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Cook_FQXiEssayNDCook_2 - Unification of Nuclear Structure...

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1 Unification of Nuclear Structure Theory Is Possible Norman D. Cook Informatics, Kansai University, Osaka, Japan Abstract The impossibility of achieving a unified theory of nuclear structure has been the conventional wisdom in nuclear physics since the 1960s. However, already in 1937 Eugene Wigner indicated a way forward in theoretical work that eventually led to a Nobel Prize, but not directly to unification. Specifically, he showed that the symmetries of the Schrodinger equation have an intrinsic face-centered-cubic (FCC) geometry. Those symmetries provide for a fully quantum mechanical unification of the diverse models of nuclear structure theory, as indicated by the following facts: (i) The FCC lattice reproduces the properties of the liquid-drop model due to short-range nucleon-nucleon interactions (constant core density, saturation of binding energies, nuclear radii dependent on the number of nucleons, vibrational states, etc.). (ii) There is an inherent tetrahedral subgrouping of nucleons in the close-packed lattice (producing configurations of alpha clusters identical to those in the cluster models). And, most importantly, (iii) all of the quantum n-shells, and j- and m-subshells of the independent-particle model are reproduced as spherical, cylindrical and conical substructures within the FCC lattice – with, moreover, proton and neutron occupancies in each shell and subshell identical to those known from the shell model. These facts were established in the 1970s and 1980s, but the “impossibility of unification” had already achieved the status of dogma by the 1960s. Here, I present the case for viewing the lattice model as a unification of traditional nuclear structure theory – an unambiguous example of how declarations of the “impossibility” of progress can impede progress. I. Introduction There is no greater obstacle to progress than a belief that progress is impossible. Unsolved puzzles and indecipherable mysteries can be found in any academic field in any era – and textbook authors inevitably treat the unsolved problems as beyond the powers of “modern” science. Today is no exception. For example, the advances in quantum chromodynamics (QCD) have brought theoretical coherency to the world of particle physics, but, despite remarkable precision of the experimental data, the masses of the 200+ elementary particles remain a puzzle beyond the scope of QCD. As Feynman (1985) has commented: “There remains one especially unsatisfactory feature: the observed masses of the particles. There is no theory that adequately explains these numbers… This is a very serious problem” (p. 152). But it is an unsolved problem primarily because it is so rarely addressed (e.g., MacGregor, 2007; Palazzi, 2003; 2004). At the level of nuclear structure, the textbooks state that the nucleus is such a complex many-body problem that inherently-incomplete, mutually-contradictory “models” are necessary to explain the diverse properties of nuclei, and that a truly unified theory is not possible. That
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