Confusion about the cross-section

Physics, Transport and Magnetic Fields
1

Dear experts,
I have recently been studying the use of FLUKA to calculate reaction cross-sections and reaction yields.
While learning on the forum, I came across this discussion Measurement of cross section that mentioned…

sigma[mb] = A[g/mol]/(λ[cm] ∗ ρ[g/cm3] ∗ NA[mol−1]) ∗ 10^27

“ You need to divide the RESNUCLE results by Number of stars generated per beam particle: Prompt radiation generated by PROTON, and multiply by sigma where lambda [cm] is also printed in the output file ( Inelastic Scattering Length for PROTON at Beam energy ).”

  • I don’t understand what "λ" refers to, and I’m also unclear about " Prompt radiation generated by PROTON." Could you help clarify my confusion?

Additionally, I consulted books and articles.

The books provide a definition of nuclear reaction cross-section:
σ = N / INs [1]
N is the number of reactions occurring per unit time,
I is the number of incident particles per unit time,
and Ns is the number of target nuclei per unit area.

The articleTransport model predictions of 225Ac production cross sections via energetic p, d and α irradiation of 232Th targets provide a definition of nuclear reaction cross-section:
σ = - ln( 1 − φ_int / φ_o) / nx [2]
Simplify it:
σ = (φ_int) / (φ_o * n * x) [3]
φ_int is the number of product nuclei,
φ_o is the number of incident particles incident on the target,
n is the number of target nuclei per unit volume,
and x is the thickness of the target.

It can be seen that Equation [1] and Equation [3] are equivalent.
（ nx = Nx/V = x[cm] ∗ ρ[g/cm3] ∗ N_A[mol−1] / A[g/mol] )

  • Can I consider that…
    In the forum:
    " RESNUCLE results " is φ_int，
    " Prompt radiation generated by PROTON " is φ_o ，
    " sigma " is 1/nx
    Is this understanding correct? If it is correct, why does it say in the forum that λ is "Inelastic Scattering Length for PROTON at Beam energy" ? I have checked the .out file. It is stated in the "Material" section that the value of λ is in the teens, which is not the same as the target thickness x.
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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).

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Thank you so much for valuable comments…I think I roughly understand now.…if I have problem…I will get back. Best regards