San José State University

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Thayer Watkins
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The Spin Pairing of Nucleons Due to the
Magnetic Fields Generated by their Spinnings

Moving charges generate magnetic fields. Consider the spherical coordinates (r, φ, θ). A spherical charge of radius R with surface charge density σ spinning about the axis φ=0 at a rate of Ω times per second generates a magnetic field according to the formula

For r≥R B = μ0RΩσ/(6π)(R/r)³[2cos(φ)ur + sin(φ)uφ]

where ur and uφ are the unit vectrors in the directions of increasing r and φ, respectively.

The field is perfectly symmetric with respect to the angle θ

For the interior of the sphere B is constant and points to the spin axis. Its value is

For r≤R B = 2μ0RΩσ/(6π)[cos(φ)ur − sin(φ)uφ]

There is a discontinuity in B at r=R.

The Attraction of Spinning Spherical Charges

The force between two magnets which have magnetic field strengts of B1 and B2 at their poles is

F = CB1B2R4[1/s² + 1/(2R+s)² − 1/(R+s)²

where C is a constant, R is the scale of the magnets and s is the separation distance between the poles.

The Alignment of Spinning Spherical Charges

The spinning spherical charges are like magnets with two poles. Thus opposite poles attract and two spinning spherical charges up>form some sort linked entity. The effect of the charges must be taken into account. If the spheres have the same charge then they must have opposite spins. If they have opposite charges then they must have the same direction of spin.

There is the possibility that two charged spheres could align themselves like two bar magnets with the opposite poles matched together. This would be like the animation shown below where the yellow arrows denote the direction of the spin..

The alternative is an end-to-end alignment as shown below.

The different colors denotes different charges.

The fact that one nucleon can form at most two spin pairs suggest that the end-to-end alignment is the one that prevails,

The Distributions of Electrostatic Charges of Nucleona

Although the neutron has zero net electrostatic charge that does not mean it has no charges at all. The graph gives the distributions.

A proton has a measuredmagnetic moment of 2.793 magnetrons and a neutron's is −1.913 magnetrons.


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