S-wave resonances below the Ps( $$n=2$$ n = 2 ) threshold in positronic sodium interacting with screened Coulomb poten
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ORIGINAL PAPER
S-wave resonances below the Ps(n ¼ 2) threshold in positronic sodium interacting with screened Coulomb potentials N Masanta1, A Ghoshal1*
and Y K Ho2
1
Department of Mathematics, Burdwan University, Golapbag, Burdwan, West Bengal 713 104, India
2
Institute of Atomic and Molecular Sciences, Academia Sinica, P.O. Box 23-166, Taipei 106, Taiwan Received: 18 May 2019 / Accepted: 26 July 2019
Abstract: S-wave resonance states of the positronic sodium atom (eþ Na) interacting with screened Coulomb potentials (SCP) are studied. Two different SCPs are tested, namely static screened Coulomb potential (SSCP) and exponential cosine screened Coulomb potential (ECSCP). Resonance states are calculated by the stabilization method. Four S-wave resonance Psð2Þ states are found to exist lying below the Ps(n ¼ 2) excitation threshold (Eex ). For free atomic system, our reported results of resonance energy compare nicely with the reliable results available in the literature. To the best of our knowledge, our present results will be the first reported results of resonance of positronic–sodium atom under a screened environment. Keywords: Positron; Sodium; Resonance; Stabilization method; Screened Coulomb potential PACS Nos.: 32.10.-f; 34.80.Uvc; 36.10.Dr; 52.20.Hv
1. Introduction Substantial efforts have been made to study the formation and structure of positronic atoms (atoms formed by the attachment of a positron to a neutral atom) over the past few years [1–21]. Ryzhikh and Mitroy were the first who conclusively proved the existence of electronically stable bound state of a positronic lithium atom (eþ Li) by performing a large variational calculation using the stochastic variational method in 1997 [21]. So far, there exists a plenty of reliable calculations which show that many atoms in their ground state (and even in excited states) can bind a positron forming an electronically stable system [4, 5]. As positron is the anti-particle of electron, positronic atoms show different nature from ordinary atoms, such as a halo structure [14] and an enhancement of relativistic effects [2, 3]. A positronic alkali atom can be regarded as one of the best systems for investigating the nature of positronic atoms. Positronic alkali atoms have at most one bound state and a number of resonance states associated with various positronium (Ps) formation thresholds [1]. A number of theoretical
investigations have been made to study the bound states of positronic alkali atoms [4–11]. Being the quasi bound states of an excited Ps and atomic ion, or an excited atom and a positron, resonance states of positronic atoms have more exotic structures than bound states. These states can be viewed as intermediate states in the formation of bound states of positronic atoms by charge-transfer reaction and laser-assisted photo-recombination [1]. Existence of resonant structures associated with atomic excited states in the positron scattering spectrum also serves as a possible signature for positron-atom binding [4]. Effects of screened interact
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