Eur. Phys. J. Plus (2015) 130: 156
https://doi.org/10.1140/epjp/i2015-15156-7

Regular Article

Improvement of the envelope theory with the dominantly orbital state method

Service de Physique Nucléaire et Subnucléaire, Université de Mons, UMONS Research Institute for Complex Systems, Place du Parc 20, 7000, Mons, Belgium

^* e-mail: claude.semay@umons.ac.be

Received: 27 April 2015
Revised: 22 June 2015
Accepted: 8 July 2015
Published online: 30 July 2015

Abstract

The envelope theory, also known as the auxiliary field method, is a simple technique to compute approximate solutions of Hamiltonians for N identical particles in D dimensions. The quality of the approximate eigenvalues can be improved by adding a free parameter in the characteristic global quantum number of the solutions. A method is proposed to determine the value of this parameter by comparing the eigenvalues computed with the envelope theory to the corresponding ones computed with a N-body generalization of the dominantly orbital state method. The accuracy of the procedure is tested with several systems.