Hydrogen-like ions in plasma environment

Behaviour of H-like atoms embedded in astrophysical plasmas in the dense plasma, strongly and weekly coupled plasmas have been investigated. In these plasmas, the change in temperature is impacted with the change in confinement radius $(r_{c})$. Two independent and generalised scaling ideas have been applied to modulate the effect of plasma screening constant ($\lambda$) and charge of ion ($Z$) on such systems. Several new equations related to various physico-chemical properties are derived to interconnect the original Hamiltonian and these two scaled Hamiltonian. A new Virial-like theorem has been established for plasma systems. Particularly, plasmas in strong spherical confinement does not obey the conventional Virial theorem. But this new form can serve the purpose successfully. In dense plasma (DP) and weekly couple plasma (WCP) these scaling idea have provided the opportunity to propose a linear equation connecting the critical screening constant $(\lambda_{c})$ and $Z$. Their ratio provides a state dependent constant, after which that particular state vanishes. Shannon entropy has been employed to understand the plasma effect on the ion. The competing effect of plasma charge density ($n_e$) and temperature in WCP is also investigated. Multipole ($k=1-4$) oscillator strength (OS) and polarizabilies for these three systems are studies considering $1s, 2s$ states. Detailed study reveals various interesting features for almost all the systems.