The method of complex-coordinate rotation is applied to investigate autoionization states of positronium molecules. Using elaborate Hylleraas-type wave functions in which all six interparticle coordinates are used, resonance parameters for six S-wave resonant states are determined. It is believed that three of them belong to a Rydberg series in which the two positrons form a singlet spin state, and the other three resonances belong to the triplet spin state for the two positrons. All these two Rydberg series are converging on the ground state of the ${\mathrm{Ps}}^{\mathrm{\ensuremath{-}}}$ threshold.The method of complex-coordinate rotation is applied to investigate autoionization states of positronium molecules. Using elaborate Hylleraas-type wave functions in which all six interparticle coordinates are used, resonance parameters for six S-wave resonant states are determined. It is believed that three of them belong to a Rydberg series in which the two positrons form a singlet spin state, and the other three resonances belong to the triplet spin state for the two positrons. All these two Rydberg series are converging on the ground state of the ${\mathrm{Ps}}^{\mathrm{\ensuremath{-}}}$ threshold.

Physical Review AMar 1, 198922 citations

Ground state andS-wave autodissociating resonant states of positronium hydride

Zong-Chao Yan, Y. K. Ho

The fully correlated calculations in Hylleraas coordinates for the nonrelativistic ground-state energy and the first three S-wave resonances of positronium hydride are reported. For the resonances, the positions and widths are determined using the method of complex-coordinate rotation. Our results significantly improve previous work. For example, the ground-state energy is about five parts in ${10}^{9}$ in accuracy, the lowest variational upper bound reported to date. A comparison with other previous work is made.The fully correlated calculations in Hylleraas coordinates for the nonrelativistic ground-state energy and the first three S-wave resonances of positronium hydride are reported. For the resonances, the positions and widths are determined using the method of complex-coordinate rotation. Our results significantly improve previous work. For example, the ground-state energy is about five parts in ${10}^{9}$ in accuracy, the lowest variational upper bound reported to date. A comparison with other previous work is made.

Physical Review AApr 1, 199972 citations

Positronium-hydrogen elastic scattering

Richard J. Drachman, S. K. Houston

We have investigated the elastic scattering of positronium atoms by hydrogen atoms below the excitation threshold at 5.1 eV, limiting the investigation to the spin-zero (singlet) state of the two electrons. Nonresonant $S$ -wave phase shifts have been obtained from normalizable trial functions by extracting the center-of-mass wave function and examining its spatial behavior. An effective-range expansion is fitted to the phase shifts and the previously obtained positronium-hydride bound-state energy to yield a scattering length $a\ensuremath{\cong}5.3{a}_{0}$ compared with Fraser's corrected exchange result, $a=7.28{a}_{0}$ ( ${a}_{0}$ is the Bohr radius). The stabilization method suggests that a resonance occurs at a scattering energy of 4.5 eV, about 0.6 eV below the excitation threshold. Using the complex rotation method, we have obtained evidence confirming the existence of the resonance and an estimate of its width of about 6 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}2}$ eV.We have investigated the elastic scattering of positronium atoms by hydrogen atoms below the excitation threshold at 5.1 eV, limiting the investigation to the spin-zero (singlet) state of the two electrons. Nonresonant $S$-wave phase shifts have been obtained from normalizable trial functions by extracting the center-of-mass wave function and examining its spatial behavior. An effective-range expansion is fitted to the phase shifts and the previously obtained positronium-hydride bound-state energy to yield a scattering length $a\ensuremath{\cong}5.3{a}_{0}$ compared with Fraser's corrected exchange result, $a=7.28{a}_{0}$ (${a}_{0}$ is the Bohr radius). The stabilization method suggests that a resonance occurs at a scattering energy of 4.5 eV, about 0.6 eV below the excitation threshold. Using the complex rotation method, we have obtained evidence confirming the existence of the resonance and an estimate of its width of about 6 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}2}$ eV.

