# The central density of a nucleus remains roughly constant?

Let A be the atomic number

The density of a nucleus is computed using the ratio of the number of protons and neutrons, A, to the volume of the nucleus (which at my current level, is assumed to be a sphere)

The math is trivial.

Conceptually, the argument for the central density of a nucleus remaining roughly constant stems from the suggestion (from my text) that each nucleons feels a force only from it's nearest neighbour. As more nucleons are added to the nucleus, the central density increases but still lies within a range sufficient to be classified as being 'constant'.

This does not convince me. Is it necessarily true that a nucleon experiences constant force only from it's nearest neighbour? Suppose there exists a finite number number of nucleons, n, in the nucleus. Each nucleon then experiences a force from (n-1) number of nucleons. The other nucleon experiences also a force from (n-1) number of nucleons. By induction, and since these particles are indistinguishable-protons and neutrons are fermions- is it also not true then that every $$nucleon_i$$ experiences a constant force?

Could someone fill me in conceptually?