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Physical Review A

Stability of the (m2+,e−,e−,e+) system

Jim Mitroy

Published Jul 19, 2002• 11 citations
Publisher

Abstract

The stability of the ${(m}^{2+}{,e}^{\ensuremath{-}}{,e}^{\ensuremath{-}}{,e}^{+})$ system is studied as a function of the mass of the ${m}^{2+}$ particle. The system is found to be stable for all values of ${m}^{2+}<{0.68m}_{e}.$ At the smallest values of ${m}^{2+}$ the system evolves into a ${m}^{2+}+{\mathrm{Ps}}^{\ensuremath{-}}$ configuration, which is absolutely stable since both fragments are electrically charged. This suggests that a positron can be expected to bind to all the group II and IIB atoms with the possible exception of mercury.

DOI
10.1103/physreva.66.010501

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Physical Review A•Dec 1, 1981•44 citations
The stability of the (m2+,e\ensuremath−,e\ensuremath−,e+){(m}^{2+}{,e}^{\ensuremath{-}}{,e}^{\ensuremath{-}}{,e}^{+})(m2+,e\ensuremath−,e\ensuremath−,e+) system is studied as a function of the mass of the m2+{m}^{2+}m2+ particle. The system is found to be stable for all values of m2+<0.68me.{m}^{2+}<{0.68m}_{e}.m2+<0.68me​. At the smallest values of m2+{m}^{2+}m2+ the system evolves into a m2++Ps\ensuremath−{m}^{2+}+{\mathrm{Ps}}^{\ensuremath{-}}m2++Ps\ensuremath− configuration, which is absolutely stable since both fragments are electrically charged. This suggests that a positron can be expected to bind to all the group II and IIB atoms with the possible exception of mercury.
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.
The stability of tripositronium, a system consisting of three electrons and three positrons, has been investigated systematically by varying the repulsion strength between like-charged particles. The possibility of the existence of a Ps3{}_{3}3​ bound state that is stable against dissociation appears utterly unlikely based on the results of variational calculations employing all-particle explicitly correlated Gaussian basis functions.
The effect of an electric quadrupole moment QQQ is studied for positron-atom bound systems. It is demonstrated that for Q>50Q>50Q>50 a.u. the electric quadrupole potential is sufficiently strong to bind a positron (or an electron) even in the absence of the dipole polarization potential. Such large values of QQQ are not known for atomic ground states; however, they exist in molecules and excited atoms. In the 2s2p3P2o2s2{p}^{3}{P}_{2}^{o}2s2p3P2o​ state of beryllium, the quadrupole contribution makes the difference between a stable bound state and an unstable state, which decays to a Be+\mathrm{Be}{}^{+}Be+ ion and positronium. In the majority of atoms the quadrupole contribution is small and can be neglected.
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 $L\ensuremath{\rightarrow}\ensuremath{\infty}$ limit of the energy. Incorporating corrections that compensate for the finite range of the radial basis increased the binding energies of e+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 positronium ion Ps−−{\mathrm{Ps}}^{--}Ps−− is often qualitative described as a positronium Ps with a loosely bound second electron, since the value of the annihilation rate for Ps−−{\mathrm{Ps}}^{--}Ps−− is nearly equal to that of the spin-averaged neutral positronium. This similarity however has never been fully explained. To study its internal structure, we decompose the electron-positron distribution function of Ps−−{\mathrm{Ps}}^{--}Ps−− into the sum of two terms: one for the electron closest to the positron and the other for the farthest. We show that the inner electron behaves almost as if the outer electron were not present, forming a Ps substructure inside Ps−−{\mathrm{Ps}}^{--}Ps−− and that the effect of electron correlation is such that the outer electron tries to stay as close as possible to the positron but without interfering too much with the distribution of the inner electron. We show that this phenomenon is closely related to the problem of the critical stability of the system (Z+,e−−,e−−)({Z}^{+},\phantom{\rule{0.28em}{0ex}}{e}^{--},\phantom{\rule{0.28em}{0ex}}{e}^{--})(Z+,e−−,e−−) with varying ZZZ charge.
The ${\mathrm{H}}^{\ensuremath{-}}$ ion is known to have a metastable $2{p}^{2}^{3}P^{e}$ triplet excited state. To see if an analog of this state is present in the positronium negative ion ${\mathrm{Ps}}^{\ensuremath{-}}$ the Coulomb binding energy Eb{E}_{b}Eb​ of the lowest-energy even-parity L=1L=1L=1 configuration of two identical-charge $\ensuremath{-}e$ fermions of mass m1{m}_{1}m1​ plus one spinless particle of mass m2{m}_{2}m2​ and charge +e+e+e is calculated. We find a value of Eb{E}_{b}Eb​ below the n=2n=2n=2 level of the neutral atom for $\frac{0\ensuremath{\le}{m}_{2}}{M\ensuremath{\le}0.17}$ and $\frac{0.90<{m}_{2}}{M\ensuremath{\le}1}$, where M=2m1+m2M=2{m}_{1}+{m}_{2}M=2m1​+m2​ is the total mass of the ion. However, we cannot say that the 3Pe^{3}P^{e}3Pe state exists for ${\mathrm{Ps}}^{\ensuremath{-}}$, where m2M=13\frac{{m}_{2}}{M}=\frac{1}{3}Mm2​​=31​.