1. Isospin symmetry breaking corrections to the superallowed beta decays from the angular momentum and isospin projected DFT: brief overview focusing on sources of theoretical errors and on limitations of the „static” MR DFT Extension of the static approach: Summary & perspectives  examples: 32 Cl- 32 S, 62 Zn- 62 Ga, 38 Ca- 38 K  towards NO CORE shell model with basis cutoff dictated by the self-consistent p-h configurations

2. 10 cases measured with accuracy ft ~0.1% 3 cases measured with accuracy ft ~0.3% ~2.4% 1.5% 0.3% - 1.5% (Conserved Vector Current) Towner & Hardy Phys. Rev. C77, 025501 (2008) weak eigenstates mass eigenstates CKM Cabibbo-Kobayashi -Maskawa 0.9490(4) 0.0507(4) <0.0001 |V ud | 2 +|V us | 2 +|V ub | 2 =0.9997(6) |V ud | = 0.97418 + 0.00026 - adopted from J.Hardy’s, ENAM’08 presentation

3. ~ ~ | ground state in N-Z=+/-2 (e-e) nucleus antialigned state in N=Z (o-o) nucleus Project on good isospin (T=1) and angular momentum (I=0) ( and perform Coulomb rediagonalization) <T~1,T z =+/-1,I=0| |I=0,T~1,T z =0> T +/- Project on good isospin (T=1) and angular momentum (I=0) ( and perform Coulomb rediagonalization) | 2 =2(1-  C ) I=0 +,T=1,T z =-1 I=0 +,T=1, T z =0

4. superallowed 0 +  0 +  -decay |V ud | (a)  -decay mirror T=1/2 nuclei -decay 0.970 0.971 0.972 0.973 0.974 0.975 0.976 (b) (c) (d) 0.9925 0.9950 0.9975 1.0000 1.0025 |V ud | 2 +|V us | 2 +|V ub | 2 superallowed 0 +  0 +  -decay  -decay -decay mirror T=1/2 nuclei (a) (b) (c) (d) -0.5 0 0.5 10203040506070 A  C -  C [%] (SV) (HT) W. Satuła, J. Dobaczewski, W. Nazarewicz, M. Rafalski, Phys. Rev. Lett. 106, 132502 (2011); Phys. Rev. C 86, 054314(2012). I.S. Towner and J. C. Hardy, Phys. Rev. C 77, 025501(2008). (a) (b) (c,d) O. Naviliat-Cuncic and N. Severijns, Eur. Phys. J. A 42, 327 (2009); Phys. Rev. Lett. 102, 142302 (2009). V ud =0.97418(26) Ft=3071.4(8)+0.85(85); Ft=3070.4(9); V ud =0.97444(23) PRL Ft=3073.6(12); V ud =0.97397(27) PRC H. Liang, N. V. Giai, and J. Meng, Phys. Rev. C 79,064316 (2009). 62 10 38

5. jj 0.5 1.0 1.5 j j j jj jj l s i ll i s s -0.3 -0.2 -0.1 0 Relative orientation of shape and current  E [MeV]  C [%] i A=34 SV A=34 SV 34 Ar  34 Cl 34 Cl  34 S  E I=0,T=1  E HF  E IV (TO) x x x y y y V ud =0.97397(27) Ft=3073.6(12) |V ud | 2 +|V us | 2 +|V ub | 2 = =0.99935(67) Functional dependence: SV: V ud =0.97374(27) Ft=3075.0(12) |V ud | 2 +|V us | 2 +|V ub | 2 = =0.99890(67) SHZ2: a sym =42.2MeV!!! Basis-size dependence: ~10% Configuration dependence:

6.    nn ………… {|I> (1) } k 1 {|I> (2) } k 2 {|I> (3) } k 3 {|I> (n) } k n ………….. E i |I i >

7. 32 Cl I=1 + I=0 + I=2 + (2 + ) (0 + ) 0 1 2 3 4 5 6  E (MeV) I=3 + theory exp W.Satula, J.Dobaczewski, M.Konieczka, W.Nazarewicz, Acta Phys. Polonica B45, 167 (2014)

8. 0 1000 2000 3000 4000 (keV) 1 1 1 T 1 1 32 Cl I=1 + theory 0 1000 2000 3000 4000 (keV) theoryexperiment T 0 0 1 1 1 4622, 4636 32 S I=1 + experiment 7002keV W.Satula, J.Dobaczewski, M.Konieczka, W.Nazarewicz, Acta Phys. Polonica B45, 167 (2014) 0keV D. Melconian et al., Phys. Rev. Lett. 107, 182301 (2011). Experiment: δ C ≈ 5.3(9)% SM+WS calculations: δ C ≈ 4.6(5)%.

9. 0 1 2 3 4 5 0 + ground state EXP (old) SM (MSDI3) SM (GXPF1) Excitation energy of 0 + states [MeV] SV mix (6 Slaters) HF  ph  ph  ph  2p2h  ph I=0 + before mixing EXP (new) K.G. Leach et al. PRC88, 031306 (2013)

10. -526 -525 -524 -523 -522 EXP 11 1 2 22  1 + +++ g.s. + Energy (MeV) normalized 0 1 2 3 4 5 6  C [%] -512 -511 -510 E HF (MeV) 11 1 Z X~YX~Y ~200keV

11. Static approach gives:  C =8.9% I=0 +, T=1 0.0 0.5 1.0 1.5 2.0 2.5 3.0 38 Ca 38 K EXP  C =1.5%  C =1.7%  E [MeV] mixing: 4 Slaters 3 Slaters

12. We have to go BEYOND STATIC MR-EDF in order to address high-quality spectroscopic data available today. First attempts are very encouraging at least concerning energy spectra!!! Isospin symmetry breaking corrections from the „static” double-projected DFT are in very good agreement with the Hardy–Towner results.

13. 0 0.5 1.0 1.5 10141822263034 T z =-1  T z =0 mixing the X,Y,Z orientations in light nuclei A  C [%] averages mixing T&H W.Satula, J.Dobaczewski, M.Konieczka, W.Nazarewicz, Acta Phys. Polonica B45, 167 (2014)

14. 0 0.5 1.0 1.5 2.0 2.5 3.0 02461357 Excitation energy [MeV] angular momentum T=1 T=0 Mixing of states projected from the antialigned configurations: nK pK 0 0.2 0.4 0.6 1/2 3/25/27/2 SV SHZ2  E (MeV) K 42 Sc ( )

15. T=1 states are not representable in a „separable” mean-field! T=0  T=0 T=1  Mean-field can differentiate between  and  only through time-odd polarizations! aligned configurations     anti-aligned configurations or  or    CORE T z =-/+1 I=0 +,T=1 (N-Z=-/+2) (N-Z=0) T z =0 | | 2 =2(1-  C )

16.  anti-aligned configurations or    E-E CORE T=1 states are not representable in a „separable” mean-field!!! T=0 T=1 