1. 1 Gamow-Teller strength in deformed QRPA with np-pairing Eun Ja Ha (Soongsil University) in collaboration with Myung-Ki Cheoun (Soongsil University) F. Simkovic (Comenius University, Slovakia) ECT * -APCTP Joint Workshop, Sep. 15, 2015

2. Motivation - Deformation & Neutron-proton(np) pairing correlation Formalism - Deformed Woods-Saxon (MF) - Deformed Bardeen Cooper Schrieffer (DBCS) ; without (with) np-pairing - Deformed quasi-particle random phase approximation (DQRPA) ; pn-QRPA (without np-pairing) ; pp+nn+pn QRPA (with np-pairing) Results - Gamow-Teller (GT) strength with deformation - np-pairing effect in DBCS approach Summary 2 Contents ECT*-APCTP Joint Workshop, Sep. 15, 2015

3. site 1 : Supernovae Type II 3 MotivationsResultsSummaryFormalism ECT*-APCTP Joint Workshop, Sep. 15, 2015 Known nuclides : 2,500 Stable nuclides : 270 Unstable nuclides : 6,000~8,000

4. site 1 : Supernovae Type II 4 MotivationsResultsSummaryFormalism ECT*-APCTP Joint Workshop, Sep. 15, 2015  In the core collapsing supernovae(SNe), medium and heavy elements are believed to be produced by r-process and s-process.  Since most of these nuclei are thought to be more or less deformed, we need to explicitly take into account of the deformation in the nuclear structure. Why do we consider the deformation in the nuclear structure?

5. ECT*-APCTP Joint Workshop, Sep. 15, 2015  Since the high density (≈10 4 g/cm 3 )and low temperature on the neutron star crust make electrons degenerated. The degenerated electrons block the beta decay and induce electric captures.  Therefore, the valley of stability is shifted toward neutron-rich nuclei.  Ordinary nuclei become highly unstable, and RI become the normal stable nuclei at the neutron-star crusts !! site 2 : Neutron star crusts 5 MotivationsResultsSummaryFormalism  The rapid proton process(rp-process) is thought to be occurred on the binary star system composed of a massive compact star and a companion star. Deformation could be of practical importance on the understanding of the nucleosynthesis.

6. 6 MotivationsResultsSummaryFormalism Are the np-pairing correlations restricted only to the vicinity of the N = Z ? ECT*-APCTP Joint Workshop, Sep. 15, 2015 proton-drip line PRL 106, 252502(2011)  The neutron-proton (np) pairing correlations are important in nuclear structure and decay for proton-rich nuclei with N ≈ Z : protons and neutrons occupy identical orbitals and have maximal spatial overlap. S=1,T=0,J=1 S=0,T=1,J=0 T=0,1

7. 7 MotivationsResultsSummaryFormalism Are the np-pairing correlations restricted only to the vicinity of the N = Z ? ECT*-APCTP Joint Workshop, Sep. 15, 2015 PRL 106, 252502(2011) (±20, 0) S=0 (T=1) (0, ±22) S=1 (T=0) (±11, ±22) S=0,1 (T=0,1) (a) 132 60 Nd 72 (b) 132 66 Dy 66 (c) 132 64 Gd 68 Neodymium Dysprosium Gadolinium  The nuclear structure of the N ≠ Z nuclei may also be affected by np pairing correlations.  Does the np-pairing depends on the nuclear deformation ?

8. 8  ℓ is a distance function of a given point r to the nuclear surface as  In experimental side, β 2 can be extracted from E2 transition probability.  How to include the deformation? MotivationsResultsSummaryFormalism ECT*-APCTP Joint Workshop, Sep. 15, 2015 Deformed Woods-Saxon potential (cylindrical WS, Damgaard et al 1969) distance function surface function  In our calculation, β 2 value is the input parameter.

9. 9  Shell evolution change according to deformation. ECT*-APCTP Joint Workshop, Sep. 15, 2015 0f 7/2 : 3301/2 0d 3/2 : 2001/2 The breaking of magic number comes from the burrowing of f 7/2 state below d 3/2 state by the deformation. E. Ha and MK Cheoun, Phys. Rev. C88(2013) MotivationsResultsSummaryFormalism

10. 10 MotivationsResultsSummaryFormalism  To exploit G-matrix elements, which is calculated on the spherical basis, deformed bases are expanded in terms of the spherical bases.  Deformed single particle state (SPS) ECT*-APCTP Joint Workshop, Sep. 15, 2015  As the deformation increase, expansion term is also increasing.

11.  Deformed BCS 11 MotivationsResultsSummaryFormalism J=0 T=1 j m j -mΩ -Ω J=0,1, 2, 3 ∙∙∙ T=0 J=1, 3, 5, ∙∙∙ T=1 J=0, 2, 4, ∙∙∙ BCS deformed BCS Ω= ½ j ≥ Ω K=0 ECT*-APCTP Joint Workshop, Sep. 15, 2015 K J Laboratory frame Intrinsic frame  Since the deformed SPS are expanded in terms of the spherical SP bases the different total angular momenta of the SP basis states would be mixed.

