Adiabatic Representation for Atomic Dimers and Trimers in Collinear Configuration
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ELEMENTARY PARTICLES AND FIELDS Theory
Adiabatic Representation for Atomic Dimers and Trimers in Collinear Configuration∗ A. A. Gusev1)** , S. I. Vinitsky1), 2) , O. Chuluunbaatar1), 3) , ´ z´ 4) , V. L. Derbov5) , and P. M. Krassovitskiy6) A. Go´ zd Received April 17, 2018
Abstract—We considered collinear models for a trimer of identical atoms with molecular pair interactions and for an atomic dimer scattered by an atom or tunneling through potential barriers. The models are formulated as 2D boundary-value problems in the Jacobi and polar coordinates. In the adiabatic representation the problems are reduced to a system of second-order ordinary differential equations (SODEs) with respect to the radial variable using the expansion of the desired solutions in the set of angular basis functions that depend on the radial variable as a parameter. The efficiency of the elaborated method, algorithms and programs is demonstrated by benchmark calculations of the asymptotic expansions of basis functions, effective potentials, fundamental solutions of the SODEs, and corresponding asymptotic scattering states, as well as the resonance scattering, metastable and bound states. DOI: 10.1134/S1063778818060169
1. INTRODUCTION At present the resonance scattering of diatomic molecules(dimers) by atoms via three-particle metastable trimer states and the molecular dissociation induced by collisions with atoms are a subject of extensive theoretical and experimental studies [1–5]. To analyze such processes it is conventional to use triatomic model systems with atoms of rare gases bound by pair interactions described, e.g., by realistic molecular and van der Waals potentials, that possess bound and metastable states in the vicinity of the dissociation threshold of the diatomic molecule [6– 8]. To extend the class of conventional models we proposed to consider the beryllium dimer [9, 10], in which the bond is covalent in the low-lying (0–4) vibrational energy states and van der Waals in the upper (5–11) states [11, 12], and to investigate the collisions of beryllium dimers with surrounding atoms or the near-surface diffusion [13–15]. Further study ∗
The text was submitted by the authors in English. Joint Institute for Nuclear Research, Dubna, 141980 Russia. 2) Peoples’ Friendship University of Russia (RUDN University), Moscow, 117198 Russia. 3) National University of Mongolia, Ulaanbaatar, Mongolia. 4) Institute of Physics, University of M. Curie-Skłodowska, Lublin, Poland. 5) Saratov State University, Saratov, Russia. 6) Institute of Nuclear Physics, Almaty, Kazakhstan. ** E-mail: [email protected] 1)
of these models and processes stimulates the development and application of the known and new methods and symbolic–numerical algorithms for solving multidimensional boundary-value problems (BVPs) with non-separable variables and the construction of asymptotic states of the triatomic scattering problem below and above the breakup threshold [16–45]. In the present paper, the application of the adiabatic representation to the solution of the above p
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