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Physical Review A

Electron-spin amplitudes in the exchange quenching of orthopositronium

Sudha R. Swaminathan, Wyatt G. Merrill, Stephen Glynn, Joseph G. Quattrucci

Published Sep 21, 2012• 1 citation
Publisher

Abstract

We study single collisions between orthopositronium beams and targets with unpaired electrons, in which the conversion (quenching) of the long-lived orthopositronium into the short-lived parapositronium occurs as a result of electron exchange. We consider unpolarized and polarized targets with one and two unpaired electrons. Angular-momentum coupling and density-matrix techniques are used to calculate the probabilities of obtaining either para- or orthopositronium after the collisions. The probability of the initial orthopositronium being converted to parapositronium (quenching probability) is given in terms of complex scattering amplitudes labeled with total electron spin. Quenching probabilities are calculated for polarized and unpolarized targets, with and without detection of the spins of the targets after the collisions. Ratios of the probabilities of producing parapositronium to that of obtaining orthopositronium are given in terms of electron-spin amplitudes.

DOI
10.1103/physreva.86.032504

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We study single collisions between orthopositronium beams and targets with unpaired electrons, in which the conversion (quenching) of the long-lived orthopositronium into the short-lived parapositronium occurs as a result of electron exchange. We consider unpolarized and polarized targets with one and two unpaired electrons. Angular-momentum coupling and density-matrix techniques are used to calculate the probabilities of obtaining either para- or orthopositronium after the collisions. The probability of the initial orthopositronium being converted to parapositronium (quenching probability) is given in terms of complex scattering amplitudes labeled with total electron spin. Quenching probabilities are calculated for polarized and unpolarized targets, with and without detection of the spins of the targets after the collisions. Ratios of the probabilities of producing parapositronium to that of obtaining orthopositronium are given in terms of electron-spin amplitudes.
Abstract A single rearrangement collision between two spin-polarized orthopositronium beams leading to the production of either negative or positive positronium ions is studied. Negative or positive ions can be produced by the attachment of an electron or positron to a positronium atom, respectively. The probabilities for the formation of all possible spin states for both types of positronium ions are determined. The spin scattering matrix constructed using angular-momentum coupling as well as the spin density matrix containing the probabilities are given. The probabilities depend on the angle between the polarization vectors of the incoming beams and the real parts of complex scattering amplitudes labeled with total electron and total positron spin. We describe the effect of the spin alignment between the two beams on the probabilities and how the annihilation rates for ion decay and the real parts of the amplitudes can be obtained.
Polarization phenomena in collisions between one-electron (alkali-like) atoms are calculated with density-matrix techniques. The kinetic energies for which this treatment is valid are limited from above by the use of the Born-Oppenheimer approximation, and from below by the assumed degeneracy of the hyperfine states. The basic mechanism for polarization changes is the electron-exchange effect, as suggested by Purcell and Field and by Wittke and Dicke. The special situation of unpolarized targets is treated in some detail. In this case, there are two numbers which characterize the scattering through any angle: the absolute values of certain direct and exchange scattering amplitudes, Fd{F}_{d}Fd​ and Fx{F}_{x}Fx​. All cross sections must be expressible in terms of ∣Fd∣|{F}_{d}|∣Fd​∣ and ∣Fx∣|{F}_{x}|∣Fx​∣, and this is explicitly carried out in two cases of special interest. One refers to the case in which only the electron-spin polarization is measured, and the other to measurements of the polarization of the hyperfine states of the scattered atom. Effects of the identity of the atoms are also studied in detail.
The quenching processes of the thermalized orthopositronium $(o\ensuremath{-}\mathrm{Ps})$ on an oxygen molecule have been studied by the positron annihilation age-momentum correlation technique. The Doppler-broadening spectrum of the 511-kev $\ensuremath{\gamma}$ rays from the $2\ensuremath{\gamma}$ annihilation of $o\ensuremath{-}\mathrm{Ps}$ in O2{\mathrm{O}}_{2}O2​ has been measured as a function of the $o\ensuremath{-}\mathrm{Ps}$ age. The rate of the quenching, consisting of the pickoff and the spin conversion, is estimated from the positron lifetime spectrum. The ratio of the pickoff quenching rate to the spin-conversion rate is deduced from the Doppler broadening of the 511-kev $\ensuremath{\gamma}$ rays from the annihilation of the $o\ensuremath{-}\mathrm{Ps}.$ The pickoff parameter 1Zeff,{}^{1}{Z}_{\mathrm{eff}},1Zeff​, the effective number of the electrons per molecule that contribute to the pickoff quenching, for O2{\mathrm{O}}_{2}O2​ is determined to be $0.6\ifmmode\pm\else\textpm\fi{}0.4.$ The cross section for the elastic spin-conversion quenching is determined to be $(1.16\ifmmode\pm\else\textpm\fi{}0.01)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19} {\mathrm{cm}}^{2}.$
We consider electron spin-exchange collisions between an atom with an electron spin of \textonehalf{} and a target atom with an arbitrary electron spin. The cross sections that describe the collision are expressed in terms of generalized direct and exchange amplitudes and are shown to depend only on the electron spin, polarization, and alignment of the target atom. We include the effects of an external magnetic field and the nuclear spin of the spin-\textonehalf{} atom on the collision. We calculate the cross sections connecting the initial and final states of the free Hamiltonian describing the spin-\textonehalf{} atom, with analytic results being displayed for the two limiting cases of the external magnetic field. For the general case, graphical results are presented for several common values of nuclear spin that allow the cross sections to be evaluated for arbitrary magnetic fields. The results are applied to several situations of current interest.
The measurement by Duff and Heymann in 1962 of the pressure-proportional pick-off quenching rate of orthopositronium in helium gas may be interpreted as giving an effective number of electrons per atom in a singlet state relative to the positron of 0 108 ± 0 010 for thermal orthopositronium kinetic energies. A trial wave function used in the study of collisions of orthopositronium with helium, arising from an extension of work by Fraser in 1962, is employed to calculate this effective number of electrons. The unsatisfactory result at low energies is 0.019. A possible improvement in the collision trial wave function is suggested.
The role of a uniform magnetic field in the collision of two one-electron atoms is analyzed using previously developed density-matrix techniques. During the collision, all magnetic-moment interactions are small compared to the usual singlet and triplet potentials, and the only effect of the magnetic field is to alter the asymptotic states. This effect may be described in terms of the unitary transformation which diagonalizes the Breit-Rabi Hamiltonian. The properties of this transformation are given in detail for electronic spin \textonehalf{} and arbitrary nuclear spin. In addition to presenting a general formulation for this scattering problem, explicit formulas are given for spin exchange in the scattering of polarized beams from unpolarized targets.