Pauli Exclusion Effects in Reactions Involving Multinucleon Systems

To investigate the importance of effects of Pauli exclusion principle in reactions involving multinucleon systems, we consider reactions in which deuterons are incident on a recoilless nucleus. First, the binding energy of a model deuteron in the presence of a nuclear Fermi gas (an infinite nucleus) is calculated as a function of nuclear density and deuteron kinetic energy so as to provide some clues to the range of incident energies and nuclear densities where exclusion effects can be expected to be important. The results show that this model deuteron is unbound in the presence of infinite nuclear matter, unless it has a kinetic energy, at least, of the order of 100 MeV. Making some simplifying assumptions, then, we pose a model problem and obtain for the deuteron breakup, elastic scattering, and stripping reactions, Hilbert-Schmidt integral equations in which the Pauli term, in each case, can be identified. Corresponding to Pauli breakup term, Pauli breakup cross sections for deuterons on ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ nucleus have been calculated in a simple model. The dependence of cross sections on directions along which the breakup products emerge and the energy partition among them is investigated. The variation of cross section with incident deuterons' kinetic energy and with nuclear density is also studied. The most prominent and important feature of Pauli breakup is the sharp peaking of cross sections for very asymmetric partition of energy among outgoing particles and is very encouraging for an experimental test. Finally, by considering Pauli breakup of an artifically tightly bound deuteron, we conclude that the Pauli mechanism should be of importance in $\alpha$-particle reactions as well.