Programme

O.32 -- Oral, VCTP-50

Date: Thursday, 7 August 2025

Time: 16:50 - 17:15

The Stark effect calculations in spherical coordinates

Luong Le Hai (1), Nguyen Minh Nhut (2), Oleg O. Kovalev (3), Alexander A. Gusev (3), Ochbadrakh Chuluunbaatar (3), Sergue I. Vinitsky (3)

(1) Ho Chi Minh city University of Education; (2) Ho Chi Minh City University of Science; (3) Joint Institute for Nulear Research

The methods for calculating the real or complex eigenenergies and the corresponding eigenfunctions of a hydrogen-like atom with one electron in a uniform electric field directed along the third axis of the Cartesian coordinate system, the Stark effect, are presented. A two-dimensional boundary value problem in partial derivatives in a spherical coordinate system for a fixed magnetic quantum number is solved by the Kantorovich method, which is a reduction in a system of second-order ODEs in the radial variable using the expansion of the desired solution in the basis of angular functions that depend on the radial variable of the ODE as a parameter. The presented method is implemented as algorithms and programs in the Maple system for calculating a set of parametric angular eigenfunctions and eigenvalues, and effective potentials of the ODE system in the radial variable. Estimates of the complex eigenvalues of the energy of the lower part of the Stark effect spectrum are obtained by solving a finite number of equations of the ODE system in the radial variable using the KANTBP 5M program, which implements the finite element method (FEM) in the Maple system.

Presenter: Luong Le Hai