Low-energy neutrons

How can I calculate the capture cross-section of neutrons in a given target material?

In principle, you can get all the information you need on the FLUKA neutron cross sections by setting a printing flag in option LOW-NEUT. From the manual:

WHAT(4) = printing flag: from 0.0 to 3.0 increases the amount of
               output about cross-sections, kerma factors, etc.
               Default: 0.0 (minimum output)

However, the information is given in a form that is difficult to understand unless one is familiar with multigroup neutron transport codes. Anyway, one will get a table of which a few lines are reproduced here:

1                     CROSS SECTIONS FOR MEDIA     1
                      (RESIDUAL NUCLEI INFORMATIONS AVAILABLE)
 GROUP    SIGT    SIGST   PNUP   PNABS  GAMGEN NU*FIS   EDEP
DOWNSCATTER MATRIX 
          barn     barn  (PNEL    PXN   PFISS  PNGAM)  GeV/col
    1 5.826E+00 9.287E+00  .0000 1.5939 1.2904  .3886 1.536E-02   .3228
.0079   .0021   .0023   .0020   .0013   .0011   .0035
.......................................................................

   26 6.861E+00 6.697E+00  .0000  .9761 1.0609  .0181 1.458E-03
.......................................................................

Explanation of the relevant quantities:

Group 1 (the highest): Total cross section (SIGT) = 5.826E+00 barn
                      "Scattering" cross. s. (SIGST) = 9.287E+00 barn
                      Probability of Non Absorption (PNABS) = 1.5939

Group 26             : Total cross section (SIGT) = 6.861E+00 barn
                      "Scattering" cross. s. (SIGST) = 6.697E+00 barn
                      Probability of Non Absorption (PNABS) = .9761

The data for the first groups will probably look strange (scattering cross section larger than total cross section): the reason is that there is neutron production through (n,xn) reactions (fission is accounted for separately), and here "scattering" means "number of outgoing neutrons times cross section" or also "changing energy group". Since more than one neutron on average is exiting a collision, the probability of non absorption is larger than 1.

But looking at the lower groups (group 26 has been copied here as an example) one will see that the data make more sense. The absorption cross sections (all of them included) will be = total - scattering = 6.861 - 6.697 = 0.164 barn

Suppose that A=(number of neutrons created)+(number of neutrons absorbed) and B=(number of neutrons created)-(number of neutrons absorbed). Is it true that neutron balance (particle number 222) neut-bala is related to A and neutron (particle number 8) is related to B?

The neutron balance according to your definition is related to B. Is the term that enters in the diffusion equation for a steady in time solution. The diffusion equation is described as:

d(Flux(r))/dt = D*\Delta2(Flux(r)) + S(r) - \Sigma_abs*Flux(r)

where S(r) term describing the sources and \Sigma_abs the absorption cross section.
With words the diffusion equation is (per unit volume):

dFlux(r)/dt = -[outflow rate] + [production rate] - [absorption rate]

and for a steady state solution

[outflow rate] = [production rate] - [absorption rate] = neutron balance

The particle 8=neutron is scoring the neutron fluence, the quantity most frequently used for describing neutron fields. Fluence is defined as the number of particles that penetrate a sphere with a cross section of pi*r^2 = 1cm2 per unit of time and/or energy. Otherwise, the particles crossing a surface of 1cm2 that is ALWAYS perpendicular to the direction of the particle.

How do I define transport thresholds for low-energy neutrons?

In order to kill all low-energy neutrons below the group transport boundary one should use LOW-BIAS with WHAT(1) set to 1, i.e., selecting the highest energy group as cut-off boundary (inclusive). If you want to select a even higher neutron cut-off PART-THR has to be used which will then also stop the low-energy neutron group transport.

Example:
no neutron transport below 19.6 MeV

LOW-BIAS       1.0       0.0               Reg1     Reg2

no neutron transport below 500.0 MeV

PART-THR      -0.5   NEUTRON

Are cross section data for low-energy neutron transport available in FLUKA with take into account molecular bindings?

Yes, there are low-energy neutron cross section data sets available in FLUKA which take into account molecular bindings. The cross section data set has to be associated with the material by the card LOW-MAT. See Chapter 10 of the manual for a list of available data sets.