Direct two-nucleon transfer reactions and their interpretation in terms of the nuclear shell model

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Abstract
The distorted wave Born approximation (DWBA) treatment for direct two-nucleon transfer reactions has been derived following the formalism of Satchler, spin-orbit coupling being included in the distorted wave expansions. Methods for the evaluation of the integrals involved are described, and in particular a discussion is given of two different ‘zero-range’ approximations, one involving an assumption that the heaviest projectile has zero extent, the other assuming the interaction to have zero range. These two approaches are compared. The main emphasis, however, is directed towards extracting from experimental two-nucleon transfer reactions, reliable spectroscopic information, and to this end, shell model expressions for the spectroscopic amplitude have been derived, together with closed formulae for two-particle coefficients of fractional parentage (cfp). The JT representation is used principally throughout, but expressions are given for the LSJT representation as well as for the separate treatment of neutrons and protons. Examples illustrating (i) excitation of analogue states; (ii) comparison of (p, t) and (p, 3He) reactions to mirror states; and (iii) coherence effects between different shell model orbitals, indicate the usefulness of two-nucleon transfer reactions in determining nuclear structure information such as spins, parities, two-body matrix elements, etc. As a further aid to the analysis of experimental data, numerical tables of two-particle cfp's in the isospin formalism for j = 1/2, 3/2 and 5/2 are given for states of low seniority, and in the non-isospin formalism for j = 3/2, 5/2, 7/2 and 9/2 shells.