Beta- decay studies in N~Z nuclei using no- core configuration-interaction model

1. Beta-decaystudies in N~Z nucleiusing no-core configuration-interaction model WojciechSatuła in collaboration with: J. Dobaczewski, W. Nazarewicz, M. Rafalski & M. Konieczka Isospinsymmetrybreakingcorrections to the superallowed beta decays from the angularmomentum and isospinprojected DFT: briefoverviewfocusing on sources of theoreticalerrors and on limitations of the „static” MR DFT Extension of the staticapproach: • towards NO CORE shell model with basiscutoff • dictated by the self-consistent p-h configurations • examples: • 32Cl-32S, 62Zn-62Ga, • 38Ca-38K Summary & perspectives

2. Superallowed I=0+ T=1 I=0+T=1 Fermi beta decays (testing the Standard Model of elementaryparticles) 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

3. How to calculate the superallowed Fermi beta decay ME using the double-projected DFT framework? I=0+,T=1,Tz=-1 Skyrme-Hartree-Fock DF t1/2 Qb I=0+,T=1, Tz=0 BR antialigned state inN=Z (o-o) nucleus ground state inN-Z=+/-2 (e-e) nucleus Project on goodisospin (T=1) and angularmomentum (I=0) (and perform Coulomb rediagonalization) Project on goodisospin (T=1) and angularmomentum (I=0) (and perform Coulomb rediagonalization) |2=2(1-dC) |I=0,T~1,Tz=0> T+/- <T~1,Tz=+/-1,I=0| | ~ ~

4. |Vud| & unitarity of the CKM – a survey dC- dC [%] (HT) (SV) 10 20 30 40 50 60 70 (a) I.S. Towner and J. C. Hardy, Phys. Rev. C 77, 025501(2008). Ft=3071.4(8)+0.85(85); Vud=0.97418(26) 0.5 (b) 1.0025 (c,d) W. Satuła,J. Dobaczewski, W. Nazarewicz, M. Rafalski, Phys. Rev. Lett. 106, 132502 (2011); Phys. Rev. C 86, 054314(2012). 1.0000 0 (a) (a) (c) (c) |Vud|2+|Vus|2+|Vub|2 |Vud| (d) (d) 0.9975 0.976 Vud=0.97444(23) PRL Ft=3070.4(9); n-decay (b) n-decay (b) -0.5 0.975 Vud=0.97397(27) PRC Ft=3073.6(12); 0.9950 0.974 superallowed 0+0+ b-decay superallowed 0+0+ b-decay O. Naviliat-Cuncic and N. Severijns, Eur. Phys. J. A 42, 327 (2009); Phys. Rev. Lett. 102, 142302 (2009). 0.9925 mirror T=1/2 nuclei 0.973 mirror T=1/2 nuclei p-decay A p-decay 0.972 0.971 62 10 0.970 H. Liang, N. V. Giai, and J. Meng, Phys. Rev. C 79,064316 (2009). 38

5. 1.5 1.0 0.5 0 -0.1 -0.2 -0.3 SOURCES OF THEORETICAL ERRORS Configurationdependence: Basis-sizedependence: l l l jn jp s s s jp y y y ~10% i i jn i jn jp Functionaldependence: x x x A=34 SV Ft=3073.6(12) SV: 34Ar  34Cl Vud=0.97397(27) dC [%] |Vud|2+|Vus|2+|Vub|2= =0.99935(67) 34Cl  34S Ft=3075.0(12) SHZ2: DEI=0,T=1 Vud=0.97374(27) |Vud|2+|Vus|2+|Vub|2= =0.99890(67) DE [MeV] DEHF (TO) DEIV asym=42.2MeV!!! Relative orientation of shape and current

6. MEAN-FIELD compute „n” self-consistentSlaterdeterminants corresponding to low-lying p-h excitations jn j2 j1 j3 ………… PROJECTION non-orthogonal set of K- and T-mixedstates {|I>(2)}k2 {|I>(1)}k1 {|I>(3)}k3 {|I>(n)}kn ………….. STATE MIXING Hill-Wheeler equation : Hu=ENu Ei |Ii>

