Transformation coefficients in the hyperspherical approach to the three-body problem

Halo nuclei, stepping stones across the drip-lines

“…An excited state is found at 4 MeV, which can be attributed to a 2 + resonance. The 8 He-n scattering length is determined to be only a s =−3.17 (66) fm, in accordance with the predictions made in [63]. Further Gamov states at 1.33 and 2.42 MeV have been adopted from an earlier multinucleon transfer experiment [67].…”

“…The extracted coefficients need to obey particular transformation properties between the two choices of coordinates. The Raynal-Revai coefficients [66] define a unitary transformation between the T and the Y system. The fits to the data in figures 7 and 8 are performed independently and were successfully checked for consistency in the presence of effects from the finite resolution and efficiency in the setup by comparison to the nominal values.…”

Similarity renormalization group evolution of three-nucleon forces in a hyperspherical momentum representation

“…For identical particles (equal mass), all dependence of any orthogonal transformation operator (O), such as permutation operators, is completely encoded between the partial waves and is block diagonal in G [19], therefore they are independent of the remaining continuous coordinate Q,…”

Three-particle bound states in a finite volume: Unequal masses and higher partial waves

“…In general, the transformation between the wave functions, depending on different sets of Jacobi coordinates, is given by the Raynal-Revai coefficients [38]. An explicit expression for these coefficients is known in the literature (see, e.g., Ref.…”

“…(26) and (27) and Eqs. (38) and (39) in the case of arbitrary l. To this end, using the explicit form of ϕ l ðαÞ, it suffices to represent the wave function ϕ i lm ðx i ; y i Þ in Eq. (52) as…”