Coulomb problem for a nucleus. (August 2015)

• Record Type: Journal Article
• Authors: Kuleshov, V M; Mur, V D; Narozhny, N B; Fedotov, A M; Lozovik, Yu E; Popov, V S
• Is Part Of: Physics Uspekhi. Volume 58:Number 8(2015:Aug.)
• Page Start: 785
• Page End: 791
• Publication Date: 2015-08
• Subjects: 03.65.Pm -- 12.20. − m -- 73.22.Pr; Coulomb problem -- point-like nucleus -- boundary conditions -- critical charge -- scattering phase -- Breit–Wigner resonance; Physics -- Periodicals; 530.05
• DOI: 10.3367/UFNe.0185.201508d.0845
• Languages: English
• ISSNs: 1063-7869

Abstract

Abstract: A closed-form equation is derived for the critical nucleus charge at which a discrete level with the Dirac quantum number touches the lower continuum of the Dirac equation solutions. For the Coulomb potential cut off rectangularly at the short distance, the critical nucleus charge values are obtained for several values of and . It is shown that the partial scattering matrix of elastic positron–nucleus scattering, , is also unitary for . For this range, the scattering phase is calculated as a function of the positron energy, as are the positions and widths of quasidiscrete levels corresponding to the scattering matrix poles. The implication is that the single-particle approximation for the Dirac equation is valid not only for but also for and that there is no spontaneous creation of pairs from the vacuum.