Design calculations are presented for a pulsed neutron source comprising polychromatic protons accelerated from a metal foil by a short-pulse laser, and a LiF converter in which (p,n) reactions occur. Although the proton pulse is directional, neutrons are predicted to be emitted relatively isotropically. The neutron spectrum was predicted to be similar to the proton spectrum, but with more neutrons of low energy in the opposite direction to the incident protons. The angular depen- dence of spectrum and intensity was predicted. The (p,n) reactions generate unstable nuclei which decay predominantly by positron emission to the original 7Li and 19F isotopes. For the initial planned experiments using a converter 1mm thick, we predict that 0.1% of the protons will undergo a (p,n) reaction, producing 109 neutrons. Ignoring the unreacted protons, neutrons, and prompt gamma emission as excited nuclear states decay, residual positron radioactiv- ity (and production of pairs of 511 keV annihilation photons) is initially 4.2MBq decaying with a half-life of 17.22 s for 6mins (19Ne decays), then 135Bq decaying with a half-life of 53.22 days (7Be decays).