Comparison theorems for the Dirac equation with spin-symmetric and pseudo-spin-symmetric interactions
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, cilt.43, sa.19, 2010 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 43 Sayı: 19
- Basım Tarihi: 2010
- Doi Numarası: 10.1088/1751-8113/43/19/195303
- Dergi Adı: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Gazi Üniversitesi Adresli: Evet
Özet
A single Dirac particle is bound in d dimensions by vector V (r) and scalar S(r) central potentials. The spin-symmetric S = V and pseudo-spin-symmetric S = -V cases are studied and it is shown that if two such potentials are ordered V((1)) <= V((2)), then corresponding discrete eigenvalues are all similarly ordered E(kappa nu)((1)) <= E(kappa nu)((2)). This comparison theorem allows us to use envelope theory to generate spectral approximations with the aid of known exact solutions, such as those for Coulombic, harmonic-oscillator and Kratzer potentials. The example of the log potential V (r) = v ln(r) is presented. Since V (r) is a convex transformation of the soluble Coulomb potential, this leads to a compact analytical formula for lower-bounds to the discrete spectrum. The resulting ground-state lower-bound curve E(L)(v) is compared with an accurate graph found by direct numerical integration.