Isospin Symmetry Breaking Effects in Atomic Nuclei within Extended Density Functional Theory

1. Isospinsymmetrybreakingeffects in atomicnuclei withinextendedDensityFunctionalTheory WojciechSatuła In colaboration with: Jacek Dobaczewski, Paweł Bączyk, Maciek Konieczka, KoichiSato, TakashiNakatsukasa Frontiers in nuclearstructuretheory: goldendecadeof ab initio methods spectaculardevelopments in (SR) DFT, TD-DFT and MR-DFT-rootedapproaches • newdevelopments: DFT-rooted NCCI • pn-mixed SR functionals • charge-dependent functionals • physicshighlights:nuclearstructure • beta decays • strongisospinsymmetrybreaking • effects (TED/MED) Finalremarks and perspectives

2. Hot and dense quark-gluon matter Hadron structure LQCD Resolution quark models Hadron-Nuclearinterface ab initio Nuclear structure & reactions CI Effective (field) theories Third Law of Progress in Theoretical Physics by Weinberg: “You may use any degrees of freedom you like to describe a physical system, but if you use the wrong ones, you’ll be sorry!” DFT collective and algebraic models

3. Effectiveorlow-energy (low-resolution) theoryexploresseparation of scales. Itsformulationrequires: in coordinatespace: defineR to separateshort- and long-distancephysics or, in momentumspace: defineL (1/R) to separatelow and high momenta replace (complicated and, in nuclearphysics, unknown) shortdistance (orhigh momentum) physics by a LCP (localcorrectingpotential) (thereis a lot of freedomhowthisisdoneconcerningboth the scale and form but physicsis (should be!) independent on the scheme!!!) emergence of 3NF due to finite resolution from Hammer et al. RMP 85, 197 (2013)

4. Nucleareffectivetheory for EDF (nuclear DFT) Thereexistan „infinite” number of equivalentrealizations of effectivetheories isbased on the same simpleand veryintuitiveassumptionthatlow-energynucleartheoryis independent on high-energy dynamics ultraviolet cut-off L Fourier regularization Coulomb Long-range part of the NN interaction (must be treated exactly!!!) hierarchy of scales: 2roA1/3 2A1/3 ~ local correcting potential ro ~ 10 denotes an arbitrary Dirac-delta model where Gaussian regulator J. Dobaczewski, K. Bennaceur, F. Raimondi, J. Phys. G 39, 125103 (2012)

5. Proof of principle of the regularizationrange(scale) independence for the gaussian-regularizeddensity-independent EDFs J. Dobaczewski, K. Bennaceur, F. Raimondi, J. Phys. G 39, 125103 (2012)

6. Havingdefined the generator, the nuclear EDF isbuiltusing mean-field (HF orKohn-Sham) methodology Skyrmeinteraction - specific (local) realization of the nucleareffectiveinteraction: lim da a 0 spin exchange relative momenta LO NLO 10(11) density dependence parameters direct term exchange term spin-orbit

7. Lookverysimilarexcept of „three-body” contributions! Fractionalpowers of the densitylead to singularities in extensions involvingrestoration of brokensymmetries:  rotational(spherical) symmetry  isospinsymmetry(approximate)  particlenumber… and subsequentconfigurationmixing. NCCI MR-DFT SR-DFT

8. Our NCCI scheme: Skyrme SV (density independent) isusedatthisstage W.Satuła, P.Bączyk, J.Dobaczewski & M.Konieczka, Phys. Rev. C94, 024306 (2016) Skyrme SV (density independent) isusedatthisstage

9. -20 -25 -30 -35 -40 -45 -50 -55 -60 mixing of statesprojected from three-four p-h configurations For detailssee: W.Satuła, P.Bączyk, J.Dobaczewski & M.Konieczka, Phys. Rev. C94, 024306 (2016) 6Li TH 2+ 0+ 3+ 1+ TH 8Li 1+ 3+ Energy [MeV] 1+ 2+

