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.