Physical Review ASep 1, 197591 citations

Autodissociating Rydberg states of positronium hydride

Richard J. Drachman

The "molecule" positronium hydride (PsH), consisting of one atom each of positronium and hydrogen, has one well-known particle-stable state of total energy $E=\ensuremath{-}1.575$ Ry. In addition, for each $L$ it must have an infinite Rydberg series of excited states whose principal configuration is (${e}^{+}{\mathrm{H}}^{\ensuremath{-}}$), converging to a limit at $E=\ensuremath{-}1.0555$ Ry, the energy of ${\mathrm{H}}^{\ensuremath{-}}$. All of these excited states are energetically able to dissociate into ground-state Ps + H, and the higher-lying states can also decay with emission of excited Ps and ground-state H. These Rydberg states should appear as resonances in Ps + H scattering. In this paper I compute the lowest $S$ -wave resonance parameters, using an optical-potential formalism based on the (${e}^{+}{\mathrm{H}}^{\ensuremath{-}}$) configuration. The results are in rough agreement with those previously obtained using Kohn variational or complex-rotation techniques with highly correlated trial functions. The physical description of the PsH excited states is thus clarified.The "molecule" positronium hydride (PsH), consisting of one atom each of positronium and hydrogen, has one well-known particle-stable state of total energy $E=\ensuremath{-}1.575$ Ry. In addition, for each $L$ it must have an infinite Rydberg series of excited states whose principal configuration is (${e}^{+}{\mathrm{H}}^{\ensuremath{-}}$), converging to a limit at $E=\ensuremath{-}1.0555$ Ry, the energy of ${\mathrm{H}}^{\ensuremath{-}}$. All of these excited states are energetically able to dissociate into ground-state Ps + H, and the higher-lying states can also decay with emission of excited Ps and ground-state H. These Rydberg states should appear as resonances in Ps + H scattering. In this paper I compute the lowest $S$-wave resonance parameters, using an optical-potential formalism based on the (${e}^{+}{\mathrm{H}}^{\ensuremath{-}}$) configuration. The results are in rough agreement with those previously obtained using Kohn variational or complex-rotation techniques with highly correlated trial functions. The physical description of the PsH excited states is thus clarified.

Physical Review AMay 1, 197952 citations

Positronium-hydrogen elastic scattering: The electronic S=1 state

Richard J. Drachman, S. K. Houston

We have continued our investigation into the elastic scattering of positronium atoms by hydrogen atoms, extending the work to include the spin-one (triplet) state of the two electrons. Once again we have extracted the $S$ -wave phase shifts from normalizable trial functions by examining the spatial behavior of the center-of-mass wave functions. An effective-range expansion linear in the positronium energy fits the results very well and leads to a scattering length ${a}^{(\ensuremath{-})}\ensuremath{\simeq}2.36{a}_{0}$, compared with the static result ${a}^{(\ensuremath{-})}=2.476{a}_{0}$ of Hara and Fraser. The $S$ -wave total and ortho-para conversion cross sections are calculated by making use of both $^{1}S$ and $^{3}S$ results. In the $^{3}S$ case, we see no indication of any resonances below the excitation threshold at 5.1 eV.We have continued our investigation into the elastic scattering of positronium atoms by hydrogen atoms, extending the work to include the spin-one (triplet) state of the two electrons. Once again we have extracted the $S$-wave phase shifts from normalizable trial functions by examining the spatial behavior of the center-of-mass wave functions. An effective-range expansion linear in the positronium energy fits the results very well and leads to a scattering length ${a}^{(\ensuremath{-})}\ensuremath{\simeq}2.36{a}_{0}$, compared with the static result ${a}^{(\ensuremath{-})}=2.476{a}_{0}$ of Hara and Fraser. The $S$-wave total and ortho-para conversion cross sections are calculated by making use of both $^{1}S$ and $^{3}S$ results. In the $^{3}S$ case, we see no indication of any resonances below the excitation threshold at 5.1 eV.

