrations were done using a standard 15'Eu y point source of known strength by keeping it at target position. Above the threshold energy of each reaction under study, all the characteristic y rays in the decay of their product nuclei were identified in each foil by their relative intensities. All the decay parameters of the nuclei studied here were taken from the table of isotopes by Lederer and Shirley (13).

The following expression was used for computing the exper- imentally measured reaction cross sections (14):

Ah exp (At,) 4 E ) =

No . @ (GE) ' 0 . K[1 - exp( - At,)] [I - exp( - ~ t , ) ]

where A is the counts under the photopeak of the characteristic y-rays, A is the decay constant of the product nucleus, No is the number of nuclei of the isotope under investigation, Q, is the incident a-particle flux, (GE) is the geometry-dependent efficiency of Ge(Li) detector, 0 is the absolute intensity of the characteristic y-rays, K is the self-absorption correction factor for the y-rays in the sample, t , is the irradiation time, t, is the time elapsed between stopping the beam and the start of count- ing, and t3 is the counting time.

The activation cross section for a given reaction was deter- mined from the intensities of the various y-rays identified as arising from the same residual nucleus. For cross section mea- surement we considered only those y-rays that have good sta- tistics. The reported value is the weighted average (15) of the various cross section values so obtained. The statistical error given in the results is the larger one of the internal and external errors (15). In general these are less than 12%, except for a few points.

3. Results and discussion The measured excitation functions for the reactions

69Ga(a,n), 69Ga(a,2n), 69Ga(a,3n), 69Ga(a,p3n), 71Ga(a,n),

----PURE EQ -PE WITH EQ

(GDH MODEL)

FIG. 2. Experimental and theoretical excitation function for the reaction 69Ga(a ,n) "As.

and 71Ga(a,4n) are shown in Figs. 2-8. The horizontal bars show the estimated total energy spread associated with each incident a-particle energy while the vertical bars represent the total estimated errors in cross section. If no bar is depicted, the size of the circle includes the magnitude of the statistical

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872 CAN. J . PHYS. VOL. 67, 1989

/ 0 PRESENT WORK /

FIG. 3. Experimentally measured excitation function for the reac- tions 69Ga(a,2n) 7'As + "Ga(a,4n) 7 1 A ~ .

L 0 50 60 30 E m (MeV, -

FIG. 4. Experimental and theoretical excitation function for the reaction 69Ga(a,2n) 71As.

FIG. 5. Experimental and theoretical excitation function for the reaction 69Ga(a,3n) 70As.

O PRESENT WORK -----PURE EQ -PE WlTH EQ

(GDH hlODEU

FIG. 6. Experimental and theoretical excitation function for the reaction 69Ga(a,p3n) 69Ge.

.----PURE EQ -PE WlTH EQ

FIG. 7. Experimental and theoretical excitation function for the reaction 71Ga(a,n) 74As.

errors. Straggling effects are expected to be negligibly small (16).

The experimental excitation functions were also compared with those predicted by theory, on the basis of the compound and preequilibrium (PE) reaction mechanisms. Comparison with theory is made only for those reactions in which total cross section (i.e., both isomers m (metastable state) and g (ground state)) is measured in the present work. For the equi- librium part of the analysis, the compound nucleus model of Weisskopf-Ewing (17) was adopted, while the geometry- dependent hybrid (GDH) model of Blann (6) was used for sim-

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---- PURE EQ -PE WITH EQ

FIG. 8. Experimental and theoretical excitation function for the reaction "Ga(a,4n) "As.

ulating preequilibrium (PE) decay of the compound system. A computer code ALICE/LIVERMORE-82 (18) was used for these calculations. The excitation functions are represented by a solid curve for the cross sections obtained by consideration of both the compound and preequilibrium contributions (GDH model calculations), and by a broken line for the compound nucleus (Weisskopf-Ewing calculation) cross sections.

In the equilibrium calculations the evaporation of protons, neutrons, deuterons, and a particles has been allowed for. The Q values for the formation of the compound nucleus and the neutron, proton, a-particle, and deuteron binding energies for all nuclides of interest were calculated using the Myers- Swiatecki/Lysekil mass formula (19). The pair energy 6 was calculated from the back-shifted model. The inverse cross sec- tions were calculated from the optical model subroutine of ALICE/LIVERMORE-82 (18), which uses the Becchetti and Greenlees (20) optical parameters. The intranuclear transition rates were calculated using the Pauli-corrected nucleon- nucleon (N-N) scattering cross sections, and adjustment of the mean free path for the intranuclear transitions was made, keeping the so-called mean-free-path multiplier (K) constant and equal to 3.0.

