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

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, (2008) weak eigenstates mass eigenstates CKM Cabibbo-Kobayashi -Maskawa (4) (4) < |V ud | 2 +|V us | 2 +|V ub | 2 =0.9997(6) |V ud | = adopted from J.Hardy’s, ENAM’08 presentation

~ ~ | 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

superallowed 0 +  0 +  -decay |V ud | (a)  -decay mirror T=1/2 nuclei -decay (b) (c) (d) |V ud | 2 +|V us | 2 +|V ub | 2 superallowed 0 +  0 +  -decay  -decay -decay mirror T=1/2 nuclei (a) (b) (c) (d) A  C -  C [%] (SV) (HT) W. Satuła, J. Dobaczewski, W. Nazarewicz, M. Rafalski, Phys. Rev. Lett. 106, (2011); Phys. Rev. C 86, (2012). I.S. Towner and J. C. Hardy, Phys. Rev. C 77, (2008). (a) (b) (c,d) O. Naviliat-Cuncic and N. Severijns, Eur. Phys. J. A 42, 327 (2009); Phys. Rev. Lett. 102, (2009). V ud = (26) Ft=3071.4(8)+0.85(85); Ft=3070.4(9); V ud = (23) PRL Ft=3073.6(12); V ud = (27) PRC H. Liang, N. V. Giai, and J. Meng, Phys. Rev. C 79, (2009)

jj j j j jj jj l s i ll i s s 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 = (27) Ft=3073.6(12) |V ud | 2 +|V us | 2 +|V ub | 2 = = (67) Functional dependence: SV: V ud = (27) Ft=3075.0(12) |V ud | 2 +|V us | 2 +|V ub | 2 = = (67) SHZ2: a sym =42.2MeV!!! Basis-size dependence: ~10% Configuration dependence:

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

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

(keV) T Cl I=1 + theory (keV) theoryexperiment T , 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, (2011). Experiment: δ C ≈ 5.3(9)% SM+WS calculations: δ C ≈ 4.6(5)%.

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, (2013)

EXP 11 1 2 22  g.s. + Energy (MeV) normalized  C [%] E HF (MeV) 11 1 Z X~YX~Y ~200keV

Static approach gives:  C =8.9% I=0 +, T= Ca 38 K EXP  C =1.5%  C =1.7%  E [MeV] mixing: 4 Slaters 3 Slaters

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.

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)

Excitation energy [MeV] angular momentum T=1 T=0 Mixing of states projected from the antialigned configurations: nK pK /2 3/25/27/2 SV SHZ2  E (MeV) K 42 Sc ( )

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 )

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