Text Box: The Nuclear Field
 Within the nucleus, the speed of the body radiaton becomes sub-c. Therefore, if v be the mid-mode speed of such a radiaton, 
then, again, by classical mechanical analysis pertinent to the situation, 
the force field within the atomic nucleus at radius r will be given by,
Fr = mv2/2r                          (5)

The derivation of this expression is given in section 11.01 of the book. (It requires a little calculus since v is not constant over the vibrational length. The exercise, though, is a simple one, the likes of which one would find in high-school textbooks.)

The body radiatons of the nucleus (unlike their speed-c counterparts outside) have a vibrational speed that is variable. That is, for instance, their mid-mode speed, v, will not be a constant. And this (sub-c) speed is determined purely by the extent of natural compaction of the radiatons within the nucleus. The most stable state for any body is its lowest potential state, also known as the body’s ground state. For the vibrant radiaton, therefore, this will correspond to movement with maximum possible amplitude, in which mode the perfectly elastic particle would attain its least possible potential energy (cyclically). And in the atomic nucleus, this lowest potential state results when the constituent particles are all in resonance (that is, vibrant at a common frequency) whereby the individual particles would maximize their amplitudes. (This is also the fundamental reason for a material body, in general, to have a single frequency of vibration, which we call the natural frequency of vibration, in its ground-state mode.)  

 At ground state, therefore, all nuclear body radiatons have a common vibrational frequency. To make this possible within the nucleus, the vibrational lengths vary linearly with radius. (Recall that body radiatons are vibrant perpendicularly and symmetrically about the atomic radius.) Consequently, at, say, any fractional displacement from mid mode, the speed of the nuclear body radiaton, too, would show a linear variation with atomic radius. 
 This translates also to the linear variation of v with radius. That is, the mid-mode speed (v) of the nuclear body radiaton divided by its radial distance (r cosa, in Fig 4) will be a constant. Hence,

v / (r cosa) = c / [(ln/2) cosa]       (6)

where, (ln/2) cosa  is the radius at which v just becomes equal to c. (Note: ln/2 will be the atomic radius at each end mode for the outermost nuclear body radiaton; ln will thus be the effective diameter of the nuclear surface.) 
 Whence, from equations (5) and (6), we get for the basic nuclear interior,

Fr = (mc2/ln2)d                                    (7)

showing the force field at a point within the nucleus to vary directly with the diameter, d (= 2r), at that point.
And replacing r with d/2 in equation (4) of the previous part, we would get for the basic nuclear exterior,

Fr = 2mc2/d                                          (8)

showing the force field outside the nucleus to vary inversely with diameter.
          Go to Part 4 of 6
A Synopsis The Cosmos The Spin
ADDENDA The Cosmological Redshift The Neutrino
Two-Slit Tests The Galaxy Nuclear Reactions
NASA Tests Gravity The Sun
KamLAND Test Anti-Gravity The Pulsar
UCLA Test Relativity Superconductivity
Q and A Mass-Energy Fusion Energy
 Eugene Sittampalam
 27 June 2007