Nuclear Landscape not fully known

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2 Nuclear Landscape not fully known Heaviest Elements? Known Nuclei Limit of proton rich nuclei? Fission Limit? Possible Nuclei Limit of Neutron Rich Nuclei?

3 Nuclear Radii Textbooks: R = r 00 A 1/3 1/3 I. Tanihata

4 Weakly Bound Nulcei Quantum mechanical penetration of weakly bound nucleons leads to a new class of nuclei. Example: 42 Mg 4πr 2 x density (nucleons/fm) πr 2 x density Neutron Proton Radius (fm) 42 Mg - 40 Mg Difference Neutron Proton Radius Science to Study: Pairing in lowdensity material Interaction with continuum states Efimov States Reactions

5 Change of Shell Structure J. Dobaczewski and W. Nazarewicz h 9/2 f 5/2 p 1/2 p 3/2 f 7/2 h 11/ 2 g 7/2 d 3/2 s 1/2 d 5/2 g 9/2 very diffuse surface neutron drip line N=5 3p 2f 1h 3s N=4 2d harmonic oscillator 1g no spin orbit exotic nuclei/ hypernuclei around the valley of β-stability p 1/2 f 5/2 i 13/2 p 3/2 h 9/2 f 7/2 d 3/2 h 11/2 s 1/2 g 7/2 d 5/2 g 9/2 The nuclear mean field potential is dependent on the number and type of nucleons present in the nucleus. Shell structure for very asymmetric nuclear matter will be different than for normal N=Z nuclear material.

6 New Shell Structure Z=8?? N=20 N=8 N=16?

7 N=8, Z=8 shell closure?

8 Vanishing of Shell Closure N=20 shell gap vanishes New shell closure at N=16 N=8 shell closure 1s 1/2 1s 1/2, 0p 1/2 N=8 0p 1/2 N=6 0p 3/2 0p 3/2 16 O, 14 C 12 Be, 11 Li Removing 0p 3/2 protons Spin-flip, isopspin-flip NN interaction Vts is strongly attractive T. Otsuka et al., PRL 87 (2001)

9 Pygmy Dipole Resonance Occurrence of a collective soft dipole mode in Neutronrich nuclei A strong impact on nuclear astrophysics

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11 Open Problem in Nuclear Structure Theory

12 From simplicity to Complexity RHIC quarks gluons CEBAF bare nucleons RIA heavy nuclei vacuum quark-gluon plasma QCD nucleon QCD few-body systems free NN force many-body systems effective NN force

13 From NN int to Finite Nuclei Brueckner theory of nuclear many-body systems (BHF) was introduced about 50 years ago a powerful tool the bare N N interaction V the effective inmedium interaction G a meson-exchange type of interaction V is strongly repulsive at short distances Behaves smoothly a nuclear system can be described by an ensemble of nucleons moving in a mean field created self-consistently by the two-body effective interaction G

14 Good Predictions for NM in DBHF All BHF predictions of the NM saturation point lie along the Coester band which misses the empirical saturation point With 3-body force BHF gives right saturation properties These three-body terms are mainly effects of the vacuum virtual N N excitations, leading to the so-called Z graphs Coester band DBHF approach based on meson-exchange potentials predicts NM saturation point without the need for a three-body force

15 Dirac Brueckner Hartree-Fock Theory bare NN interaction of the mesonexchange type. predict properties of finite nuclei A promising starting point consists in DBHF calculations using realistic nucleon nucleon interactions like the Bonn potentials Difficulties in Brueckner theory double selfconsistency Construct effective Lagrangians with density-dependent nucleon meson coupling vertices, which can be used in the relativistic mean field (RMF) or preferably in the relativistic Hartree Fock (RHF) approach.

16 Limitations of DBHF Limitations of DBHF A three-dimensional Thompson reduction of BS eq. Neglecting the negative energy states (no-sea approximation) the Lorentz structure of the self-energy is either lost or ambiguous At very low densities: unstable because of the deuteron pole or cluster effects and noninhomogeneities of NM At high densities several times of the saturation density the description in terms of nucleons and mesons may not be valid subnuclear degrees of freedom have to be included Valid at ρ (1 2)ρ 0.1ρ to 0 0

17 Lorentz Structure of the G matrix DBHF calculations do not yield identical results the reduced BS equation (3-dimension) projected on the positive-energy Dirac spinors The Lorentz structure of the G matrix is lost must be reconstructed in some manner The simplest method Brockmann R and Machleidt R 1990 Phys. Rev. C analyzing the momentum dependence of the single-particle energies Neglect the momentum dep. of the nucleon self-energies

18 Isospin dependence This method gives reasonable results for symmetric nuclear matter it leads to incorrect results in asymmetric matter, even giving the wrong sign for the isospin dependence of the effective interaction

19 Methods to extract Lorentz Structure A decomposition of the DBHF G matrix of the form Bare NN int. ΔG is treated by a projection method the Lorentz structure can be derived explicitly in the HF approximation for the OBE interaction yield the most reliable results at present another method consists in performing the projection on the full space of positive and negative energy Dirac states de Jong F and Lenske H 1998 Phys. Rev. C

20 Effective Lagrangian To build an effective Hamiltonian of HF or RHF (RMF) that can reproduce the results of BHF (+ corrections) or DBHF in infinite NM DBHF self-energies are density and momentum dependent

21 Density and Momentum dependence At present DDRMF have been done in this direction g i have to be density dependent Brockmann R and Toki H 1992 Phys. Rev. Lett Ma Z Y and Liu L 2002 Phys. Rev. C Nucleon self-energies are not momentum dep in RMF RHF in NM are momentum dependent ~1/k matching to the DBHF self-energies in a more consistent way. DDRHF are performed in a phenomenological way Long W H, Ring P, Van Giai N and Meng J 2010 Phys. Rev. C

22 Conclusion There are not yet completely satisfactory RHF calculations of finite nuclei based on effective Lagrangians deduced from DBHF nuclear matter studies The next step to establish a link between N N interactions like the Bonn potentials and the properties of finite nuclei is at hand

23 Thank you

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