  We analyze the scattering problem of identical bosonic particles confined on
a spherical surface. At low scattering energies and for a radius much larger
than the healing length, we express the contact interaction strength in terms
of the s-wave scattering length. Adopting this relation, we are then able to
regularize the zero-point energy of the spherical Bose gas and to obtain its
equation of state, which includes the corrections due to the finite radius of
the sphere and coincides with the flat-case result in the infinite-radius
limit. We also provide a microscopic derivation of the superfluid density of
the system, reproducing a result postulated in a previous work. Our results are
relevant for modeling the ongoing microgravity experiments with two-dimensional
bubble-trapped Bose-Einstein condensates.
