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Physical Review A

The stability and structure of the (mZ+,e−,e−,e+) system

J. Mitroy, S. A. Novikov

Published Sep 28, 2004• 15 citations
Publisher

Abstract

The stability and structure of the $({m}^{Z+},{e}^{\ensuremath{-}},{e}^{\ensuremath{-}},{e}^{+})$ system is studied as a function of the mass of the ${m}^{Z+}$ particle and for $Z=1$, 2, 3, and 10. The $Z=1$ system can be regarded as an analog of the $A\mathrm{Ps}$ system (where $A$ is a group I or IB atom of the periodic table) and was found to be stable for all values of ${m}^{+}$. 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 ${m}^{10+}∕{m}_{e}=0.002\phantom{\rule{0.2em}{0ex}}54$, 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.

DOI
10.1103/physreva.70.032511

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•Aug 1, 2005•0 citations
The stability and structure of the (mZ+,e\ensuremath−,e\ensuremath−,e+)({m}^{Z+},{e}^{\ensuremath{-}},{e}^{\ensuremath{-}},{e}^{+})(mZ+,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 (m2+,e\ensuremath−,e\ensuremath−,e+)({m}^{2+},{e}^{\ensuremath{-}},{e}^{\ensuremath{-}},{e}^{+})(m2+,e\ensuremath−,e\ensuremath−,e+) system is stable for all m2+∕me\ensuremath⩽0.68{m}^{2+}∕{m}_{e}\ensuremath{\leqslant}0.68m2+∕me​\ensuremath⩽0.68 and evolves into a configuration best described as (m2+,Ps\ensuremath−)({m}^{2+},{\mathrm{Ps}}^{\ensuremath{-}})(m2+,Ps\ensuremath−) when m2+∕me\ensuremath→0{m}^{2+}∕{m}_{e}\ensuremath{\rightarrow}0m2+∕me​\ensuremath→0. The (m3+,e\ensuremath−,e\ensuremath−,e+)({m}^{3+},{e}^{\ensuremath{-}},{e}^{\ensuremath{-}},{e}^{+})(m3+,e\ensuremath−,e\ensuremath−,e+) system was stable for a mass range given by m3+∕me\ensuremath⩽0.06632{m}^{3+}∕{m}_{e}\ensuremath{\leqslant}0.066\phantom{\rule{0.2em}{0ex}}32m3+∕me​\ensuremath⩽0.06632, 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 (m3+,e\ensuremath−,e\ensuremath−,e+)({m}^{3+},{e}^{\ensuremath{-}},{e}^{\ensuremath{-}},{e}^{+})(m3+,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 (m10+,e\ensuremath−,e\ensuremath−,e+)({m}^{10+},{e}^{\ensuremath{-}},{e}^{\ensuremath{-}},{e}^{+})(m10+,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 (mZ+,e\ensuremath−,e\ensuremath−,e+)({m}^{Z+},{e}^{\ensuremath{-}},{e}^{\ensuremath{-}},{e}^{+})(mZ+,e\ensuremath−,e\ensuremath−,e+) system is stable whenever the mZ++Ps\ensuremath−{m}^{Z+}+{\mathrm{Ps}}^{\ensuremath{-}}mZ++Ps\ensuremath− or (mZ+,e\ensuremath−)+Ps({m}^{Z+},{e}^{\ensuremath{-}})+\mathrm{Ps}(mZ+,e\ensuremath−)+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.
Various geometrical and energetical (bound-state) properties of the positronium negative ion $({\mathrm{Ps}}^{\ensuremath{-}}$ or ${e}^{\ensuremath{-}}{e}^{+}{e}^{\ensuremath{-}})$ are determined by using highly accurate variational wave functions. These wave functions have been constructed by applying the advanced two-stage strategy proposed by Frolov [Phys. Rev. A 57, 2436 (1998)]. The determined total energy of the ground state $E=\ensuremath{-}0.2620050702329757\mathrm{a}.\mathrm{u}.$ is the lowest and most accurate value obtained for this system to date (the corresponding binding energy equals $\ensuremath{-}0.326674721317821\mathrm{eV}).$ The computation of the second-order relativistic corrections $(\ensuremath{\simeq}{\ensuremath{\alpha}}^{2})$ to the total energy is discussed also. The general form of the Breit-Pauli Hamiltonian in the relative coordinates for the ${\mathrm{Ps}}^{\ensuremath{-}}$ ion is presented.
