Solving Hyperspherical Basis Transformation Problem for Four-, Five-, and Six-Body Systems by the Use of Recurrence Method
Abstract— The study of barion-barion interactions is an important problem of nuclear physics. Principal information about hyperon-nuclear interactions may be obtained by exploring the structure and decay of few-body hypernuclear systems. While investigating few-body systems with the use of Hyperspherical Function Method, the problem of hyperspherical basis transformation between different sets of Jacobi coordinates arises. As number of particles increases, these transformations include not only particle permutations but also transitions between different configurations. This article proposes a recurrence method of determination of transformation coefficients for four-,five-, and six-body systems. The complete set of recurrence relations for the transformation coefficients of N particle hyperspherical funtions (N=4,5,6) under particle permutations is obtained and transformation coefficients for specific values of quantum numbers are calculated. Significant advantage of the proposed method is that no principal difficulties arise when increasing number of particles. Furthermore, recurrence relations contain numerical coefficients that are easy to evaluate by substituting appropriate quantum numbers.
Keywords— Few-body systems, Hyperspherical basis, Recurrence relations, Transformation coefficients
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