A theoretic model to investigate the dynamics of the longitudinal nucleus-acoustic waves (NAWs) in gyrogravitating electrostatically confined degenerate quantum plasma (DQP) system in spherically symmetric geometry is constructed. The model setup consists of non-degenerate heavy nuclear species (HNS), lighter nuclear species (LNS), and quantum degenerate electronic species (DES). It specifically considers the influences of the Bohm potential, Coriolis rotation, viscoelasticity, and electrostatic confinement pressure (ECP, scaling quadratically in density). A standard normal spherical mode analysis gives a generalized dispersion relation (septic). It highlights the dependency of various atypical instability response on the equilibrium plasma parameters. A numerical illustrative platform portrays that the relative nuclear charge-to-mass coupling parameter (\(\beta\)) acts as a destabilizing agency and the heavy-to-light nuclear charge density ratio (\(\mu\)) acts as a stabilizing agency in both the non-relativistic (NR) and ultra-relativistic (UR) limits. Another interesting conjuncture is that the Coriolis rotation introduces a destabilizing influence on the system in both the limits. The progressive analysis presented herein has correlations and consistencies in the dynamic growth backdrop of various compact astro objects and their circumvent atmospheres, such as white dwarfs, neutron stars, etc.

构建了一个理论模型，用于研究球对称几何中旋转引力静电约束简并量子等离子体 (DQP) 系统中纵向核声波 (NAW) 的动力学。模型设置由非简并重核物种 (HNS)、轻核物种 (LNS) 和量子简并电子物种 (DES) 组成。它特别考虑了玻姆势、科里奥利旋转、粘弹性和静电限制压力（ECP，密度按二次方缩放）的影响。标准法向球面模式分析给出了广义色散关系（化粪池）。它强调了各种非典型不稳定性响应对平衡等离子体参数的依赖性。\(\beta\) ) 充当不稳定机构，而重轻核电荷密度比 ( \(\mu\) ) 在非相对论 (NR) 和超相对论 ( NR ) 中充当稳定机构 ( UR) 限制。另一个有趣的结合是科里奥利旋转在两个极限中都对系统产生了不稳定的影响。本文提出的渐进分析在各种致密天体及其周围大气（如白矮星、中子星等）的动态增长背景中具有相关性和一致性。