Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8254Research ArticleThe Model of Tunneling of Clusters Through Repulsive Barriers in Symmetrized Coordinates RepresentationGusevA ALaboratory of Information Technologiesgooseff@jinr.ruJoint Institute for Nuclear Research150120141527008092016Copyright © 2014,2014Formulation of a mathematical model for the system A identical particles with pair interaction of oscillator type in the repulsive barrier potentials in the form of a boundary-value problem for elliptic equations in new symmetrized coordinates, eﬀective methods, algorithms and program complexes for the analysis of its solutions are presented. Reduction of the problem for a cluster of A identical particles to subsystems “(one particle) + (cluster of (A − 1) particles)” and “(a cluster of Ab1 particles) + (cluster of Ab2 particles)” is considered. The solution of the boundary-value problem for a cluster of A identical particles sought the form of an expansion over the cluster (A − 1)-dimensional oscillator basis functions, symmetric and antisymmetric with respect to permutations of A identical particles, i.e. in the symmetrized coordinates representation [Gusev A.A. // Bulletin of PFUR. Series “Mathematics, Information Sciences. Physics”. — 2013. — No 3. — P. 52–67]. The problem is reduced to the boundary value problem for a set of coupled second-order ordinary diﬀerential equations with the R-matrix third type boundary conditions in the close coupling channel method. The amplitude matrix of transmission and reﬂection and the eigenfunctions of the continuous spectrum of the scattering problem with respect to the center of mass are calculated with help of the program complex KANTBP 3.0. The eﬀectiveness of the approach is demonstrated by the analysis of the solutions of the quantum tunneling of clusters consisting of a number of identical particles with oscillator-type pair interaction through a repulsive barrier in the s-wave approximation. The analysis of the eﬀect of quantum transparency, i.e. resonant tunneling of a cluster of several identical particles through the repulsive barriers, which is due to the presence of quasi-stationary states embedded in a continuum is given. To calculate the positions of the energy of quasistationary states and their classiﬁcation, the algorithm of solving the boundary value problems for elliptic equations in A-dimensional domain of a special type based on the decomposition of solutions A-dimensional oscillator basis is developed. The developed approach and set of programs focused on the analysis of the quantum diﬀusion of molecules, channeling and tunneling clusters and ions in crystals, as well as tetrahedral and octahedral symmetry of the nuclei.cluster modelsnuclear reaction models and methodscoupled channel modelsquantum tunnelingкластерные моделимодели ядерных реакций и методымодели связанных каналовквантовое туннелирование