  Spontaneous parametric down conversion has been shown to be a reliable source
of entangled photons. Amongst the wide range of properties that have been shown
to be entangled, it is the orbital angular momentum that is the focus of our
study. We investigate, in particular, the bi-photon state generated using a
Gaussian pump beam. We derive an expression for the simultaneous correlations
in the orbital angular momentum and radial momentum of the down-converted
Laguerre-Gaussian beams. Our result allows us, for example, to calculate the
spiral bandwidth with no restriction on the geometry of the beams: $\ell$, $p$
and the beam widths are all free parameters. Moreover, we show that, with the
usual paraxial and collinear approximations, a fully analytic expression for
the correlations can be derived.
