AI 中文总结
研究中重核$^{48}$Ti、$^{56}$Ni、$^{60}$Zn和$^{64}$Ge中电子俘获率，通过形变准粒子随机相位近似计算GT强度分布，评估恒星EC率，发现形变对GT强度分布影响大，对EC率影响除特定情况外较小，为恒星弱率中形变和形状共存作用提供微观约束。
AI 中文摘要
中重核中的电子俘获（EC）率由伽莫夫-泰勒（GT）强度分布决定，为恒星弱相互作用过程提供重要输入。本文研究了$pf$壳层及其附近选定中重核（即$^{48}$Ti、$^{56}$Ni、$^{60}$Zn和$^{64}$Ge）中GT强度和恒星EC率的形变依赖性。通过Skyrme SGII相互作用得到单粒子基，在形变准粒子随机相位近似（DQRPA）中计算GT$^{(+/-)}$强度分布，利用标准相空间形式从所得$B(\mathrm{GT}^+)$强度评估恒星EC率。用势能曲线识别所考虑核中的形状柔软性和可能的形状共存。发现形变通过改变质心能量等等强烈改变GT强度分布，特别是$^{56}$Ni和$^{64}$Ge的GT$^{(+/-)}$强度有明显形状依赖性，$^{60}$Zn有偏好的长椭球最小值，$^{48}$Ti呈现柔软的近球形/长椭球态势。除低温低密度处因电子相空间中负的EC $Q$值导致低能GT$^+$强度起决定性作用外，相应的EC率通常对形变的敏感性远低于微分GT响应本身。用$^{48}$Ti和$^{56}$Ni的可用电荷交换数据作为模型预测的基准。本结果为选定中重核（包括$N = Z$线附近的富质子同位素）恒星弱率中形变和形状共存的作用提供微观约束。
英文摘要
Electron-capture (EC) rates in medium-mass nuclei are governed by Gamow--Teller (GT) strength distributions and provide important input for stellar weak-interaction processes. In this work, we investigate the deformation dependence of the GT strengths and stellar EC rates in selected medium-mass nuclei in and near the $pf$ shell, namely $^{48}$Ti, $^{56}$Ni, $^{60}$Zn, and $^{64}$Ge. The GT$^{(+/-)}$ strength distributions are calculated in the deformed quasiparticle random-phase approximation (DQRPA) on a single-particle basis obtained by the Skyrme SGII interaction, while the stellar EC rates are evaluated from the resulting $B(\mathrm{GT}^+)$ strengths using the standard phase-space formalism. The potential-energy curves are used to identify shape softness and possible shape coexistence in the nuclei under consideration. We find that deformation strongly modifies the GT strength distributions by changing the centroid energies, resonance splitting, and fragmentation patterns. In particular, a pronounced shape dependence of the GT$^{(+/-)}$ strengths is found for $^{56}$Ni and $^{64}$Ge, whereas $^{60}$Zn is characterized by a favoured prolate minimum and $^{48}$Ti exhibits a soft near-spherical/prolate landscape. By contrast, the corresponding EC rates are generally much less sensitive to deformation than the differential GT response itself, except at low temperatures and low densities where the low-lying GT$^+$ strength becomes decisive because of the negative EC $Q$-value in the electron phase space. Available charge-exchange data for $^{48}$Ti and $^{56}$Ni are used as benchmarks of the model predictions. The present results provide microscopic constraints on the role of deformation and shape coexistence in stellar weak rates for selected medium-mass nuclei, including proton-rich isotopes near the $N = Z$ line.
Comments21pages, 11 figures
