Effects of collisions on the magnetic quenching of positronium

A theory describing the behavior of positronium (Ps) in a magnetic field is presented including the effects of Ps collisions. Such effects are especially important if the Ps is formed in a medium containing unpaired electrons since Ps collisions with these electrons can provide an effective spin exchange mechanism. By integrating the equation of motion for the density matrix, it is shown that the dependence of any annihilation yield N on the static magnetic field x is of the form N (x) = (g + hx + kx2) / (l + mx2) for a wide class of quenching mechanisms with time independent reaction rates. The coefficients g, h, k, l, and m are evaluated explicitly for the 2γ and 3γ yields from Ps formed from polarized positrons assuming that the quenching mechanisms can be characterized by an effective spin exchange rate and an effective pickoff rate. The yields are also evaluated assuming zero positron polarization in formulas which include the interesting Ps chemical reaction rates directly. The formulas derived can be used to obtain information about such chemical reaction rates from magnetic quenching data. Diagrams which permit the quick estimation of magnetic quenching effects as a function of the quenching rates are presented. The formalism has also been extended to include an rf magnetic field and is used to compute the shift of the measured Ps hyperfine structure interval as a function of quenching and microwave power. The shifts are found to be extremely small as expected.