10. 5 4 3 2 1 0 No-coreconfiguration-interactionformalismbased on the isospinand angularmomentumprojectedDFT 62Zn, I=0+statesbelow 5MeV p2 SM (GXPF1) SM (MSDI3) EXP (new) p|312 5/2>-1 p|310 1/2> n2 SVmix (6 Slaters) EXP (old) n|312 3/2>-1 n|321 1/2> pp1 W.Satuła, J.Dobaczewski & M.Konieczka, arXiv:1408.4982; JPS Conf. Proc. 6, 020015 (2015) n1 p1 Excitationenergy of 0+states [MeV] K.G. Leach et al. PRC88, 031306 (2013) p|312 5/2>-2 p|312 3/2>2 p|312 5/2>-1 p|312 3/2> n|312 3/2>-1 n|310 1/2> W.S., J. Dobaczewski, M. Konieczka arXiv:1408.4982 (2014) JPS Conf. Proc. 6, 020015 (2015) HF I=0+ before mixing 0+groundstate

11. Testing the fundamental symmetries of nature Temporaldependence of the fine structure constantstudies in 229Th 126 82 Weak interaction studies in N=Z nuclei superallowedb-decay EDM search in radium bb0n searches 50 protons 82 • Specific nuclei offer new opportunities for precision tests of: • CP and P violation • Unitarity of the CKM matrix • Possibletemporaldependence • of the fine structureconstant in 229Th 28 20 50 8 28 neutrons 2 20 8 2 neutron EDM

12. Superallowed 0+>0+Fermi beta decays (testing the Standard Model) 10 casesmeasuredwithaccuracyft ~0.1% 3 casesmeasuredwithaccuracyft ~0.3%  test of the CVC hypothesis (ConservedVectorCurrent) 0.3% - 1.5% 1.5% ~2.4% adopted from J.Hardy’s, ENAM’08 presentation  test of unitarity of the CKM matrix Towner & Hardy Phys. Rev. C77, 025501 (2008) |Vud|2+|Vus|2+|Vub|2=0.9997(6) |Vud| = 0.97418 + 0.00026 - 0.9490(4) 0.0507(4) <0.0001 mass eigenstates CKM Cabibbo-Kobayashi -Maskawa weak eigenstates

13. dC- dC [%] (HT) (SV) 1.0025 1.0000 0.9975 0.9950 0.9925 10 20 30 40 50 60 70 0.5 0 (a) I.S. Towner and J. C. Hardy, Phys. Rev. C 77, 025501(2008). NCCI: 0.976 M. Konieczka, P. Bączyk, W. Satuła, Phys. Rev. C 93, 042501(R) (2016). (b) H. Liang, N. V. Giai, and J. Meng, Phys. Rev. C 79,064316 (2009). -0.5 0.975 0.974 W. Satuła,J. Dobaczewski, W. Nazarewicz, M. Rafalski Phys. Rev. C 86, 054314 (2012) (a) (c,d) (a) O. Naviliat-Cuncic and N. Severijns, Eur. Phys. J. A 42, 327 (2009); Phys. Rev. Lett. 102, 142302 (2009). (c) (c) |Vud| (d) (d) 0.973 A n-decay (b) n-decay (b) 0.972 |Vud| & unitarity - worldsurvey 0.971 superallowed 0+0+ b-decay superallowed 0+0+ b-decay 0.970 mirror T=1/2 nuclei mirror T=1/2 nuclei p-decay p-decay |Vud|2+|Vus|2+|Vub|2

14. Gamow-Teller and Fermi matrix elementsin T=1/2 sd- and ft- mirrors. The NCCI study M.Konieczka, P.Bączyk, W.Satuła, Phys. Rev. C93, 042501(R) (2016); arXiv:1509.04480 Proof-of-principlecalculation: 6He(0+) 6Li(1+) 2.5 |MGT| Knecht et al. PRL108, 122502 (2012) 2.0 NCCI in 6Li 6He isfixed NCCI in 6He 6Li isfixed T=1/2 mirrors: Tz=-1/2 Tz= 1/2 1.5 masses: 1.0 20 30 40 50 0.5 (EEXP-ETH)/EEXP (%) 0 -0.5 -1.0 -1.5 A

