The origin of the dramatic shifts observed in the temperature dependence of positron-annihilation characteristics (particularly lifetime and Doppler-broadening line shape) near $T_c$ in the cuprates is not presently clear. Both intrinsic and extrinsic (i.e., defect-related) mechanisms have been proposed. To help clarify whether Cooper pairing is responsible for these shifts, we present an approximate formulation of the positron characteristics in a BCS superconductor. Relations are derived for the zeroth- and first-order terms in the ladder summation for the two-photon momentum density, with electron propagators represented in the Nambu-Gorkov form. The momentum densities in the normal and superconducting states differ appreciably only within the pairing shell centered at $p_F$. Numerical calculations are performed for two- and three-dimensional models. The differences increase with increasing Δ/μ but are relatively small in the first-order calculation. We also estimate an upper bound to the effect of BCS pairing on the positron characteristics, including terms to all orders in the electron-positron interaction. Based on comparisons of our model calculations with experiment, it seems unlikely that BCS pairing is responsible for the measured shifts in positron properties near $T_c$.

• Received 18 August 1989

DOI:https://doi.org/10.1103/PhysRevB.41.1789