Properties of alpha-particle solutions to the many-nucleon problem
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BIRTHDAY OF Yu.F. SMIRNOV Theory
Properties of Alpha-Particle Solutions to the Many-Nucleon Problem I. А. Gnilozub1)* , S. D. Kurgalin2)** , and Yu. M. Tchuvil’sky1), 3)*** Received August 19, 2005
Abstract—A class of A-nucleon (for even N = Z) Hamiltonians is found such that they admit, among others, solutions that can be exactly related to solutions to the problem of A/4 alpha particles in the sense that the respective eigenvalues of the two problems coincide and that the A-nucleon solutions can be constructed from the alpha-particle solutions within a procedure that follows from the resonating-group model. It is shown that an effective nuclear Hamiltonian close to a realistic one possesses these properties, the alpha-particle states in nuclei having basic properties of an alpha condensate and, frequently, a normal nuclear density. The statistics of alpha particles (and other composite bosons) proves to be different from Bose–Einstein and Fermi–Dirac statistics and from parastatistics. PACS numbers : 21.60.-n, 21.45.+v DOI: 10.1134/S1063778806060123
1. INTRODUCTION Searches for methods that can provide an exact or an approximate description of the properties of a multiparticle system on the basis of equations that are specified in terms of variables characterizing the relative motion of its subsystems (clusters, interacting bosons, and so on) have been performed since the appearance of Wheeler’s classic studies [1]. Many achievements of theoretical nuclear physics, such as the unified theory of the nucleus [2] and the interacting-boson model [3, 4], are based on precisely this principle of description of nuclear dynamics. The problem of constructing, from constituent particles (these may be elementary particles, atoms, and so on), more complicated subsystems is far beyond the scope of traditional nuclear physics, being of importance for particle physics (for example, the theory of quark–gluon plasma), the physics of mesic systems (metallic clusters and fullerenes), and condensedmatter physics. In seeking structures into which one would be tempted to break down the system being considered, attention is given primarily to subsystems that stand out in what is concerned with their energy or spatial features, as well as in what is concerned with their properties in momentum space. In the present 1)
Institute of Nuclear Physics, Moscow State University, Vorob’evy gory, Moscow, 119899 Russia. 2) Voronezh State University, Universitetskaya pl. 1, Voronezh, 394693 Russia. 3) ¨ D-35392 Giessen, Germany. Justus-Liebig-Universitat, * E-mail: [email protected] ** E-mail: [email protected] *** E-mail: [email protected]
study, we will basically restrict ourselves to nuclearphysics problems and demonstrate that there exist subtler properties stemming from the symmetry of the Hamiltonian of the A-nucleon system and resulting in that a reduced Hamiltonian (that is, a Hamiltonian written in terms of variables of the relative motion of subsystems constituting the system being considered) exactly reproduces a specific
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