Rapid-ionization approach based on the factorization method

Abstract

The factorization method of Bar-Shalom, Klapisch, and Oreg [Phys. Rev. A 38, 1773 (1988)] is extended to relativistic-distorted-wave cross sections for ionization by electron impact. This leads to a very great simplification for complex ions. In particular, when mixing is confined to the states in a complex (having the same set of n values, parity, and J value), the ionization cross section takes the form of a summation over states of the product of a readily calculated quantity that depends only on target-ion properties, such as mixing coe%cients and angular momenta, and a cross section having exactly the same form as a hydrogenic cross section except that the radial functions should be calculated using the appropriate potential for the ion being considered. Similar results are obtained for intermediate coupling using LS-coupling notation and for totally nonrelativistic calcu1ations. On1y slightly more complicated formulas apply when mixing is included outside a complex. It is also noted that similar expressions apply for photoionization. Sample numerical results are obtained and compared with relativistic calculations of Moores and Pindzola [Phys. Rev. A 42, 5384 (1990)]. Quite good agreement is obtained when mixing is included among the same set of states.PACS number{s): 34.80.Kw

Electron Impact Excitation Cross Sections in F-Like Selenium

“…The total collision strength is computed by summing over the partial collision strengths, which are computed from the transition matrix T. T can be expressed in terms of the reactance matrix K. For highly charged ions of interest here, the elements of K are small, so that the weak-coupling approximation made in the RDWB method gives a good treatment. After applying the factorization method proposed by Bar-Shalom et al [25] to the RDWB model by Sampson et al [26], the final expression obtained for the collision strength ⍀ if can be written as (6) contains the radial scattering matrix elements and is obtained by summation over initial and final orbitals and total angular momenta of the free electron within them. Therefore, Eq.…”

FULLY RELATIVISTIC DISTORTED-WAVE CROSS SECTIONS FOR ELECTRON IMPACT IONIZATION FROM THE 2s, 2p1/2, AND 2p3/2 SUBSHELLS IN IONS WITH Z − N ≥ 3, Z ≤ 92, AND N ≤ 12

“…The ionization cross sections were calculated fully relativistically using the distorted-wave program of [1] and [2], modified to include the generalized Breit interaction (GBI) between bound and free electrons, as described in [3]. The atomic structure data used in the calculations were obtained with the Dirac-Fock-Slater (DFS) program of [4] with the improvements discussed in [5].…”

“…The quantities directly calculated are the pseudohydrogenic cross sections Q H PS (nlj) described in [2], which in turn can be used to provide more useful cross sections or rate coefficients. The notation nlj refers to the quantum numbers of the active subshell from which ionization takes place.…”

“…If the active subshell is not occupied in the ground state, a single electron is promoted from the outermost, occupied subshell, and equally split between the active subshell and the 9h orbital. For example, 1s 2 2s 2 2p 1/ 2 1 2p 3/ 2 0.5 9h 11/ 2 0.5 (2) was the mean configuration used to determine the DFS potential for ionization of the 2p 3/ 2 subshell in C-like ions. It should be mentioned that the resulting cross sections are insensitive to the precise choice for the highly excited subshell as well as to slight adjustments to the occupation numbers of the remaining subshells that make up the mean configuration.…”

“…which was originally derived in [2]. In the above equation S and S 1 are pure states contributing to initial level U, while SЉ and S Љ 1 are pure states contributing to final level UЉ with one less bound electron.…”