New Model Potential for Pseudopotential Calculations

Abstract

The use of model potentials in pseudopotential calculations is discussed, and a set of desirable criteria for model potentials is suggested. The Hellmann potential and the Abarenkov and Heine potential are examined, and it is shown that both potentials are useful, but neither fully satisfies the suggested desiderata. A new potential of the form, V(r) =-Z!r+"1:,IBIPI!r 2 , where PI is the projection operator over the subspace of spherical harmonics of a given I, is proposed. A physical interpretation of the potential in terms of a "Pauli force" and a polarized core is given. Ionization energies for excited S, P, D, and F states for onevalence-electron atoms are calculated. The new potential is also applied to two-valence-electron atoms, and their calculated valence-state energies are shown to be in good agreement with experimental values.

Radiative Lifetimes for Singly Ionized Beryllium

“…The QDO theory is based on analytical solution of the one-electron Schrödinger equation with an effective central-field potential [11]. This formalism gives exact solutions for the radial orbital and analytical expressions for transition integrals.…”

Integral transform functions and separable potentials

“…This should be an interesting alternative to the usual Hellmann or Fues potentials used in pseudopotential calculations [14,21]. We plan to apply this model function and potential to such calculations.…”

“…But due to imperfect screening of the residual Coulomb potential by the shorter range interactions between electrons, the general asymptotic wave functions will deviate from the hydrogenic solutions, i.e., y will not be integral and hence the appropriate solutions will be of the form (21). This can be further generalized by adding a dipolar term A/r2, converting the effective potential into a Fues potential [14] to simulate Pauli repulsions or dipolar polarizations: V ( r ) = -1 / r + A/r2. The net effect of this is to change 1 to a nonintegral value A by the relation 2mA/h2 + l(1 + 1) = i Z(1 + 1).…”

“…The net effect of this is to change 1 to a nonintegral value A by the relation 2mA/h2 + l(1 + 1) = i Z(1 + 1). This does not change the asymptotic expressions (14) and (22). The asymptotic solutions, (13) and (21), are obtained from scattering boundary conditions at r = 03 which depend on solutions irregular at the origin.…”

Зарядовое распределение ионов Kr, образуемых при рентгеновском облучении 1.3 keV

“…В этом случае он в литера-туре известен как потенциал Саймонса [12]. Несмотря на неверное асимптотическое поведение при r → ∞, потенциал Саймонса в ряде случаев дает разумные радиационные характеристики атомов, близкие к тем, что получаются при использовании известного метода квантового дефекта [13].…”