二维三粒子超球绝热基的解析表达式
Analytical Expressions for a Hyperspherical Adiabatic Basis Three Particles in 2 Dimensions
摘要：
对于一个特定的情况下，在2维三体散射，我们证明了分析的行为的绝热势是不同的超球耦合矩阵元素，从而导致相移趋于零，能量为零，而不是一个常数。我们考虑两个粒子相互作用的二元排斥阶跃电位，作为一个旁观者，并解析求解绝热本征值和本征向量，所有的ρ值。因此，我们能够获得的有效电位的长期行为的领先条款，并确认其逆对数的性质，建议从以前的数值研究。
英文摘要：
For a particular case of three-body scattering in 2 dimensions, we demonstrate analytically that the behaviour of the adiabatic potential is different from that of the hyperspherical coupling matrix elements, thereby leading to a phase shift that tends to zero, as the energy goes to zero, instead of to a constant. We consider two particles interacting with binary repulsive step potentials, one acting as a spectator, and solve analytically for the adiabatic eigenvalues and eigenvectors, for all values of rho. We are thereby able to obtain the leading terms in the long range behaviour of the effective potentials, and confirm its inverse logarithmic nature, suggested from a previous numerical study.
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