Single particle spin-orbit interaction energy problem in nuclear shell structure is solved through negative harmonic oscillator in the self-similar-structure shell model (SSM) [4] and considering quarks contributions on single particle spin and orbit
momentum. The paper demonstrates that single particle motion in normal nuclei is described better by SSM negative harmonic oscillator than conventional shell model positive harmonic oscillator[1][2][3]. The proposed theoretical formula for spin orbit interaction energy agrees well to experiment measurements.
The Self-similar-structure shell model (SSM) comes from the evolution of the conventional shell model (SM) and keeps the energy level of SM single particle harmonic oscillation motion. In SM, single particle motion is the positive harmonic oscillatio
n and in SSM, the single particle motion is the negative harmonic oscillation. In this paper a nuclear evolution equation (NEE) is proposed. NEE describes the nuclear evolution process from gas state to liquid state and reveals the relations among SM, SSM and liquid drop model (DM). Based upon SSM and NEE theory, we propose the solution to long-standing problem of nuclear shell model single particle spin-orbit interaction energy . We demonstrate that the single particle motion in normal nuclear ground state is the negative harmonic oscillation of SSM[1][2][3][4] Key words: negative harmonic oscillation, nuclear evolution equation, self-similar shell model