15. |gAMGT| 4 3 2 1 20 30 40 50 0 1 2 3 4 5 SM NCCI Shell-model: (TH) |gAMGT| B. A. Brown and B. H. Wildenthal, Atomic Data andNuclear Data Tables 33, 347 (1985). G. Martinez-Pinedoet al., Phys. Rev. C 53, R2602 (1996). A T. Sekineet al., Nucl. Phys. A 467, (1987). 5 quenching q~25%!!! NCCI SM NCCI vs shell-model: 4 The NCCI takesintoaccount a coreand itspolarization 3 (TH) |gAMGT| SM Completelydifferent model spaces NCCI 2 Differenttreatment of correlations 1 Differentinteractions 0 (EXP) |MGT |

16. Renormalization of axial-vectorcouplingconstant by 2B-currents ci from N and NN: cD, cE fit to 3H, 4He properties Menendez et al. PRL107, 062501 (2011) β−decays of 14C and 22;24O Ekstrom et al. PRL 113, 262504 (2014) q2~0.84-0.92 (from Ikeda sum rule) Seealso: Klos et al. PRC89, 029901 (2013) q~0.9 Engel et al. PRC89, 064308 (2013)

17. 24Al;4+ g.s. beta Decay |p202 5/2> GT strength M.Konieczka, M.Kortelainen, W.S., in preparation

18. 8 7 6 5 4 3 2 1 0 100In 100Sn NCCI LSSM*) exp NCCI ~ ~ BGT = 10.2 for qgA=0.6 +2.6 EXP BGT = 9.1 -3.0 NCCI 0+ 1+ ENERGY (MeV) 1+ 2+ 3+ 4+ 5+ 2+ 4+ 3+ 7+ 5+ 6+ GROUND STATE *) C.B. Hinkeet al. Nature 486, 341, (2012) „Superallowed GT decay of the doublymagicnucleus100Sn”

19. T=1,I=0+isobaricanaloguestates from self-consistent 3D-isocranked HF: hl=h-lT K. Sato, J. Dobaczewski, T. Nakatsukasa, and W. Satuła, Phys. Rev. C88 (2013), 061301 hl=h-lT + - normalized: theory (red curve) shifted by 3.2MeV lx lz p-n mixed solution separable solution separable solution |n> |p>

20. CD local (strong) corrections to the Skyrmeforce (class II (CIB) and III (CSB) Henley-Miller forces) Class II corrects for TDE Class III corrects for MDE

21. Mirror displacementenergies with class II and III local corrections to the Skyrmeforce P.Bączyk, J.Dobaczewski,M.Konieczka, W.Satuła, T.Nakatsukasa, K. Sato, arXiv:1701.04628

22. Triplet DisplacementEnergies (TDE) with class II and III localcorrections to the Skyrmeforce

23. Challenges for Low-EnergyNuclear Theory • Perform proof-of-principlelattice QCD calculation for the lightestnuclei • Develop first-principles framework for light, medium-mass nuclei, and nuclear matter from 0.1 to twice the saturation density • Derivepredictive nuclear energy density functional rooted in first-principles theory • Carry out predictive and quantified calculations of nuclear matrix elements for fundamental symmetry tests. • Unify the fields of nuclear structure and reactions. • Develop predictive microscopic model of fusion and fission that will provide the missing data for astrophysicsand nuclearenergy research. • Develop and utilize tools forquantification of theoreticaluncertainties. • Provide the microscopic explanationfor observed, and new, (partial-) dynamical symmetries and simple patterns

24. Isobaric Multiplet Mass Equation (IMME) EXP 3.5 GFMC 0.3 SVT CD 3.0 SVT 0.2 2.5 aA,T,I (MeV) aA,T,I (MeV) 0.1 2.0 (2) (1) 0 P.Bączyk, J.Dobaczewski, M.Konieczka, W.Satuła, in preparation 10,1,0 12,1,1 14,1,0 8,1,2 A,T,I

25. Staggering in a(2) isdue to TIME-ODD part of CIB (type II) short-rangefunctional |K|=1 |K|=2 0.2 time-even CIB 0.1 time-odd CSB daA,T,I (MeV) [CSB=0] (2) 0 -0.1 10,1,0 12,1,I 14,1,0 8,1,2 A,T,I