arXiv subjects

John H. Connell

Publications and source records attributed to John H. Connell.

3 recordsLinked to original sources

arXiv2017

Atomic Two-Body $(Zα)^6$ Predictions

For muonic hydrogen, positronium, and ordinary hydrogen, we show that the existence of a relativistic two-body wave equation whose energy levels are physically accurate to order $(Zα)^4$ (where $Zα$ is the binding coupling constant) implies a previously unknown two-body Sommerfeld energy formula which can be used to predict energy terms to order $(Zα)^6$ using simple algebra. Two such terms are verified to be physically correct by earlier $(Zα)^6$ calculations for positronium. For muonic hydrogen and ordinary hydrogen, these terms are predictions.

hep-ph↗

arXiv2013

Sommerfeld Fine-Structure Formula for Two-Body Atoms

For relativistic atomic two-body systems such as the hydrogen atom, positronium, and muon-proton bound states, a two-body generalisation of the single-particle Sommerfeld fine-structure formula for the relativistic bound-state energies is found. The two-body Sommerfeld bound-state energy formula is obtained from a two-body wave equation which is physically correct to order $(Zα)^4$. The two-body Sommerfeld formula makes two predictions in order $(Zα)^6$ for every bound state and every mass ratio. With $N$ the Bohr quantum number: (a) The coefficient of the $(Zα)^6/N^6$ energy term has a specified value which depends only on the masses of the bound particles, not on angular quantum numbers; (b) The coefficient of the $(Zα)^6/N^4$ energy term is a specified multiple of the {\em square} of the coefficient of the $(Zα)^4/N^3$ energy term. Both these predictions are verified in positronium by previous calculations to order $(Zα)^6$ which used second-order perturbation theory. They are also correct in the Coulomb-Dirac limit. The effect of the two-body Sommerfeld formula on calculations of muon-proton bound-state energies is examined.

physics.atom-ph↗

arXiv2001

Solution of the Scalar Coulomb Bethe-Salpeter Equation

A relativistic two-body wave equation, local in configuration space, is derived from the Bethe-Salpeter equation for two scalar particles bound by a scalar Coulomb interaction. The two-body bound-state wave equation is solved analytically, giving a two-body Bohr-Sommerfeld formula whose energies agree with the Bethe-Salpeter equation to order alpha^4 for all quantum states. From the Bohr-Sommerfeld formula, along with the expectation values of two remaining small corrections, the energy levels of the scalar Coulomb Bethe-Salpeter equation are worked out to order alpha^6 for all states.

hep-th↗