A theoretical study is conducted on the stability of exotic antiproton-hydrogen molecular anions ( $\overline{p}\mathrm{H}$ ), which in the separated atom limit correlate with $\overline{p}+\mathrm{H}(n=2)$ ( $n$ being the principal quantum number). The $\overline{p}\mathrm{H}$ molecule in the electronic ground state is highly unstable due to pair annihilation and autodetachment ($\ensuremath{\rightarrow}\overline{p}p+e$). However, if the $\overline{p}\mathrm{H}$ molecule is electronically excited, the molecular stability can be drastically improved. Since the excited states of the $\mathrm{H}$ atom have accidental degeneracy, the asymptotic form of the Born-Oppenheimer potential curve of $\overline{p}+\mathrm{H}(n=2)$ behaves as $1/{R}^{2}$ ( $R$ being the relative distance), which can play a critical role in the bonding and stability of the molecule. It is found that the $\overline{p}\mathrm{H}$ molecule in the first electronic excited state and in a high rotational state is sufficiently stable and has a lifetime dominated by spontaneous radiative emission ($\ensuremath{\rightarrow}\overline{p}+\mathrm{H}+h\ensuremath{\nu}$). The $\overline{p}\mathrm{H}$ system is dynamically similar to ${\mathrm{H}}_{2}{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{-}}$, which had been commonly considered to be unstable due to autodetachment. However, recent measurements of ion-beam sputtering unambiguously verified the existence of long-lived ${\mathrm{H}}_{2}{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{-}}$ molecules in high rotational states. This suggests that the $\overline{p}\mathrm{H}$ molecules may actually be created if one employs experimental means such as the chemical sputtering of hydrogen-rich targets with $\overline{p}$ beams.A theoretical study is conducted on the stability of exotic antiproton-hydrogen molecular anions ($\overline{p}\mathrm{H}$), which in the separated atom limit correlate with $\overline{p}+\mathrm{H}(n=2)$ ($n$ being the principal quantum number). The $\overline{p}\mathrm{H}$ molecule in the electronic ground state is highly unstable due to pair annihilation and autodetachment ($\ensuremath{\rightarrow}\overline{p}p+e$). However, if the $\overline{p}\mathrm{H}$ molecule is electronically excited, the molecular stability can be drastically improved. Since the excited states of the $\mathrm{H}$ atom have accidental degeneracy, the asymptotic form of the Born-Oppenheimer potential curve of $\overline{p}+\mathrm{H}(n=2)$ behaves as $1/{R}^{2}$ ($R$ being the relative distance), which can play a critical role in the bonding and stability of the molecule. It is found that the $\overline{p}\mathrm{H}$ molecule in the first electronic excited state and in a high rotational state is sufficiently stable and has a lifetime dominated by spontaneous radiative emission ($\ensuremath{\rightarrow}\overline{p}+\mathrm{H}+h\ensuremath{\nu}$). The $\overline{p}\mathrm{H}$ system is dynamically similar to ${\mathrm{H}}_{2}{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{-}}$, which had been commonly considered to be unstable due to autodetachment. However, recent measurements of ion-beam sputtering unambiguously verified the existence of long-lived ${\mathrm{H}}_{2}{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{-}}$ molecules in high rotational states. This suggests that the $\overline{p}\mathrm{H}$ molecules may actually be created if one employs experimental means such as the chemical sputtering of hydrogen-rich targets with $\overline{p}$ beams.

Physical Review AOct 8, 20183 citations

Positronium–hydrogen-atom scattering in a five-state model

Sadhan K. Adhikari, Priyanka Biswas

The scattering of orthopositronium (Ps) by hydrogen atoms has been investigated in a five-state coupled-channel model allowing for $\mathrm{Ps}(1s)\mathrm{H}(2s,2p)$ and $\mathrm{Ps}(2s,2p)\mathrm{H}(1s)$ excitations using a recently proposed electron-exchange model potential. The higher $(n>~3)$ excitations and ionization of the Ps atom are calculated using the first Born approximation. Calculations are reported of scattering lengths, phase shifts, elastic, Ps and H excitation, and total cross sections. Remarkable correlations are observed between the S-wave Ps-H binding energy and the singlet scattering length, effective range, and resonance energy obtained in various model calculations. These correlations suggest that if a Ps-H dynamical model yields the correct result for one of these four observables, it is expected to lead to the correct result for the other three. The present model, which is constructed so as to reproduce the Ps-H resonance at 4.01 eV, automatically yields a Ps-H bound state at $\ensuremath{-}1.05$ eV that compares well with the accurate value of $\ensuremath{-}1.067$ eV. The model leads to a singlet scattering length of ${3.72a}_{0}$ and effective range of ${1.67a}_{0},$ whereas the correlations suggest the precise values of ${3.50a}_{0}$ and ${1.65a}_{0}$ for these observables, respectively.The scattering of orthopositronium (Ps) by hydrogen atoms has been investigated in a five-state coupled-channel model allowing for $\mathrm{Ps}(1s)\mathrm{H}(2s,2p)$ and $\mathrm{Ps}(2s,2p)\mathrm{H}(1s)$ excitations using a recently proposed electron-exchange model potential. The higher $(n>~3)$ excitations and ionization of the Ps atom are calculated using the first Born approximation. Calculations are reported of scattering lengths, phase shifts, elastic, Ps and H excitation, and total cross sections. Remarkable correlations are observed between the S-wave Ps-H binding energy and the singlet scattering length, effective range, and resonance energy obtained in various model calculations. These correlations suggest that if a Ps-H dynamical model yields the correct result for one of these four observables, it is expected to lead to the correct result for the other three. The present model, which is constructed so as to reproduce the Ps-H resonance at 4.01 eV, automatically yields a Ps-H bound state at $\ensuremath{-}1.05$ eV that compares well with the accurate value of $\ensuremath{-}1.067$ eV. The model leads to a singlet scattering length of ${3.72a}_{0}$ and effective range of ${1.67a}_{0},$ whereas the correlations suggest the precise values of ${3.50a}_{0}$ and ${1.65a}_{0}$ for these observables, respectively.

