  We present a study of the electronic structure, phonon frequencies and
electron-phonon coupling in hcp Sc under pressure. The electron-phonon coupling
constant is found to increase steadily with pressure in the hcp phase, until
the pressure reaches a value where the hcp phase becomes unstable. Calculations
for the normal pressure $c/a$ ratio predict a phase change somewhere between
calculated pressures of 22 and 30 GPa. The calculated frequencies for the
equilibrium hcp lattice parameters are in good agreement with the inelastic
neutron scattering results. From the measured value of the electronic specific
heat constant and the calculated values of the Fermi level density of states
and electron-phonon coupling constant, we conclude that the electron-paramagnon
coupling constant in hcp Sc should be comparable to the electron-phonon
coupling constant. This indicates that the spin fluctuation effects are strong
enough to suppress superconductivity completely in hcp Sc. Based on estimates
of the electron-paramagnon coupling constants and the calculated or estimated
electron-phonon coupling constants, we argue that the hcp phase may become
superconducting with a very low transition temperature immediately prior to the
transition to the Sc-II phase and that the Sc-II phase should indeed be
superconducting.
