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arXiv 2211.09448nucl-th
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用能量密度泛函计算原子核和非均匀物质的费米算符展开方法

Fermi operator expansion method for nuclei and inhomogeneous matter with nuclear energy density functional

Takashi Nakatsukasa

备注：
14 pages, 16 figures
发表信息：
Phys. Rev. C 107, 015802 (2023)
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摘要：

有限温度下的能量密度泛函方法是研究高激发下原子核结构、恒星爆炸现象中的核物质和中子星的有用工具。然而，它的无限制计算需要大量的计算成本的三维坐标空间求解器，特别是对于哈密顿矩阵对角化和（或）的Gram-Schmidt正交归一化的单粒子波函数。我们测试的费米算子展开方法的数值性能，既不需要对角化，也不需要Gram-Schmidt正交归一化，有限核和非均匀核物质。将该方法应用于有限温度下孤立的有限N=Z核和非均匀对称核物质，结果表明，该方法在三维坐标空间表示下是非常有效的，特别是在高温下。费米算符展开方法是研究有限温度下各种核相的能量密度泛函计算的有效工具。该方法适用于分布式存储的大规模并行计算。此外，当空间大小较大时，计算可以受益于其N阶缩放属性。

英文摘要：

The nuclear energy density functional method at finite temperature is a useful tool for studies of nuclear structure at high excitation, and also for researches of nuclear matter involved in explosive stellar phenomena and neutron stars. However, its unrestricted calculation requires large computational costs for the three-dimensional coordinate-space solvers, especially for the Hamiltonian matrix diagonalization and (or) the Gram-Schmidt orthonormalization of the single-particle wave functions. We test numerical performance of the Fermi operator expansion method, that requires neither the diagonalization nor the Gram-Schmidt orthonormalization, for finite nuclei and inhomogeneous nuclear matter. The method is applied to isolated finite N=Z nuclei and to non-uniform symmetric nuclear matter at finite temperature, which turns out be very effective with the three-dimensional coordinate-space representation, especially at high temperature. The Fermi operator expansion method is a useful tool for studies of various nuclear phases at finite temperature with the energy density functional calculations. The method is suitable for massively parallel computing with distributed memory. Furthermore, when the space size is large, the calculation may benefit from its order-N scaling property.

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