Extension of the Siegert theorem for photon emission

Abstract

When the long wavelength approximation is not performed, extensions of the Siegert theorem can take various forms. An alternative expression is derived for the electric multipole fields, that is inspired by earlier works on photonuclear reactions. It is applied to the Siegert transformation of electric transition operators for single photon emission. In the particular case of isospin forbidden E1 transitions that can be useful for some important radiative capture reactions, an approximation of this electric transition operator is established and discussed. * dbaye@ulb.ac.be

Relativistic polarizabilities with the Lagrange-mesh method

“…The results for the hydrogen atom are obtained with only 6 mesh points for λ = 1 and 8 mesh points for λ = 2. For low Z values, the dipole polarizabilities are very close to the exact nonrelativistic ones [5,7]. Indeed, the relativistic effects are very weak.…”

“…Hence it is useful to use a more compact expression. For partial wave l, the radial functions ψ (1) nll ′ at the first order of perturbation theory are solutions of the inhomogeneous radial equations [7,18,19]…”

“…nll ′ does not contain the degenerate component. The reduced polarizabilities can be rewritten as [7,18]…”

“…The Lagrange-mesh method is definitely accurate for estimating relativistic polarizabilities of hydrogen-like systems, as it was already shown for non-relativistic polarizabilities [7] and for relativistic energies and wave functions [16]. As such, Lagrange bases could find their room in the large family of finite basis sets to which B-splines and B-polynomials belong, to investigate twophoton processes in hydrogen-like ions [33,34].…”

Analytical expressions of non-relativistic static multipole polarizabilities for hydrogen-like ions*

“…where the Sturmian polynomials are also used in their work to describe the wave functions and the Green function. Analytical expressions for the dipole polarizabilities of hydrogen in an arbitrary atomic state have been obtained by Baye [9]. However, analytical results for multipole polarizabilities of hydrogen are still less investigated, which will be the main focus of the present work.…”