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The Isospin Dependence of the Nuclear Force and its Impact on the Many-Body System

The Isospin Dependence of the Nuclear Force and its Impact on the Many-Body System. 11 th International Spring Seminar on Nuclear Theory In honor of Aldo Covello Ischia, May 12-16, 2014. Francesca Sammarruca University of Idaho.

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The Isospin Dependence of the Nuclear Force and its Impact on the Many-Body System

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  1. The Isospin Dependence of the Nuclear Force and its Impact on the Many-Body System 11th International Spring Seminar on Nuclear Theory In honor of Aldo Covello Ischia, May 12-16, 2014 Francesca Sammarruca University of Idaho Research supported in part by the US Department of Energy.

  2. After more than 8 decades of nuclear physics, still a lot is unknown about the nuclear chart. Particularly so for systems with large isospin asymmetry

  3. Open questions : Nuclear properties under extreme neutron/proton ratio? Are present nuclear models still valid for nuclei with large neutron excess? Properties of “halo nuclei”?

  4. Experimental programs at RIBF (and the upcoming FRIB) will have widespread impact, filling some of the gaps in our incomplete knowledge of the nuclear chart. Isospin-Asymmetric Nuclear Matter (IANM) is closely related to neutron-rich nuclei and is a convenient theoretical laboratory. Studies of IANM (particularly the symmetry energy contribution to the EoS), are now particularly timely, as they support rich on-going and future experimental effort.

  5. The goal of microscopic nuclear physics: To derive the properties of nuclear systems from the basic nuclear interaction (AB INITIO)

  6. How to develop basic interactions? Our present (incomplete) knowledge of the nuclear force is the results of decades of struggle. QCD and its symmetries led to the development of chiral effective theories. Chiral potentials are based on a low-momentum expansion and are of limited use for applications in dense matter.

  7. Two-body sector: a realistic meson-theoretic potential developed within a relativistic scattering equation (Bonn B) Our traditional many-body framework: The Dirac-Brueckner-Hartree-Fock(DBHF)approach to (symmetric and asymmetric) nuclear matter. Microscopic DB gives validation to the success of RMF theories. Microscopic relativistic nuclear physics: A paradigm which is important to pursue, reliable over a broad range of momenta/densities.

  8. Starting with a historical note: The “mass formula”, Bethe-Weizaecker: B/A = Binding energy/nucleon (N – Z)/A = neutron excess or isospin asymmetry

  9. Symmetry energy

  10. This is consistent with the results of a proper (microscopic) calculation of the energy/particle in nuclear matter: EoS= Equation of state= energy/particle as a function of density

  11. The symmetry energy as predicted by three meson-theoretic NN potentials:

  12. The density dependence of the symmetry energy from various parametrizations of the (phenomenological) Skyrme models. The shaded area corresponds to constraints from heavy-ion collisions.

  13. In any fundamental theory of nuclear forces, the pion is the most important ingredient (crucial for NN scattering data or the deuteron!), followed by heavier mesons. As demonstrated in F.S., PRC84, 044307 (2011), the pion gives the main contribution to the symmetry energy.

  14. The slope of the symmetry energy at saturation density is represented by the parameter: Note that the pressure in neutron matter (at saturation density) is: So:

  15. In a neutron-rich nucleus, this pressure pushes neutrons outwards against surface tension to form the neutron skin. Thus: L Pn.m. Neutron skin Skin=Rn- Rp r.m.s. radii of the n(p) distributions

  16. A simple determination of n and p densities directly from the EoS of IANM: Neutron excess parameter n and p densities in 208-Pb predicted through our EoS

  17. There is a nearly linear relation between the L parameter and the thickness of the neutron skin in a heavy nucleus: ID= Isospin diffusion

  18. Electroweak (parity-violating) experiment: PREX: Skin = 0.33 (+0.16,-0.18) fm PREX II : will come soon

  19. Perhaps the most “isospin-asymmetric” system in nature is a Neutron star Very “exotic” objects, with mass of about 2 solar masses and radius about 10 km. The structure of NS is determined by the EoS of stellar matter. TOV equations EoS

  20. J1614-2230 (Demorest et al., 2010) has a mass of 1.97 (0.04) solar masses. This value is the highest yet measured with this certainty and represents a challenge for theoretical models of the EoS. Mass-radius relation over a broad range of masses would provide the necessary constraint on the EoS of IANM.

  21. Whereas some NS masses are accurately known, (e.g. pulsar in Hulse-Taylor binary system, with M=1.4408(0.0003) solar masses), precise measurements of their radii are not available. (No direct measurements exist for NS radii.) NS radii can provide stringent constraints on the density dependence of the symmetry energy. Studies suggest: the larger the skin of a heavy nucleus, the larger the predicted stellar radius. Therefore, constraints from both neutron skins and NS radii would be extremely useful.

  22. Correlation coefficient between A quantity A and the neutron skin thickness in 208-Pb L 0.9952 P(at saturation density) 0.9882 P(twice saturation density) 0.8016 R0.6 0.9953 R0.8 0.9931 R1.0 0.9866 R1.4 0.9486 R1.6 0.8361 (Fattoyev, Piekarewicz, PRC86, 015802 (20012))

  23. Moving on to other applications of the nuclear force in the medium: Nuclear/neutron matter Structure of nuclei Reactions

  24. Our link with reactions: In-medium NN collisions

  25. Transport models of HI collisions are sensitive to both NN collisions and the average nuclear matter potential. NN collisions are described by NN effective xsections. Our in-medium NN xsections are microscopic (i.e. driven by the NN scattering amplitudes.) (Chen, Sammarruca, Bertulani, PRC87, 054616 (2013)) Using microscopic input has the advantage that different ingredients are internally consistent, as they all originate from the NN scattering amplitudes in the medium.

  26. Effective NN cross section suitable for nucleus-nucleus collisions: Microscopic DBHF Geometric Pauli blocking in collisions of two Fermi spheres.

  27. Future plans/work in progress include: Single-nucleon knockout reactions at intermediate energies involving unstable beams. (with Carlos Bertulani) (c + N) + T c + X (A very sensitive tool to study s.p. occupancies in the shell model through measurements of the momentum distribution.)

  28. In conclusions: Using microscopic input has several advantages: Internal consistency of different ingredients Better insight into the physics All microscopic models have at least one thing in common….. ….they describe the nucleon-nucleon system

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