Title:

Study of reactions between heavy nuclei

A semi classical approach, has been used to study those reactions between heavy nuclei (or "heavy ions" as they are more commonly referred to) in which a single nucleon or a single cluster of nucleons is transferred from one nucleus to the other. A method has been developed for evaluating transfer amplitudes for the transfer of a neutron using the semi classical theory of Brink and Pixton. As this leads to a tedious three dimensional integral, we have developed another method for the same calculation. It is found that if we work in momentum space and assume a straight line trajectory for the relative motion, the expressions simplify considerably and we are left with a straightforward single integral for the transfer amplitude. An added advantage is that the formulae are exactly the same in the post and prior representations. The theory has then been generalised for the transfer of a charged particle. Some numerical calculations have been performed for the reaction ^{208}Pb(^{11}B, ^{10}B)^{209}Pb at 114 MeV laboratory energy. A comparison of the transfer amplitudes calculated in the post and prior representations using the first method has been made. The agreement is reasonably good between these two results as well as between these and the results using the second method. We go on to set up a semi classical theory for evaluating angular distributions. The starting point is the expression of the transition matrix in DWBA. A partial wave expansion is made for the distorted waves and the WKB approximation used for the radial wave functions. Further simplifications are made resulting in a formula for the transition amplitude which is a partial wave sum containing a term recognisable as the semi classical transfer amplitude evaluated earlier. The method has been used to calculate angular distributions for the reactions ^{26}Mg(^{11}B, ^{10}B)^{27}Mg and ^{26}Mg(^{11}B, ^{10}Be)^{27}Ai at 114MeV laboratory energy. A detailed numerical study of the formula shows some interesting features which enable us to approximate the transfer amplitude by a simple parametrised exponential formula. The resulting angular distributions are compared with experiment showing good agreement. A parametrisation of the elastic scattering phase shifts as well make it possible to obtain a closed expression for the angular distribution. A numerical comparison of the angular distribution obtained from this formula is made with former results. The agreement is good. We also study the theoretical reaction ^{16}0(^{17}0*, ^{16}0)^{17}0* for a range of energies from 212.5 MeV to 37.1875 MeV and compare our results with that using the quantum mechanical code LOLA of De Vries (DeVries, 1973). The elastic scattering phase shifts are calculated in a potential with an energy dependent imaginary part. The agreement is good till 53.125 MeV. At 37.1875 MeV there is disagreement. This is attributed to the breakdown of our formalism for weakly absorbing potentials. Some calculations have been performed for the αparticle transfer reaction ^{16}0(^{16}0, ^{12}C)^{20}Ne. Comparison with LOLA shows disagreement which we have not been able to explain.
