Model in FLUKA for p-B fusion

Dear expert

I am studying the p-b fusion reaction shown in following equation with proton energy 675 keV.

p + 11B  → 12C* → 3 α

I also read the PEANUT model from The Physics of High Energy Reactions and ppt.

The INC model simulate reaction for energy range above 50 MeV, than the excited residual nucleus undergoes pre-equilibrium, Fermi break-up and final gamma de-excitation.

Following is my question.

1. What is the model in FLUKA to simulate the reaction p + 11B → 12C* for proton energy < 50 MeV. I mean the cross section of this reaction depending on energy of proton and relation between excitation energy of 12C* and energy of proton.

2. Does the Fermi Break-up modeling the reaction that 12C* becomes alpha particles?

3. For Fermi break-up, I only see the probability for break up into n fragment. How to determine the energy, momentum and excitation energy of each fragment. Does there are any document describes this problem in detail?

Dear Jeff,

The integrated cross section for protons on target nuclei in FLUKA is implemented as a general effective parametrized expression fitted to experimental nuclear reaction data. For p on ^{11}\textrm{B} at the particularly low energies you care about, it was directly fitted on EXFOR data.

and relation between excitation energy of 12C* and energy of proton.

This follows from elementary kinematics: you start with a proton at a given kinetic energy E_\textrm{p}, a target ^{11}\textrm{B} at rest, you evaluate the invariant mass of this system of particles, you subtract from it the rest mass of ^{12}\textrm{C} and this gives you the excitation energy of ^{12}\textrm{C}^* . In your case, with E_\textrm{p}=675 keV, you should get to an excitation energy of 16.575 MeV.

Does the Fermi Break-up modeling the reaction that 12C* becomes alpha particles? For Fermi break-up, I only see the probability for break up into n fragment. How to determine the energy, momentum and excitation energy of each fragment. Does there are any document describes this problem in detail?

Indeed, Fermi break-up is the model which describes the split of the formed compound ^{12}\textrm{C}^* into three alphas. This is done on phase-space considerations. Indeed, the probability for break-up into n\geq2 fragments follows from e.g. Eq (1) of this paper https://www.sciencedirect.com/science/article/pii/S0090375214005018?via%3Dihub , while the angular distribution for n-body emission is based on the n-body phase-space distribution, see e.g. https://cds.cern.ch/record/864958/files/p1.pdf as a general reference.

The possible excitation energy of the fragments is taken from nuclear level information and is explicitly fixed when a Fermi break-up channel is defined. E.g. we have (among other) both

p+11B -> a + 8Be_gs  -> a + a + a

and

p+11B -> a + 8Be_1st -> a + a + a

with respective excitation energies of 0 and 3.3 MeV for ^8\textrm{Be} as per its nuclear-level structure (see e.g. ENSDF) and respective likelihoods set by the prescrition above.

With kind regards,

Cesc

Dear Cesc