Level densities of residual nuclei play an important role in deciding the shapes and absolute values of the excitation func- tions. For the calculations, the level density formula proposed by Lang and Le Couteur (21) was used. In general, for the level density parameter a value of a = A / K was applied, where A denotes the nucleon number and K a constant for which values spread over a wide region have been given in the lit- erature (22-24). In our calculations, a best fit was obtained by using a value of 10 for 69.7'Ga.

In preequilibrium reactions, the initial exciton configuration is a crucial quantity (25). The influence of this initial exciton configuration on the results of the preequilibrium calculations was investigated by varying the initial exciton configuration, no (n-p-h), which is described by the number of neutrons (n) and protons (p ) in excited states, and the number of holes (h)

after the first collision. The total exciton number, no, equals the sum of n, p , and h. For a-induced reactions, the initial exciton number no = 4 or 5 was suggested by Blann (3). How- ever, it was found by many investigators (26-29) that no = 4 fits experimental data better than no = 5. We performed the calculations with an initial exciton configuration no = 4 (2n + 2p + Oh, i.e., pure particle state), which appears to give the best fit to our experimental data for a-induced reactions.

The agreement between the experimental and the theoretical excitation functions can be judged from their peak positions and widths. As can be seen from Figs. 2 and 4-8, the exci- tation functions calculated theoretically have their peaks at energies lower than the experimental ones. This is reasonable, since Weisskopf-Ewing calculations (17) refer to a lower limit for both these parameters (30), because of the angular momen- tum effects. Compound systems attained with incident parti- cles of different masses have appreciably different angular momenta when excited to the same excitation energy. This, in principle, can lead to differences in the excitation functions. If, in the last stages of nucleon de-excitation, high angular momentum inhibits particle emission more than it does y-ray emission, then the peak of the excitation function, correspond- ing to the particle emitting mode, will be shifted to the higher energy side (3 1). Such a shift could also be produced if the mean energy of the evaporated particles increases with increas- ing nucleon spin. The order of magnitude of this shift can be obtained from nuclear rotational energy (3 1). Blann and Mer- kel (32) have indicated that inclusion of angular momentum effects broadens the excitation functions. Excitation functions calculated with and without the inclusion of preequilibrium emission of particles are shown in Figs. 2 and 4-8. As can be seen, excitation functions calculated by considering the preequilibrium emission of particles are in better agreement, in general, with those measured currently over the full energy range. However, some composite excitation functions now measured require special mention.

Figure 2 shows the theoretical and experimental excitation function for the reaction 69Ga(a,n) "As. The excitation func- tion for this reaction was studied only up to 21.1-MeV a-par- ticle energy, because above this energy three more reaction channels, ie., 69Ga(a,a3n) 66Ga(T,12 = 9.45 h, Q = - 29.7 10 MeV), 7LGa(a,3n) 72As = 26.01 h, Q = -25.030 MeV), and 71Ga(a,2pn) 72Ga(Tll, = 14.12 h, Q = - 21.780 MeV), occur at the same time and decay with the same y-rays, ie., 0.630 MeV and 0.834 MeV, as obtained in the case of the 69Ga(a,n) 72As reaction. The four reactions cannot be sep- arated simultaneously.

The measured excitation function for the reactions 69Ga- (a,2n) 71As and 71Ga(a,4n) 71As is shown in Fig. 3. Because the product nucleus is the same in both reactions, it is obvious that above the threshold energy of the 71Ga(a,4n) reaction (ie., 33.920 MeV), the experimentally measured cross sections are the sum of the above-mentioned two reactions. Therefore the observed activity of 0.175-MeV and 1.096-MeV y-rays, aris- ing from the decay of the residual nucleus 71As, with a half- life of 61.0 h, into the irradiated samples, is the composite activity due to the two reactions, ie., 69Ga(a,2n) and 71Ga(a,4n). The two contributions can be separated quite accurately, using either the known theoretical ratio of cross sections, or by subtracting the contribution of one of the reac- tions measured with an enriched isotope (33). Efforts were made to separate the contributions (34) for these two reactions using the theoretical excitation function for the reaction

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874 CAN. I. PHYS.

