In this paper we have discussed all possible boundary values used in the ordinary Skyrme model. Among the solutions to these boundary conditions the non-skyrmion and skyrmion one exist according to certain choices. The free parameter R in the boundary value conditions is shown to be related to the density of the nuclear matter in its Wigner-Seitz model. | Communications in Physics, Vol. 24, No. 2 (2014), pp. 124-134 THE PHASE TRANSITION OF HALF-SKYRMIONS IN THE DENSE NUCLEAR MATTER1 NGUYEN AI VIET Information Technology Institute, Vietnam National University, Hanoi, Vietnam Received 15 March 2014 Accepted for publication 10 May 2014 E-mail: naviet@ Abstract. In this paper we have discussed all possible boundary values used in the ordinary Skyrme model. Among the solutions to these boundary conditions the non-skyrmion and skyrmion one exist according to certain choices. The free parameter R in the boundary value conditions is shown to be related to the density of the nuclear matter in its Wigner-Seitz model. All three types of skyrmion can describe the nucleon in a good agreement with the experimental values of the axial coupling constant and isoscalar radii. However, all three types of skyrmion lead to a large value of the nucleon mass and a too small mass splitting between the nucleon and delta particles. The phase transitions of the skyrmions of Type III are also observed in the numerical computations as the density of the nuclear matter varies. Keywords: quantum field theories, nonlinear chiral model, Skyrme model, computational physics, dense nuclear matter. I. INTRODUCTION It was Skyrme who has shown long ago for the first time that nucleons can be treated as solitons in the non-linear sigma model [1]. The interest toward the Skyrme model has revived after Adkins, Nappi and Witten [2] have successfully derived the static properties of nucleons from the model within 30% of the experimental values. However, if the calculations are carried out more precisely, the model has two main problems. First, since the pion mass is taken as zero, one can prove that the mass splitting between nucleon and delta is zero. The non-zero result is obtained only if one truncate the large distant contribution of a divergent integral. The lesson learned from this problem is that one must be more careful with the numerical