Physical Review AAug 1, 197661 citations

Variational treatment of positronium molecules

M. M. H. El-Gogary, M. A. Abdel-Raouf, M Y H Hassan +1 more

A variational treatment for obtaining the binding energies, wavefunctions and internal distances of the positronium molecule (Ps 2 ) is presented. For this purpose, very modern Hylleraas-type trial wavefunctions, as well as different envelope functions ( upsilon m6 e - gamma upsilon where m 6 =0, 1, 2, 3 and upsilon is the distance between the two positrons), are employed. The resulting binding energies show excellent convergence when the number of components of the wavefunction considered is increased. Our results at m 6 =2 show that only 22 components of our wavefunction are sufficient for obtaining the binding energy omega P(s 2 )=-0.03 Ryd (=-0.41 eV) which is identical to the binding energy calculated by Ho via 400 components of his trial wavefunctions. The best convergence, however, has been achieved via 22 components of our wavefunctions at m 6 =1. In this case, omega P(s 2 )=-0.042 Ryd (=-0.573 eV). Comparison with the very recent value of omega P(s 2 )(=-0.435 eV) determined by Kinghorn and Poshusta (1993) and Kozlowski and Adamowicz (1993), using 300 components of their trial wavefunctions, supports the opinion that the exact binding energy of Ps 2 is less than -0.41 eV. Our average values for the internal distances of Ps 2 agree quite well with those determined by previous authors and emphasize the argument that the size of the molecule is decreased when the binding energy is lowered.A variational treatment for obtaining the binding energies, wavefunctions and internal distances of the positronium molecule (Ps 2 ) is presented. For this purpose, very modern Hylleraas-type trial wavefunctions, as well as different envelope functions ( upsilon m6 e - gamma upsilon where m 6 =0, 1, 2, 3 and upsilon is the distance between the two positrons), are employed. The resulting binding energies show excellent convergence when the number of components of the wavefunction considered is increased. Our results at m 6 =2 show that only 22 components of our wavefunction are sufficient for obtaining the binding energy omega P(s 2 )=-0.03 Ryd (=-0.41 eV) which is identical to the binding energy calculated by Ho via 400 components of his trial wavefunctions. The best convergence, however, has been achieved via 22 components of our wavefunctions at m 6 =1. In this case, omega P(s 2 )=-0.042 Ryd (=-0.573 eV). Comparison with the very recent value of omega P(s 2 )(=-0.435 eV) determined by Kinghorn and Poshusta (1993) and Kozlowski and Adamowicz (1993), using 300 components of their trial wavefunctions, supports the opinion that the exact binding energy of Ps 2 is less than -0.41 eV. Our average values for the internal distances of Ps 2 agree quite well with those determined by previous authors and emphasize the argument that the size of the molecule is decreased when the binding energy is lowered.

Journal of Physics B Atomic Molecular and Optical PhysicsNov 28, 199510 citations

{10}^{9}

in accuracy, the lowest variational upper bound reported to date. A comparison with other previous work is made.

S

-wave phase shifts have been obtained from normalizable trial functions by extracting the center-of-mass wave function and examining its spatial behavior. An effective-range expansion is fitted to the phase shifts and the previously obtained positronium-hydride bound-state energy to yield a scattering length $a\ensuremath{\cong}5.3{a}_{0}$ compared with Fraser's corrected exchange result,

a=7.28{a}_{0}

(

{a}_{0}

is the Bohr radius). The stabilization method suggests that a resonance occurs at a scattering energy of 4.5 eV, about 0.6 eV below the excitation threshold. Using the complex rotation method, we have obtained evidence confirming the existence of the resonance and an estimate of its width of about 6 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}2}$ eV.

L

it must have an infinite Rydberg series of excited states whose principal configuration is (${e}^{+}{\mathrm{H}}^{\ensuremath{-}}$), converging to a limit at $E=\ensuremath{-}1.0555$ Ry, the energy of ${\mathrm{H}}^{\ensuremath{-}}$. All of these excited states are energetically able to dissociate into ground-state Ps + H, and the higher-lying states can also decay with emission of excited Ps and ground-state H. These Rydberg states should appear as resonances in Ps + H scattering. In this paper I compute the lowest

S

-wave resonance parameters, using an optical-potential formalism based on the (${e}^{+}{\mathrm{H}}^{\ensuremath{-}}$) configuration. The results are in rough agreement with those previously obtained using Kohn variational or complex-rotation techniques with highly correlated trial functions. The physical description of the PsH excited states is thus clarified.

S

-wave phase shifts from normalizable trial functions by examining the spatial behavior of the center-of-mass wave functions. An effective-range expansion linear in the positronium energy fits the results very well and leads to a scattering length ${a}^{(\ensuremath{-})}\ensuremath{\simeq}2.36{a}_{0}$, compared with the static result ${a}^{(\ensuremath{-})}=2.476{a}_{0}$ of Hara and Fraser. The

S

-wave total and ortho-para conversion cross sections are calculated by making use of both

^{1}S

and

^{3}S

results. In the

^{3}S

case, we see no indication of any resonances below the excitation threshold at 5.1 eV.