Binding energies, oscillator strengths, and polarizabilities of hydrogen-like atoms embedded in dense quantum plasmas are calculated in high precision by employing the generalized pseudospectral method. Benchmark predictions of these quantities are obtained for both the ground and excited states including high-order transitions. The critical behaviour of system eigenenergies, radial mean values, oscillator strengths, and multipole polarizabilities for bound states when they approach to the corresponding continuum limit as increasing the plasma screening strength are investigated in detail. It is shown that near the critical screening parameters the quantities in s-wave states show distinct behaviour from those in non-s states and such phenomenon is attributed to the divergent asymptotic form of wave functions caused by the centrifugal potential of orbital angular momentum. Based on the power laws of energies and radial mean values extracted from numerical calculations and the approximate formulae for dipole polarizabilities, the critical behaviour of the 2 ^k -pole polarizability of s-wave states is explicitly derived and numerically validated to follow a power law with the exponent −2(k + 1).

通过使用广义伪光谱方法，可以高精度计算嵌入密集量子等离子体中的类氢原子的结合能、振荡器强度和极化率。这些量的基准预测是针对基态和激发态（包括高阶跃迁）获得的。详细研究了系统特征能量、径向平均值、振子强度和束缚态多极极化率随着等离子体屏蔽强度的增加而接近相应的连续介质极限时的临界行为。结果表明，在临界筛选参数附近，s波状态的量表现出与非s波状态不同的行为。状态和这种现象归因于由轨道角动量的离心势引起的波函数的发散渐近形式。基于从数值计算中提取的能量幂律和径向平均值以及偶极极化率的近似公式，明确推导出s波态的 2 ^k极极化率的临界行为并通过数值验证遵循幂律指数 -2( k + 1)。