轴呼吸模式下核费米液体的超平均场有效质量
Beyond--mean--field effective masses in the nuclear Fermi liquid from axial breathing modes
摘要：
本文用核能密度泛函理论研究了轴向呼吸模，讨论了平均场近似下核子有效质量的修正。用减二次无规相位近似（SSRPA）模型对$^{48}$ Ca和$^{90}$ Zr两个核进行了分析。通过分析基于平均场的随机相位近似和超平均场SSRPA模型得到的轴向呼吸模式的质心能量，我们估计了在平均场之外引起的有效质量的修正（增强）。这是通过使用由朗道费米液体理论获得的轴向模式的激发频率与$\sqrt{m/m^*}$之间的关系来完成的，其中$m$（$m^*$）是裸（有效）质量。这种增强的有效质量进行了讨论与单粒子激发能的能量相关的SSRPA自能校正所产生的重整化。我们发现，自能修正产生的单粒子谱的有效超平均场压缩与轴向呼吸模估计的有效质量的增加是一致的。
英文摘要：
Axial breathing modes are studied within the nuclear energy--density--functional theory to discuss the modification of the nucleon effective mass produced beyond the mean--field approximation. This analysis is peformed with the subtracted second random--phase--approximation (SSRPA) model applied to two nuclei, $^{48}$Ca and $^{90}$Zr. Analyzing the centroid energies of axial breathing modes obtained with the mean--field--based random--phase approximation and with the beyond--mean--field SSRPA model, we estimate the modification (enhancement) of the effective mass which is induced beyond the mean field. This is done by employing a relation, obtained with the Landau's Fermi liquid theory, between the excitation frequency of axial modes to $\sqrt{m/m^*}$, where $m$ ($m^*$) is the bare (effective) mass. Such an enhancement of the effective mass is discussed in connection with the renormalization of single--particle excitation energies generated by the energy--dependent SSRPA self-energy correction. We find that the effective beyond--mean--field compression of the single--particle spectrum produced by the self--energy correction is coherent with the increase of the effective mass estimated from the analysis of axial breathing modes.
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