1 3 J IRAN CHEM SOC DOI 10.1007/s13738-017-1090-4 ORIGINAL PAPER Theoretical investigation of scattering of an atomic projectile confined in a harmonic surface potential Maryam Mansoori Kermani 1 · Ali Maghari 1 Received: 6 January 2017 / Accepted: 28 February 2017 © Iranian Chemical Society 2017 model does agree surprisingly well with the experimental results was proposed by Logan and Stickney [5]. A hard- cube model of gas-surface collision, in which the surface is assumed a cube to move only in the direction normal to the surface, was introduced by Grimmelmann et al. [6], Good- man [7] and later by Goodman and Tan [8, 9]. Within the classical Wigner formalism about the scattering of atoms from surface, a new analytic expression for angular distri- bution and its surface temperature dependence was studied by Adelman and Doll [10]. The first study of the scatter- ing quantum theory of gas/solid interactions was done by Jackson and Mott [11]. This investigation developed by Lennard-Jones, Devonshire and Strachan via considering the Morse potential interactions [12, 13]. Washboard model of gas-surface scattering that was an extension of hard and soft cube models of gas-surface scattering was considered by Tully [14] and was extended by Yan et al. [15]. An ana- lytic model for the scattering intensity pattern via first order in the inelastic atom-surface interactions was presented by Adams and Miller [16] that is in qualitative agreement with experimental results. Winter studied the scattering of fast atoms and ions from solid surfaces under a grazing angle of incidence [17]. The energy transfer in gas-surface collision from gas-phase models was investigated by Nogueira et al. [18]. Once a beam of atomic projectiles collides with a sur- face, a fraction of atoms may be directly scattered and the other atoms can be trapped in the potential well of the sur- face. At low incident particle energies, trapping into the physisorption well at the surface is significant, whereas at higher energies the scattering from the surface should become important process. The scattering of atomic gas in extremely low density from the solids including the effects of lattice motions is a useful tool to study the struc- ture of surfaces [19]. If the energy of incident beam is in Abstract In this paper, scattering of a projectile atomic gas confined in an atomic harmonic surface is studied using the Lippmann–Schwinger. The nonlocal separable potential of rank one has been assumed between the pro- jectile gas and surface, because this potential is useful to investigate the few-body systems. The analytical solution of Lippmann–Schwinger equation has been derived, and the scattering properties including transition and scattering matrices, phase shift, scattering amplitude and time delay are calculated analytically as a function of incident atomic gas energies. Keywords Lippmann–Schwinger equation · Nonlocal separable potential · Harmonic confinement Introduction Understanding the gas-surface collision via a simple math- ematical model is of much interest and can help to interpret the experimental and simulation data. Structural defects that prepare discrete centers in the lattice of crystals act- ing as the trapping/scattering centers are made during the fabrication process of surfaces. The collision of a gas atom with a solid surface is a fundamental inelastic process. The- oretical investigation of gas-surface interactions has been done by both classical [1] and quantum viewpoint [2–4]. A simple classical model for the scattering of gas atoms from a solid surface in which the qualitative behavior of the * Ali Maghari maghari@ut.ac.ir 1 Department of Physical Chemistry, College of Science, University of Tehran, Tehran 14155-6619, Iran