Intermediate mass Higgs bosons at TeV $e\gamma$ colliders in the ${\cal {MSSM}}$

We study the cross sections for the production of intermediate mass Higgs bosons via the reactions $e^-\gamma\rightarrow \nu_eW^-\Phi^0$, $e^-\gamma\rightarrow \nu_eH^-\Phi^0$, $e^-\gamma\rightarrow e^-Z^0\Phi^0$ and $e^-\gamma\rightarrow e^-H^+H^-$ in the Minimal Supersymmetric Standard Model (with $\Phi^0=H^0,h^0$ and, where possible, $A^0$) at TeV energies, taking into account $b$--tagging capabilities. We find that the rates for $e^-\gamma\rightarrow \nu_eW^-\Phi^0$ are large enough to permit the discovery of at least one between $h^0$ and $H^0$ over the whole intermediate mass range of $M_{A^0}$, at all $\tan\beta$, using the $(jj)(b\bar b)$ final state. The ${\cal {CP}}$-odd neutral $A^0$ and the charged $H^\pm$'s can be detected via the processes $e^-\gamma\rightarrow \nu_eH^-A^0$, with $A^0\rightarrow b\bar b$, and $e^-\gamma\rightarrow e^-H^+H^-$, resorting to the leptonic decay $H^\pm\rightarrow \nu_\tau\tau^+(\bar\nu_\tau\tau^-)$, but only for $M_{A^0}\approx60$ GeV. Finally, we present explicit formulae for the helicity amplitudes of these processes.