生成团簇本征函数的符号-数值算法：团簇通过排斥势垒的隧穿
Symbolic-numerical Algorithm for Generating Cluster Eigenfunctions: Tunneling of Clusters Through Repulsive Barriers
摘要：
在新的对称坐标表象中，首次引入了一个由A全同粒子组成的团簇，通过短程排斥势垒，在散射型势耦合下的量子隧穿模型，并在s波近似下进行了研究.利用Maple计算机代数系统，给出了用团簇波函数和势垒准定态能量计算紧耦合方程有效势的符号-数值算法.分析了量子透明性的影响，表现在透射系数对粒子能量、粒子数A= 2，3，4及其对称性的非单调共振型依赖性。结果表明，总透射系数的共振行为是由于存在的势垒准定态嵌入连续。
英文摘要：
A model for quantum tunnelling of a cluster comprising A identical particles, coupled by oscillator-type potential, through short-range repulsive potential barriers is introduced for the first time in the new symmetrized-coordinate representation and studied within the s-wave approximation. The symbolic-numerical algorithms for calculating the effective potentials of the close-coupling equations in terms of the cluster wave functions and the energy of the barrier quasistationary states are formulated and implemented using the Maple computer algebra system. The effect of quantum transparency, manifesting itself in nonmonotonic resonance-type dependence of the transmission coefficient upon the energy of the particles, the number of the particles A=2,3,4, and their symmetry type, is analyzed. It is shown that the resonance behavior of the total transmission coefficient is due to the existence of barrier quasistationary states imbedded in the continuum.
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