by G. Sardin
Copyright © 10 March 2000. All right reserved
Introduction
Here we will focus on a specific feature of the deuteron consisting in the presence of a hole in the center of its structure, i.e. a charge density deficiency in the center of the deuteron. But we will first briefly review the more significant aspects of the deuteron quantum structure and nuclear forces.
Experimental Data
Let us start with a short quotation from reference (1) that represents the topic epicenter of our present concern:
"Scattering experiments of high energy electrons on deuterons have provided an independent evidence of the presence of a highly repulsive zone in the nucleonic potential. These experiments have also demonstrated that there is a hole in the center of the deuteron charge distribution, i.e. the proton avoid the center of the deuteron, presumably due to the intense repulsion from the nucleonic potential when getting too close to the neutron. The analysis of the electron-deuteron scattering experiments as well as the proton-proton ones indicate that the repulsive range if of the order of half a Fermi."
Main features of nuclear forces
Nuclear forces are strong, of short range, charge independent, spin dependent, subject to saturation and their most peculiar feature stands on their double attractive and repulsive behavior. In effect, their main role is indeed a cohesive one with an attractive range of a few Fermi, however at a range lower than the nucleons size i.e. below 1 Fm nuclear forces become repulsive. The cohesive factor is evidently the one incharged of building the high number of nuclear structures and of fixing their stability, while the repulsive factor leads to their saturation and instability.
Let us recall the high similitude between proton-proton and proton-neutron scattering experiments. It is of fundamental significance that both proton and neutron exhibit a repulsive positive core when getting in close contact in deep collisions, as shown in the experimental data of figure 1. From the orbital model neutron-proton scattering should effectively show similar patterns to the proton-proton scattering since the neutron core is considered to be a proton. As a consequence in both cases the dominant effect is a proton-proton collision, since the neutron shell with a quite low energy of only 1.29 MeV has a marginal energetic influence in regard to the high kinetic energies involved in the collision and the high massive energies of the protons. These facts strongly support the orbital structure attributed to the neutron and whose extension applies easily to the deuteron structure.
Fig. 1: Proton and Neutron Experimental Charge Distributions (1). Both exhibit a positive core (+) but the neutron exhibits also a negative shell (- ). The charge distribution of the shell has been represented by substracting the neutron and proton experimental charge distributions.
Deuteron structure from a quantum point of view
The simplest quanto-mechanical approach to a nuclear cohesive system is provided by the deuteron since it is a two bodies system, composed of only a proton and a neutron bound together by the nuclear force. Essential experimental data on the deuteron (1,3) stand on its bonding energy: D E = - 2.22 MeV, its nuclear spin: i = 1, its nuclear parity which is even, its magnetic moment: m = + 0.857 n.m., its radius of its charge distribution: r @ 1.1 Fm (2) and its quadrupolar electric moment: q = + 2.7 x 10-31 m2.
The fact the deuteron having an electric quadrupolar moment means that the distribution of its structure probability density goes off spherical symmetry which implies that the nuclear potential representative of the forces acting on the two nucleons has not a perfect spherical symmetry. The deviation q / r'2 is small and equal to about 6%, from which it is considered that the deuteron is in the L = 0 state during 96% of the time and the remaining 4% in the L= 2 state (1).
In short, the nucleic potential is not perfectly symmetrical since it has not a pure base 3S1 state and has a small 3D1 component. This result provides moreover the correct magnetic moment of the deuteron: m = + 0.857 n.m which differs of about 3% from the value m = + 0.8793 n.m that it would give if the deuteron was in a pure S state, since then it would just be equal to the sum of the neutron and proton magnetic moments, respectively equal to: mp = + 2.7896 n.m and: mn = - 1.9103 n.m (1). Following this brief review of the main characteristics of the deuteron let us now introduce the orbital approach applied to it (2).
