Principal-axis hyperspherical coordinates

ABSTRACT. Adiabatically adjusting Principal-axis Hyperspherical(APH) coordinates are used in a fully 3-dimensional quantum mechanical formulation of reactive scattering. Exact results will be presented for the following systems ... 

The Adiabatically adjusting Principal axis Hyperspherical (APH) coordinate method of Pack and Parker is well known [52, 72, 120, 121, 122, 123]. The APH coordinates were first introduced by Pack, in 1984, as a route to an optimum centrifugal sudden approximation for reactions [112]. These coordinates are similar to the earlier PA hyperspherical coordinates of Smith and Whitten [117] and of Johnson [119], but differ in that they do not require the use of half-integer angular momenta [117, 119] and are better suited to... 

Mass-scaled Jacobi coordinates associated to a generic arrangement X — a for A -I- BC, /I for B + CA and ) for C + AB) cU c denoted by r (diatom vector) and R (atom-molecule vector). They are used in the definition of hyperspherical coordinates which parametrize the nuclear motion of the system, namely the principal axis body frame hyperspherical coordinates [3, 4, 5]. These coordinates are ... 

The symmetric parametrization can be achieved by taking as internal reference system the one that diagonalizes the inertia tensor, placing the principal axis in correspondence with that of maximal inertia [6,64], The symmetric hyperspherical coordinates can be calculated from the asymmetric hyperspherical coordinates ... 

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