Resonances in the electron scattering from a calcium atom

Резонансна Структура Перерізів Розсіяння Повільних Електронів На Атомі Кальцію

“…The essence of the method aimed at the discretization of the continuum of the (𝑁 + 1)-electron system "atom + incident electron", which was proposed in our works [6][7][8][9][10][11][12][13][21][22][23][24][25][26], consists in the expansion of the target bound orbitals 𝑃 𝑛𝑗 𝑙𝑗 (𝑟) and the scattered electron orbitals 𝐹 Γ 𝑖𝛼 (𝑟) (r) in a complete finite set {𝐵 𝑖 } 𝑛 𝑖=1 of the basis splines 𝐵 𝑖 and the following single diagonalization of the matrix of the self-conjugated system Hamiltonian 𝐻 𝑁 +1 + 𝐿 𝑁 +1 in the discrete basis (13). The main advantage of this method of continuum discretization is based on the fact that the matrix of the total Hamiltonian 𝐻 𝑁 +1 + 𝐿 𝑁 +1 has a very sparse -namely, band -structure in the 𝐵-spline basis, which considerably simplifies the solution of the corresponding system of algebraic equations.…”

“…This condition does not follow from the basic requirements of quantum mechanics and was introduced in the SCC method proceeding from the reasons of calculation convenience. As a result of constraints imposed on the collision function Ψ Γ 𝛼 by the orthogonality condition (8), the incident electron cannot be virtually captured in one of the unfilled subshells participating in expansion (5) of the target states and pseudostates. In the framework of the standard SCC method, the possibility of such a capture, as was marked above, is taken into consideration by including special additional correlation functions 𝜒 Γ 𝑗 into expansion (2).…”

“…However, this method of making allowance for resonance effects is not the most advantageous one and often leads to the appearance of a nonphysical pseudoresonance structure in scattering cross-sections, as well as to the necessity to solve a cumbersome system of coupled integrodifferential equations for 𝐹 Γ 𝑖𝛼 . In order to avoid these difficulties, increase the accuracy of the theory, and extend the scope of its application, we must abandon the "forced" condition (8) of orthogonality between the continuum functions 𝐹 Γ 𝑖𝛼 and the radial target orbitals 𝑃 𝑛𝑗 𝑙𝑗 . Now, there is no need to separately introduce a special set of correlation functions 𝜒 Γ 𝑗 , which would account for the influence of some autoionization states, into the second sum in expansion (2) because the first sum in this expansion will already contain the wave functions of those states.…”

“…Although this potential strongly simplifies calculations and allows the excitation energies and oscillator strenghts to be determined with sufficient accuracy, the question remains as to how accurately the model potential can mimic the covalent correlation, including the nonlocal and non-dipole contributions. For this reason, correlation effects are taken into account in our approach [6][7][8][9][10][11][12][13] (see Section 2) by including special additional electronic configurations with an excited core into the expansion of the target states and pseudostates.…”

“…In this paper, to study the resonance effects occurring at the collisions of slow electrons with Ca atoms, we used a new version of the 𝑅-matrix method [briefly, the 𝐵-Spline 𝑅-matrix (BSR) method], which was developed in works [6][7][8][9][10][11][12][13][21][22][23][24][25][26]. In the framework of this version, a new method was proposed to take resonance effects into account.…”