My Articles

References (and discussion of their relevance) for my article:
    “Nuclear Fusion Mass Loss, Crevices between Nucleons,
    and an Improved Method of Calculating Binding Energies

       ((These articles in Wikipedia describe the authors of the much used early
textbook, “College Physics”.  Much is covered in that book, including a part on
estimating with reasonable accuracy, “the energy emitted when a neutral
Helium-4 atom is formed by the fusing together of (4) Hydrogen-1 atoms”.  See
next reference for more details.))

2…  Sears, F., and Zemansky, M., College Physics, 49-10, pp. 989-991, and in
particular p.990, Addison Wesley Publishing Co., Inc., Reading, MA., 3rd Ed.,
(1960).  ((Those pages 989-991 cover a simple way of estimating the energy
released when Helium-4 is conceived as formed from (4) Hydrogen-1 atoms.))

3…   At the present time, the relative atomic weights of the various isotopes is standardized by designating the atomic weight of a Carbon-12 atom to be ’12 u’, which is a nice whole number.  But the resulting relative atomic weights of the many other isotopes then do not come out nice whole numbers.  For example, then Hydrogen-1 atom comes out ‘1.00782503207 u’, instead of ‘1 u’ as discussed in my article.  (When Sears & Zemansky published their ‘College Physics’ textbook, however; Oxygen-16, not Carbon-12, was used for the standard.)

Important:  To find out the relative atomic weight of any isotope or particle, go to the Wikipedia online encyclopedia at: and then enter the desired isotope or subject, ‘Electron’, ‘Proton’, ‘Isotopes of Hydrogen’, ‘etc.’, in their ‘search box’ and click.  That brings up an appropriate article, that generally includes the sought-after ‘atomic weight’, along with other key data, and all that is usually listed inside a prominent rectangular box.  Note, data provided may change since my article was drafted in June 2015.

            ((This presents the “Weizsacker’s formula”, also known as the “Bethe-  
   Weizsacker formula”.   That is a semi-empirical mathematical formula for   
    estimating the ‘Binding Energy’ for the over 200 stable isotopes.  Various
    numbers, each describing details for the particular isotope, are inserted into the
 formula, which then gives an estimate for the binding energy of the isotope.))  

5…  Pauling, L., General Chemistry, Nuclear Chemistry, 26-7 to 26-10, Dover Publications, Inc., Mineola, New York (1988).  ((Some topics covered in these sections include the traditional concept or method for calculating and treating nuclear ‘binding energies’.  But also, near the end of Section 26-7, Pauling describes a ‘Helion-Triton model of nuclear structure’.  I reference that now, because in my very elementary treatment I also focus mainly on nuclei with 4 and 3 nucleons, respectively.  And because I think those also have some traits that we associate with the basic tetrahedron and triangle, structures respectively.))

6… Mayer, M. G., and Jensen, J. H. D., Elementary Theory of Nuclear Shell Structure, John Wiley & Sons, New York (1955).  ((That is mentioned here because those authors were likely the main pioneers of the sort of refined ‘shell’ modeling that mainstream physics commonly uses today, pretty effectively -- for nuclei with many nucleons and of increased complexity.))

7…  The following two references below are given because they show how small spheres just barely fit into the grooves between large spheres in abstract patterns. And how that generates a volume ratio (big to small sphere) that corresponds, proportionally, to actual mass particles ratios in the real world -- the ratio of large mass particles to small mass particles!  (Although the two below mostly address particles that decay, still those references might somewhat relate to mass ‘lost’ during fusion.)

Littmann, C., Booklet of Large & Small Spheres in Pattern and Large & Small Mass Particles,  ((This booklet is found and viewable online at, or just click above long booklet’s title.))
Littmann, C., “Particle Mass Ratios and Similar Volume Ratios in Geometry”, J. Chem. Inf. Comput. Sci. 35 (3) 579-580 (1995)

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Carl R. Littmann

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