柱谐振子基中的高斯矩阵元
Gaussian matrix elements in a cylindrical harmonic oscillator basis
摘要：
我们推导出一种形式主义，分离法，在圆柱谐振子基础上的高斯势的两体矩阵元的有效和准确的计算。这种形式主义是至关重要的Hartree-Fock和Hartree-Fock-Bogoliubov计算在变形核中使用现实的，有限范围的有效相互作用核子。这里给出的结果也与原子和分子物理中的微观多体计算有关，因为形式主义可以应用于高斯形式之外的其他类型的相互作用。推导非常详细地强调的方法，它依赖于生成函数。由此产生的高斯矩阵元素的解析表达式检查的速度和精度作为振荡器壳的数量的函数，并对直接数值积分。
英文摘要：
We derive a formalism, the separation method, for the efficient and accurate calculation of two-body matrix elements for a Gaussian potential in the cylindrical harmonic-oscillator basis. This formalism is of critical importance for Hartree-Fock and Hartree-Fock-Bogoliubov calculations in deformed nuclei using realistic, finite-range effective interactions between nucleons. The results given here are also relevant for microscopic many-body calculations in atomic and molecular physics, as the formalism can be applied to other types of interactions beyond the Gaussian form. The derivation is presented in great detail to emphasize the methodology, which relies on generating functions. The resulting analytical expressions for the Gaussian matrix elements are checked for speed and accuracy as a function of the number of oscillator shells and against direct numerical integration.
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