Bound and resonance states of positronic copper atoms

Abstract

We report a theoretical calculation for the bound and S-wave resonance states of the positronic copper atom (e + Cu). A positron is a positively charged particle; therefore, a positronic atom has an attractive correlation between the positron and electron. A Gaussian expansion method is adopted to directly describe this correlation as well as the strong repulsive interaction with the nucleus. The correlation between the positron and electron is much more important than that between electrons in an analogous system of Cu − , although the formation of a positronium (Ps) in e + Cu is not expressed in the ground state structure explicitly. Resonance states are calculated with a complex scaling method and identified above the first excited state of the copper atom. Resonance states below Ps (n=2) + Cu + classified to a dipole series show agreement with a simple analytical law. Comparison of the resonance energies and widths of e + Cu with those of e + K, of which the potential energy of the host atom resembles that of e + Cu, reveals that the positions of the resonance for the e + Cu dipole series deviate equally from those of e + K.

Four-body variational calculation of a hydrogen-like atom involving an excited muonic molecule

“…In the present calculation, we consider a Schrödinger equation (H − E ν )Ψ ν = 0 where the fourbody Hamiltonian H contains kinetic energy operators (separated from the center-of-mass motion) and all inter-particle Coulomb potential energy operators. We adopt a Gaussian expansion method (see reviews [17][18][19] and our recent calculations [20][21][22][23][24]) for the four-body wave function Ψ ν . The Ψ ν is expanded in terms of Gaussian basis functions ϕ il (r) = N il r l exp(−r 2 ) (N il is a normalization constant) and spherical harmonics as follows:…”

Three-body resonance states just below the antiproton and hydrogen dissociation threshold

“…The total Hamiltonian for pH is written as In order to describe the all inter-particle correlation of the near-threshold resonance states precisely, we adopt a Gaussian expansion method (GEM) [34]. Recently the GEM approach successfully revealed the near-threshold resonances in positronic atom systems [35][36][37]. Besides, this approach can be applied to the four-body system HH in the same theoretical framework [33,38].…”

Coupled channel study of antihydrogen-hydrogen molecular resonance state

“…It has been pointed out that the positron cannot form a bound state with a neutral hydrogen atom and helium atom; therefore, the simplest positronic atom is a positronic lithium atom (e + Li) whose electronically stable bound state was theoretically proved by a precise calculation in 1997 [5,6]. Theoretical investigations performed since then have revealed that positronium (Ps, a bound state of e + and e − ) formation by configuration rearrangement can contribute to the binding mechanism of the positronic atoms [7][8][9][10][11]. A host atom like lithium, whose ionization energy is smaller than the binding energy of positronium, can capture the Ps by the electric field of the residual ion.…”