Chiral interac,ons in nucleonic ma1er and nuclei

Transcription

1 Chiral interac,ons in nucleonic ma1er and nuclei Thomas Papenbrock and G. Baardsen, A. Ekström, C. Forssen, G. Hagen, M. Hjorth Jensen, G. R. Jansen, R. Machleidt, W. Nazarewicz, J. Sarich, S. M. Wild Inelas,c Reac,ons in Light Nuclei Ins6tute for Advanced Studies, Hebrew University October 10, 2013 Research partly funded by the US Department of Energy

2 Op6miza6on of chiral interac6on at NNLO Ekström et al., Phys. Rev. Le^. 110, (2013) Kept fixed Adjusted parameters Weinberg; van Kolck; Epelbaum, Glöckle & Meiβner; Entem & Machleidt; Krebs;

3 Op6miza6on of NN poten6al to phase shics; χ 2 from data Weights for contacts scale as Q 3 ; for pion nucleon couplings from Nijmegen analysis Pion nucleon couplings determined from fits to peripheral d, f, g par6al waves (NNLO contacts do not contribute for L 2)

4 Results: χ 2 and NN proper6es NN proper6es

5 Phase shics of NNLOopt

6 A. Ekström et al (2012), unpublished Differen6al cross sec6ons at 90 MeV

7 Oxygen isotopes (NN only)

8 Calcium isotopes (NN only)

9 Neutron ma^er with chiral NN interac6on NNLO opt Pauli operator from [Suzuki et al. (2000)]; coupled cluster with pp and hh ladders; par6al wave decomposi6on of chiral NN interac6on GCR=Gandolfi, Carlson, Reddy, Phys. Rev. C 85, (2012) EGM=I. Tews, T. Krüger, K. Hebeler, and A. Schwenk, Phys. Rev. Le^. 110, (2013) Ekström et al., Phys. Rev. Le^. 110, (2013)

10 Nucleonic ma^er Use plane wave basis with generalized boundary condi6ons (Bloch waves) Basis respects momentum conserva6on CCD (no singles) for closed shell references Three nucleon forces much simpler to implement than in shell model basis Shell effects dominate finite size correc6ons Related studies with chiral interac6ons: Soma & Bozek (2008); Epelbaum, Krebs, Lee, & Meissner (2009); Hebeler & Schwenk (2010); Hebeler, Bogner, Furnstahl, Nogga, & Schwenk (2011); Holt, Kaiser, & Weise (2012); Carbone, Polls, & Rios (2013); Gezerlis, Tews, Epelbaum, Gandolfi, Hebeler, Nogga, & Schwenk (2013);

11 Mi6gate shell oscilla6ons Twist averaged boundary condi6ons: average over all possible phases of Bloch waves. Exactly removes finite size effects for free Fermi gas. [Gros, Z. Phys. B 86, 359 (1992); Lin, Zong, and Ceperley, Phys. Rev. E 64, (2001)] Discrete momenta are

12 Shell effects reduced considerably Shell effects depend on interac6on Twist average boundary condi6ons make extrapola6ons A possible A=66 (neutron ma^er) or A=132 (symmetric nuclear ma^er) are closed shells with small finite size correc6ons

13 Comparison with a con6nuum coupled cluster method The con6nuum coupled cluster method employs a par6al wave decomposi6on of the interac6on, integrates over rela6ve CoM momenta (with angular averages), and includes the exact Pauli operator. Neutron ma^er Finite size effects are controlled. Two different implementa6ons of the coupled cluster method agree well with each other. Sym. nuclear ma^er

14 Benchmark for Minnesota poten6al with Auxiliary Field Diffusion Monte Carlo

15 Three nucleon force Local form of 3NF [Navra6l, Few Body Syst. 41, 117 (2007)], i.e. cutoff is in the momentum transfer based on [Epelbaum et al., Phys. Rev. C 66, (2002)]. Fit to A=3,4 binding energies and triton half life (Gazit, Navra6l, & Quaglioni) c D =0.389 c E =0.39

16 Inclusion of three nucleon forces 3NFs s6ll require considerable computer 6me but less human 6me Normal ordered (w.r.t. HF vacuum) Hamiltonian Normal ordered 1 body interac6on (contains informa6on about NN force and 3NF) Normal ordered 2 body interac6on (contains informa6on of 3NF) Residual 3NF

17 Role of 3NF in neutron ma^er

18 Neutron ma^er is perturba6ve (NN only)

19 3NF acts repulsively in neutron ma^er

20 Nuclear ma^er is not perturba6ve (NN only) Overbinding and satura6on at too high densi6es

21 3NFs add repulsion 3NFs yields (too) large contribu6ons in triples correc6ons

22 Regulariza6on scheme dependence of 3NF Reduced cutoff in 3NF or non local regulator yields small triples correc6ons from 3NF Varia6on of c D and c E not sufficient to get interac6on that binds light nuclei and nuclear ma^er sa6sfactorily

23 Where actually does the cutoff cut off?

24 Summary Op6miza6on of chiral interac6on NNLO opt acceptable χ 2 1 per degree of freedom for lab energies < 125 MeV πn constants c i finely tuned, outside recommended intervals (?) NN interac6ons alone reproduce some essen6al features in isotopes of oxygen and calcium Nucleonic ma^er in momentum space with NNLO opt Finite size correc6ons under control Neutron ma^er is perturba6ve nuclear ma^er is not 3NF adds repulsion Varia6on of cd and ce not sufficient to fit light nuclei and ma^er 3NF with local regulator not without problems

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28 A. Ekström et al (2012), unpublished Differen6al cross sec6ons at 144 MeV

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30 3 H

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32 4 He

33 Nucleon nucleon proper6es

34 Three nucleon forces Matrix elements of 3NFs up to energies E 3max = 14 ħω Insufficient to reach converged results for binding energies Convergence of energy differences somewhat be^er Error es6mates based on varia6on 16 MeV ħω 22 MeV First 2+ state 22 O 24 O 48 Ca NN +3NF 2.3(3) MeV 3.5(5) MeV 4.8(7) MeV NN only 2.5 MeV 5.0 MeV 4.5 MeV Experiment 3.2 MeV 4.7 MeV 3.8 MeV