12. Realistic two body interaction was taken by Brueckner G-matrix, which is a solution of the Bethe-Goldstone Eq., derived from the Bonn-CD one-boson exchange potential.  DQRPA eq (nn+pp+pn DQRPA). 12 MotivationsResultsSummaryFormalism ECT*-APCTP Joint Workshop, Sep. 15, 2015 without np-pairing (pn-DQRPA)

13. MotivationsSummaryFormalismResults 13 ECT*-APCTP Joint Workshop, Sep. 15, 2015

14. 14 ECT*-APCTP Joint Workshop, Sep. 15, 2015 The particle model space 5 ħω is not enough to reproduce the empirical pairing gap. Therefore, the particle model space can be used beyond 6 ħω in G−matrix. In this calculation we use N max =10 ħω in G−matrix. (5 ħω in deformed basis) MotivationsResultsSummaryFormalism  Particle model space N max : pairing strength g pair

15. 15ECT*-APCTP Joint Workshop, Sep. 15, 2015 MotivationsResultsSummaryFormalism  GT strength in deformed basis & expanded basis ISR = 98.4 % ISR = 98.5 %  Since we will apply our DQRPA to other transition, such as electric or magnetic transition, the calculation expanded in spherical basis is more proper than in deformed basis to calculate Wigner Ecart theorem.

16. 16 ECT*-APCTP Joint Workshop, Sep. 15, 2015  Particle-hole strength g ph ; determined from the GTGR MotivationsResultsSummaryFormalism  Particle-particle strength g pp ; tuned from the double beta decay The position of the GTGR energy is roughly reproduced. All GT peaks get shifted to smaller energies as g pp increase.

17. 17 ECT*-APCTP Joint Workshop, Sep. 15, 2015 The high-lying GT excited states beyond one nucleon threshold were already measured at the charge exchange reaction experiments. It is consistent with our calculation. β 2 = 0.157 by RMF 0.262 from B(E2)  GT(-) strength for 76 Ge with different β 2 value MotivationsSummaryFormalismResults

18. 18ECT*-APCTP Joint Workshop, Sep. 15, 2015  Running sum of GT(-) strength for 76 Ge ISR exp = 55% (up to 12MeV) There may be a possibility of the high-lying GT state above 12.0 MeV. ISR DQRPA ≈ 98 % Results by DQRPA reproduce well experimental data without quenching factor. MotivationsSummaryFormalismResults

19. MotivationsSummaryFormalismResults 19 ECT*-APCTP Joint Workshop, Sep. 15, 2015  GT(+) strength for 76 Se with different β 2 value β 2 = -0.244 by RMF, 0.309 from B(E2) (2008) (1997)

20. 20ECT*-APCTP Joint Workshop, Sep. 15, 2015  Running sum of GT(+) strength for 76 Se Results by DQRPA reproduce well experimental data. MotivationsSummaryFormalismResults

21. 21ECT*-APCTP Joint Workshop, Sep. 15, 2015  GT(-) strength for 82 Se with different β 2 value β 2 = 0.133 by RMF 0.193 from B(E2) MotivationsSummaryFormalismResults

22. 22ECT*-APCTP Joint Workshop, Sep. 15, 2015  Running sum of GT(-) strength for 82 Se Results by DQRPA reproduce well experimental data. MotivationsSummaryFormalismResults

23. MotivationsSummaryFormalismResults 23ECT*-APCTP Joint Workshop, Sep. 15, 2015

24. 24 MotivationsSummaryResultsFormalism ECT*-APCTP Joint Workshop, Sep. 15, 2015  Empirical neutron-proton pairing gaps N=Z N Z The values of np pairing gaps are not negligible even for large neutron excess isotopes

25. 25 MotivationsSummary  The values of np pairing gaps δ pn emp are not negligible even for large neutron excess isotopes.  The attractive short-range interaction between one unpaired proton and neutron with energies close to the Fermi surface is considered to be the origin of the np paring interaction.  The np-pairing interaction can be associated with the deformation effect, which is changing the distribution of proton and neutron SP levels. ResultsFormalism  Empirical pairing gaps for 64 Ge ~ 76 Ge ECT*-APCTP Joint Workshop, Sep. 15, 2015

26. 26 MotivationsSummaryFormalismResults  β 2 =0.217 (RMF),  In (a), below some critical value (~0.97) : only pp & nn-pairing modes.  Above this value : the system prefers to form only np-pair.  In (a) pp, nn, and np-pairs coexist in the narrow region.  In (b) the coexistence region is more wide and the phase transition becomes less sharp. ECT*-APCTP Joint Workshop, Sep. 15, 2015 simple schematic phenomenological force  Pairing gap for 64 Ge (Z=N)

