Problem of levels in the lower continuum

Journal Article · Wed Feb 01 04:00:00 EST 1978 · Sov. J. Nucl. Phys. (Engl. Transl.); (United States)

OSTI ID:6773689

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

Quasistationary levels in the lower (negative) continuum of solutions of the Dirac equation are considered. The potential V (r) is assumed deep enough ( vertical-barV/sub max/vertical-bar>2mc/sup 2/) so that the levels of the discrete spectrum may cross the boundary epsilon =-mc/sup 2/ and dive into the lower continuum. Application of the WKB approximation allows complete solution of the problem of the real part of the level energy. Explicit equations are obtained for the spectrum of levels with energies epsilon<-mc/sup 2/, their number, and their angular-momentum distribution. Comparison with numerical calculations shows that the WKB method is satisfactorily accurate even at zeta=Ze/sup 2//hc> or approx. =2. However, the WKB method does not allow one to find the width of deep levels with low angular momenta. The exact solutions of the dirac equation are analyzed to elucidate this problem. It is shown that for zeta>>1 the width ..gamma../sub n/ is much smaller than both the level energies epsilon/sub n/ and the separation between close levels epsilon/sub n/+1--epsilon/sub n/; the levels are, thus, isolated. The change in the asymptotics (r..-->..infinity) of solutions of the Dirac equation upon crossing the boundary of the lower continuum is clarified.

• Research Organization: Institute of Theoretical and Experimental Physics, State Atomic Energy Commission
• OSTI ID: 6773689
• Journal Information: Sov. J. Nucl. Phys. (Engl. Transl.); (United States), Journal Name: Sov. J. Nucl. Phys. (Engl. Transl.); (United States) Vol. 27:2; ISSN SJNCA
• 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
ANGULAR MOMENTUM
CHARGE STATE
CRITICAL SIZE
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
ENERGY LEVELS
EQUATIONS
SIZE
WAVE EQUATIONS
WKB APPROXIMATION