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.
In other words the diffusion equation (per unit volume) can be understood as follows:
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. Flux 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.