Ground state and resonant states of helium in exponential cosine screened Coulomb potential

We have investigated the ground state and a resonance state of normal helium atom in exponential cosine screened Coulomb potential (ECSCP) with screening parameter$\lambda $: $V(r)\,=\,-\,\frac{1}{r}\,e^{-\lambda r}\cos (\lambda r)$ (in a.u.), where $r$ denotes the inter-particle distance. Within the framework of Ritz's variational principle and making use of a highly correlated wave function, we have determined the ground state energies and wave functions of the helium atom for different values of the screening parameter$\lambda $. Furthermore, we have shown that the ground state energy of helium for a particular value of $\lambda $ does converge with increasing number of terms in the wave function. In addition, using the stabilization method, we have investigated the doubly excited $2s^{2} \quad ^{1}S^{e}$ resonance state in helium with ECSCP. Resonance energy and width for various $\lambda $ values are calculated. Our present work will play a useful role in the investigations of atomic structures in quantum plasmas [1]. [1]. P.K. Shukla and B. Eliasson, \textit{Phys. Lett. A} \textbf{372,} 2899 (2008).