WKB method at Z>137 and its applications to the theory of supercritical atoms

Journal Article · Thu Feb 01 04:00:00 EST 1979 · Sov. Phys. - JETP (Engl. Transl.); (United States)

OSTI ID:6037468

Popov, V S; Voskresenskii, D N; Eletskii, V L; Mur, V D

Formulas are obtained in the WKB approximation for the Dirac equation in a strong external field (defined as a field in which the electron binding energy exceeds 2m/sub e/c/sup 2/ and the discrete-spectrum level can drop to the lower continuum). The forms of the wave functions in the classically allowed and forbidden regions are obtained, and conditions for their joining at the turning point are obtained. The following applications of the WKB method are considered: 1) Generalization of the Bohr-Sommerfeld quantization condition with allowance for relativistic effects and spin. 2) Calculation of the pre-exponential factor in the probability of spontaneous positron production. 3) The level energy and width in the relativistic two-center problems. 4) The effect of screening on the critical distance R/sub c/r between colliding nuclei. 5) Tunneling through a nonspherical barrier and the angular distribution of positrons. 6) Allowance for the finite velocity of nuclei. Some problems outside the scope of the WKB method are also considered, viz., the electron spectrum at Ze/sup 2/=1 and deep level in the lower continuum (Ze/sup 2/>>1, j< or approx. = (Ze/sup 2/) /sup 1/2/).

• Research Organization: Institute of Theoretical and Experimental Physics
• OSTI ID: 6037468
• Journal Information: Sov. Phys. - JETP (Engl. Transl.); (United States), Journal Name: Sov. Phys. - JETP (Engl. Transl.); (United States) Vol. 49:2; ISSN SPHJA
• Country of Publication: United States
• Language: English

Related Subjects

640305* -- Atomic
Molecular &amp; Chemical Physics-- Atomic &amp; Molecular Theory-- (-1987)
74 ATOMIC AND MOLECULAR PHYSICS
ANTILEPTONS
ANTIMATTER
ANTIPARTICLES
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
ELEMENTARY PARTICLES
ELEMENTS
ENERGY LEVELS
EQUATIONS
FERMIONS
FUNCTIONS
INTERACTIONS
LEPTONS
LEVEL WIDTHS
PARTICLE INTERACTIONS
PARTICLE PRODUCTION
POSITRONS
TRANS 104 ELEMENTS
TRANSPLUTONIUM ELEMENTS
TRANSURANIUM ELEMENTS
WAVE EQUATIONS
WAVE FUNCTIONS
WKB APPROXIMATION