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Relativistic corrections of order $mα^6$: singular operators and regularization

Vladimir I Korobov

Abstract

The finite operators are derived for the nonrecoil (leading order in the $(m/M)$ expansion) relativistic corrections in hydrogen-like atoms and ions at orders $mα^6$ in the two- and three-body formalism beyond the adiabatic approximation. Singular operators that appear in the derivation are analysed, and various regularization methods are discussed.

Relativistic corrections of order $mα^6$: singular operators and regularization

Abstract

The finite operators are derived for the nonrecoil (leading order in the expansion) relativistic corrections in hydrogen-like atoms and ions at orders in the two- and three-body formalism beyond the adiabatic approximation. Singular operators that appear in the derivation are analysed, and various regularization methods are discussed.

Paper Structure

This paper contains 19 sections, 76 equations.

Table of Contents

  1. Introduction
  2. Nonrecoil corrections at $m\alpha^6$ order
  3. Separation of singularities from the first-order contribution
  4. Separation of singularities from the second-order contribution
  5. Modifications to the effective Hamiltonian resulting from the second-order contributions
  6. Singular identities
  7. Regularization
  8. Coordinate cutoff regularization
  9. Mass regularization
  10. Dimensional regularization
  11. Nonrecoil relativistic corrections at $m\alpha^6$ order for hydrogen molecular ions
  12. Separation of singularities from the first-order contribution
  13. Separation of singularities from the second-order contributions
  14. Conclusions
  15. $V(r)(4\pi\delta(\mathbf{r}))$ distribution in the dimensional regularization.
  16. ...and 4 more sections