Input parameters
Every number of particles for filled shells defines also the number of particles to be used in a given calculation. We use the number of particles to define the density of the system
$$
\rho = g \frac{k_F^3}{6\pi^2},
$$
where you need to define \( k_F \) and the degeneracy \( g \), which is two for one type of spin-\( 1/2 \) particles and four for symmetric nuclear matter.
With the density we can define the length \( L \) of the box used with periodic boundary contributions, that is use the relation
$$
V= L^3= \frac{A}{\rho}.
$$
Finally we can use \( L \) to define the spacing to set up the spacing between varipus \( k \)-values, that is
$$
\Delta k = \frac{2\pi}{L}.
$$
Here, \( A \) can be the number of nucleons.