Monte Carlo calculations of angular momentum projected many-body matrix elements in the Pairing Plus Quadrupole Model

G. Puddu

doi:doi:10.1007/s100500070034

2022 Impact factor 2.7

Hadrons and Nuclei

Eur. Phys. J. A 9, 171-181

Monte Carlo calculations of angular momentum projected many-body matrix elements in the Pairing Plus Quadrupole Model

G. Puddu

Dipartimento di Fisica dell'Universitá di Milano, I-20133 Milano, Italy
giovanni.puddu@mi.infn.it

Received: 28 April 2000 / Revised version: 6 July 2000
Communicated by P. Schuck

Abstract
We extend the recently presented formalism for Monte Carlo calculations of the partition function, for both even and odd particle number systems (Phys. Rev. C 59, 2500 (1999)), to the
calculation of many-body matrix elements of the type $\langle\psi\vert e^{-\beta\hat H}\vert\psi\rangle$ where $\vert\psi\rangle$ is a many-body state with a definite angular momentum, parity, neutron and proton numbers. For large $\beta$ such matrix elements are dominated by the lowest eigenstate of the many-body Hamiltonian $\hat H$ , corresponding with a given angular momentum parity and particle number. Emphasis is placed on odd-mass nuclei. Negligible sign fluctuations in the Monte Carlo calculation are found provided the neutron and proton chemical potentials are properly adjusted. The formalism is applied to the $J^{\pi}=0^+$ state in ${}^{166}{\rm Er}$ and to the $J^{\pi}=9/2^-,\;\; 13/2^+,\;\; 5/2^-$ states in ${}^{165}{\rm Er}$ using the pairing-plus-quadrupole model.