Abstract
Hyperspherical harmonics (HH) expansion method is introduced for the three-body system. Jacobi coordinates are defined, in terms of which the center of mass motion separates for a mutually interacting system. Hyperspherical coordinates and hyperangular momentum are introduced. Analytical expression for the eigenfunction (called HH) of the latter is derived. Expanding the relative wave function in the complete basis of HH and substituting in the Schrodinger equation, a system of coupled differential equation is derived. Symmetrization of the HH basis using the Raynal–Revai coefficients (RRC) is discussed. Calculation of the potential matrix elements (PME) is facilitated by multipolar expansion of the potential in the HH basis. Then PME becomes a sum of products of potential multipoles and geometrical structure coefficients (GSC). An elegant method for calculation of GSC is developed using the completeness property of the Jacobi polynomials. An explicit expression is obtained for central potentials.
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