scholarly journals Eigenvalues of the Breit equation

2013 ◽  
Vol 2013 (6) ◽  
pp. 63B03-0
Author(s):  
Y. Yamaguchi ◽  
H. Kasari
Keyword(s):  
Breit Equation

scholarly journals SINGULARITY-FREE BREIT EQUATION FROM CONSTRAINT TWO-BODY DIRAC EQUATIONS

1996 ◽  
Vol 05 (04) ◽  
pp. 589-615 ◽  
Author(s):  
HORACE W. CRATER ◽  
CHUN WA WONG ◽  
CHEUK-YIN WONG
Keyword(s):  
Quantum Electrodynamics ◽  
Bound States ◽  
Two Body Problem ◽  
Dirac Equations ◽  
Coupled Equations ◽  
Interaction Terms ◽  
Potential Form ◽  
Orthogonality Constraint ◽  
Hyperbolic Form ◽  
Breit Equation

We examine the relation between two approaches to the quantum relativistic two-body problem: (1) the Breit equation, and (2) the two-body Dirac equations derived from constraint dynamics. In applications to quantum electrodynamics, the former equation becomes pathological if certain interaction terms are not treated as perturbations. The difficulty comes from singularities which appear at finite separations r in the reduced set of coupled equations for attractive potentials even when the potentials themselves are not singular there. They are known to give rise to unphysical bound states and resonances. In contrast, the two-body Dirac equations of constraint dynamics do not have these pathologies in many nonperturbative treatments. To understand these marked differences we first express these contraint equations, which have an “external potential” form, similar to coupled one-body Dirac equations, in a hyperbolic form. These coupled equations are then recast into two equivalent equations: (1) a covariant Breit-like equation with potentials that are exponential functions of certain “generator” functions, and (2) a covariant orthogonality constraint on the relative momentum. This reduction enables us to show in a transparent way that finite-r singularities do not appear as long as the exponential structure is not tampered with and the exponential generators of the interaction are themselves nonsingular for finite r. These Dirac or Breit equations, free of the structural singularities which plague the usual Breit equation, can then be used safely under all circumstances, encompassing numerous applications in the fields of particle, nuclear, and atomic physics which involve highly relativistic and strong binding configurations.

scholarly journals On the Breit equation

2001 ◽  
Vol 508 (1-2) ◽  
pp. 198-202 ◽  
Author(s):  
Hikoya Kasari ◽  
Yoshio Yamaguchi
Keyword(s):  
Breit Equation

Normalization of bound-state solutions to the Breit equation

1989 ◽  
Vol 39 (6) ◽  
pp. 1787-1790 ◽  
Author(s):  
Jerome Malenfant
Keyword(s):  
Bound State ◽  
Breit Equation

scholarly journals Two-Body Dirac Equation Approach to the Deuteron

1998 ◽  
Vol 07 (01) ◽  
pp. 89-106
Author(s):  
A. P. Galeão ◽  
J. A. Castilho Alcarás ◽  
P. Leal Ferreira
Keyword(s):  
Exchange Potential ◽  
Equation Approach ◽  
Deuteron Binding Energy ◽  
Coupling Constant ◽  
Radial Functions ◽  
First Order ◽  
Pion Nucleon ◽  
Component Wave ◽  
Breit Equation ◽  
Conditions At Infinity

The two-body Dirac(Breit) equation with potentials associated to one-boson-exchanges with cutoff masses is solved for the deuteron and its observables calculated. The 16-component wave-function for the Jπ=1+ state contains four independent radial functions which satisfy a system of four coupled differential equations of first order. This system is numerically integrated, from infinity towards the origin, by fixing the value of the deuteron binding energy and imposing appropriate boundary conditions at infinity. For the exchange potential of the pion, a mixture of direct plus derivative couplings to the nucleon is considered. We varied the pion-nucleon coupling constant, and the best results of our calculations agree with the lower values recently determined for this constant.

scholarly journals Variational wave equations of two fermions interacting via scalar, pseudoscalar, vector, pseudovector and tensor fields

Open Physics ◽  
2005 ◽  
Vol 3 (4) ◽  
Author(s):  
Askold Duviryak ◽  
Jurij Darewych
Keyword(s):  
Wave Equations ◽  
Body Wave ◽  
Vacuum State ◽  
Nonlocal Interaction ◽  
Tensor Fields ◽  
Tensor Coupling ◽  
Coordinate Representation ◽  
Interaction Terms ◽  
Breit Equation ◽  
Variational Wave

AbstractWe consider a method for deriving relativistic two-body wave equations for fermions in the coordinate representation. The Lagrangian of the theory is reformulated by eliminating the mediating fields by means of covariant Green's functions. Then, the nonlocal interaction terms in the Lagrangian are reduced to local expressions which take into account retardation effects approximately. We construct the Hamiltonian and two-fermion states of the quantized theory, employing an unconventional “empty” vacuum state, and derive relativistic two-fermion wave equations. These equations are a generalization of the Breit equation for systems with scalar, pseudoscalar, vector, pseudovector and tensor coupling.

Klein paradox in the Breit equation

1979 ◽  
Vol 1 (4) ◽  
pp. 369-375 ◽  
Author(s):  
W. Kr�likowski ◽  
A. Turski ◽  
J. Rzewuski
Keyword(s):  
Klein Paradox ◽  
Breit Equation

scholarly journals Breit equation with form factors in the hydrogen atom

2012 ◽  
Vol 39 (3) ◽  
pp. 035103 ◽  
Author(s):  
F García Daza ◽  
N G Kelkar ◽  
M Nowakowski
Keyword(s):  
Hydrogen Atom ◽  
Form Factors ◽  
Breit Equation

scholarly journals Breit Equation versus Salpeter Equation in One Dimension

1989 ◽  
Vol 81 (3) ◽  
pp. 706-714 ◽  
Author(s):  
W. Glockle ◽  
Y. Nogami ◽  
F. M. Toyama
Keyword(s):  
One Dimension ◽  
Equation Versus ◽  
Breit Equation
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