thought on the "Random close packing of binary hard spheres predicts the stability of atomic nuclei"

 There was an interesting article in arxiv. https://arxiv.org/abs/2405.11268

Apparently , it claims that the mean ratio between proton and neutron in stable nuclei can be explained by the Random close packing of two hard spheres with different size. 

According to the article, Z/N ~ 0.75 gives maximal packing/maximul number density for protons(r~ 0.84 fm) and neutrons(r~ 1fm) without any adjustable parameters. This is roughly the same as the slope of stable line in nuclear chart. 

This is interesting. However, is it really correct approach? The estimation does not involves any Coulomb repulsion or interaction between nucleons. (It may corresponds to the very hard repulsive core and very attractive interaction so that the maimal packing gives minimum energy.) 

As far as I can understand, the ratio between total volume and the sum of volumes of hard spheres  is estimated as $\phi ~ 0.661 ~ 1/8 (sum of volumes of hard spheres)/(total volume)$. Using $r_p~0.84$fm , $r_n~1$fm and maximal packing condition $Z/N~0.75$, one would get the number density of inifinite nuclear matter as ~ 1.5 nucleons/fm^3. This seems to be not right. Right?  (Or should one remove 1/8? in that case, it will be about 0.19 nucleons/fm^3 roughly correct value.) I am not sure whether it is a correct estimation...