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Posted: May 28, 2005
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Two recent publications dealing with nucleon clusters are: "Recent advances in study of nuclear clusters", Annual Review of Nuclear and Particle Science, 1995 (see link), and "Clustering aspects of nuclear structure and dynamics", 1999 (see link).
The concept that the atomic nucleus is composed of "nucleon groups or clusters" has a long history in physics. Perhaps the first mention of possible nucleon group structure was by Dr. John A. Wheeler in 1937 (Phys. Rev. 52, 1083, 1107), with other early papers by Perring and Skyrme (Proc. Phys. Soc. A, 69, 600, (1956) and Wildermuth and Kanelopoulos (Nucl. Phys. 9, 449 (1958).
Webmaster update: June 3, 2005. In his classic 1937 papers in Physical Review (vol 52) titled "On the mathematical description of light nuclei by the method of resonating group structure" , and "Molecular viewpoints in nuclear structure" Dr. John Wheeler presented his hypothesis of the "resonating group structure" to explain the nucleon structure of atomic nuclei. This classic paper rejected the present day hypothesis that N and P follow the mathematics of the "Hartree-Fock" procedure in a mean-field. Instead, Wheeler takes the perspective that the wave function of a composite nucleus is a combination of partial wave functions "corresponding to the various ways that N and P can be distributed into groups". These groups of Wheeler directly correspond to the Nucleon Clusters of the Brightsen Model, such as [N-P], [N-P-N], [P-N-P], [N-N], [P-P], and the alpha which is comprised of two [N-P] clusters according to the Brightsen Model. Thus it is suggested that the Brightsen Model follows the theoretical thinking of John Wheeler's "resonating group structure" model of the atomic nucleus, and that the Wheeler wave function dynamics may help explain the cluster dynamics of the Brightsen Model.
In 1965, Dr. Linus Pauling published his "close-packed spheron model" of the atomic nucleus, which is based on the hypothesis that the protons and neutrons exist in fundamental clusters and are not independent particles moving in a mean field (see What's New for 2005 link).
Evidence for "nucleon clusters" including a proposed wave function equation (adapted from Wheeler, 1937, see above) for two interacting clusters was published in 1969 by Neudatchin and Smirnov in "Progress in Nuclear Physics, Vol. 10, Brink & Mulvey, eds. "Evidence for nucleon clusters in the lightest nuclei of the 1p-shell from data on reactions at high energies". In this paper detailed wave functions are given for the nucleon cluster structure for lithium-6, lithium-7, and beryllium-9. The authors refer to a "nucleon cluster model" to explain both experimental and theoretical aspects of their hypothesis. For example, consider two clusters, such as [N-P] bound to [N-P], the well known alpha or helium-4. Let the first [N-P] cluster be {1}, the second {2}. Then, the wave function of Neudatchin and Smirnov that explains the nucleon binding of helium-4 is:
wave function of {[N-P]-[N-P]} = [1/sr.rt. (Ni)] A [{1} {2} (R) (S-I)]
where {Ni} is the normalization factor, A is the antisymmetrization operator, {1} is the internal orbital wave function of the first [N-P] cluster, {2} is the internal orbital wave function of the second [N-P] cluster, (R) is the wave function of the relative motion of the two clusters, and (S-I) is the spin-isospin function of the helium-4 nucleus as a whole. Thus, the primary "wave functions" within the helium-4 isotope divide the nucleus into subsystems (e.g. nucleon cluster structures) moving relative to each other, not independent protons and neutrons moving in a mean field--which conforms to the hypothesis of the Brightsen Model. Comments are welcome.
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