Physical Review A

Expectation values of the e+Li system

J. Mitroy

Published Aug 25, 2004• 39 citations

Abstract

Close to converged energies and expectation values for ${e}^{+}\mathrm{Li}$ are computed using a ground state wave function consisting of 1200 explicitly correlated Gaussians. The best estimate of the ${e}^{+}\mathrm{Li}$ energy was $\ensuremath{-}7.532 895 5$ hartree which has a binding energy of 0.002 482 hartree against dissociation into $\mathrm{Ps}+{\mathrm{Li}}^{+}$. The $2\ensuremath{\gamma}$ annihilation rate for the spin singlet state was $6.996\ifmmode\times\else\texttimes\fi{}{10}^{9}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. The annihilation rate for the triplet state, taking into account core annihilation and the $3\ensuremath{\gamma}$ decay, was $9.36\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$.

DOI: 10.1103/physreva.70.024502

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Physical Review A

Expectation values of the e+Li system

J. Mitroy

Published Aug 25, 2004• 39 citations

Publisher

Abstract

Close to converged energies and expectation values for

{e}^{+}\mathrm{Li}

are computed using a ground state wave function consisting of 1200 explicitly correlated Gaussians. The best estimate of the

{e}^{+}\mathrm{Li}

energy was

\ensuremath{-}7.532 895 5

hartree which has a binding energy of 0.002 482 hartree against dissociation into

\mathrm{Ps}+{\mathrm{Li}}^{+}

. The

2\ensuremath{\gamma}

annihilation rate for the spin singlet state was

6.996\ifmmode\times\else\texttimes\fi{}{10}^{9}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}

. The annihilation rate for the triplet state, taking into account core annihilation and the

3\ensuremath{\gamma}

decay, was

9.36\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}

DOI: 10.1103/physreva.70.024502

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Expectation values of the e+He(Se3) system

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Close to converged energies and expectation values for ${e}^{+}\mathrm{He}(^{3}S^{e})$ are computed using a ground state wave function consisting of 1500 explicitly correlated Gaussians. The best estimate of the ${e}^{+}\mathrm{He}(^{3}S^{e})$ energy was $\ensuremath{-}2.250\phantom{\rule{0.2em}{0ex}}595\phantom{\rule{0.2em}{0ex}}08\phantom{\rule{0.3em}{0ex}}\text{hartree}$, which has a binding energy of $0.000\phantom{\rule{0.2em}{0ex}}595\phantom{\rule{0.2em}{0ex}}08\phantom{\rule{0.3em}{0ex}}\text{hartree}$ against dissociation into $\mathrm{Ps}+{\mathrm{He}}^{+}$ . The $2\ensuremath{\gamma}$ annihilation rate for the spin doublet state was $5.713\ifmmode\times\else\texttimes\fi{}{10}^{9}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. The estimated annihilation rate with the core ${\mathrm{He}}^{+}$ electron was $2.506\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. The derived enhancement factor for annihilation with the ${\mathrm{He}}^{+}(1s)$ core was 2.29, just over 10% smaller than the enhancement factor derived from analyses of annihilation during ${e}^{+}\text{\ensuremath{-}}{\mathrm{He}}^{+}$ scattering. The diffuse nature of the wave function, with well separated ${\mathrm{He}}^{+}$ and Ps subsystems, is demonstarted to be on the threshold of satisfying the formal criteria that define a quantum halo state.Close to converged energies and expectation values for ${e}^{+}\mathrm{He}(^{3}S^{e})$ are computed using a ground state wave function consisting of 1500 explicitly correlated Gaussians. The best estimate of the ${e}^{+}\mathrm{He}(^{3}S^{e})$ energy was $\ensuremath{-}2.250\phantom{\rule{0.2em}{0ex}}595\phantom{\rule{0.2em}{0ex}}08\phantom{\rule{0.3em}{0ex}}\text{hartree}$, which has a binding energy of $0.000\phantom{\rule{0.2em}{0ex}}595\phantom{\rule{0.2em}{0ex}}08\phantom{\rule{0.3em}{0ex}}\text{hartree}$ against dissociation into $\mathrm{Ps}+{\mathrm{He}}^{+}$. The $2\ensuremath{\gamma}$ annihilation rate for the spin doublet state was $5.713\ifmmode\times\else\texttimes\fi{}{10}^{9}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. The estimated annihilation rate with the core ${\mathrm{He}}^{+}$ electron was $2.506\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. The derived enhancement factor for annihilation with the ${\mathrm{He}}^{+}(1s)$ core was 2.29, just over 10% smaller than the enhancement factor derived from analyses of annihilation during ${e}^{+}\text{\ensuremath{-}}{\mathrm{He}}^{+}$ scattering. The diffuse nature of the wave function, with well separated ${\mathrm{He}}^{+}$ and Ps subsystems, is demonstarted to be on the threshold of satisfying the formal criteria that define a quantum halo state.

