Isospin symmetry breaking effects in atomic nuclei within extended Density Functional Theory Wojciech Satuła In colaboration with: Jacek Dobaczewski, Paweł Bączyk, Maciek Konieczka, Koichi Sato, Takashi Nakatsukasa Frontiers in nuclear structure theory: golden decade of ab initio methods spectacular developments in (SR) DFT, TD-DFT and MR-DFT-rooted approaches new developments: DFT-rooted NCCI pn-mixed SR functionals charge-dependent functionals physics highlights: nuclear structure beta decays strong isospin symmetry breaking effects (TED/MED) Final remarks and perspectives

Resolution Effective (field) theories Hot and dense quark-gluon matter Hadron structure DFT collective and algebraic models CI ab initio LQCD quark models Resolution Hadron-Nuclear interface Nuclear structure & reactions 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!”

emergence of 3NF due to finite resolution Effective or low-energy (low-resolution) theory explores separation of scales. Its formulation requires: in coordinate space: define R to separate short- and long-distance physics or, in momentum space: define L (1/R) to separate low and high momenta replace (complicated and, in nuclear physics, unknown) short distance (or high momentum) physics by a LCP (local correcting potential) (there is a lot of freedom how this is done concerning both the scale and form but physics is (should be!) independent on the scheme!!!) from Hammer et al. RMP 85, 197 (2013) emergence of 3NF due to finite resolution

Nuclear effective theory for EDF (nuclear DFT) is based on the same simple and very intuitive assumption that low-energy nuclear theory is independent on high-energy dynamics ultraviolet cut-off L regularization Fourier Coulomb Long-range part of the NN interaction (must be treated exactly!!!) hierarchy of scales: 2roA1/3 ~ 2A1/3 ro correcting potential local ~ 10 There exist an „infinite” number of equivalent realizations of effective theories where denotes an arbitrary Dirac-delta model Gaussian regulator J. Dobaczewski, K. Bennaceur, F. Raimondi, J. Phys. G 39, 125103 (2012)

Proof of principle of the regularization range (scale) independence for the gaussian-regularized density-independent EDFs J. Dobaczewski, K. Bennaceur, F. Raimondi, J. Phys. G 39, 125103 (2012)

Having defined the generator, the nuclear EDF is built using mean-field (HF or Kohn-Sham) methodology direct term exchange term lim da a 0 Skyrme interaction - specific (local) realization of the nuclear effective interaction: spin-orbit density dependence 10(11) parameters relative momenta spin exchange LO NLO

Look very similar except of „three-body” contributions! Fractional powers of the density lead to singularities in extensions involving restoration of broken symmetries:  rotational (spherical) symmetry  isospin symmetry (approximate)  particle number… and subsequent configuration mixing. NCCI SR-DFT MR-DFT

(density independent) (density independent) Our NCCI scheme: Skyrme SV (density independent) is used at this stage W.Satuła, P.Bączyk, J.Dobaczewski & M.Konieczka, Phys. Rev. C94, 024306 (2016) Skyrme SV (density independent) is used at this stage

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

Excitation energy of 0+ states [MeV] No-core configuration-interaction formalism based on the isospin and angular momentum projected DFT 62Zn, I=0+ states below 5MeV HF p1 n1 n2 pp1 p2 I=0+ before mixing p|312 5/2>-1 p|312 3/2> p|312 5/2>-2 p|312 3/2>2 p|310 1/2> n|312 3/2>-1 n|310 1/2> n|321 1/2> EXP (old) SM (MSDI3) (GXPF1) EXP (new) K.G. Leach et al. PRC88, 031306 (2013) SVmix (6 Slaters) 1 2 3 4 5 W.Satuła, J.Dobaczewski & M.Konieczka, arXiv:1408.4982; JPS Conf. Proc. 6, 020015 (2015) Excitation energy of 0+ states [MeV] W.S., J. Dobaczewski, M. Konieczka arXiv:1408.4982 (2014) JPS Conf. Proc. 6, 020015 (2015) 0+ ground state

Testing the fundamental symmetries of nature Temporal dependence of the fine structure constant studies in 229Th 126 Weak interaction studies in N=Z nuclei superallowed b-decay 82 EDM search in radium bb0n searches 50 protons 82 28 Specific nuclei offer new opportunities for precision tests of: CP and P violation Unitarity of the CKM matrix Possible temporal dependence of the fine structure constant in 229Th 20 50 8 28 neutrons 2 20 2 8 neutron EDM

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

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

|MGT| 6He(0+) 6Li(1+) Proof-of-principle calculation: 2.5 2.0 Gamow-Teller and Fermi matrix elements in 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-principle calculation: 6He(0+) 6Li(1+) 2.5 |MGT| Knecht et al. PRL108, 122502 (2012) 2.0 NCCI in 6Li 6He is fixed NCCI in 6He 6Li is fixed T=1/2 mirrors: -1.5 -1.0 -0.5 0.5 1.0 1.5 20 30 40 50 (EEXP-ETH)/EEXP (%) A Tz= 1/2 Tz=-1/2 masses:

|gAMGT| A |gAMGT| |MGT | 1 2 3 4 5 SM NCCI 20 30 40 50 SM NCCI 1 2 3 4 5 SM NCCI |gAMGT| 20 30 40 50 A (TH) |MGT | (EXP) SM NCCI Shell-model: B. A. Brown and B. H. Wildenthal, Atomic Data and Nuclear Data Tables 33, 347 (1985). G. Martinez-Pinedo et al., Phys. Rev. C 53, R2602 (1996). T. Sekine et al., Nucl. Phys. A 467, (1987). quenching q~25%!!! NCCI vs shell-model: The NCCI takes into account a core and its polarization Completely different model spaces Different treatment of correlations Different interactions

Renormalization of axial-vector coupling constant 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) See also: Klos et al. PRC89, 029901 (2013) q~0.9 Engel et al. PRC89, 064308 (2013)

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

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

T=1,I=0+ isobaric analogue states 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 lx lz normalized: theory (red curve) shifted by 3.2MeV separable solution p-n mixed |n> |p> + -

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

Mirror displacement energies with class II and III local corrections to the Skyrme force P.Bączyk, J.Dobaczewski, M.Konieczka, W.Satuła, T.Nakatsukasa, K. Sato, arXiv:1701.04628

Triplet Displacement Energies (TDE) with class II and III local corrections to the Skyrme force

Challenges for Low-Energy Nuclear Theory Perform proof-of-principle lattice QCD calculation for the lightest nuclei Develop first-principles framework for light, medium-mass nuclei, and nuclear matter from 0.1 to twice the saturation density Derive predictive 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 astrophysics and nuclear energy research. Develop and utilize tools for quantification of theoretical uncertainties. Provide the microscopic explanation for observed, and new, (partial-) dynamical symmetries and simple patterns

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

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