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Model of diatomic homonuclear molecule scattering by atom or barriers. (English) Zbl 1392.81214
Vishnevskiy, Vladimir M. (ed.) et al., Distributed computer and communication networks. 19th international conference, DCCN 2016, Moscow, Russia, November 21–25, 2016. Revised selected papers. Cham: Springer (ISBN 978-3-319-51916-6/pbk; 978-3-319-51917-3/ebook). Communications in Computer and Information Science 678, 511-524 (2016).
Summary: The mathematical model of quantum tunnelling of diatomic homonuclear molecules through repulsive barriers or scattering by an atom is formulated in the s-wave approximation. The 2D boundary-value problem (BVP) in polar coordinates is reduced to a 1D BVP for a set of second-order ODEs by means of Kantorovich expansion over the set of parametric basis functions. The algorithm for calculating the asymptotic form of the parametric basis functions and effective potentials of the ODEs at large values of the parameter (hyperradial variable) is presented. The solution is sought by matching the numerical solution in one of the subintervals with the analytical solution in the adjacent one. The efficiency of the algorithm is confirmed by comparing the calculated solutions with those of the parametric eigenvalue problem obtained by applying the finite element method in the entire domain of definition at large values of the parameter. The applicability of algorithms and software are demonstrated by the example of benchmark calculations of discrete energy spectrum of the trimer \(\mathrm{Be}_3\) in collinear configuration.
For the entire collection see [Zbl 1386.68012].
MSC:
81U05 \(2\)-body potential quantum scattering theory
81V55 Molecular physics
81V45 Atomic physics
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
Software:
KANTBP; KANTBP 2.0
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References:
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