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arXiv 0906.5239nucl-th
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核光吸收截面的自洽计算:三维实空间中Skyrme泛函有限振幅法

Self-consistent calculation of nuclear photoabsorption cross section: Finite amplitude method with Skyrme functionals in the three-dimensional real space

Tsunenori Inakura, Takashi Nakatsukasa, Kazuhiro Yabana

摘要:

我们最近提出的有限振幅法(FAM)(T。Nakatsukasa,T. Inakura和K. Yabana,Phys.Rev.C76,024318(2007))显著简化了完全自洽的RPA计算。采用FAM,我们正在进行系统的,完全自洽的响应计算广泛的质量区域。本文的目的是提出一个计算方案中使用的系统的调查,并显示一个现实的Skyrme能量泛函的FAM的性能。我们实现的方法在混合表示,其中的前向和后向RPA振幅表示的指数的单粒子轨道的占用状态和未占用状态的空间网格点。我们求解给定频率的线性响应方程。该方程是一个具有稀疏非厄米矩阵的线性代数问题,用迭代法求解。我们显示的偶极子响应选定的球形和变形核的结果。巨偶极共振的峰值能量与重核的测量结果吻合得很好,而轻核的峰值能量则被系统地低估了。我们还讨论了在完全自洽RPA计算中巨偶极共振的宽度。

英文摘要:

The finite amplitude method (FAM), which we have recently proposed (T. Nakatsukasa, T. Inakura, and K. Yabana, Phys. Rev. C 76, 024318 (2007)), simplifies significantly the fully self-consistent RPA calculation. Employing the FAM, we are conducting systematic, fully self-consistent response calculations for a wide mass region. This paper is intended to present a computational scheme to be used in the systematic investigation and to show the performance of the FAM for a realistic Skyrme energy functional. We implemented the method in the mixed representation in which the forward and backward RPA amplitudes are represented by indices of single-particle orbitals for occupied states and the spatial grid points for unoccupied states. We solve the linear response equation for a given frequency. The equation is a linear algebraic problem with a sparse non-hermitian matrix, which is solved with an iterative method. We show results of the dipole response for selected spherical and deformed nuclei. The peak energies of the giant dipole resonance agree well with measurements for heavy nuclei, while they are systematically underestimated for light nuclei. We also discuss the width of the giant dipole resonance in the fully self-consistent RPA calculation.

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