Phonons and superconducting p -state pairing in Pd

We present an analytical calculation of the electron-phonon parameters for s- and p-state pairing in Pd, λ₀ᵖʰ and λ₁ᵖʰ. The calculation is based on Doniach's six half-sphere Fermi-surface model for the heavy d electrons, a Debye and an Einstein model for intra- and intersphere phonon-scattering processes, respectively, and the LCMTO (linear combination of muffin-tin orbitals) representation to obtain the electron-phonon matrix elements. The group-theoretical method of Allen is employed in solving the anisotropic gap equation at the multiply sheeted Fermi surface for s- and p-state pairing interactions. The phonon-mediated interaction, Iᵖʰ(→k,→k^') is attractive for all momentum transfers, →k-→k^', and yields the BCS parameter, λ₀ᵖʰ=0.153, in agreement with Papaconstantopoulos et al. Our results for p-state pairing is λ₁ᵖʰ=0, when Einstein phonon model is used for both intra- and intersheet scattering processes and λ₁ᵖʰ=0.089λ₀ᵖʰ when the Debye model is applied to the small-momentum intrasheet transitions of the Cooper pairs. The weakness of the p-state interaction is due to the cancellation between the contributions from intrasheet scattering and from large-momentum intersheet scattering processes. A detailed discussion of the results is presented in terms of the parameters of our electron-phonon model.