The NEUTRON CHARGE DENSITY and its CLASSICAL RADIUS

1. The neutron and proton radial charge density

Let us focus here on an experimental information concerned with the radial dependance of the charge density of the proton and the neutron, as shown in figure 1. Although it has been a text book knowledge for years, its deep relevance and significance has not been clearly understood and still less satisfactorily used.

Fig.1: Radial dependance of the charge density of the proton and the neutron. The neutron clearly shows a positive core (zone +) and a negative shell (zone -). The radial charge distribution of the neutron shell has been deduced from the neutron and the proton charge distribution.

It is well known that the nucleonic potential becomes repulsive at a distance of the order half a Fermi, evidencing hence the presence of a repulsive core. In the orbital conception of elementary particles it has been conferred to this experimental information all the relevance that it deserves. Within its context, the neutron is considered to be formed by a positive core, which is nothing else but a proton, and by a negative shell. The proton is itself structured by the orbital spun by a c+ corpuscular carrier. The shell is instead structured by an orbital spun by a c- carrier. It is considered to be very reactive due to its affinity to be shared with other neighboring protons. For example the neutron shell (unstable) has a strong trend to accommodate a second proton in its core, which increases its stability, leading to the deuteron (stable). In further building steps the primary trend is to preserve two protons for each c- wrapping carrier, which acts as the cohesive element of the nuclear structure. The departure from this primary trend is due to secondary effects, e.g. shielding and saturation.

The orbital conception of the neutron is in agreement with Fig.1 in which its radial distribution of the charge density clearly evidences a positive core (zone +) and a negative shell (zone -). The proton core is the cause of the repulsive potential at a distance of about 0.5 Fermi and the shell plays the role of an attractive bonding element. The added charge distribution of the shell has been directly deduced from the one of the proton and the neutron.

The quark model of the neutron (u,d,d) with fractional charges (+2/3, - 1/3, -1/3) does not implicitly predict a positive core and a negative shell neither the nucleonic repulsive core potential, and is hardly able to account for it without appealing to highly artificial and twisted arguments, as always do the quark model and its supporting QCD, such as all their ad hoc properties e.g. fractional electric charges, colors, gluonic interactions, and ad hoc etc...

2. The neutron classical radius

The classical radius of the neutron can be derived straightforwardly from the potential energy. The orbital conception of the neutron assumes that it is made of a core and a shell. The core corresponds to a proton whose structural orbital is spun by a corpuscular carrier (c+) with positive electric charge. The structuring orbital of the shell is instead spun by a corpuscular carrier (c-) of negative electric charge. In such a frame, the shell has hence a mass which corresponds to the mass difference between the neutron and the proton, i.e. 1.29 MeV/c2. Let us now consider a corpuscle c- falling from infinity into the field of a proton, until acquiring a potential energy of 1.29 MeV.

The potential energy E = Integral of F(x)dx. In a Coulomb field E = Integral of (q^2/x^2)dx. Hence, a unitary electric charge q falling in a Coulomb field from infinity down to a distance r to the field epicenter (e.g. a proton) will acquire a potential energy: E = q^2/r. Since the neutron shell has an energy of 1.29 MeV, thus r = q^2/E = 1.1*10^-15 m, i.e. the classical radius of the neutron is equal to about 1.1 Fermi. The orbital approach to the neutron structure provides a simple way to get its classical radius, whose value is in good agreement with experimental data.