Regarding the issue with lambda

[20244220042 (keying zhu)]

Continuing the discussion from Confusion about the cross-section:

Dear fluka experts,

Continuing the discussion from Confusion about the cross-section:

@ceruttif

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).

1. In FLUKA, is x << λ used to define a thin target? I’d like to know what order of magnitude this implies.
2. As referenced in literature OVERVIEW OF SECONDARY NEUTRON PRODUCTION RELEVANT TO SHIELDING IN SPACE: " Thin targets (thin enough to limit the energy loss in the target to 5% or less) are used for cross section measurements." LISE++ calculations confirm that a 30~MeV proton beam loses 1.176~MeV (3.92% of incident energy) when traversing a 0.0125~cm thorium target, satisfying the thin-target criterion. For proton energies above 30 MeV incident on a 0.0125 cm thorium target, the thin-target criterion defined in the literature is satisfied.However, when I examine the lambda values printed in the output file (“Inelastic Scattering Length for PROTON at Beam energy”), I find that lambda increases as the incident proton energy decreases. This would imply that lower incident proton energies better satisfy the x << λ condition. This contradicts the conclusion I obtained from LISE++ calculations (where energy loss decreases at higher energies). I believe there must be an error in my understanding and would appreciate correct guidance.
3. Additionally, upon inspecting the output file, I observed that the “Inelastic Scattering Length for PROTON at Beam energy” values are normal (tens of cm) for energies above 15 MeV . However, at 10 MeV , it shows an extremely peculiar value: 0.8532E+29 cm. I would like to understand the reason for this. Is it because, at 10 MeV, the incident proton energy is completely deposited within the thorium target, rendering the calculation of cross sections meaningless at this energy? Can the 0.0125 cm thorium target be considered a thin target in FLUKA for 15 MeV proton incidence?
4. Additionally, upon re-examining my input file, I noticed I used the default BEAMPOS card, placing the incident protons at (0, 0, 0), which coincides with the defined surface of the thorium target. Could this potentially affect my results?
   
   
   
   
   
   
   
   
   
   
   
   
   
   

This is my output file.
550.inp (2.0 KB)

I apologize for the numerous questions and sincerely appreciate the time you have taken to review my inquiries. I look forward to your guidance.
Wishing you all the best with your work.

[ceruttif (Francesco Cerutti)]

1. In FLUKA, there is no definition of ‘thin target’ whatsoever, since it’s not a concept required by the code.

2. Energy loss and inelastic scattering length are two independent quantities, whose respective behavior at lower energies does not imply any contradiction. The choice of the target thickness shall take into account both, which determine the reaction probability at the initial energy and the energy variation along the target.

3. The peculiar value you report should be read as infinite, i.e., corresponding to zero reaction cross section (being the incident energy below the Coulomb barrier). This implies that no reaction takes place and has nothing to do with the proton range in the target.

4. No, being the beam direction orthogonal to your target surface.