Computer Physics Communications 182 (2011) 122–124 Contents lists available at ScienceDirect Computer Physics Communications www.elsevier.com/locate/cpc Doubly excited resonance states of two-electron systems in exponential cosine-screened Coulomb potentials Arijit Ghoshal ∗,1 , Y.K. Ho Institute of Atomic and Molecular Sciences, Academia Sinica, P.O. Box 23-166, Taipei, Taiwan 106 article info abstract Article history: Received 28 January 2010 Accepted 27 May 2010 Available online 4 June 2010 Keywords: Doubly excited resonance states Stabilization method Density of the resonance states Exponential cosine-screened Coulomb potential Correlated wave function We have made an investigation on the 2s 21 S e resonance states in two-electron systems interacting with exponential cosine-screened Coulomb potentials (ECSCP) within the framework of stabilization method. Highly correlated wave functions are used to take into account the correlations of the charge particles. Results for resonance energies and widths are reported for Z = 1, 2 and 3. For the unscreened case, our reported results are in nice agreement with the results so far available in the literature.  2010 Elsevier B.V. All rights reserved. 1. Introduction The study of atomic processes for which particles are interact- ing with exponential-cosine screened Coulomb potential (ECSCP) with screening parameter μ, V (r ) = (1/r )e −μr cos (μr ) (in a.u.), (1) is currently an interesting topic of research [1–5] (and further ref- erences therein). The screening parameter μ shortens the range of the potential in comparison to the Coulomb potential. Exponential cosine-screened Coulomb potentials are widespread in many dif- ferent areas of physics, such as, solid-state physics, nuclear physics, plasma physics [2–5]. These potentials differ from the well-known screened Coulomb potentials (SCP) with screening parameter μ, V (r ) = (1/r )e −μr (in a.u.), (2) from the existence of the cos (μr ) term, as a result an ECSCP ex- hibits stronger screening effect than an SCP. In this paper our objective is to investigate the 2s 21 S e autoion- ization resonance states of a system consisting of a nucleus of charge Ze and two electrons interacting via ECSCP. Investigation of the autoionization states of an atomic system is of utmost im- portance in several respects [6] and indeed there is a continuous * Corresponding author. E-mail address: arijit98@yahoo.com (A. Ghoshal). 1 Permanent affiliation: Department of Mathematics, Burdwan University, Golap- bag, Burdwan 713 104, West Bengal, India. interest to investigate autoionization states of two-electron sys- tems [3–5,7]. Moreover, investigation on two-electron systems in ECSCP is also important role owing to the role played by the cor- relation effects between the charged particles. We have designed this paper as follows. Describing the underlying theory and calcu- lations of our investigation in Section 2 we present and discuss our computed results in Section 3. Finally, in Section 4 we give our concluding remarks. The atomic units (a.u.) are used throughout the present work, and all calculations are performed in quadruple precision (32 sig- nificant figures) on IBM–AMD workstations in UNIX environment. 2. Theory and calculations The non-relativistic Hamiltonian of a system consisting of a nu- cleus of charge Ze and two electrons interacting via ECSCP is given by H =− 1 2 ∇ 2 1 − 1 2 ∇ 2 2 − Z  e −μr 1 r 1 cos (μr 1 ) + e −μr 2 r 2 cos (μr 2 )  + e −μr 12 r 12 cos (μr 12 ), (3) where r 1 and r 2 are the coordinates of the two electrons relative to the nucleus (assumed to be at rest), and r 12 is their relative distance. In order to determine 1 S e states, we have employed the wave function 0010-4655/$ – see front matter  2010 Elsevier B.V. All rights reserved. doi:10.1016/j.cpc.2010.05.010