It is shown that solutions of the second-order decoupled radial Dirac equations satisfy Ermakov-type invariants. These invariants lead to amplitude-phase-type representations of the radial spinor solutions, with exact relations between their amplitudes and phases. Implications leading to a Bohr-Sommerfeld quantization condition for bound states, and a few particular atomic/ionic and nuclear/hadronic bound-state situations are discussed.
Received 11 March 2013Accepted 15 April 2013Published online 02 May 2013
Article outline: I. INTRODUCTION II. DIRAC EQUATION AND AN ERMAKOV INVARIANT III. JWKB-TYPE APPROXIMATION IV. DERIVATION OF A BOHR-SOMMERFELD QUANTIZATION CONDITION V. NOTES ON APPLICATIONS A. General remarks B. Case study of an iso-scalar tensor interaction gr, with a real coupling constant g > 0 VI. CONCLUSION