The stability of the ground state for positronic sodium

Abstract

The existence of a stable ground state for the exotic Nae + atom is demonstrated by using a modified version of the stochastic variational method to solve the Schrödinger equation for a positron and valence electron moving under the influence of a model potential. The model potential consists of the direct interaction between the positronium and the Hartree-Fock wavefunction for the alkali ion. The exchange potential between the valence electron and the core electrons is approximated with a local potential. The structure of positronic sodium is best described as a slightly stretched and polarized positronium atom orbiting the Na + core at distances of the order of 10-30 a 0 . It is found that positronic sodium is stable against decay into Ps + Na + with a binding energy of 0.000 177 Hartree.

Theory and application of explicitly correlated Gaussians

“…The effective interaction can be based on a microscopic model of the core wave function, or a more empirical model potential approach can be adopted. An example of the microscopic approach is the series of calculations demonstrating positron binding to a variety of atoms (Ryzhikh, Mitroy, and Varga, 1998b). The core wave function was represented by a HF wave function.…”

“…The direct interaction with the core was straightforward to compute since this was effectively a single-particle potential. The exchange interaction with the core could also be computed provided the core single electron orbitals were expanded as a linear combination of Gaussians (Ryzhikh, Mitroy, and Varga, 1998b). Model potentials used to describe interactions with closed-shell systems tend to be more phenomenological in nature.…”

“…This makes the ECG basis sets suitable for treating systems with attractive interactions that result in strong interparticle correlations. Examples of such systems include small nuclear systems with tendencies to form -particle clusters (Varga, Suzuki, and Tanihata, 1995), exotic positron-atom systems with a tendency to form positronium clusters (Ryzhikh, Mitroy, and Varga, 1998b), and excitonic systems Varga, 2000, 2001). The ECG basis has also been generalized to handle systems with strongly repulsive interactions (or ''hard-core'' potentials) (Kinghorn and Adamowicz, 1999b;Stanke et al, 2006).…”

Positron-Atom Complexes as Quantum Halo States

“…The wave functions for e Li [11,12], e He 3 S e [13,14], e Na [11,15], e Be [11,16], e Cu [17,18], and e Mg [11,16] were all computed using the fixed core stochastic variational method (FCSVM) [11,19].…”

“…The FCSVM uses a basis of explicitly correlated Gaussians (ECG) [11,19]. In the FCSVM, the Hamiltonian is diagonalized in a large basis of energy optimized ECGs.…”