Levinson's theorem for Dirac particles

Journal Article · Mon Nov 01 04:00:00 EST 1993 · Physical Review, C (Nuclear Physics); (United States)

DOI:https://doi.org/10.1103/PhysRevC.48.2174· OSTI ID:6049998

Piekarewicz, J ^[1]

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1. Supercomputer Computations Research Institute, Florida State University, Tallahassee, Florida 32306 (United States)

Levinson's theorem for Dirac particles constrains the sum of the phase shifts at threshold by the total number of bound states of the Dirac equation. Recently, a stronger version of Levinson's theorem has been proven in which the value of the positive- and negative-energy phase shifts are separately constrained by the number of bound states of an appropriate set of Schroedinger-like equations. In this work we elaborate on these ideas and show that the stronger form of Levinson's theorem relates the individual phase shifts directly to the number of bound states of the Dirac equation having an even or odd number of nodes. We use a mean-field approximation to Walecka's scalar-vector model to illustrate this stronger form of Levinson's theorem. We show that the assignment of bound states to a particular phase shift should be done, not on the basis of the sign of the bound-state energy, but rather, in terms of the nodal structure (even/odd number of nodes) of the bound state.

• DOE Contract Number: FC05-85ER25000; FG05-92ER40750
• OSTI ID: 6049998
• Journal Information: Physical Review, C (Nuclear Physics); (United States), Journal Name: Physical Review, C (Nuclear Physics); (United States) Vol. 48:5; ISSN 0556-2813; ISSN PRVCAN
• Country of Publication: United States
• Language: English

Related Subjects

663300* -- Nuclear Reactions & Scattering
General-- (1992-)
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
BOUND STATE
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
EQUATIONS
FERMIONS
LEVINSON THEOREM
MATHEMATICAL MODELS
MEAN-FIELD THEORY
NUCLEAR MODELS
PARTIAL DIFFERENTIAL EQUATIONS
PHASE SHIFT
WALECKA MODEL
WAVE EQUATIONS