Various kinds of kinematical constraints of pair operators play important roles in an algebraic approach to the theory of nuclear collective motion. The algebraic foundation of these constraints is given with the use of algebraic recursion formulas.
The program of the algebraic approach to nuclear collective motion is summarized. In essence, it should permit an accurate solution of the many-body problem within a subspace of the many-particle space if the conditions defining collective motion are present. The formulation, containing both dynamical and kinematical aspects, leads to coupled nonlinear algebraic equations for the matrix elements between collective states of fermion pair operators. An explicit set of equations is given for the problem of N (even) particles confined to a single-j shell and described by the conventional pairing plus quadrupole-quadrupole interaction Hamiltonian. This formulation is designed to be nearly exact in the pairing-dominant (seniority) limit and to be accurate enough (based on plausibility arguments) to describe the transition from spherical to deformed shape. That this is so is verified for configurations, the largest being jN=(221)6, for which exact solutions are available. The present method can be viewed as an angular momentum conserving alternative to the description of the transition based on the Hartree-Bogoliubov-BCS method. Qualitative and detailed comparisons of the two methods are carried out. In particular, it is shown from approximate analytic results that the two theories predict the transition to occur for almost identical values of the parameters. Over-all agreement with exact results is much better for the algebraic method, however, confirming its status as an approximate method of variation after projection.
We study symmetric nuclear matter using bare nucleon-nucleon (NN) interactions with the finite particle-number approach within finite cubic boxes. Due to the NN correlations originating from the bare NN interaction, two nucleons can be excited to the high-momentum region, leading to the increase of the kinetic energy in nuclear matter. We further consider the spin excitations in the nucleon pairs, where the spins of the two nucleons are changed, and this excitation is important for the tensor correlation. The unitary correlation operator method (UCOM) is used to treat the short-range correlation. The tail correction coming from the neighboring boxes is also included. We demonstrate the contributions of various excitations of nucleon pairs as well as the tail correction to the total energy at normal density. We also discuss the effects of UCOM and correlated nucleon pairs on the density dependence of the total energy. We calculate the equations of state of symmetric nuclear matter using two kinds of the Argonne potentials and the results agree with those from other many-body theories. The density dependences of the Hamiltonian components are also shown.