Eur. Phys. J. D 55, 581–589 (2009) DOI: 10.1140/epjd/e2009-00238-x Regular Article T HE EUROPEAN P HYSICAL JOURNAL D Positron scattering from hydrogen atom embedded in weakly-coupled plasmas A. Ghoshal a and Y.K. Ho Institute of Atomic and Molecular Sciences, Academia Sinica, P.O. Box 23-166, Taipei, Taiwan 106, P.R. China Received 7 June 2009 / Received in final form 14 July 2009 Published online 4 September 2009 – c  EDP Sciences, Societ`a Italiana di Fisica, Springer-Verlag 2009 Abstract. Elastic scattering of positrons from the hydrogen atoms in weakly-coupled plasmas has been studied using an expression for partial wave scattering amplitude that has been derived within the frame- work second order distorted wave Born approximation. The interactions among the charged particles in the plasma have been represented by Debye-H¨ uckel potentials. A detailed study has been made on differential and total cross sections in the energy range 20–300 eV. To the best of our knowledge such a study on the differential and total cross sections for elastic positron-hydrogen collisions in a weakly-coupled plasma environment is reported for the first time in the literature. PACS. 34.80.Bm Elastic scattering – 52.20.Hv Atomic, molecular, ion, and heavy-particle collisions 1 Introduction Atomic collision processes in hot, dense plasmas have been the subject of continuous interest during the last several years [1–14] (and further references therein). The motiva- tion behind this interest is mostly due to the spectroscopy of such plasmas [5]. Moreover, the collision processes in plasmas play a crucial role in determining radiation and transport properties of the plasmas. Among the collision processes, excitation and ionization processes have been paid much emphasis theoretically [2,6,7,9–14], and in most of these studies, plasmas screening effect has been repre- sented by Debye-H¨ uckel potential. Of course, there are increasing activities to study the effect of Debye screening on atomic processes [15–27]. A classical plasma is said to be collisionless or ideal when long-range self-consistent interactions (described by the Poisson equation) dominate over short-range two- particle interactions (collisions). This takes place when the potential energy of two particle separated by an average interparticle distance is small compared to the average ki- netic energy. In other words, the ratio of the potential energy to the average kinetic energy, called the coupling parameter, is much less than unity. Such plasmas are also known as weakly-coupled plasmas. The effect of such plas- mas on a test charge is to replace the Coulomb potential by an effective screened potential. This effective screened Coulomb potential (SCP) is known as the Debye-H¨ uckel a Permanent address: Department of Mathematics, Burdwan University, Golapbag, Burdwan 713104, West Bengal, India e-mail: arijit98@yahoo.com potential and is given by [1,2]: V (r) = (1/r)e -λr (in a.u.), (1) where 1/λ(= D = v T /ω p ) is the Debye length, v T and ω p are the thermal velocity and plasma frequency respec- tively. A particular value of D corresponds to a range of plasma conditions. Smaller values of D or larger val- ues of λ correspond to stronger screening. However, the Debye-H¨ uckel model would not be reliable to investigate the physical properties of the plasmas with the increase of plasma density due to the multi-particle cooperative in- teractions [28]. Recently Shukla and Eliasson [29] have showed that the effective screened potential of a test charge of mass m in a dense quantum plasma can be mod- eled by a modified Debye-H¨ uckel potential or exponential- cosine-screened Coulomb potential (ECSCP), V (r) = (1/r)e -λr cos (λr) (in a.u.), (2) rather than Debye-H¨ uckel potential (1). Here λ is related to the plasma frequency ω p by means of the relation λ = ω p /(ω p /m) 1/2 . Basically, when the de Broglie wave- length of the charge carriers is comparable to the Debye length, the quantum mechanical effect is significant in the Debye shielding. If a plasma is cooled to low-temperature, the de Broglie wavelength of the charge carriers may be comparable to the various scale-lengths of the systems, e.g., the Debye length, Larmor radius, etc. Again, the static Debye screening formula (1) would not be reliable when the thermal velocity is smaller than the velocity of the projectile since the projectile polarizes the surround- ing plasma medium [30]. The dynamic interaction poten- tial between a projectile (say electron) with velocity v and