27. 27  Pairing gap for 70 Ge (Z ǂ N) MotivationsSummaryFormalismResults  β 2 = - 0.261 (RMF),  The realistic interaction by the G-matrix makes the phase transitions more slowly than the schematic force.  np-pairing mode does exist only in coexistence with pp & nn-pairing mode. ECT*-APCTP Joint Workshop, Sep. 15, 2015

28. 28 MotivationsSummaryFormalismResults  G np =0.275 in (a), g np =1.75 in (b)  The np-pairing gap decreases with neutron excess.  It heavily depends on the deformation parameter β 2 for 64 Ge.  If we use G np ≥ 0.275(g np ≥ 1.75), np-pairing gap is not zero for N-Z =8~10 nuclei. ECT*-APCTP Joint Workshop, Sep. 15, 2015  np-pairing gap with a fixed pairing strength for 64 Ge ~ 76 Ge

29. 29 MotivationsSummary Formalism Results  Does the δ pn depend on the deformation parameter β 2 ? ECT*-APCTP Joint Workshop, Sep. 15, 2015  The np pairing gap is sensitive to the β 2.  Since the spherical SPS are split by the deformation, the energy gaps of protons and neutrons are also scattered. Therefore the overlap of wave functions becomes smaller and energy gaps becomes larger.  The np pairing gaps decrease with the deformation.

30. 30 MotivationsSummaryFormalismResults  ISR(Ikeda sum rule) = 3( N - Z ) =0 for 64 Ge : spherical nucleus  :: : deformed nucleus  ISR de /3(N-Z) =100% for 64 Ge with pn-pairing at BCS process.  The modified smearing of Fermi surface were found with np-pairing for N = Z. ECT*-APCTP Joint Workshop, Sep. 15, 2015

31. 31 MotivationsSummaryFormalismResults  How about N ≠ Z nucleus ? ECT*-APCTP Joint Workshop, Sep. 15, 2015  The modified smearing of Fermi surface were found with np-pairing for N ≠ Z but not as much as 64 Ge.

32. 32 MotivationsSummaryFormalismResults ECT*-APCTP Joint Workshop, Sep. 15, 2015

33. 33  GT(-) strength for 24 Mg (nn+pp+pn DQRPA) MotivationsSummary Formalism Results preliminary ECT*-APCTP Joint Workshop, Sep. 15, 2015  There is a particle number fluctuation in QRPA formalism in (b).  We need a correction of the excitation energy in (d).

34. 34  Excitation Energy correction MotivationsSummary Formalism Results ECT*-APCTP Joint Workshop, Sep. 15, 2015 Correction term

35. 35 MotivationsResultsFormalismSummary 1. We used the deformed WS potential and then performed the deformed BCS and deformed QRPA with realistic two-body interaction calculated by Brueckner G- matrix based on Bonn potential. 2. Results of the Gamow-Teller strength, B(GT±), for 76 Ge and 76,82 Se show that the deformation effect leads to a fragmentation of the GT strength into high-lying GT excited states. 3. We examined isovector(T=1) and isoscalar(T=0) np-pairing correlations for the ground state of even-even Ge isotopes, A=64–76, within the deformed BCS approach. 4. For N=Z 64 Ge a sharp phase transition from the pp(nn)-pairing mode to the np -pairing mode is observed. 5.The T=0,1 np-pairing correlations should be considered also for medium- heavy nuclei with large neutron excess since the np-pairing effect is not negligible. 6.The change of Fermi level and the modified smearing of Fermi surface were found for N ≠ Z as well as N = Z nuclei. These variations may affect many important nuclear electro-magnetic and weak transitions in nuclear physics. 7.The GT strength for 24 Mg in DQRPA with np-pairing reproduce well experimental data. Summary ECT*-APCTP Joint Workshop, Sep. 15, 2015

36. 36 MotivationsResultsSummaryFormalism ECT*-APCTP Joint Workshop, Sep. 15, 2015 Mean Field (Deformed WS ) Deformed BCS w/o np-pairing (O) (T=1) with np-pairing (O) Generalized DBCS(X) (T=0,1 ) (T=0) 64~76 Ge Deformed QRPA w/o np-pairing (O): pn-DQRPA with np-pairing (O): nn+pp+pn DQRPA for only light nuclei Medium and heavy nuclei (X) Calculation: Gamow-Teller(GT) transition (pn-DQRPA)(O) : all nucleus GT transition with np (nn+pp+DQRPA) (O) : 24,26 Mg M1 spin (X)  Status The gray colored letters are next work !!

37. Thanks for your attention !! 37 ECT*-APCTP Joint Workshop, Sep. 15, 2015