2023 Impact factor 2.6
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

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

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.

05.30.-d Quantum statistical mechanics - 02.70.Lq Monte Carlo and statistical methods - 21.60.Ka Monte Carlo models

Copyright Società Italiana di Fisica, Springer-Verlag 2000