J. Sapirstein

The use of basis splines in theoretical atomic physics

The use of basis sets formed from B-splines in non-relativistic and relativistic atomic calculations is described.

Contributions to helium fine structure of order mα7

An effective Hamiltonian approach is used to analyse QED contributions to the fine structure of 2 3PJ levels in helium to order mα7. Formulae for leading contributions are derived and their numerical values presented.

Higher-order recoil corrections to helium fine structure

A class of recoil corrections of order α4 me mαRy∞ c to the fine structure of helium is calculated. The present status of the fine structure constant determined from comparison of theory with recent accurate experiments of the large interval ν01 is described, and possible explanations for significant discrepancies between theory and experiment for ν01, as well as the small interval ν12, discussed.

Quantum electrodynamics of many-electron atoms

The question of the validity of many body perturbation theory (MBPT) calculations that start from the Dirac-Coulomb Hamiltonian is addressed. An extension of the Furry representation of Quantum Electrodynamics (QED) is introduced in which the nuclear Coulomb field is replaced by a potential more relevant to many-electron atoms. QED perturbation theory for energies and matrix elements is set up and evaluated for exchanges of up to two photons. It is shown that in lowest and first order the expressions used in MBPT starting from the Dirac-Coulomb Hamiltonian are reproduced along with additional Lamb shift and Breit interaction contributions. In second order use of QED gives rise to slight differences with MBPT: however, simple rules pertaining to sums over negative energy states are given that eliminate possible difficulties corresponding to continuum dissolution.

Order alpha(2) corrections to the decay rate of orthopositronium

Order alpha(2) corrections to the decay rate of orthopositronium are calculated in the framework of nonrelativistic QED. The resulting contribution is found to be in significant disagreement with one set of experimental measurements, though another experiment is in agreement with theory.

Determination of the fine structure constant from helium spectroscopy

The fine structure of the 23PJ levels in helium is recalculated and the present status of theoretical predictions is summarized. Comparison with a recent high-accuracy measurement then allows the determination of the fine structure constant α. A detailed analysis of the higher-order terms which affect this determination is presented.

Many-body theory applied to negative ions

The quasiparticle orbital for the valence electron in a negative ion having one electron outside closed shells is determined from the Dyson equation. The authors replace the proper self-energy in the Dyson equation by an approximation derived from second-order many-body perturbation theory. Solving the resulting equation for the 4d105s state of the negative palladium ion they obtain a value of 0.525 eV for the electron affinity, compared with the measured value 0.558+or-0.008 eV; for the 4s24p state of the calcium negative ion the authors obtain an affinity 0.056 eV, compared with the measured value 0.043+or-0.007 eV; for the strontium negative ion the authors predict a 5s25p state having an affinity 0.093 eV; and for the barium negative ion they predict a 6s26p state with affinity 0.192 eV.

Radiative corrections to one photon decays of hydrogenic ions

Radiative corrections to the decay rate of n = 2 states of hydrogenic ions are calculated. The transitions considered are the M1 decay of the 2s state to the ground state and the E1(M2) decays of the 2p{sub 1/2} and 2p{sub 3/2} states to the ground state. The radiative corrections start in order {alpha}(Z{alpha}){sup 2}, but the method used sums all orders of Z{alpha}. The leading {alpha}(Z{alpha}){sup 2} correction for the E1 decays is calculated and compared with the exact result. The extension of the calculational method to parity nonconserving transitions in neutral atoms is discussed.

Recoil corrections to the Lamb shift in helium

Nuclear recoil corrections to the energies of helium S levels of order m 2 /M 5 are presented. They are shown to contribute only a small amount to the ionization energies of the 2 1 S and 2 3 S states, but to contribute significantly on the scale of accuracy of modern 4 He-3 He isotope shift experiments.

Calculations of the parity non-conserving 6s→7s transition in caesium

SummaryThe electroweak interaction between electrons and nucleons destroys the mirror symmetry of an atom. The size of the effect depends on the weak interaction constants as well as on the atomic structure. Small-scale experiments studying atomic parity non-conservation can thus give a quantitative test of the standard model for the electro-weak interaction — provided the atomic structure is sufficiently well understood. The increasing experimental accuracy, in particular for Cs, raises new demands on atomic theory. The various contributions to the parity non-conserving electric dipole transition matrix element are discussed together with the methods used to calculate them. The uncertainty in the atomic calculation is estimated. A discussion of radiative corrections with emphasis on the role of the top quark mass is also given.