Doubly Excited 1,3Fe States of Two-Electron Atoms under Weakly Coupled Plasma Environment *

Precise energy eigenvalues of metastable bound doubly excited $^{1,3}{\rm F}^{e}$ states originating from $2pnf$,($n=4$--6) configuration of helium-like ions $(Z=\text{2--4})$ under weakly coupled plasma (WCP) environment have been estimated within the framework of Ritz variational method. The wavefunction is expanded in explicitly correlated Hylleraas type basis set. The screened Coulomb potential is considered mimic the WCP environment. The atomic systems tend towards gradual instability and the number of excited metastable bound states reduces with increasing plasma strength. The wavelengths corresponding to $2pnf (^{1,3}{\rm F}^{e}) \rightarrow 2pn^\prime d (^{1,3}{\rm D}^{o})$ ($n=4$--6; $n^\prime=3$--6) transitions occurring between doubly excited states of plasma embedded two-electron ions are also reported.