Baryonium with a phenomenological Skyrmion-type potential

In this paper, we investigate the nucleon-antinucleon static energies in the Skyrme model with the product Anzatz. The calculation shows that, in the ungroomed S (S) over bar (Skyrmion and anti-Skyrmion) channel which leads to rapid annihilation, there exists a quasistable bound state which may give a natural explanation for the near-threshold enhancement in the proton-antiproton (p (p) over bar) mass spectrum reported by the BES Collaboration and the Belle Collaboration. Similar to the phenomenological well potential of the deuteron, we construct a phenomenological Skyrmion-type potential to study this narrow p (p) over bar -resonance in J/psi ->gamma p (p) over bar. By this potential model, a p (p) over bar baryonium with small binding energies is suggested and the decay width of this state is calculated by WKB approximation. In this picture the decay is attributed to quantum tunneling and p (p) over bar annihilation. Prediction on the decay mode from the baryonium annihilation at rest is also pointed out.