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Register a new userToward Chiral Theory of NN interactions in nuclear matter
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B.Krippa
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The effective chiral theory of the in-medium NN interactions is considered. The shallow bound states, which complicate the effective field theory analysis in vacuum do not exist in matter. We show that the next-to-leading order terms in the chiral expansion of the effective Lagrangian can be interpreted as corrections so that the expansion is systematic. The Low Energy Effective Constants of this Lagrangian are found to satisfy the concept of naturalness. The potential energy per particle is calculated. The problems and challenges in constructing the chiral theory of nuclear matter are outlined.
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The effective field theory of NN interactions in nuclear matter is considered. Due to the Pauli principle the effective NN amplitude is not affected by the shallow bound states. We show that the next-to-leading order terms in the chiral expansion of the effective NN potential can be interpreted as corrections so the expansion is systematic. The value of potential energy per particle is calculated and some issues concerning the chiral effective theory of nuclear matter are outlined.
The nuclear symmetry energy is a key quantity in nuclear (astro)physics. It describes the isospin dependence of the nuclear equation of state (EOS), which is commonly assumed to be almost quadratic. In this work, we confront this standard quadratic expansion of the EOS with explicit asymmetric nuclear-matter calculations based on a set of commonly used Hamiltonians including two- and three-nucleon forces derived from chiral effective field theory. We study, in particular, the importance of non-quadratic contributions to the symmetry energy, including the non-analytic logarithmic term introduced by Kaiser [Phys.~Rev.~C textbf{91}, 065201 (2015)]. Our results suggest that the quartic contribution to the symmetry energy can be robustly determined from the various Hamiltonians employed, and we obtain 1.00(8) MeV (or 0.55(8) MeV for the potential part) at saturation density, while the logarithmic contribution to the symmetry energy is relatively small and model-dependent. We finally employ the meta-model approach to study the impact of the higher-order contributions on the neutron-star crust-core transition density, and find a small 5% correction.
In this talk, we report on two recent studies of relativistic nucleon-nucleon and hyperon-nucleon interactions in covariant chiral perturbation theory, where they are constructed up to leading order. The relevant unknown low energy constants are fixed by fitting to the nucleon-nucleon and hyperon-nucleon scattering data. It is shown that these interactions can describe the scattering data with a quality similar to their next-to-leading order non-relativistic counterparts. These studies show that it is technically feasible to construct relativist baryon-baryon interactions, and in addition, after further refinements, these interactions may provide important inputs to {it ab initio} relativistic nuclear structure and reaction studies and help improve our understanding of low energy strong interactions.
We study the equation of state for symmetric nuclear matter using a ring-diagram approach in which the particle-particle hole-hole ($pphh$) ring diagrams within a momentum model space of decimation scale $Lambda$ are summed to all orders. The calculation is carried out using the renormalized low-momentum nucleon-nucleon (NN) interaction $V_{low-k}$, which is obtained from a bare NN potential by integrating out the high-momentum components beyond $Lambda$. The bare NN potentials of CD-Bonn, Nijmegen and Idaho have been employed. The choice of $Lambda$ and its influence on the single particle spectrum are discussed. Ring-diagram correlations at intermediate momenta ($ksimeq$ 2 fm$^{-1}$) are found to be particularly important for nuclear saturation, suggesting the necessity of using a sufficiently large decimation scale so that the above momentum region is not integrated out. Using $V_{low-k}$ with $Lambda sim 3$ fm$^{-1}$, we perform a ring-diagram computation with the above potentials, which all yield saturation energies $E/A$ and Fermi momenta $k_F^{(0)}$ considerably larger than the empirical values. On the other hand, similar computations with the medium-dependent Brown-Rho scaled NN potentials give satisfactory results of $E/A simeq -15$ MeV and $k_F^{(0)}simeq 1.4$ fm$^{-1}$. The effect of this medium dependence is well reproduced by an empirical 3-body force of the Skyrme type.
Chiral expansions of the two-pion exchange components of both two- and three-nucleon forces are reviewed and a discussion is made of the predicted pattern of hierarchies. The strength of the scalar-isoscalar central potential is found to be too large and to defy expectations from the symmetry. The causes of this effect can be understood by studying the nucleon scalar form factor.
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