Spurious solutions in few-body equations

Journal Article · Thu Mar 01 04:00:00 EST 1979 · Phys. Rev., C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.19.616· OSTI ID:6307567

Adhikari, S K; Gloeckle, W

After Faddeev and Yakubovskii showed how to write connected few-body equations which are free from discrete spurious solutions various authors have proposed different connected few-body scattering equations. Federbush first pointed out that Weinberg's formulation admits the existence of discrete spurious solutions. In this paper we investigate the possibility and consequence of the existence of spurious solutions in some of the few-body formulations. Contrary to a proof by Hahn, Kouri, and Levin and by Bencze and Tandy the channel coupling array scheme of Kouri, Levin, and Tobocman which is also the starting point of a formulation by Hahn is shown to admit spurious solutions. We can show that the set of six coupled four-body equations proposed independently by Mitra, Gillespie, Sugar, and Panchapakesan, by Rosenberg, by Alessandrini, and by Takahashi and Mishima and the seven coupled four-body equations proposed by Sloan and related by matrix multipliers to basic sets which correspond uniquely to the Schroedinger equation. These multipliers are likely to give spurious solutions to these equations. In all these cases spuriosities are shown to have no hazardous consequence if one is interested in studying the scattering problem.

• Research Organization: Departamento de Fisica, Universidade Federal de Pernambuco, 50 000, Recife, Pe, Brazil
• OSTI ID: 6307567
• Journal Information: Phys. Rev., C; (United States), Journal Name: Phys. Rev., C; (United States) Vol. 19:3; ISSN PRVCA
• Country of Publication: United States
• Language: English

Related Subjects

653003* -- Nuclear Theory-- Nuclear Reactions & Scattering
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
AMPLITUDES
DIFFERENTIAL EQUATIONS
EQUATIONS
FADDEEV EQUATIONS
FOUR-BODY PROBLEM
FUNCTIONS
KERNELS
MANY-BODY PROBLEM
MATRIX ELEMENTS
SCATTERING AMPLITUDES
SCHROEDINGER EQUATION
THREE-BODY PROBLEM
WAVE EQUATIONS
WAVE FUNCTIONS