No.
" RESNUCLE results " is φ_int / φ_o，
" Number of stars generated per beam particle " is x/λ (if x<<λ) ，
" sigma " is 1/nλ.
λ is the mean free path and is a property of the target material (and the particle type and energy).
x, being the target thickness, is a property of the target geometry, which σ has no vocation to depend on.
Number of stars generated by prompt PROTON (which is how it should be read) is the nuclear reaction rate, i.e., the probability that a proton undergoes a nuclear reaction, in the thin target assumption (x<<λ; for thick targets instead, all this does not apply in view of the energy degradation of the beam particles, which changes λ along the target thickness, and the re-interaction of reaction products inside the target).