# MODEL ELECTRON-POSITRON CORRELATION POTENTIAL FOR LOW-ENERGY POSITRON-ATOM ELASTIC SCATTERING

#### Abstract

The wave function for positron-atom scattering is approximated in the trial form of (UNFORMATTED TABLE FOLLOWS) (PSI)((')r(,e),(')r(,p)) = (psi)((')r(,e),(')r(,p))(psi)(r(,p)). (1)(TABLE ENDS) The closed-channel function (psi)((')r(,e),(')r(,p)), a determinant of electronic function (phi)(,i), and the open-channel function (psi)((')r(,p)) can be found by applying the Hartree-Fock (HF) variational principle, (delta) (INT) (PSI)H(PSI)d(tau) = 0, subject to orthonormality constraints on the (phi)(,i)'s leads to uncoupled Schrodinger equations for the electrons and the positron. The positronic operators are replaced by a model potential V(,mp) in the Schrodinger equation for the electronic part, (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) where the Coulomb ((')J(,j)) and exchange ((')K(,j)) integrals are r(,p)-dependent. The proposed functional form of V(,mp) is (UNFORMATTED TABLE FOLLOWS) V(,mp)(r(,p),r(,(mu)p)) = 1 - ce(,n)('x)e('-x) (be('-ar(,(mu)p))/r(,(mu)p)), x = r(,p)/r(,0), (3)(TABLE ENDS) where a, b, c, r(,0), and n are disposable parameters and (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) The Schrodinger equation for the positron is a potential scattering equation: (UNFORMATTED TABLE FOLLOWS) -1/2(DEL)(,p)('2) + Z/r(,p) + V(,ep)(r(,p)) - k('2)/2 (phi)(,p)((')k,(')r(,p)). (4)(TABLE ENDS) The effective electron-positron interaction potential V(,ep) is obtained by subtracting the HF ground-state energy from the r(,p)-dependent electronic energy obtained by solving eq. (2). The parameters for V(,mp) are found such that the calculated V(,ep) leads to the known scattering lengths for the H-e('+) and He-e('+) systems. The calculated results for cross sections and annihilation parameters for both test systems are reasonably good as compared to other variational and approximate methods. The present results also suggest the model framework can be extended to other larger positron-atom systems.

#### Recommended Citation

CHIU, SEE-WING, "MODEL ELECTRON-POSITRON CORRELATION POTENTIAL FOR LOW-ENERGY POSITRON-ATOM ELASTIC SCATTERING" (1985). *Dissertations (1962 - 2010) Access via Proquest Digital Dissertations*. AAI8604950.

https://epublications.marquette.edu/dissertations/AAI8604950