The ground state and doubly excited $^{1,3}$\textit{P}$^{o}$ states of the plasma-embedded Li$^{+}$ ion*

With the recent advancement for laser plasmas in laser fusion laboratories [1] and with the recent experimental measurement on the doubly excited resonances in photo-ionization spectrum of Li$^{+}$ using the photon-ion merged-beam at the Advanced Light Source [2], it is of interest to investigate the bound states and resonance states of Li$^{+}$ under the influence external environments produced by the charge-neutral background such as that of a plasma. The plasma effect is taken care of by using a screened Coulomb potential obtained from the Debye model. A correlated wave function has been used to represent the correlation effect between the charged particles. The ground state of Li$^{+}$ in plasmas for different screening parameters has been estimated in the framework of Rayleigh-Ritz variational principle. In addition, a total of 18 resonances (9 each for $^{1}P^{o}$ and $^{3}P^{o}$ states) below the $n=$2 Li$^{+}$ thresholds has been estimated by calculating the density of states using the stabilization method. The resonance energies and widths for various Debye parameters ranging from infinity to a small value for these $^{1,3}P^{o}$ resonance states are reported. [1] S . NaKai, K. Mima\textbf{,} \textit{Rep. Prog. Phys. }\textbf{67}, 321 (2004). [2] S. W. J. Scully \textit{et al},\textit{ J. Phys. B} \textbf{39}, 3957 (2006).