We reexamine the binding energies of three-particle systems containing two electrons and one positive particle of mass M, in an attempt to understand the approximate proportionality of the 1Se^{1}\mathrm{S}^{\mathrm{e}}1Se ground-state binding energies to the reduced masses, as pointed out by Botero and Greene [Phys. Rev. 56, 1366 (1986)]. Our investigation involves a careful evaluation of the contribution to the energy of the mass-polarization term ${H}_{\mathrm{mp}=\mathrm{\ensuremath{-}}(2/\mathrm{M}){\ensuremath{\nabla}}_{1}\mathrm{\ensuremath{\cdot}}{\ensuremath{\nabla}}_{2}}$ which is the only part of the Hamiltonian not scaling like the reduced mass. It does not appear that any fundamental principle is involved, since we find merely that the mass polarization decreases somewhat as the mass of the positive particle is reduced below the proton mass. In the case of the excited 3Pe^{3}\mathrm{P}^{\mathrm{e}}3Pe state, this reduction is not sufficient to allow binding when M approaches the electron mass. As a by-product, we compute accurately some properties of the recently observed negative muonium ion (${e}^{\mathrm{\ensuremath{-}}}$${\ensuremath{\mu}}^{+}$${e}^{\mathrm{\ensuremath{-}}}$).
The stability of the ${(m}^{2+}{,e}^{\ensuremath{-}}{,e}^{\ensuremath{-}}{,e}^{+})$ 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 ${m}^{2+}+{\mathrm{Ps}}^{\ensuremath{-}}$ 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.
The fixed-core stochastic variational method has been used to demonstrate the existence of an electronically stable ground state for the Li + Ps 2 and Na + Ps 2 systems. The stability of Li + Ps 2 has been indicated previously in an ab initio calculation by Varga, but the present estimate of the binding energy is much closer to convergence. The Li + Ps 2 system has a binding energy of 0.013 149 Hartree and a 2 annihilation rate of 3.86 × 10 9 s -1 . The Na + Ps 2 system has a binding energy of 0.005 736 Hartree and an annihilation rate of 4.02 × 10 9 s -1 . Examination of the interparticle expectation values, correlation functions and the annihilation rates suggests that both of these systems can be best described as a Ps 2 molecule weakly bound to an alkali atom cation.
The following dissertation consists of three parts. The first two concern ground - state properties of one - dimensional matter, while the third describes an experimental realization of the Zel'dovich effect in Rydberg atoms. Motivated by emerging experimental possibilities to confine atoms and molecules in quasi - one -dimensional geometries, in Chapters 1 and 2 we analyze ground - state properties of strictly onedimensional molecular matter comprised of identical particles of mass m interacting by a Morse potential between nearest neighbors. We find that due to zero - point motion, the system first undergoes a discontinuous evaporation transition into a diatomic gas followed by a continuous dissociation transition into a monoatomic gas. In particular we find that spin - polarized isotopes of hydrogen and 3He are monoatomic gases, 4H6 is a diatomic gas, while molecular hydrogen and heavier substances are Luttinger liquids. We also investigate the effect of finite pressure on the properties of the liquid and monoatomic gas phases. In particular we estimate a pressure at which molecular hydrogen undergoes an inverse Peierls transition into a metallic state which is a one - dimensional analog of the transition predicted by Wigner and Huntington in 1935. In Chapter 2, we show that dissociar tion of the Luttinger liquid is a process initiated at the system edge. The latter becomes unstable against quantum fluctuations at a value of De Boer's number which is smaller than that of the bulk instability which parallels the classical phenomenon of surface melting. In 1959 Ya. B. Zel'dovich predicted that the bound - state spectrum of the non - relativistic Coulomb problem distorted at small distances by a short - range potential undergoes a peculiar reconstruction whenever this potential alone supports a low - energy scattering resonance. However documented experimental evidence of this effect has been lacking. In Chapter 3 we demonstrate that along the Periodic Table of elements the Zel'dovich effect manifests itself as a systematic periodic variation of the Rydberg spectra with a period proportional to the cubic root of the atomic number. This dependence, which is supported by analysis of experimental and numerical data, has its origin in the binding properties of the ionic core of the atom. Note: Abstract extracted from PDF file via OCR