Generalized routhian calculations within the Skyrme-Hartree-Fock approximation Original Research Article

We consider here variational solutions in the Hartree-Fock approximation upon breaking time reversal and axial symmetries. When decomposed on axial harmonic oscillator functions, the corresponding single particle triaxial eigenstates as functions of the usual cylindrical coordinates (r, θ, z) are evaluated on a mesh in r and z to be integrated within Gauss-Hermite and Gauss-Laguerre approaches and as Fourier decompositions in the angular variable θ. Using an effective interaction of the Skyrme type, the Hartree-Fock Hamiltonian is also obtained as a Fourier series allowing a two-dimensional calculation of its matrix elements. This particular choice is shown to lead in most cases to shorter computation times compared to the usual decomposition on triaxial harmonic oscillator states. We apply this method to the case of the semi-quantal approach of large amplitude collective motion corresponding to a generalized routhian formalism and present results in the A = 150 superdeformed region for the coupling of global rotation and intrinsic vortical modes in what is known after Chandrasekhar as the S-ellipsoid coupling case.