Shifted 1/N Expansion Within the Framework of the SO(2,1) Pseudo-spin Formalism

Abstract

The shifted 1/N expansion is organized within the framework of the SO(2, 1) pseudo-spin formalism and the method is formulated to derive the ground state energies of a class of power law potentials.Keywords Shifted large-N expansion · Pseudo-spin formalism · Power-law potentialsThe method of large-N expansion has won acceptance as a powerful non-perturbative approach in quantum mechanics, atomic physics, statistical mechanics and field theory (for a review see [1][2][3][4][5][6][7]). Notwithstanding its proven efficacy in dealing with a wide variety of problems the method is at times plagued with slow convergence. To improve the situation, Sukhatme and Imbo [33] have developed the so called shifted 1/N expansion scheme introducing an extra degree of freedom, called the shift parameter. Sukhatme and collaborators [34] have given a prescription for the choice of the shift parameter which is physically motivated and developed their theory in the framework of the perturbed oscillator technique. The shifted 1/N expansion method [33] has been used by several authors with overwhelming success [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49]. There have also been several other formulations [50-54] to obtain improved convergence in the 1/N expansion.In the present paper we have made an attempt to introduce the idea of the shifted 1/N expansion of Sukhatme and Imbo [34] in a wider framework namely in the pseudo-spin formulation [55,56]. It is well-known that the pseudo-spin formalism is a very powerful and versatile technique which finds applications in various branches of physics [57-60] and therefore it is expected that the shifted 1/N expansion in the pseudo-spin formalism would have a much wider applicability. We shall formulate the theory for a class of spherically symmetric potentials and compare the results with those obtained by Sukhatme and Imbo [33] with the perturbed oscillator method.

Detailed description of exclusive muon capture rates using realistic two-body forces

“…As it is well known, when negative muons, µ − , pro- * Electronic address: pgiannak@cc.uoi.gr † Electronic address: hkosmas@uoi.gr duced in a meson factory, slow down in matter, it is possible for them to be captured in atomic orbits. Afterwards, fast electromagnetic cascades bring these muons down to the innermost (1s or 2p) quantum orbits (in this way muonic atoms are produced) [3][4][5][6][7]. A bound muon in the muonic atom may disappear either by decay known as muon decay in orbit or by capture by the nucleus the main channel of which is the ordinary muon capture represented by the reaction [8][9][10]…”

“…As muon-capture in nuclei presents many advantages for the study of both nuclear structure and the fundamental electro-weak interactions [11][12][13][14], process (1) has been the subject of extensive experimental and theoretical investigations started early on 50's using closure approximation or sum-over partial rates to find the total µ − -capture rate (the measured quantity). [3][4][5][6][16][17][18][19][20][21][22]. In the plethora of the relevant papers, the most important motivation was rested on the hope to explain how nucleons (hadronic current) inside the nucleus couple weakly to the lepton field (leptonic current).…”