Master equations for thermal unimolecular reactions and the reverse thermal recombination reactions are solved for a series of model reaction systems and evaluated with respect to broadening factors. It is shown that weak collision center broadening factors F(cent) (wc) can approximately be related to the collision efficiencies β(c) through a relation F(cent) (wc) ≈ max {β(c) (0.14), 0.64(±0.03)}. In addition, it is investigated to what extent weak collision falloff curves in general can be expressed by the limiting low and high pressure rate coefficients together with central broadening factors F(cent) only. It is shown that there cannot be one "best" analytical expression for broadening factors F(x) as a function of the reduced pressure scale x = k(0)∕k(∞). Instead, modelled falloff curves of various reaction systems, for given k(0), k(∞), and F(cent), fall into a band of about 10% width in F(x). A series of analytical expressions for F(x), from simple symmetric to more elaborate asymmetric broadening factors, are compared and shown to reproduce the band of modelled broadening factors with satisfactory accuracy.