Energy and Stability Related to Composition of Atomic Nuclei

Abstract

Examination of the postulates of Heisenberg concerning the energy of binding of neutrons and protons to atomic nuclei shows that factors not included in the primary considerations are of appreciable effect in determining nuclear composition and stability, and result in deviations of a periodic character from the requirements of the theory. Nevertheless, the formulation of binding energies as linear functions of the neutron-proton ratio of the nucleus is adequate as a rough approximation over a large range of elements, as is also the proportionality assumed between the radius and the cube root of the mass number. For evaluation of the various constants, it is assumed that the boundary of stability in emission of beta-particles should be centrally placed with respect to existing nuclear species. Reasons supporting this placement, and the manner of adjustment of the alpha-boundary, for which the distribution of nuclei alone is not an adequate guide, are outlined. The application in various fields of nuclear physics and chemistry of the constants thus determined is discussed and illustrated. The nuclear radii resulting in these calculations agree excellently with those found by other methods. An equation for the energy of formation of nuclei from neutrons and protons is obtained and found to hold, within experimental error, for all elements above ${}_{24}{}^{}{}_{}{}^{}\mathrm{Cr}$ for which data are available for comparison. Calculated energies of spontaneously emitted alpha- and beta-particles and energies of capture of various particles by light nuclei, are in rough agreement with known values. Energies in nuclear collision processes are calculated with fair average agreement with experimental values, and the indications of the theory regarding critical energies and nuclear composition in such reactions discussed. Specific characteristics are not faithfully predicted in the various nuclear changes above, but the average accuracy of calculated energies is superior, for all but the light elements, to that obtainable from present values of atomic masses. In addition, these calculations are possible in cases where the masses are not yet measured. Spontaneous emission of protons from any existing nuclei is indicated to be impossible. A chart is given showing in what region of nuclear composition this and other similar changes might occur. The alpha-disintegration is considered to be possible in elements as low as ${}_{51}{}^{}{}_{}{}^{}\mathrm{Sb}$. The possibility of beta-changes, or their reverse, in certain isobaric pairs among the "non-radioactive" elements is pointed out. The "end" of the periodic system and the limiting spread in mass numbers of isotopes as influenced by the various types of nuclear instability are also discussed.