Added January, 27, 2004, revised January 28, 2004


The Structure of Matter as of 1955

The recent article in the Meta Research Bulletin, Volume 12, No. 4, "The Structure of Matter in the Meta Model", is an interesting attempt to push deductive reasoning into a new area - the very small world of the nucleus. It got me to get out and review my old 1955 textbook, The Atomic Nucleus, by Robley D. Evans. That was the first Nuclear Physics course I took at MIT in 1957, taught by Robert A. Dudley and Robley Evans himself. In the preface, Evans states that the book is an experimentalist's 20 year confrontation with the current theory of that time, which was before quarks were introduced but after a great deal of work on nuclear structure and nuclear systematics had been done. The Big Bang was only mentioned once in passing, but it was called a "Great Event", 3 billion years ago, in the context of Alpher and Herman's analysis of nuclear abundances in meteorites.

1955 Nuclear Physics

Evans started out with chapters on: Charge; Nuclear Radius; Mass; Nuclear Moments, Parity and Statistics; and then on to Hyperfine Structure; Conservation Laws; Isotopic Abundance; Nuclear Systematics; Binding Energy; Nuclear Forces; and Nuclear Models including the Shell and Liquid Drop models. Everything was subject to extensive experimental data that led to the same answer from many different directions, like the fundamental radius of a single nucleon.

Of most interest to me was the 4th chapter discussing angular momentum, nuclear magnetic moments and electric quadrupole moments. Angular momentum is made up of individual nucleon spins, often paired, plus orbital angular momentum. The allowed combinations are quantized, and only appear with fixed quantum numbers. This leads to nuclei obeying Fermi-Dirac statistics with Pauli exclusion, or Bose-Einstein statistics without Pauli exclusion. Parity, which has to do with a reflection of coordinates, also has to be conserved.

The magnetic moment is due to moving charge in a spinning nucleus. The proton has a magnetic moment of +2.793 nuclear magnetons. The interesting thing is that the uncharged neutron also has an appreciable negative magnetic moment of -1.913 nuclear magnetons.

Aside comments If the quark model of a nucleon is valid, a proton is made up of a diquark containing an up quark with a charge of +2/3 and a down quark of -1/3 (net charge +1/3), and a valence up quark with a charge of +2/3, leading to a total charge of +1. One obtains a concept of the strong force as attracting the diquark and the valence quark together against the centrifugal force trying to separate them, spilling over to adjacent nucleons, and the concept of the weak force providing a repulsive and possibly disruptive restraint. In this regard, the weak force supplies a type of incompressability to a nucleon. The heavier diquark would lie closer to the axis of rotation than the valence quark in order to balance centrifugal force, so the valence quark would give the major contribution to the nuclear moment. On the other hand, a neutron consists of a diquark and a valence down quark with a charge of -1/3, leading to a total charge of 0. But the valence down quark would be the major contributor to the magnetic moment. If we totally ignored the diquarks, the ratio of the magnetic moments of a neutron and a proton would be -1/3 divided by +2/3, or -0.5. The actual ratio is -1.913/2.793 = -0.66, which is qualitatively similar and supports this idea of an internal charge distribution inside a nucleon.

Chapter 8 on nuclear forces demonstrates that there is a strong short-range attraction between nucleons, and that the (n,n), (n,p) and (p,p) forces are almost identical. At that time, this force was envisioned as a pi-meson exchange, but we now call it the Strong Force and attribute it to very heavy exchange entities called gluons. Chapter 8 also shows that an electron or positron cannot exist independently inside the nucleus, but must be formed at the moment of decay along with an appropriate neutrino to conserve spin and parity.

The Shell Model of the nucleus was invoked to explain the so-called "magic" numbers of 2, 8, 20, 28, 50, 82 and 126, that do not form any logical sequence, where sudden discontinuities in nuclear mass systematics occur and nuclei are exceptionally tightly bound. The number 2 corresponds to the double-magic alpha particle He4, the number 8 corresponds to the double-magic O16 which is extremely stable, and 82-126 corresponds to double-magic Pb208, the heaviest stable isotope in the periodic table except for Bi209, which is singly-magic.

The Liquid Drop Model of the nucleus attempts to explain the shape of the Binding Energy curve, with Iron having the largest binding energy per nucleon. This shape explains why fusion works for light elements and fission works for heavy elements. It also explains why stars stop working when their centers become pure Iron, leading in some cases to a supernova. The major contributor is the Strong Force between nucleons, called the Volume term, minus a Surface term for no nearby neighbors. This balances the repulsive Coulomb or Electromagnetic Force negative term that tries to break up the nucleus. An Asymmetry term proportional to (N - Z)2 is also subtracted to explain why radioactive isotopes of any given Z lie in a narrow band around the stable isotopes in parabolic energy diagrams. Asymmetry was explained in the shell model as having little coupling between nucleons at different energy levels lying in different shells. This repulsive force can now be recognized as the Weak Force that fosters radioactive decay, although this does not logically lead to massive W-particles as the theoretical exchange partners. There is no measurable contribution of the Gravity Force, which is 36 orders of magnitude smaller than the other forces. The Liquid Drop Model is completed by adding a Magic term for big discontinuities, and a Pairing term that adds a small saw-tooth-like variation and recognizes that most stable isotopes are even N and even Z, while the rest are even-odd. There are only four stable odd-odd isotopes.

Binding Energy per Nucleon, Explained by the Liquid Drop Model
From R. D. Evans, The Atomic Nucleus, McGraw Hill, 1955


Example of Mass Parabolas for Double Beta Decay
From R. D. Evans, The Atomic Nucleus, McGraw Hill, 1955

I do not for one moment believe that the Standard Model of the nucleus is correct as presently formulated. The various heavy sub-nuclear particles may indeed fit into a geometric pattern, and they have been observed if enough energy is added, but that does not mean that they are virtual actors in everyday life. Specifically, I don't believe that the Fehnman diagrams that are used to explain the exchange forces meet conditions of distance and speed of motion, let alone the energy conditions. So I don't think that they can explain gravity by graviton exchange, any more than they explain electrostatic force by photon exchange.