KANTBP 3.1: a program for computing energy levels, reflection and transmission matrices, and corresponding wave functions in the coupled-channel and adiabatic approaches. (English) Zbl 1522.81679

Summary: A FORTRAN program for calculating energy values, reflection and transmission matrices, and corresponding wave functions in a coupled-channel approximation of the adiabatic approach is presented. In this approach, a multidimensional Schrödinger equation is reduced to a system of the coupled second-order ordinary differential equations on a finite interval with the homogeneous boundary conditions of the third type at left- and right-boundary points for the discrete spectrum and scattering problems. The resulting system of such equations, containing potential matrix elements and first-derivative coupling terms is solved using high-order accuracy approximations of the finite element method. The scattering problem is solved with non-diagonal potential matrix elements in the left and/or right asymptotic regions and different left and right threshold values. Benchmark calculations for the fusion cross sections of \(^{36}\mathrm{S}+{}^{48}\mathrm{Ca}\), \(^{64}\mathrm{Ni}+{}^{100}\mathrm{Mo}\) reactions are presented. As a test desk, the program is applied to the calculation of the reflection and transmission matrices and corresponding wave functions of the exact solvable wave-guide model, and also the fusion cross sections and mean angular momenta of the \(^{16}\mathrm{O}+{}^{144}\mathrm{Sm}\) reaction.


81U05 \(2\)-body potential quantum scattering theory
94A40 Channel models (including quantum) in information and communication theory
70F10 \(n\)-body problems
35P15 Estimates of eigenvalues in context of PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
70H11 Adiabatic invariants for problems in Hamiltonian and Lagrangian mechanics
14G12 Hasse principle, weak and strong approximation, Brauer-Manin obstruction
34L16 Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators
81Q37 Quantum dots, waveguides, ratchets, etc.


Full Text: DOI


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