69Ga(a,2n). Below the threshold for the 71Ga(a,4n) reaction (i.e., 33.920 MeV), the measured excitation function is due to the 69Ga(a,2n) reaction only. Therefore, the measured exci- tation function for the 69Ga(a,2n) reaction, below the threshold for the 71Ga(a,4n) reaction, was reproduced first from the the- oretical calculations. The calculated excitation function was then extended in the region of overlap, i.e., above 33.920 MeV, using the same set of parameters. The contribution of the extrapolated part of the excitation function, beyond 33.920 MeV, for the 69Ga(a,2n) reaction was subtracted from the composite decay curve to get the counting rate for the 71Ga(a,4n) reaction. This method for separating the two activ- ities is justified, since the excitation functions for the reactions "Ga(a,2n) (Fig. 4) and for 71Ga(a,4n) (Fig. 8), so resolved, can be reproduced individually by theoretical calculations using the same set of parameters. It can be seen from Figs. 4 and 8 that there is agreement between theory (GDH model) and experiment.

Figure 5 shows the present experimental values and the the- oretical predictions for the reaction 69Ga(a,3n). One more reaction channel 7'Ga(a,5n) opens at the offset of available a - particle energy (i.e., at 46.2 MeV), whereas the same product nucleus is produced. By theoretical calculations we find that the cross section for the reaction 71Ga(a,5n) is of the order of a few millibarns up to 60 MeV, and hence the contribution from the first reaction, ie., 69Ga(a,3n), of the order of 55.0 mb, is predominant. It can be seen that the trend of our exper- imental values is generally reproduced by the GDH model.

Figure 6 shows the experimental and theoretical excitation functions for the 69Ga(a,p3n) 69Ge reaction. The same product nucleus 69Ge is also produced by the 71GA (a,p5n) reaction at the offset of the available a-particle energy (ie., 50.98 MeV). From theoretical calculations, it is important to note that the cross section for the reaction 71Ga(a,p5n) is <1 mb, up to 60 MeV, and hence the contribution from the 69Ga(a,p3n) reac- tion, which is of the order of hundreds of millibarns, is pre- dominant. It can be seen that our results are in better agreement with GDH model calculations. The theoretical and experimen- tal excitation functions for the reaction 7'Ga(a,n) are shown in Fig. 7. It can be seen that there is good agreement between theory (GDH model) and experiment.

4. Conclusions From an overall com~arison of the ex~erimental and theo-

reticzl excitation functions for all six reactions studied in the present work one may conclude that the quantitative agreement is not very good in general, but qualitatively it is satisfactory, especially in the high-energy tail portion of the excitation func- tions. In spite of this poor quantitative agreement, it is quite evident from Figs. 2 and 4-8 that preequilibrium (PE) emis- sion of multiparticles is necessary before the system is equi- librated, and hence the experimentally observed high-energy tail of the excitation function can be explained only when the combination of semiclassically treated preequilibrium emis- sion (geometry-dependent hybrid model) followed by particle evaporation from the equilibrated system (Weisskopf-Ewing model) is taken into account. The pure equilibrium reaction, in its decay, is unable to explain the experimental data in the high-energy tail portion of the excitation function. It is clear from Figs. 2 and 4-8 that the calculated values shown by broken lines (based on the pure equilibrium model) do not reproduce the experimental data well. These data are repro-

FIG. 9. heequilibrium fraction (f,,) of the total reaction cross sec- tion as a function of a-particle energy.

duced well only when the preequilibrium emission is also taken into account, as shown by the solid lines. One may also infer that the initial exciton configuration no = 4 (2n + 2p + Oh) gives the best fit to our experimental data and supports the findings of many earlier investigators (26-29). The preequi- librium fraction Cf,,) of total reaction cross section has also been computed and is shown in Fig. 9. It is inferred from the trend of the curves that fpE increases very fast as the excitation energy of the a particle increases; at higher excitation energy, when the multiplicity of the outgoing particle increases, the preequilibrium fraction becomes more or less constant. Fur- ther, the threshold for preequilibrium emission is higher for the system of lower mass number.

Acknowledgements The authors are grateful to the Chairman of the Department

of Physics, Aligarh Muslim University, for providing the facil- ities to carry out this work. We also thank Dr. S . N. Chinta- lapudi and Variable Energy CyclotrQn Centre personnel for their cooperation during the ceurse of this experiment. One of the authors (I.A.R.) gratefully acknowledges the financial sup- port given by Aligarh Muslim University.

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