一种改进的求解三体问题的超球方法

提出了一种改进的在超球坐标下高精度、高效率求解库仑三体束缚态的方法,并计算了弱束缚库仑三体体系氢负离子的基态能量.该方法利用B样条函数的高局域性和高可塑性质,通过优化样条节点分布得到了小基组情况下高精度的超球势曲线与道函数;利用离散变量表示（DVR）把超径耦合微分方程转化为超径本征值问题的求解,不仅减少了计算量也提高了数值计算的精度与稳定性,克服了以往直接求解超径耦合微分方程精度不高、计算量大的缺点.所得结果的迄今超球方法框架下最精确的结果之一,即8位有效数字的精度.

The Improved Hyperspherical Calculations of Three-Body Problem

In this paper, a highly accurate and effective method is proposed to solve the three body coulomb system in the hyperspherical coordinate and the energy of weakly bound ground states of the typical three body coulomb system is calculated. Applying the special feature of the B-spline function like the localization and flexibility a highly accurate hyper radius potential and the channel function is obtained by modifying the knots distribution of the B-spline basis, and it can be transformed into a hyper-radius generalized algebraic eigenvalue problem with discrete variable representation. Therefore we successfully reduce the calculation expense and improve the precision and stabilization for numerical calculation, overcome the defect of ordinary method such as low precision and the giant calculation expense, which is caused by direct solving the hyper-radius coupling differential equation. High accurate results with 8 digits precision is obtained, which is one of most accurate results of the hyperspherical coordinate up to now.