Equations-of-motion approach to the neutron-proton pairing problem

The J=0, T=1 charge-independent pairing Hamiltonian is treated by means of the equations of motion for pair creation operators. Exact equations for the seniority-zero states of N nucleons are derived. It is shown that these equations can be solved by a stepby-step procedure which consists of progressively adding pairs of nucleons to a core. A method is given which removes the spurious effects arising from the redundancy of the set of basis vectors. The theory can be applied at several levels of approximation depending on the number of core states which are chosen to build up the basis vectors. Of special interest are the lowest orders of approximation, which are very simple in application. To assess the practical value of the present work, a three-level model calculation is performed using the first-order theory, wherein the core states are restricted to the lowest energy state for each value of the total isospin. Comparison shows that the energies, occupation probabilities, and two-nucleon transfer amplitudes for the lowest states of natural isospin are in very good agreement with the exact results for all values of N.