7. No-coreshell model withbasiscutoffdictated by the self-consistent p-h DFT states theory 32Cl exp 6 5 4 DE (MeV) (2+) 3 (2+) 2 (2+) 1 (0+) (2+) 0 I=1+ I=2+ I=3+ I=0+ W.Satula, J.Dobaczewski, M.Konieczka, W.Nazarewicz, Acta Phys. Polonica B45, 167 (2014)

8. 32Cl I=1+ T 4622, 4636 32S I=1+ (keV) (keV) 1 4000 4000 1 T 3000 3000 1 W.Satula, J.Dobaczewski, M.Konieczka, W.Nazarewicz, Acta Phys. Polonica B45, 167 (2014) 1 2000 2000 0 1000 1000 1 1 0 1 1 0 0 7002keV 0keV theory experiment theory experiment our:δC≈ 6(2)% Experiment: δC≈ 5.3(9)% SM+WS calculations: δC≈ 4.6(5)%. D. Melconian et al., Phys. Rev. Lett. 107, 182301 (2011).

9. 5 4 3 2 1 0 62Zn, I=0+statesbelow 5MeV SM (GXPF1) SM (MSDI3) SVmix (6 Slaters) EXP (new) EXP (old) 2pph 2nph 1pp2p2h 1nph Excitationenergy of 0+states [MeV] K.G. Leach et al. PRC88, 031306 (2013) 1pph I=0+ before mixing HF 0+groundstate

10. -522 -510 -523 -511 -524 -525 -512 -526 Stability of configuration – interactioncalculations + g.s. EXP Energy (MeV) ~200keV normalized 6 n1 5 + + + + pp1 n1 n2 p1 p2 4 p1 dC [%] 3 2 EHF (MeV) 1 Z 0 X~Y

11. 3.0 2.5 2.0 1.5 1.0 0.5 0.0 A case of A=38 (38Ca38K) Staticapproachgives: dC=8.9% I=0+, T=1 EXP dC=1.5% DE [MeV] dC=1.7% 38K 38Ca 3Slaters 4 Slaters mixing:

12. Summary & perspectives Isospinsymmetrybreakingcorrections from the „static” double-projected DFT are in verygood agreement with the Hardy–Townerresults. We have to go BEYOND STATIC MR-EDF in order to address high-qualityspectroscopic data available today. First attemptsareveryencouragingatleast concerningenergy spectra!!!

13. 1.5 1.0 0.5 0 10 14 18 22 26 30 34 mixing the X,Y,Z orientations in lightnuclei Tz=-1  Tz=0 averages mixing dC [%] T&H A W.Satula, J.Dobaczewski, M.Konieczka, W.Nazarewicz, Acta Phys. Polonica B45, 167 (2014)

14. 0.6 0.4 0.2 0 3/2 5/2 7/2 1/2 SV SHZ2 42Sc DE (MeV) nKpK K Mixing of statesprojected from the antialignedconfigurations: 3.0 ( ) 42Sc 2.5 T=1 2.0 1.5 Excitationenergy [MeV] 1.0 0.5 T=0 0 0 1 2 3 4 5 6 7 angularmomentum

15. How to calculate the superallowed Fermi beta decayusing the projected DFT framework? n n n n p p p p n n n p p p n p n p n n p p T=0 Tz=-/+1 I=0+,T=1 |<T+/->|2=2(1-dC) (N-Z=-/+2) t1/2 Qb I=0+,T=1 (N-Z=0) BR Tz=0 MEAN FIELD CORE CORE anti-aligned configurations aligned configurations n p or or ISOSPIN PROJECTION T=1 T=0 Mean-fieldcandifferentiatebetween T=1 states are not representable in a „separable” mean-field! and onlythroughtime-oddpolarizations!

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