Extension of the correlated Gaussian hyperspherical method to more particles and dimensions
Extension of the correlated Gaussian hyperspherical method to more particles and dimensions
复制标题
将相关高斯超球面方法扩展到更多粒子和维度
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
C. Greene
中科院分区：
文献类型：
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作者：
K. Daily;C. Greene
基于显式相关高斯函数的少体系统超角Schr\ odinger方程的求解仍然具有数值挑战性。这部分是由于随着系统规模的增长所需的基函数的数量，但也由于数值积分的数量随着超角自由度的增加而增加的事实。本文表明，后一种挑战已不复存在。使用delta函数来固定超半径R，所有矩阵元素的计算都简化为单个数值积分，而不管系统大小n或维数d。在$d$为偶数的特殊情况下，非相互作用系统的矩阵元素是完全解析的。我们演示了新的矩阵元素在具有零总角动量$L$、正宇称$\pi$和可变自旋$S_+$和$S_-$的3体、4体和5体电子-正电子系统中的应用。
The solution of the hyperangular Schr\"odinger equation for few-body systems using a basis of explicitly correlated Gaussians remains numerically challenging. This is in part due to the number of basis functions needed as the system size grows, but also due to the fact that the number of numerical integrations increases with the number of hyperangular degrees of freedom. This paper shows that the latter challenge is no more. Using a delta function to fix the hyperradius $R$, all matrix element calculations are reduced to a single numerical integration regardless of system size $n$ or number of dimensions $d$. In the special case of $d$ an even number, the matrix elements of the noninteracting system are fully analytical. We demonstrate the use of the new matrix elements for the 3-, 4-, and 5-body electron-positron systems with zero total angular momentum $L$, positive parity $\pi$, and varied spins $S_+$ and $S_-$.