General-relativistic effects in hydrogenic systems

Journal Article · Fri May 15 04:00:00 EDT 1981 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.23.2157· OSTI ID:6405598

Fischbach, E; Freeman, B S; Cheng, W

We examine in detail the behavior of bound systems containing a spin-1/2 fermion (e.g., atomic hydrogen or positronium) in an external gravitational field. Starting with the generally covariant Dirac equation, we derive the effective Hamiltonian for a fermion in a weak gravitational field correct through order v/sup 2//c/sup 2/, where v is the fermion velocity. The resulting expression is then used to obtain the gravitational Hamiltonian for both hydrogen and positronium including relativistic effects. It is shown that the form of the Hamiltonian for the bound system depends on the choice of center-of-mass and relative coordinates, and several choices of these coordinates are considered. An extensive discussion is given of the relativistic variables used to describe the bound system and their physical significance. The principal focus of this paper is a relativistic gravitational analog of the Stark effect which arises from a set of post-Newtonian terms in the bound-state Hamiltonian. These are shown to mix opposite-parity states in hydrogen, such as S/sub 1/2/ and P/sub 1/2/, and lead to a correlation between the local acceleration of gravity g and the photon polarization in electromagnetic decays. We discuss the possibility that a study of this polarization could be used to discriminate among different theories of gravity at the quantum level through its dependence on one of the parametrized post-Newtonian parameters. For a fermion-antifermion system such as positronium, the interaction Hamiltonian can admix states with opposite values of P and CP, as we illustrate with several examples. Our results apply specifically to the case of a hydrogenic system supported in a gravitational field by nongravitational forces. The effects of these are not explicitly considered.

• Research Organization: Physics Department, Purdue University, West Lafayette, Indiana 47907
• OSTI ID: 6405598
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 23:10; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

640305* -- Atomic
Molecular & Chemical Physics-- Atomic & Molecular Theory-- (-1987)
657003 -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
ANGULAR MOMENTUM
BOUND STATE
COUPLING CONSTANTS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
ELEMENTS
EQUATIONS
FERMIONS
FIELD THEORIES
FUNCTIONS
GENERAL RELATIVITY THEORY
GRAVITATIONAL FIELDS
HAMILTONIANS
HYDROGEN
INVARIANCE PRINCIPLES
LAGRANGIAN FUNCTION
MATHEMATICAL OPERATORS
MATRIX ELEMENTS
MECHANICS
NONMETALS
P INVARIANCE
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE PROPERTIES
POSITRONIUM
QUANTUM MECHANICS
QUANTUM OPERATORS
RELATIVITY THEORY
SELECTION RULES
SPACE-TIME
SPIN
WAVE EQUATIONS