1. LBL 5/21/2007J.W. Holt1 Medium-modified NN interactions Jeremy W. Holt* Nuclear Theory Group State University of New York * with G.E. Brown, J.D. Holt, and T.T.S. Kuo

2. LBL 5/21/2007J.W. Holt2 Medium- modified Microscopic Foundation for density-dependent interactions Can such interactions provide a good description of nuclear systems?

3. LBL 5/21/2007J.W. Holt3 Chiral Effective Theories (e.g. Hidden Local Symmetry) Double Decimation Match T and  dependence with QCD Sum Rule correlation functions Traditional OBE potentials (e.g. Bonn, Nijmegen, etc.) EFT with intrinsic T and  dependence QCD Chiral decimation Fermi liquid decimation Describe in a unified way G. Brown and M. Rho, Phys. Rept. 396 (2004) (1) Finite nuclei (2) Nuclear matter (3) Hot/dense matter Low-momentum interaction Introduce medium modifications “by hand”

4. LBL 5/21/2007J.W. Holt4 CD-Bonn potentialNijmegen potentials  0 (135),  ± (140)  0 (135),  ± (140),  (549),  '(958)  1 (500),  2 (900)  (760), a 0 0 (983), a 0 ± (983), f 0 (976)  0 (770),  ± (770),  (782)  0 (767),  ± (768),  (782),  (1020) In-medium modifications (T = 0,   0) Change in mass at  =  0 Theory Experiment Us ,  ~ 10 – 15% decrease Yes Yes 15%  ~ small increase Yes Yes 0%  ~ 10% decrease Yes No 7% Assume linear scaling:

5. LBL 5/21/2007J.W. Holt5 RG and EFT Traditional problem: Strong short distance repulsion (a) G-matrix (b) V low-k

6. LBL 5/21/2007J.W. Holt6 Bare NN Potentials Universal interaction for  = 2.1 fm -1 k = 2.1 fm -1  E lab = 350 MeV Integrate out the experimentally unconstrained part of the NN interaction

7. LBL 5/21/2007J.W. Holt7 Nuclear matter  Easier than finite nuclei (only one density)  Saturation (E/A, k F, K )  Hartree-Fock (preliminary)  Ring diagram expansion (preliminary)  Fermi liquid theory [JWH et al., NPA 785 (2007) 322.] Outline of Results Finite nuclei  Diminishing tensor force  Beta decay of 14 C

8. LBL 5/21/2007J.W. Holt8 Saturation with low momentum interactions Fixed cutoff in Hartree-Fock approximation (no saturation) S. Bogner et al., NPA 763 (2005) 59. Add leading order chiral 3N force Empirical saturation energy and density

9. LBL 5/21/2007J.W. Holt9 Tensor force with dropping masses

10. LBL 5/21/2007J.W. Holt10 Novel saturation mechanism Hartree-Fock + Preliminary!

11. LBL 5/21/2007J.W. Holt11 Ring diagrams (pp) +++ Introduce model space  m ~ 3.0 fm –1 Choose  vlowk =  m

12. LBL 5/21/2007J.W. Holt12 Preliminary! [fm –1 ] [MeV]

13. LBL 5/21/2007J.W. Holt13 Expand: quasiparticle interaction Quasiparticles defined only near Fermi surface: k  k F Strongly interacting, normal Fermi systems at T = 0 Weakly interacting quasiparticles Fermi Liquid Theory Hartree-Fock

14. LBL 5/21/2007J.W. Holt14 Spin & Isospin Dependence: Dimensionless parameters: Correspondence between FLP and observables

15. LBL 5/21/2007J.W. Holt15 Pauli Principle  Sum Rules: + Babu-Brown induced interaction S. Babu and G. Brown, Ann. Phys. 78 (1973) 1

16. LBL 5/21/2007J.W. Holt16 FullDrivingInduced l FGF’G’FGF’G’FGF’G’ 0 -0.480.030.220.78-1.280.140.370.640.80-0.12-0.150.14 1 -0.340.260.270.17-0.530.260.280.130.200.010.000.05 Largest effect is to cut down the strong attraction in F channel Rapid convergence of iteration scheme Full Calculation: Driving Terms (V low-k CD-Bonn) F d0 = -1.20 F d1 = -0.50 G d0 = 0.14 G d1 = 0.24 F' d0 = 0.35 F' d1 = 0.26 G' d0 = 0.60 G' d1 = 0.12 Unstable (negative K ) Sum Rules:

17. LBL 5/21/2007J.W. Holt17 Nijmegen INijmegen IICD-BonnExpt. m*/m0.8870.9300.888 K [MeV] 136102136200-300  [MeV] 18.120.517.625-35 gl[N]gl[N] 0.6820.4520.6850.20-0.26 SlSl 0.200.160.27 S2S2 -0.04-0.02-0.04 How to improve? 1. Explicit three-body forces 2. In-medium modifications to NN interaction Medium modifications equivalent to a type of 3N force Extend Walecka mean field theory to constituent quarks

18. LBL 5/21/2007J.W. Holt18 V NI V NII V N93 V CDB Exp. m*/m0.7210.7630.6960.682 K [MeV] 218142190495200-300  [MeV] 20.425.523.719.225-35 gl[N]gl[N] 0.2460.1810.2830.2670.20-0.26 Full many-body calculations g A = 1.25 g A * = 1.00 quark model Decreasing g 2  NN by 20% cuts K by 50% but changes other observables by ~ 5%

19. LBL 5/21/2007J.W. Holt19 Finite nuclei Decreasing tensor force necessary! 1.Decay of 14 C 2.0 – T=1 and 0 – T=0 splitting in 16 O 3.E2 and M1 moments of 6 Li Traditional many-body effects or novel scaling mechanism?

20. LBL 5/21/2007J.W. Holt20

21. LBL 5/21/2007J.W. Holt21 14 C 14 N 0+0+ 1+1+ 2 holes in 0p-shell –– Nijmegen I Preliminary

22. LBL 5/21/2007J.W. Holt22 NN interactions with medium-modified mesons Saturation of nuclear matter and Fermi liquid parameters improved with dropping masses Summary Full analysis of ring diagrams Look for nuclear observables where tensor force plays dominant role Understand the connection between medium modifications and three- body forces Outlook