Physical Review ASep 21, 200520 citations

( e− , e+ )-pair annihilation in the positronium molecule Ps2

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Stable mixtures of $^6$ Li fermions in the three lowest energy spin statesStable mixtures of $^6$Li fermions in the three lowest energy spin states

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Bulletin of the American Physical SocietyMay 29, 20080 citations

Close to converged energies and expectation values for

{e}^{+}\mathrm{Li}

are computed using a ground state wave function consisting of 1200 explicitly correlated Gaussians. The best estimate of the

{e}^{+}\mathrm{Li}

energy was

\ensuremath{-}7.532 895 5

hartree which has a binding energy of 0.002 482 hartree against dissociation into

\mathrm{Ps}+{\mathrm{Li}}^{+}

. The

2\ensuremath{\gamma}

annihilation rate for the spin singlet state was

6.996\ifmmode\times\else\texttimes\fi{}{10}^{9}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}

. The annihilation rate for the triplet state, taking into account core annihilation and the

3\ensuremath{\gamma}

decay, was

9.36\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}

Close to converged energies and expectation values for

{e}^{+}\mathrm{He}(^{3}S^{e})

are computed using a ground state wave function consisting of 1500 explicitly correlated Gaussians. The best estimate of the

{e}^{+}\mathrm{He}(^{3}S^{e})

energy was $\ensuremath{-}2.250\phantom{\rule{0.2em}{0ex}}595\phantom{\rule{0.2em}{0ex}}08\phantom{\rule{0.3em}{0ex}}\text{hartree}$, which has a binding energy of

0.000\phantom{\rule{0.2em}{0ex}}595\phantom{\rule{0.2em}{0ex}}08\phantom{\rule{0.3em}{0ex}}\text{hartree}

against dissociation into

\mathrm{Ps}+{\mathrm{He}}^{+}

. The $2\ensuremath{\gamma}$ annihilation rate for the spin doublet state was $5.713\ifmmode\times\else\texttimes\fi{}{10}^{9}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. The estimated annihilation rate with the core

{\mathrm{He}}^{+}

electron was $2.506\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. The derived enhancement factor for annihilation with the

{\mathrm{He}}^{+}(1s)

core was 2.29, just over 10% smaller than the enhancement factor derived from analyses of annihilation during ${e}^{+}\text{\ensuremath{-}}{\mathrm{He}}^{+}$ scattering. The diffuse nature of the wave function, with well separated

{\mathrm{He}}^{+}

and Ps subsystems, is demonstarted to be on the threshold of satisfying the formal criteria that define a quantum halo state.

The (${\mathit{e}}^{\mathrm{\ensuremath{-}}}$,

{\mathit{e}}^{+}

)-pair annihilation in the bound

^{1}

{\mathit{S}}_{0}

state of the

{\mathrm{Ps}}_{2}

molecule (${\mathit{e}}^{\mathrm{\ensuremath{-}}}$

{\mathit{e}}^{+}

${\mathit{e}}^{\mathrm{\ensuremath{-}}}$

{\mathit{e}}^{+}

) is studied. It is shown that the expectation values of the two-, three-, and four-body Dirac \ensuremath{\delta} functions 〈${\mathrm{\ensuremath{\delta}}}_{+\mathrm{\ensuremath{-}}}$〉, 〈${\mathrm{\ensuremath{\delta}}}_{++\mathrm{\ensuremath{-}}}$〉 (\ensuremath{\equiv}〈${\mathrm{\ensuremath{\delta}}}_{+\mathrm{\ensuremath{-}}\mathrm{\ensuremath{-}}}$〉), and 〈${\mathrm{\ensuremath{\delta}}}_{++\mathrm{\ensuremath{-}}\mathrm{\ensuremath{-}}}$〉 determine the photonless, one- and many-photon annihilation rates, i.e., the values of ${\mathrm{\ensuremath{\Gamma}}}_{0\ensuremath{\gamma}}$, ${\mathrm{\ensuremath{\Gamma}}}_{1\ensuremath{\gamma}}$, and ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{n}\ensuremath{\gamma}}$, where n\ensuremath{\ge}2. The appropriate analytical expressions are presented together with numerical estimates. As expected, the two-photon annihilation process dominates.

This study explores the electronic structure of the CH

_2

molecule, modeled as a (6e, 23o) system using a 52-qubit quantum experiment, which is relevant for interstellar and combustion chemistry. We focused on calculating the dissociation energies for CH

_2

in the ground state triplet and the first excited state singlet, applying the Sample-based Quantum Diagonalization (SQD) method within a quantum-centric supercomputing framework. We evaluated the ability of SQD to provide accurate results compared to Selected Configuration Interaction (SCI) calculations and experimental values for the singlet-triplet gap. To our knowledge, this is the first study of an open-shell system, such as the CH

_2

triplet, using SQD. To obtain accurate energy values, we implemented post-SQD orbital optimization and employed a warm-start approach using previously converged states. While the results for the singlet state dissociation were only a few milli-Hartrees from the SCI reference values, the triplet state exhibited greater variability. This discrepancy likely arises from differences in bit-string handling within the SQD method for open- versus closed-shell systems, as well as the inherently complex wavefunction character of the triplet state. The SQD-calculated singlet-triplet energy gap matched well with experimental and SCI values. This study enhances our understanding of the SQD method for open-shell systems and lays the groundwork for future applications in large-scale electronic structure studies using quantum algorithms.

Stable mixtures of

^6

Li fermions in the three lowest energy spin states