Ground and doubly excited states of He atom in non-ideal classical plasmas: structural, entanglement and information theoretical measures

Santanu Mondal; Sujay Kr. Nayek; Jayanta K. Saha

doi:10.1140/epjp/s13360-022-02574-1

2024 Impact factor 2.9

EPJ PLUS - Condensed Matter and Complex Systems

Eur. Phys. J. Plus (2022) 137: 373
https://doi.org/10.1140/epjp/s13360-022-02574-1

Regular Article

Ground and doubly excited states of He atom in non-ideal classical plasmas: structural, entanglement and information theoretical measures

Santanu Mondal¹, Sujay Kr. Nayek² and Jayanta K. Saha¹^c

¹ Department of Physics, Aliah University, IIA/27, Newtown, 700160, Kolkata, India
² Department of Mathematics, Netaji Nagar Day College, 700092, Kolkata, India

^c jksaha.phys@aliah.ac.in

Received: 5 January 2022
Accepted: 7 March 2022
Published online: 21 March 2022

Abstract

Structural properties of ground ( $1 s^{2}$ $$1s^2$$ : $^{1}$ $$^1$$ S $^{e}$ $$^e$$ ) and first doubly excited resonance ( $2 s^{2}$ $$2s^2$$ : $^{1}$ $$^1$$ S $^{e}$ $$^e$$ ) states of He atom embedded in non-ideal classical plasma (NICP) environment are studied under the Ritz variational framework in conjunction with Hylleraas-type basis set. Suitable model potential, being an explicit function of density and temperature, is used to replicate the interaction between the charge particles inside NICP. Stabilization method is adopted to determine the resonance parameters (position and width) of the doubly excited state. The behaviour of different energy components of both the states of He atom under NICP has been examined thoroughly. We have made a comparative study on the influence of NICP and the ideal classical plasma (ICP) modelled by Debye-Hückel potential on the energy level of He atom. It is observed that the effect of NICP is much prominent as compared to the effect of ICP on the bound as well as on the resonance states of He atom. The ionization potential for both the states of He atom under NICP shows declining trend as the density of the NICP increases, and furthermore, the increment in the temperature of the NICP mitigates the rate of such declination. The effect of NICP on different geometrical properties e.g. radial moments [ $⟨ r_{1} ⟩$ $\langle r_1 \rangle$ , $⟨ r_{12} ⟩$ $\langle r_{12} \rangle$ , $⟨ r_{1}^{2} ⟩$ $\langle r_1^2 \rangle$ , $⟨ r_{12}^{2} ⟩$ $\langle r_{12}^2 \rangle$ , $⟨ r_{<} ⟩$ $\langle r_< \rangle$ and $⟨ r_{>} ⟩$ $\langle r_> \rangle$ ], angular moments [ $⟨ θ_{1} ⟩$ $\langle \theta _1 \rangle$ , $⟨ θ_{12} ⟩$ $\langle \theta _{12} \rangle$ ], one- and two-electron delta functions [ $⟨ δ ({\vec{r}}_{1}) ⟩$ $\langle \delta (\vec {r}_1) \rangle$ , $⟨ δ ({\vec{r}}_{12}) ⟩$ $\langle \delta (\vec {r}_{12}) \rangle$ ] corresponding to both the states of He atom has been estimated. The flattening of the electronic charge distribution w.r.t. the increment in plasma density is clearly demonstrated by computing the respective one- and two-electron radial charge densities. We have also reported the measures of quantum entanglement and quantum information in terms of von Neumann, Linear and Shannon entropies for different sets of NICP parameters.