Mass Corrections to the Fine Structure of Hydrogen-Like Atoms

Recoil corrections of order (Zα)6(m/M)m to the hydrogen energy levels recalculated

“…[7], but also linear in m/M parts of recoil corrections of orders (Zα) 4 and (Zα) 5 (ref. [13]) were reproduced for the 1S-state. Note that the Braun formula, despite its obvious advantages, in its present form sums only contributions linear in the mass ratio.…”

Salpeter equation and probability current in the relativistic Hamiltonian quantum mechanics

“…The most popular choices of the relativistic quantum mechanical equations for spinless massive particle are the Klein-Gordon equation [1][2][3][4] and less familiar relativistic Schrödinger equation which is usually referred to as the spinless Salpeter equation [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. The latter can be regarded as the "square root" of the Klein-Gordon equation and is based on the approach which is sometimes referred to as the relativistic Hamiltonian dynamics [24,25].…”

Solving the homogeneous Bethe-Salpeter equation

“…When we take the BS kernel to be the instantaneous (Coulomb-like) interaction, the homogeneous BS equation reduces to the Salpeter equation. [14] On the other hand, in ref. [15] the authors work for the Euclidean total momentum and solve the BS equation by expanding the BS amplitude in terms of SO(4) orthogonal Tschebyshev polynomials and dropping higher order polynomials.…”

“…In the improved ladder approximation we use the running coupling, the asymptotic form of which is given by 14) where the summation over the repeated indices is promised and…”