San José State University
Thayer Watkins
Silicon Valley
& Tornado Alley

What holds a nucleus together?

Nuclear Forces

The Interactions of Nucleons
through the Nucleonic Force

Possible Direct Evidence for the
Alpha Module Structure of Nuclei

The British science journal Nature in its online version of August 24, 2010 reported the following:

In 2002, Oak Ridge physicist Paul Koehler and his colleagues used the neutron beam to measure 'neutron resonances' in each of four different isotopes of platinum. The resonances are particular energies at which the neutrons are especially likely to be absorbed by the platinum nuclei. The motion of protons and neutrons inside the platinum nuclei affects the pattern of resonances. And according to random matrix theory, a mathematical theory that for decades has been crucial for calculating the behaviour of large nuclei, those motions should be chaotic.

Yet, as Koehler and his colleagues report this month in Physical Review Letters (P. E. Koehler et al. Phys. Rev. Lett. 105, 072502; 2010), their analysis of the ORELA data found no sign that the nucleons in platinum were moving chaotically. By looking at the strength of the resonances, rather than just their spacing, the group rejects the applicability of random matrix theory with a 99.997% probability. Instead, the nucleons seem to move in a coordinated fashion. "There's no viable model of nuclear structure that could explain this," says Koehler.

The description of the results is compatible with the Alpha Module Model of nucler structure.

  • Nuclear Stability

    An alpha module has a nucleonic charge of +2/3=(1+1-2/3-2/3). Therefore two spherical shells composed of alpha modules would be repelled from each other if the spherical shells are separated from each other. This would be a source of instability. But if the spherical shells are concentric the repulsion can be a source of stability. Here is how that works.

    Without loss of generality the force between two nucleons can be represented as

    F = Hq1q2f(s)/s²

    where s is the separation distance between them, H is a constant, q1 and q2 are the nucleonic charges and f(s) is a function of distance. For the nucleonic force it is presumed that f(s) is a positive but declining function of distance. This means that the nucleonic force drops off more rapidly than the electrostatic force between protons.

    When one spherical shell is located interior to another of the same charge the equilibrium is where the centers of the two shells coincide. If there is a deviation from this arrangement the increased repulsion from the areas of spheres which are closer together is greater than the decrease in repulsion from the areas which are farther apart. This only occurs for the case in which f(s) is a declining function. If f(s) is constant there is no net force when one sphere is entirely enclosed within the other. For more on this surprising yet obvious result see Repelling spheres.

  • There are nuclei in which there are neutron spin pairs in excess of the number of proton spin pairs. These are in orbits outside of the concentric spheres but held in orbit by the attraction through the nucleonic force between neutrons and the alpha modules. (There are a few nuclides with excess proton spin pairs and their structure is yet to be explained.)
  • Whenever a model is proposed which involves charged particles traveling in curved trajectories the issue is raised of charged particles which experience acceleration radiating energy. Since particles traveling in curved paths experience centripetal acceleration this is taken to mean the model is invalid. The proposition that accelerated charges radiate energy was formulated by J.J. Larmor in the 1890's. Its application to atomic and nuclear models is disbelieved by many if not most physicists without knowing why it does not apply. Richard Feynman in his Lectures on Gravitation says, "we have inherited a prejudice that an accelerating charge should radiate."

    The explanation of why the Larmor proposition does not apply is that it is for point particles and the radiated energy is proportional to the square of the charge. If a charge of Q is divided into M pieces which are effectively point particles the result is M pieces each having the effect of (Q/M)², which reduces to Q²/M. If M→∞, as it would for a spatially distributed charge, the effect goes to zero. Thus the Larmor proposition is irrelevant for real charged particles because they are spatially distributed rather than being point particles.

  • The Statistical Explanatory Power of the Model

    Regression equations for the binding energies almost three thousand nuclides based upon the model presented above have coefficients of determination (R²) ranging from 0.999 to 0.99995. See Statistical Performance for the details.

  • Conclusions

    In a nucleus wherever possible the nucleons are linked together through spin pair formation into rings of alpha modules which rotate in four different modes at rapid rates. This rapid rotation results in each nucleon being effectively smeared uniformly throughout a sphere shell.

    The nucleons are organized in spherical shells containing at most certain numbers of nucleons. These nuclear magic numbers are explained by a simple algorithm.

    Dynamically a nucleus is basically composed of concentric spherical shells which repel each other. This mutual repulsion results in a stable arrangement in which the centers of the concentric spherical shells coincide. This only occurs for repulsion forces that drop off faster than inverse distance squared.

    Thus a nucleus is held together by the linkages created by the formation of spin pairs. The rings of alpha modules rotate to create the dynamic appearance of concentric spherical shells which a held together through the repulsion of the nucleonic forces. Neutron spin pairs outside of the concentric spheres are held by their attraction to the concentric spheres. So all of the nuclear forces, repulsions as well as attractions, are involved in holding a nucleus together.

  • For a review and critique of the conventional theory of nuclei see Conventional theory of the nucleus

  • For more on the physics of nuclei and other things see New pages.

        Dedicated to K. Serventi
    without whose medical and
    people skills this would
    not have been written,

    HOME PAGE OF applet-magic