A Self-Consistent "Realistic" Pairing Theory with Applications to Two-Nucleon Transfer Reactions

Abstract

Scope and Contents: A generalized pairing theory has been developed which diagonalizes matrix elements of the effective nucleon-nucleon interaction in a space of one, two and three-pair excitations from a Skyrme Hartree-Fock solution for deformed rotational nuclei. The "pairing" excitation energy for the configurations of time-reversed pairs of particles is obtained from the Hartree-Fock approximation as opposed to the conventional (BCS) residual interaction point of view. The effects of the finite-range character of the effective nucleon-nucleon interaction are studied in the single-particle structure they induce in the pairing matrix elements. Microscopic form factors for (p,t) and (t, p) reactions between states of the rotational bands built on the K^π=0^+ pairing solution band-head states are constructed in the cylindrical Harmonic-Oscillator basis in which the Hartree-Fock solution is expanded. These form factors are used in DWBA calculations for the differential cross-sections. Preliminary calculations for (p,t) and (t,p) transitions between states in 172Yb and 174Yb were performed. The calculations emphasize the effects of structure in the pairing matrix elements, and the necessity for a self-consistent calculation of the diagonal pairing matrix elements sing the Hartree-Fock equations.