arXiv:physics/9911054Physical Review AMar 1, 199937 citations

Entanglement, coherence and correlation in atomic and molecular systems

Juan F. P. Mosquera

ABSTRACT: In the present work, we have computed the entanglement between the electronic and nuclear motions in two molecular model systems: the one-dimensional hydrogen molecular ion (H2+) and the Shin-Metiu model, considering the molecules as a bipartite systems: electron and nuclear motion. For that purpose, we have computed the Born-Oppenheimer and non-Born-Oppenheimer (Born-Huang) wave function in terms of the Fourier Grid Hamiltonian basis that expands both the electronic and nuclear wave functions. Also, according to the Schmidt decomposition theorem for bipartite systems, widely used in quantum-information theory, there is a much shorter but equivalent expansion in terms of the Schmidt bases for the electronic and nuclear sub-spaces. In these models of distinguishable coupled particles we have shown that the entanglements contents do not increase monotonically with the excitation energy. In the hydrogen molecular ion and in the ShinMetiu model, the entanglements contents for each Born-Oppenheimer electro-nuclear state is quantified through the von-Neumann and linear entropies and we have shown that entanglement serves as a witness of distinguishability of nuclear states related to different Born-Oppenheimer molecular energy curves or electronic excitation modes.ABSTRACT: In the present work, we have computed the entanglement between the electronic and nuclear motions in two molecular model systems: the one-dimensional hydrogen molecular ion (H2+) and the Shin-Metiu model, considering the molecules as a bipartite systems: electron and nuclear motion. For that purpose, we have computed the Born-Oppenheimer and non-Born-Oppenheimer (Born-Huang) wave function in terms of the Fourier Grid Hamiltonian basis that expands both the electronic and nuclear wave functions. Also, according to the Schmidt decomposition theorem for bipartite systems, widely used in quantum-information theory, there is a much shorter but equivalent expansion in terms of the Schmidt bases for the electronic and nuclear sub-spaces. In these models of distinguishable coupled particles we have shown that the entanglements contents do not increase monotonically with the excitation energy. In the hydrogen molecular ion and in the ShinMetiu model, the entanglements contents for each Born-Oppenheimer electro-nuclear state is quantified through the von-Neumann and linear entropies and we have shown that entanglement serves as a witness of distinguishability of nuclear states related to different Born-Oppenheimer molecular energy curves or electronic excitation modes.

Jan 1, 20200 citations

The hydrogen atom revisited

Randell L Mills

International Journal of Hydrogen EnergyDec 1, 200056 citations

A theoretical study is conducted on the stability of exotic antiproton-hydrogen molecular anions (

\overline{p}\mathrm{H}

), which in the separated atom limit correlate with

\overline{p}+\mathrm{H}(n=2)

(

n

being the principal quantum number). The

\overline{p}\mathrm{H}

molecule in the electronic ground state is highly unstable due to pair annihilation and autodetachment ($\ensuremath{\rightarrow}\overline{p}p+e$). However, if the

\overline{p}\mathrm{H}

molecule is electronically excited, the molecular stability can be drastically improved. Since the excited states of the

\mathrm{H}

atom have accidental degeneracy, the asymptotic form of the Born-Oppenheimer potential curve of

\overline{p}+\mathrm{H}(n=2)

behaves as

1/{R}^{2}

(

R

being the relative distance), which can play a critical role in the bonding and stability of the molecule. It is found that the

\overline{p}\mathrm{H}

molecule in the first electronic excited state and in a high rotational state is sufficiently stable and has a lifetime dominated by spontaneous radiative emission ($\ensuremath{\rightarrow}\overline{p}+\mathrm{H}+h\ensuremath{\nu}$). The

\overline{p}\mathrm{H}

system is dynamically similar to ${\mathrm{H}}_{2}{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{-}}$, which had been commonly considered to be unstable due to autodetachment. However, recent measurements of ion-beam sputtering unambiguously verified the existence of long-lived ${\mathrm{H}}_{2}{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{-}}$ molecules in high rotational states. This suggests that the

\overline{p}\mathrm{H}

molecules may actually be created if one employs experimental means such as the chemical sputtering of hydrogen-rich targets with

\overline{p}

beams.

The scattering of orthopositronium (Ps) by hydrogen atoms has been investigated in a five-state coupled-channel model allowing for

\mathrm{Ps}(1s)\mathrm{H}(2s,2p)

and

\mathrm{Ps}(2s,2p)\mathrm{H}(1s)

excitations using a recently proposed electron-exchange model potential. The higher

(n>~3)

excitations and ionization of the Ps atom are calculated using the first Born approximation. Calculations are reported of scattering lengths, phase shifts, elastic, Ps and H excitation, and total cross sections. Remarkable correlations are observed between the S-wave Ps-H binding energy and the singlet scattering length, effective range, and resonance energy obtained in various model calculations. These correlations suggest that if a Ps-H dynamical model yields the correct result for one of these four observables, it is expected to lead to the correct result for the other three. The present model, which is constructed so as to reproduce the Ps-H resonance at 4.01 eV, automatically yields a Ps-H bound state at $\ensuremath{-}1.05$ eV that compares well with the accurate value of $\ensuremath{-}1.067$ eV. The model leads to a singlet scattering length of

{3.72a}_{0}

and effective range of

{1.67a}_{0},

whereas the correlations suggest the precise values of

{3.50a}_{0}

and

{1.65a}_{0}

for these observables, respectively.