  Self-interacting dark matter has been proposed as a hypothesis to explain the
shallow central slopes of the density profiles of dark matter halos in
galaxies. In order to be consistent with observational studies at scales of
galaxy clusters, the cross section should scale inversely with the velocity of
collision. In this paper we consider the mass density profile of the halo of
the low surface brightness (LSB) galaxy NGC 5963 to place an upper limit on the
dark matter cross section for collisions with velocities $\sim 150$ km
s$^{-1}$, i.e. at the low velocity regime. After calibrating against
cosmological simulations, we found that the large inferred dark matter
concentration and central dark matter density in NGC 5963 are inconsistent with
an effective collisional cross section per unit of mass >0.2 cm^2/g.
Corrections were applied in order to account for reduction of the core by the
adiabatic contraction caused by cooling baryons. Our limits that involve a
number of simplifying, but always conservative, assumptions, exclude the last
permitted interval for velocity-dependent cross sections to explain the flat
density core in LSB galaxies. Implications for the nature of dark matter are
also discussed.
