Positron annihilation in liquid helium and liquid argon under an electric field

We have made new measurements of the lifetimes at 4.29 K and 2.92 K in He I, and at 2.14 K and 1.67 K in He II, without and with an electric field. At 4.19 K we have a new value of the lifetime, 2.01 +/- 0.002 ns, leading to a Z(eff) of 3.53 at zero field. In contrast to earlier reports, Z(eff) decreases very slightly as the temperature is lowered and the density increases. The orthopositronium lifetime at 4.19 K is 98.1 +/- 0.2 ns, at zero field, independent of field up to 18 kV cm(-1). At 4.19 K the free positron decay rate falls exponentially with increasing field to a value 5% below its zero-field value, the drop-off rate being 0.36 +/- 0.04 cm amagat V-1. From 28 through 50 V cm(-1) amagat(-1) the decay rate of the free component rises slowly as expected because of the increasing positronium fraction over the same range of electric field. In liquid argon there is positronium enhancement beginning at or below 3 V cm(-1) amagat(-1), which contrasts with 160 V cm(-1) amagat(-1) for argon gas. At least two lifetimes make up the long triplet component, suggesting different degrees of thermalization, or different states of positronium within the liquid. The effect of the electric field is to enhance the longer-lived, or more thermal component, in strong contrast with the findings of Charlton et al for the gas. The argon results suggest positron behaviour similar to that of electrons in the liquid phase, namely, such particles move in a conduction band subject to small effective scattering and diffusion cross sections. An analytic model in which the scattering length is an adjustable parameter yields the onset of positronium enhancement just below 3 V cm(-1) amagat(-1) when a(s) = -0.043 a(0), corresponding to an elastic scattering and diffusion cross section of 0.034 pi a(0)(2). Consequences for positron thermalization are discussed. A model of positronium losing energy slowly in the liquid without bubble formation is suggested.