When scattering anomalies involving many phase shifts are to be studied, it appears desirable to treat the amplitudes directly before combining them into differential cross sections. Amplitudes suitable for the study of elastic collisions of charged and uncharged Fermi-Dirac particles of spin \textonehalf{}, taking account of possible identity are, therefore, given in forms convenient for computation. The case of coupling between states of the same total but different orbital angular momentum is not discussed. Formulas using the spin functions usually denoted by ${\ensuremath{\chi}}_{m}$ are supplemented by forms based on spin functions which transform like the components of an ordinary space vector, the latter allowing more compact expressions in some cases.