Theory of Nuclear Matter for Neutron Stars and ... - Graduate Physics

Table 4.1: Interaction parameters when ǫ = 1/6, K = 265 MeV, S v = 28MeV, L = 54MeV.v 1L v 1U v 2L v 2U v 3L,U t ′ 3 r 0 (fm)-1.766 -3.472 0.410 0.931 0.169 1.177 1.2054.2.1 Determination of the 1+ǫ powerWe added in Eq. (4.5) the auxiliary density interaction with the 1 + ǫ power. We mightregard 1+ǫ as the many-body effect—for example, a three-body force if ǫ > 1 . It is known,2however, that interactions among more than three-bodies are unimportant in dense matter[34]. Thus we can restrict the ǫ to be less than 1 . As ǫ changes, the t 2 3 parameter changessign, which means that the three-body force can be attractive or repulsive. In the generalSkyrme model with the three-body force, the t 3 parameter is positive. We choose ǫ = 1/6 sothat the interaction has the form of ρ 7/6t 1ρ 7/6t 2. In zero-temperature, uniform matter, we haveu 7/3 terms in the energy density. From Eq. (4.18), the energy density has u 5/3 , u 2 , u 7/3 , u 8/3 ,and u 3 terms if we have ǫ = 1/6 so we can use a statistical approach in uniform matter. Fig4.1 shows the energy per baryon from GNDF and APR [35] EOS. We can see that as thedensity increases, the pressure from the two models agrees very well.Figure 4.1: The solid line represents the energy per baryon (uniform matter) using GNDF.The upper (lower) curve represents the energy perbaryon ofpure neutronmatter (symmetricnuclear matter). The energy per baryon (dotted line) from the APR [35] EOS is added forcomparison.4.2.2 The effective range of the nuclear force : r 0In the Gaussian-interaction model, we can see that the effective range of the force is givenby r 0 , which is approximately ∼ 1 to 2 fm. We do not have an analytic form of r 0 , so we58