Exact formulation and solution of the nuclear eigenvalue problem in a microscopic multiphonon space

Abstract

We propose a method for solving exactly the nuclear eigenvalue problem within a multiphonon space constructed out of Tamm-Dancoff phonons. The method consists in deriving, within a given $n$-phonon subspace, a set of equations, of simple structure for any $n$, which are solved iteratively, starting from the particle-hole vacuum, to yield a set of states covering a multiphonon space up to an arbitrary number of phonons. The intrinsic redundancy of the set so generated is removed completely and exactly by a simple and efficient prescription. Such a multiphonon basis reduces the Hamiltonian into diagonal blocks plus residual off-diagonal terms of simple form. Its diagonalization becomes straightforward and yields exact eigensolutions. $^{16}\mathrm{O}$ is adopted as numerical test ground.