Self-consistent description of the SHFB equations for 112Sn

Investigation of the Nuclear Structure of Some Ni and Zn Isotopes with Skyrme-Hartree-Fock Interaction

“…Skyrme presented an effective interaction for HF calculations of nuclei 14,15 . In describing the ground conditions properties of nuclei with approximately ten adjustable parameters, it is the more convenient force used to fit experimental nuclei data such as binding energies and charged radii 16 .…”

“…As a result, as an extended Skyrme force 17 , the Skyrme forces are unified in a single form. The interaction between two bodies in Skyrme is written as follows 14 : 𝑬 𝒔𝒌𝒚 is the energy functional of the Skyrme force and given by 15 ,…”

“…𝜌 𝑞 is the local densities for protons and neutrons (depending on the value of q), 𝜌 is the total density, 𝜏 𝑞 is the kinetic energy densities for protons and neutrons and 𝐽 𝑞 is the spin-orbit current density. They are given by these relations 15 𝜌…”

“…In the (SHF) theory using the Skyrme forces, the most general product wave functions (𝜓 𝛽 ) consist of independently moving single particles. In this method the neutron and proton densities are given in The Coulomb energy is calculated as follows 15,17 : where 𝑅 𝛽 is the radial part of the harmonics oscillator wavefunction and is given as…”

Longitudinal and Transverse form Factors from $^{65}$Cu and $^{71}$Ga Nuclei

“…Consequently, the Skyrme forces are combined in a single form as an expanded Skyrme force. The Skyrme's interaction is then written as [22,23],…”