Relativistic corrections to spin-forbidden electric-dipole transitions

Theoretical results for spin-forbidden electric-dipole transitions have recently been questioned on the grounds that relativistic corrections to the transition operator were not included. It is shown here that these corrections are automatically included when the transition operator is expressed in the dipole length form. The above criticism of previous dipole-length calculations is therefore unfounded. The 1s2p 3P1-1s21S0 and 1s2p 3P1-1s2s 1S0 transitions of helium are discussed as specific numerical examples

Angular integrals and radial recurrence relations for two-electron matrix elements in Hylleraas coordinates

General formulas are obtained for the reduction of a wide class of two-electron matrix elements in Hylleraas coordinates to finite sums of radial integrals for states of arbitrary angular momentum. Multipole transition integrals and the Breit interaction are treated as special cases. A number of recurrence relations are derived for radial integrals containing PL(cosθ) (where cosθ=r^1•r^2) in terms of radial integrals containing lower-order Legendre polynomials. The results are well suited to computer implementation. © 1978 The American Physical Society

Theory of relativistic magnetic dipole transitions: Lifetime of the metastable 2S3 state of the heliumlike ions

It has recently been established that the radiative lifetime of the metastable 2S3 state of helium and the heliumlike ions is determined by single-photon magnetic dipole (M1) transitions to the ground state, rather than the two-photon process proposed by Breit and Teller. The theory of nl-n′l M1 transitions with n ′ is developed in the Pauli approximation and extended to two-electron systems. Terms arising from relativistic energy corrections and finite-wavelength effects are included. The results for hydrogenic systems are shown to be identical to those obtained in the relativistic four-component Dirac formulation. The coefficients in the Z-1 perturbation expansion of the 1s2sS3-1s2S1 M1 transition integral are evaluated through ninth order and used to calculate the M1 emission probabilities from the 2S3 state of the two-electron ions up to Fe XXV. The emission probability for neutral helium is 1.27 × 10-4 sec-1. The results are compared with recent solar coronal observations by Gabriel and Jordan, and with a measurement of the 2S3 state lifetime in Ar XVII by Schmieder and Marrus. © 1971 The American Physical Society

Asymptotic expansion for -function matrix elements of helium

This paper extends the methods of asymptotic analysis extensively developed for energy-level calculations of Rydberg states to the evaluation of matrix elements of (r). All terms up to x-8 in the asymptotic potential are systematically derived from a simple perturbation expansion. The formalism is developed in a way that closely parallels that for the corresponding energy expansion. The results are comparable in accuracy to the energy itself. Detailed numerical comparisons with high-precision variational calculations are presented for the states of helium up to nL=10K (i.e., L=7). For L5, the accuracy of the asymptotic expansion exceeds what has been achieved variationally. The asymptotic expansion for the specific mass correction to (r) is also obtained. Here the accuracy rivals the variational results even for L=3. Similar methods can be applied to the calculation of a wide variety of other atomic properties. © 1992 The American Physical Society

Spontaneous two-photon decay rates in hydrogenlike and heliumlike ions

A theoretical study of the two-photon emission rate from the 1s2s 1S state of two-electron ions is presented. High-precision values of the nonrelativistic emission rate for ions with nuclear charge Z up to 36 are obtained by use of correlated variational wave functions of the Hylleraas type. Summations over intermediate states are performed by finite-basis-set methods. The results are used to obtain an accurate extrapolation formula and to study the convergence characteristics of a 1/Z expansion for the decay rate. The leading hydrogenic term is calculated to an accuracy which substantially exceeds Klarsfeld\u27s, and the next term is obtained for what is believed to be the first time. Relativistic effects are taken into account by means of a screened hydrogenic approximation. The predicted decay rate for two-electron Kr34+ is (2.993±0.012)×1010 s-1, where the error is the uncertainty in the relativistic correction. This lies significantly higher than the value (2.934±0.030)×1010 s-1 recently measured by Marrus et al. © 1986 The American Physical Society

Relativistic corrections to radiative transition probabilities

The rate of spontaneous emission of radiation by a loosely bound composite system is calculated from quantum electrodynamics correct through terms of relative order α2Z2. Recent criticisms by Feinberg and Sucher of the semiclassical method of deriving the higher-order radiation coupling terms are discussed. It is proved that the Breit interaction remains valid in the presence of radiation emission and that the semiclassical and quantum-electrodynamic methods of deriving the higher-order coupling terms always yield the same results to relative order α2Z2. We discuss in particular relativistic corrections to allowed and spin-forbidden electric dipole transitions and the 1s2s S13-1s2 S01 magnetic dipole transition. © 1972 The American Physical Society

Predicted energy shifts for paronic helium

It has been shown recently that one can construct a local relativistic quantum field theory which admits small violations of the Pauli exclusion principle by introducing paronic states which obey para-Fermi statistics of order 2. Paronic shifts are calculated for the low-lying states of helium to aid in the design of experiments either to detect paronic helium, or place upper limits on its possible existence. © 1989 The American Physical Society

Singlet-triplet mixing in the helium sequence

Accurate variational calculations are presented for the off-diagonal matrix elements of the Breit interaction between the 2P1 and 2P3 states of several members of the helium iso-electronic sequence. A comparison is made with recent Z-expansion calculations, which are accurate through terms of order α2Z3. The comparison shows that the Z-expansion method for off-diagonal mixing is potentially useful in the theory of many-electron atoms. The effect of singlet-triplet mixing on the 2P3 excitation cross sections is briefly discussed. © 1969 The American Physical Society