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Physical Review A

Excited states of positronic atoms

M. W. J. Bromley, J. Mitroy

Published Apr 19, 2007• 17 citations
Publisher

Abstract

The existence and structure of positronic atoms with a total angular momentum of $L=1$ is studied with the configuration interaction method. Evidence is presented that there is a $^{2}P^{o}$ state of ${e}^{+}\mathrm{Ca}$ and $^{2,4}P^{o}$ states of ${e}^{+}\mathrm{Be}(^{3}P^{o})$ that are electronically stable with binding energies of $45\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ and $2.6\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$, respectively. These predictions rely on the use of an asymptotic series analysis to estimate the angular $L\ensuremath{\rightarrow}\ensuremath{\infty}$ limit of the energy. Incorporating corrections that compensate for the finite range of the radial basis increased the binding energies of ${e}^{+}\mathrm{Ca}$ and ${e}^{+}\mathrm{Be}$ to $71\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ and $42\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$, respectively.

DOI
10.1103/physreva.75.042506

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The existence and structure of positronic atoms with a total angular momentum of L=1L=1L=1 is studied with the configuration interaction method. Evidence is presented that there is a 2Po^{2}P^{o}2Po state of e+Ca{e}^{+}\mathrm{Ca}e+Ca and 2,4Po^{2,4}P^{o}2,4Po states of e+Be(3Po){e}^{+}\mathrm{Be}(^{3}P^{o})e+Be(3Po) that are electronically stable with binding energies of 45meV45\phantom{\rule{0.3em}{0ex}}\mathrm{meV}45meV and 2.6meV2.6\phantom{\rule{0.3em}{0ex}}\mathrm{meV}2.6meV, respectively. These predictions rely on the use of an asymptotic series analysis to estimate the angular L\ensuremath→\ensuremath∞L\ensuremath{\rightarrow}\ensuremath{\infty}L\ensuremath→\ensuremath∞ limit of the energy. Incorporating corrections that compensate for the finite range of the radial basis increased the binding energies of e+Ca{e}^{+}\mathrm{Ca}e+Ca and e+Be{e}^{+}\mathrm{Be}e+Be to 71meV71\phantom{\rule{0.3em}{0ex}}\mathrm{meV}71meV and 42meV42\phantom{\rule{0.3em}{0ex}}\mathrm{meV}42meV, respectively.
The stability and structure of the $({m}^{Z+},{e}^{\ensuremath{-}},{e}^{\ensuremath{-}},{e}^{+})$ system is studied as a function of the mass of the mZ+{m}^{Z+}mZ+ particle and for Z=1Z=1Z=1, 2, 3, and 10. The Z=1Z=1Z=1 system can be regarded as an analog of the APsA\mathrm{Ps}APs system (where AAA is a group I or IB atom of the periodic table) and was found to be stable for all values of m+{m}^{+}m+. This is supportive of the idea that all the group I and IB atoms can bind Ps. The $({m}^{2+},{e}^{\ensuremath{-}},{e}^{\ensuremath{-}},{e}^{+})$ system is stable for all ${m}^{2+}∕{m}_{e}\ensuremath{\leqslant}0.68$ and evolves into a configuration best described as $({m}^{2+},{\mathrm{Ps}}^{\ensuremath{-}})$ when ${m}^{2+}∕{m}_{e}\ensuremath{\rightarrow}0$. The $({m}^{3+},{e}^{\ensuremath{-}},{e}^{\ensuremath{-}},{e}^{+})$ system was stable for a mass range given by ${m}^{3+}∕{m}_{e}\ensuremath{\leqslant}0.066\phantom{\rule{0.2em}{0ex}}32$, which suggests that positrons could form Feshbach resonances in collisions with positive ions which are isolectronic with the group II and IIB columns of the periodic table. The $({m}^{3+},{e}^{\ensuremath{-}},{e}^{\ensuremath{-}},{e}^{+})$ system has the unusual property that it has a mass range where it becomes more compact while its binding energy simultaneously decreases. The $({m}^{10+},{e}^{\ensuremath{-}},{e}^{\ensuremath{-}},{e}^{+})$ system is also stable at m10+∕me=0.00254{m}^{10+}∕{m}_{e}=0.002\phantom{\rule{0.2em}{0ex}}54m10+∕me​=0.00254, which implies stability for all mass ratios less than 0.002 54. In total, the calculations suggest that the $({m}^{Z+},{e}^{\ensuremath{-}},{e}^{\ensuremath{-}},{e}^{+})$ system is stable whenever the ${m}^{Z+}+{\mathrm{Ps}}^{\ensuremath{-}}$ or $({m}^{Z+},{e}^{\ensuremath{-}})+\mathrm{Ps}$ breakups represent the lowest energy dissociation channel. As part of the analysis some improved estimates of the properties of the KPs ground state are reported.
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The configuration-interaction method is applied to the study of positronic zinc (e+Zn){(e}^{+}\mathrm{Zn})(e+Zn) and positronic cadmium (e+Cd).{(e}^{+}\mathrm{Cd}).(e+Cd). The estimated binding energies and annihilation rates were 0.003 73 hartree and $0.42\ifmmode\times\else\texttimes\fi{}{10}^{9} {\mathrm{sec}}^{\ensuremath{-}1}$ for e+Zn{e}^{+}\mathrm{Zn}e+Zn and 0.006 10 hartree and $0.56\ifmmode\times\else\texttimes\fi{}{10}^{9} {\mathrm{sec}}^{\ensuremath{-}1}$ for e+Cd.{e}^{+}\mathrm{Cd}.e+Cd. The low-energy elastic cross section and Zeff{Z}_{\mathrm{eff}}Zeff​ were estimated from a model potential that was tuned to the binding energies and annihilation rates. Since the scattering lengths were positive (14.5a0{(14.5a}_{0}(14.5a0​ for Zn and 11.6a0{11.6a}_{0}11.6a0​ for Cd) the differential cross sections are larger at backward angles than at forward angles just above threshold. The possibilities of measuring differential cross sections to confirm positron binding to these atoms is discussed.
We report a theoretical calculation of the relativistic corrections to the binding energy of positronic alkali-metal atoms. The ground state for the positronic alkali-metal atom is a loosely bound state with the structure of an alkali-metal ion surrounded by a positronium cloud. The correlation between the valence electron and positron in the field of a residual core ion is taken into account using a three-body model. Relativistic corrections to the binding energy for positronic alkali-metal atoms are evaluated based on the Breit-Pauli perturbation theory up to the second order of the fine structure constant. The relativistic corrections caused by the interaction between the valence electron and core ion was evaluated from the decomposed expectation values of the perturbation Hamiltonian. We found that the importance of relativistic corrections to the binding energy, namely the ratio of the net relativistic correction in the total binding energy, is remarkably enhanced in the loosely bound states of positronic alkali-metal atoms, where the charge of the valence electron is screened by the positron as positronium in the outermost region, while the electron is released from the positron near the nucleus. The results imply that positronic atoms with a dominant positronium can serve as an apt testing ground for relativistic quantum mechanics.
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