  We study the vortex matter phase diagram of a layered superconductor in the
presence of columnar pinning defects, {\it tilted} with respect to the normal
to the layers. We use numerical minimization of the free energy written as a
functional of the time averaged vortex density of the Ramakrishnan-Yussouff
form, supplemented by the appropriate pinning potential. We study the case
where the pin density is smaller than the areal vortex density. At lower pin
concentrations, we find, for temperatures of the order of the melting
temperature of the unpinned lattice, a Bose glass type phase which at lower
temperatures converts, via a first order transition, to a Bragg glass, while,
at higher temperatures, it crosses over to an interstitial liquid. At somewhat
higher concentrations, no transition to a Bragg glass is found even at the
lowest temperatures studied. While qualitatively the behavior we find is
similar to that obtained using the same procedures for columnar pins normal to
the layers, there are important and observable quantitative differences, which
we discuss.
