KANTBP 3.1: A program for computing energy levels, reflection and transmission matrices, and corresponding wave functions in the coupled-channel and adiabatic approaches

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 36S+48Ca, 64Ni+100Mo 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 16O+144Sm reaction.

本文提出一款适用于绝热近似（adiabatic approach）耦合道近似（coupled-channel approximation）框架的Fortran（FORTRAN）程序，可用于计算能量本征值、反射与透射矩阵以及对应波函数。在该近似框架下，多维薛定谔方程（Schrödinger equation）被约化为有限区间上的耦合二阶常微分方程组；针对离散谱与散射问题，方程组在左右边界点均满足第三类齐次边界条件。该方程组包含势矩阵元与一阶导数耦合项，采用有限元法（Finite Element Method）的高精度近似格式进行求解。本程序可处理左、右渐近区域存在非对角势矩阵元且左右阈值各异的散射问题。本文给出了36S+48Ca、64Ni+100Mo两个核反应的熔合截面基准计算结果。作为验证测试案例，本程序被应用于精确可解波导模型（wave-guide model）的反射与透射矩阵及其对应波函数的计算，同时还完成了16O+144Sm反应的熔合截面与平均角动量计算。