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On rotational-vibrational spectrum of diatomic beryllium molecule
Author(s): A. A. Gusev; O. Chuluunbaatar; S. I. Vinitsky; V. L. Derbov; A. Góźdź; P. M. Krassovitskiy; I. Filikhin; A. V. Mitin; L. L. Hai; T. T. Lua
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Paper Abstract

The eigenvalue problem for second-order ordinary differential equation (SOODE) in a finite interval with the boundary conditions of the first, second and third kind is formulated. A computational scheme of the finite element method (FEM) is presented that allows the solution of the eigenvalue problem for a SOODE with the known potential function using the programs ODPEVP and KANTBP 4M that implement FEM in the Fortran and Maple, respectively. Numerical analysis of the solution using the KANTBP 4M program is performed for the SOODE exactly solvable eigenvalue problem. The discrete energy eigenvalues and eigenfunctions are analyzed for vibrational-rotational states of the diatomic beryllium molecule solving the eigenvalue problem for the SOODE numerically with the table-valued potential function approximated by interpolation Lagrange and Hermite polynomials and its asymptotic expansion for large values of the independent variable specified as Fortran function. The efficacy of the programs is demonstrated by the calculations of twelve eigenenergies of vibrational bound states with the required accuracy, in comparison with those known from literature, and the vibrational-rotational spectrum of the diatomic beryllium molecule.

Paper Details

Date Published: 3 June 2019
PDF: 8 pages
Proc. SPIE 11066, Saratov Fall Meeting 2018: Laser Physics, Photonic Technologies, and Molecular Modeling, 1106619 (3 June 2019); doi: 10.1117/12.2518409
Show Author Affiliations
A. A. Gusev, Joint Institute for Nuclear Research (Russian Federation)
O. Chuluunbaatar, Joint Institute for Nuclear Research (Russian Federation)
National Univ. of Mongolia (Mongolia)
S. I. Vinitsky, Joint Institute for Nuclear Research (Russian Federation)
RUDN Univ. (Russian Federation)
V. L. Derbov, Saratov State Univ. (Russian Federation)
A. Góźdź, Maria Curie-Sklodowska Univ. (Poland)
P. M. Krassovitskiy, Joint Institute for Nuclear Research (Russian Federation)
Institute of Nuclear Physics (Kazakhstan)
I. Filikhin, North Carolina Central Univ. (United States)
A. V. Mitin, Moscow Institute of Physics and Technology (Russian Federation)
Lomonosov Moscow State Univ. (Russian Federation)
Joint Institute for High Temperatures (Russian Federation)
L. L. Hai, Ho Chi Minh City Univ. of Technology (Viet Nam)
T. T. Lua, Ho Chi Minh City Univ. of Technology (Viet Nam)


Published in SPIE Proceedings Vol. 11066:
Saratov Fall Meeting 2018: Laser Physics, Photonic Technologies, and Molecular Modeling
Vladimir L. Derbov, Editor(s)

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