Skyrme models and nuclear matter equation of state

We investigate the role of pressure in a class of generalized Skyrme models. We introduce pressure as the trace of the spatial part of the energy-momentum tensor and show that it obeys the usual thermodynamical relation. Then, we compute analytically the mean-field equation of state in the high- and medium-pressure regimes by applying topological bounds on compact domains. The equation of state is further investigated numerically for the charge-one Skyrmions. We identify which term in a generalized Skyrme model is responsible for which part in the equation of state. Further, we compare our findings with the corresponding results in the Walecka model.

Figure 1

(a) Energy and (b) pressure of the $B=1$ Skyrmion as a function of the volume for $E_4$ model.

Figure 2

Energy and pressure of the $B=1$ Skyrmion as a function of the volume for $E_{04}$ and $E_{24}$ model.

Figure 3

Energy and pressure of the $B=1$ Skyrmion as a function of the volume for $E_{024}$ model. (a)–(c) with the theoretical fit. (d) with the best fitted curve.

Figure 4

Comparison plots for the $B=1$ Skyrmion: (a)–(d) mass and pressure as a function of the average baryon density; (e) mass as a function of pressure; (f)–(g) equation of state.

Figure 5

Local energy density distribution for the $B=1$ Skyrmion in the $E_{024}$ model for different values of the pressure together with the corresponding mean-field energy density.

Figure 6

Energy and pressure of the $B=1$ Skyrmions as a function of the volume for $E_{026}$ model.

Figure 7

Energy and pressure of $B=1$ Skyrmion as a function of the volume for $E_{0246}$ model.

Figure 8

Comparison plots for the $B=1$ Skyrmion: (a)–(d) mass and pressure as a function of the average baryon density; (e)–(f) mass as a function of pressure; (g)–(h) equation of state.