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arXiv:1406.1315 · Physical Review A

Effect of the atomic electric quadrupole moment on positron binding

C. Harabati, V. A. Dzuba, V. V. Flambaum

Published Jul 21, 2014• 2 citations
arXivHTMLPDF

Abstract

The effect of an electric quadrupole moment $Q$ is studied for positron-atom bound systems. It is demonstrated that for $Q>50$ 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 $Q$ are not known for atomic ground states; however, they exist in molecules and excited atoms. In the $2s2{p}^{3}{P}_{2}^{o}$ state of beryllium, the quadrupole contribution makes the difference between a stable bound state and an unstable state, which decays to a $\mathrm{Be}{}^{+}$ ion and positronium. In the majority of atoms the quadrupole contribution is small and can be neglected.

DOI
10.1103/physreva.90.014501

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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 positronium molecule (Ps2)({\mathrm{Ps}}_{2})(Ps2​) has not been experimentally observed yet because its tiny (4.5 eV) binding energy cannot be detected when the molecule annihilates by emitting two photons with energy of 0.51 MeV each. It is shown in this paper that the electric dipole transition between the recently found L=1L=1L=1 excited state and the L=0L=0L=0 ground state with its characteristic photon energy of 4.94 eV is a clear signature of the existence of the positronium molecule and the possibility of its experimental observation is realistic. The probability of this transition is about 17% of the total decay rate. Another Coulomb four-body system containing positron HPs (the positronium hydride or hydrogen positride), is also included for comparison.
The quadrupole interaction between the Rydberg electronic states of a Rydberg ion and the radio frequency electric field of the ion trap is analyzed. Such a coupling is negligible for the lowest energy levels of a trapped ion but it is important for a trapped Rydberg ion due to its large electric quadrupole moment. This coupling cannot be neglected by the standard rotating-wave approximation because it is comparable to the frequency of the trapping electric field. We investigate the effect of the quadrupole coupling by performing a suitable effective representation of the Hamiltonian. For a single ion we show that in this effective picture the quadrupole interaction is replaced by rescaled laser intensities and additional Stark shifts of the Rydberg levels. Hence this detrimental quadrupole coupling can be efficiently compensated by an appropriate increase of the Rabi frequencies. Moreover, we consider the strong dipole-dipole interaction between a pair of Rydberg ions in the presence of the quadrupole coupling. In the effective representation we observe reducing of the dipole-dipole coupling as well as additional spin-spin interaction.
This paper considers the binding of an electron or a positron to a ground-state hydrogen atom in a uniform magnetic field BBB, concentrating on states with zero orbital angular momentum JJJ. It is shown that the affinity of a positron to a hydrogen atom is 2.23b2e2∕a2.23{b}^{2}{e}^{2}∕a2.23b2e2∕a, where aaa is the Bohr radius, $b\ensuremath{\equiv}B∕{B}_{0}$, ${B}_{0}=2.3505\ifmmode\times\else\texttimes\fi{}{10}^{5}\phantom{\rule{0.3em}{0ex}}\mathrm{T}$, b⪡1b⪡1b⪡1 is assumed, and the proton is assumed to have infinite mass. With these assumptions it is also shown that no J=0J=0J=0 singlet or triplet excited state of ${\mathrm{H}}^{\ensuremath{-}}$ exists. These results are compared to a previous estimate of the electron affinity of J=0J=0J=0 magnetically bound ions [V. G. Bezchastnov, P. Schmelcher, and L. S. Cederbaum, Phys. Rev. A 61, 052152 (2000)].
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.
The positronium ion (Ps−\mathrm{Ps}^-Ps−), a coulombic three-body bound state of two electrons and a positron, predominantly decays via electron-positron annihilation into electromagnetic final states. While its radiative decay channels have been extensively studied, much less attention has been given to weak processes in this system. In this work, we investigate the rare decay Ps−→e−νμνˉμ\mathrm{Ps}^- \to e^- ν_μ\barν_μPs−→e−νμ​νˉμ​, obtained by replacing the photon in Ps−→e−γ\mathrm{Ps}^- \to e^- γPs−→e−γ with a virtual ZZZ boson. Treating the three-body process as an effective two-body transition, Ps−→e−Z∗(→νμνˉμ)\mathrm{Ps}^- \to e^- Z^*\left(\to ν_μ\barν_μ\right)Ps−→e−Z∗(→νμ​νˉμ​), we compute the decay rate by explicitly evaluating all spin configurations of the initial bound state and final particles. The result agrees with that obtained using the standard spin-summation formalism of quantum field theory. We find that the branching ratio is comparable to that of the weak decay of ortho-positronium, o-Ps→γννˉ\mathrm{o\text{-}Ps} \to γν\barνo-Ps→γννˉ.
Permanent electric dipole moments in molecules require a breaking of parity symmetry. Conventionally, this symmetry breaking relies on the presence of heteronuclear constituents. We report the observation of a permanent electric dipole moment in a homonuclear molecule in which the binding is based on asymmetric electronic excitation between the atoms. These exotic molecules consist of a ground-state rubidium (Rb) atom bound inside a second Rb atom electronically excited to a high-lying Rydberg state. Detailed calculations predict appreciable dipole moments on the order of 1 Debye, in excellent agreement with the observations.