Hiroo Kumagai

Many-body theory in terms of effective interactions and its relation to coupled-cluster method

Abstract We propose a method of describing a many-body system in terms of effective interactions and show its formal equivalence to the coupled-cluster method (CCM). A transformed hamiltonian H = e −s H e S is introduced with the cluster operator S . The hamiltonian H contains many-body interactions, and they allow to define many-body average potentials. We prove that the problem of determining the ground-state energy can be reduced to calculating two-body effective interactions and they are determined from the decoupling equation for a two-body subsystem in one- and two-body average potentials. It is shown that the exact expressions of the one- and two-body average potentials are given in terms of two-, three- and four-body cluster operators in S . The three- and four-body cluster equations and their formal solutions are also given.

Unitary-model-operator approach to nuclear many-body theory

The structure of the unitary-model-operator approach (UMOA) is discussed in the framework of general effective interaction theory. The properties of the two-body effective interaction v12, introduced as a basic element in UMOA, are clarified. The effective interaction v12 has some desirable features to be E-independent, Hermitian and decoupled between two spaces of two-particle states consisting of occupied and unoccupied orbits. It is noted that these properties of v12 are advantageous over the usual Brueckner approach. The theory is applied to the calculation of the ground-state properties in 16O with various nucleon-nucleon potentials including the Bonn potential. The result is reasonable in comparison with those obtained in the usual Brueckner-Hartree-Fock calculation. The use of the Bonn potential with rather weaker tensor component leads to a better result. It is shown that the results for the saturation property, the binding energy versus charge radius, lie beyond the Coester band and get near to the experimental value.

A new solution for effective interaction

A new method is given for the model-space effective interaction. Introducing a new operator in place of the Q-box in the Krenciglowa-Kuo (KK) method, we derive a new equation for the effective interaction. This equation can be viewed as an extension of the KK method. We show that this equation can be solved both in iterative and non-iterative ways. We observe that the iteration procedure brings about fast acceleration of convergence compared to the KK approach. We also find that the non-iterative calculation reproduces successfully any set of the true eigenvalues of the original Hamiltonian. This non-iterative calculation can be made regardless of the magnitudes of the overlaps with the model space and the energy differences between the unperturbed energy and the eigenvalues to be solved.

Recursion method for deriving an energy-independent effective interaction

The effective-interaction theory has been one of the useful and practical methods for solving nuclear many-body problems based on the shell model. Various approaches have been proposed which are constructed in terms of the so-called

Formulation of an effective interaction in terms of renormalized vertices and propagators

\widehat{Q}

Nuclear ground-state properties and nuclear forces in the unitary-model-operator approach: Application to 16O.

box and its energy derivatives introduced by Kuo {\it et al}. In order to find out a method of calculating them we make decomposition of a full Hilbert space into subspaces (the Krylov subspaces) and transform a Hamiltonian to a block-tridiagonal form. This transformation brings about much simplification of the calculation of the

Graphical Method for Effective Interaction with a New Vertex Function

\widehat{Q}

Ground-State Properties of 40Ca in Unitary-Model-Operator Approach with Realistic Nucleon-Nucleon Potentials

box. In the previous work a recursion method has been derived for calculating the

Effects of Self-Consistent Single-Particle Potential on Nuclear Effective Interaction

\widehat{Q}

Formulation of effective interaction in terms of the non-perturbative and analytic box

box analytically on the basis of such transformation of the Hamiltonian. In the present study, by extending the recursion method for the