Deuteron structure from the orbital point of view
(a)
(b) (c)
Fig.1: (a) Deuteron, (b) Neutron, (c) Proton. The neutron (b) is considered to be made of a negative shell and a positive core which is nothing else but a proton (c). The deuteron (a) is thus considered made of two core protons bonded by a shell. This shell proceeds from the neutron and is then shared by both protons. It acts as a bonding shell which is the carrier of nuclear forces.
The orbital standing attributes the hole in the center of the deuteron structure (fig.1.a) to the repulsive electrostatic forces between the two core protons. Instead, the wrapping shell stresses them together and thus an equilibrium must be reached between these two opposite forces. The separation of the two core protons at which this equilibrium is sustained corresponds to the central hole experimentally observed in the structure of the deuteron. At the corpuscular level, this hole is due to the related low density of presence of the positive carrier of the proton’s structure in the interspace of maximum repulsion between the two protons structuring orbitals.
In the standard proton-neutron standpoint of nuclear systems the origin of the repulsive force is a mystery, and in fact also the one of attractive force. How attractive forces up to some distance become repulsive at a lower one? The plain neutron-proton interaction has no straightforward answer to bring. Instead, within the orbital model the repulsive component comes from the electrostatic repulsion between the two core protons, while the attractive component rises from the shell, which being negatively charged is attracted by the two protons core and since shared by both it acts hence as a link. However, the shell cohesive energy is not purely electrostatic but is instead mainly fixed by its quantum state. This can be pictorially expressed as the shell quantum stress, i.e. the energy departure from classical electrostatic equilibrium. So, the actual system equilibrium and bonding energy are dominated by quantum mechanical rules.
Other models
Let us stress that this phenomenological analysis cannot be provided either by the Yukawa forces nor by the QCD gluonic forces.
In the Yukawa model, due to the interchange of a p– pion, the neutron alternatively transforms into a proton and vice-versa. Therefore a repulsive force cannot take place between the two nucleons since only one is charged at the time.
Similarly, from the QCD a repulsive force between the neutron and the proton is not easily conceived since the residual gluonic field which bonds them is electrically neutral and thus does not affect the nucleons electric charge but only their color charge. So, in the QCD context, the quarks cohesion within nucleons is based on the gluonic field. The origin of the attractive forces between nucleons may appeal to some external residual attraction of this field, however the origin of the repulsive forces cannot be invoked in any reliable way. So, the attraction-repulsion between nucleons and its equilibrium can hardly be conceived from QCD in terms straightforward enough to have a chance of being somewhat realistic.
In any case the assumptions made in the orbital approach are incommensurably simpler, do not appeal to strange hypothetical forces and to unobserved fractional electric charges, but to forces derived from the electric field and the unitary integer charge is preserved. So, the orbital model is the sole one which provides at once an explanation to the attractive and repulsive forces between nucleons and to their equilibrium, with an approximation to realism, i.e. without the need of appealing to a lot of conceptual jokers. Any model preserving the neutron structure within the nucleus will be in trouble for giving account of the attraction-repulsion feature of nuclear forces in a credible way.
Summary
In short, from the orbital model the
deuteron central deficiency of charge density derives straightforwardly
from the proposed orbital structure of the neutron, considered formed by
a core proton and a shell. The neutron shell sharing with an extra proton
leads to the deuteron, which has hence a two protons core. So, the deuteron
central deficiency of charge density rises from the logical separation
between the two core protons due to the mutual repulsion of their positive
charge, while the negative wrapping shell keeps them bonded. These two
opposite effects lead in the case of the deuteron to a stable equilibrium
between cohesive and dispersive forces.
References
(1) R. Eisberg & R. Resnick, Quantum Physics: Elementary Particles (Chapter 17), John Wiley & Sons, Inc. (1974)
(2) G. Sardin, Unitary Orbital conception of Elementary Particles and their Interactions, N. Segroeg editor & publisher (Barcelona), ISBN:8460580067 (1998).
(3) International Council for Science,
CODATA-Committee on Data for Science and Technology, http://www.codata.org/