HOTB: High precision parallel code for calculation of four-particle harmonic oscillator transformation brackets

Computing the coefficients of transformations between oscillator states

“…Let us mention in this connection that e.g., passing from the double precision to the quadrupole precision everywhere in the calcultion of Ref. [11] increased the running time more than 15 times. Still, products of several factorials entering the usual expressions for 3j symbols may lead to overflows.…”

“…He provided the formulae in the case of the transformation (15) at ϕ = π/4 (which corresponds to the m 1 = m 2 case in Eq. (11) type relations). Below we shall refer to such formulae pertaining to the transformations (5) and (15) at any ϕ as to Moshinsky-type relations.…”

“…Programs to calculate oscillator brackets have been published in Refs. [8,11,[17][18][19][20][21][22]. Of them, the programs [8,11,22] are written in a contemporary programming language.…”

“…[8,11,[17][18][19][20][21][22]. Of them, the programs [8,11,22] are written in a contemporary programming language. They are based on an explicit expression [23] for the brackets.…”

A Mathematica program for the calculation of five-body Moshinsky brackets

“…On the other side, many papers have been devoted to accurate and fast calculations of these transformation brackets, for two-body [13][14][15][16][17][18], three-body [19] and four-body [20][21][22] systems.…”