Chiral approach to nuclear matter: role of two-pion exchange with virtual delta-isobar excitation
✍ Scribed by S. Fritsch; N. Kaiser; W. Weise
- Publisher
- Elsevier Science
- Year
- 2005
- Tongue
- English
- Weight
- 399 KB
- Volume
- 750
- Category
- Article
- ISSN
- 0375-9474
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✦ Synopsis
We extend a recent three-loop calculation of nuclear matter by including the effects from twopion exchange with single and double virtual ∆(1232)-isobar excitation. Regularization dependent short-range contributions from pion-loops are encoded in a few NN-contact coupling constants. The empirical saturation point of isospin-symmetric nuclear matter, Ē0 = -16 MeV, ρ 0 = 0.16 fm -3 , can be well reproduced by adjusting the strength of a two-body term linear in density (and tuning an emerging three-body term quadratic in density). The nuclear matter compressibility comes out as K = 304 MeV. The real single-particle potential U(p, k f 0 ) is substantially improved by the inclusion of the chiral πN∆-dynamics: it grows now monotonically with the nucleon momentum p. The effective nucleon mass at the Fermi surface takes on a realistic value of M * (k f 0 ) = 0.88M. As a consequence of these features, the critical temperature of the liquid-gas phase transition gets lowered to the value T c 15 MeV. In this work we continue the complex-valued single-particle potential U(p, k f ) + iW (p, k f ) into the region above the Fermi surface p > k f . The effects of 2π -exchange with virtual ∆-excitation on the nuclear energy density functional are also investigated. The effective nucleon mass associated with the kinetic energy density is M * (ρ 0 ) = 0.64M. Furthermore, we find that the isospin properties of nuclear matter get significantly improved by including the chiral πN∆-dynamics. Instead of bending downward above ρ 0 as in previous calculations, the energy per particle of pure neutron matter Ēn (k n ) and the asymmetry energy A(k f ) now grow monotonically with density. In the density regime ρ = 2ρ n < 0.2 fm -3 relevant for conventional nuclear physics our results agree well with sophisticated many-body calculations and (semi)-empirical values.