Two-body bound state problem and nonsingular scattering equations

Journal Article · Sat Nov 01 04:00:00 EST 1986 · Phys. Rev. C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.34.1520· OSTI ID:7083771

Bartnik, E A; Haberzettl, H; Sandhas, W

We present a new momentum space approach to the two-body problem in partial waves. In contrast to the usual momentum space approaches, we treat the bound state case with the help of an inhomogeneous integral equation which possesses solutions for all (negative) energies. The bound state energies and corresponding wave functions are identified by an additional condition. This procedure straightforwardly leads to a nonsingular formulation of the scattering problem in terms of essentially the same equation and thus unifies the descriptions of both energy regimes. We show that the properties of our momentum-space approach can be understood in terms of the so-called regular solution of the Schroedinger equation in position space. The unified description of the bound state and scattering energy regimes in terms of one single, real, and manifestly nonsingular equation allows us to construct an exact representation of the two-body off-shell T matrix in which all the bound state pole and scattering cut information is contained in one single separable term, the remainder being real, nonsingular, and vanishing half on-shell. Such a representation may be of considerable advantage as input in three-body Faddeev-type integral equations. We demonstrate the applicability of our method by calculating bound state and scattering data for the two-nucleon system with the s-wave Malfliet--Tjon III potential.

• Research Organization: Physikalisches Institut, Universitaet Bonn, D-5300 Bonn 1, Federal Republic of Germany
• OSTI ID: 7083771
• Journal Information: Phys. Rev. C; (United States), Journal Name: Phys. Rev. C; (United States) Vol. 34:5; ISSN PRVCA
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUND STATE
BOUNDARY CONDITIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FADDEEV EQUATIONS
FUNCTIONS
INTEGRAL EQUATIONS
MANY-BODY PROBLEM
MATHEMATICAL MODELS
MATRICES
NUCLEAR MODELS
PARTIAL DIFFERENTIAL EQUATIONS
PARTIAL WAVES
S MATRIX
S WAVES
SCATTERING
SCHROEDINGER EQUATION
SHELL MODELS
THREE-BODY PROBLEM
TWO-BODY PROBLEM
WAVE EQUATIONS
WAVE FUNCTIONS