SU3HOB-cgvcs: harmonic-oscillator brackets in the SU(3) basis with isofactors from an external SU(3)$\,\supset\,$SO(3) Clebsch--Gordan library

Abstract

\DeclareRobustCommand{\Su}{\code{Su3cgvcs}} We present SU3HOB-cgvcs, a Fortran~2008 package that computes the general Talmi--Moshinsky harmonic-oscillator transformation brackets, for an arbitrary mass-ratio parameter $d$. These brackets arte constructed in the $\su{SU}(3)$ basis by the method of Kalinauskas et al. . The transformation is reduced to a single sum over Wigner $d$-functions of the reflection-containing Talmi--Moshinsky matrix weighted by products of $\su{SU}(3)\supset\su{SO}(3)$ isofactors of the chain $\su{U}(6)\supset\su{U}(3)\times\su{U}(2)$. SU3HOB-cgvcs obtains these isofactors from the established external Clebsch--Gordan library \Su{} . In this library they are computed there by the vector-coherent-state (VCS) method. We bridge \Su{} formalism to ours and this requires two fixes: reinserting a sign/phase factor that depends on each state's radial-quantum number and handling the trivial $(0,0)$ representation analytically. The package reproduces, bracket for bracket to machine precision ($\sim\!10^{-13}$), the general Talmi--Moshinsky bracket code of Kamuntavičius et al. , and demonstrates that a self-contained SU(3)-scheme HOB code can be built on top of a general-purpose SU(3) Clebsch--Gordan library.