Two-Phonon Mixed-Symmetry States in the Domain N=52

1. Two-Phonon Mixed-Symmetry States in the Domain N=52 Ch. Stoyanov Institute for Nuclear Research and Nuclear Energy Sofia, Bulgaria

2. Microscopic description of mixed-symmetry states in nearly spherical nuclei • Low-lying isovector excitations are naturally predicted in the algebraic IBM-2 as mixed symmetry states. Their main signatures are relatively weak E2 and strong M1 transition to symmetric states. • T. Otsuka , A.Arima, and Iachello, Nucl .Phys. A309, 1 (1978) • P. van Isacker, K.Heyde, J.Jolie et al., Ann. Phys. 171, 253 (1986)

3. Ch. Stoyanov U(5) limit of IBM-2

4. Ch. Stoyanov E2 and M1transitions connecting one phonon states

5. Ch. Stoyanov M1 Transitions conneting two-phonon states

6. Ch. Stoyanov General view

7. The model Hamiltonian

8. Quasiparticle RPA(collective effects)

9. Ch. Stoyanov Quasiparticle RPA (2)(quasiboson approximation)

10. Quasiparticle RPA (3)(collective effects)

11. Applications • Even-even nuclei • mixed-symmetry states

12. Mixed symmetry states Experiment • N. Pietralla et al., Phys. Rev. C 58, 796 (1998), • N. Pietralla et al., Phys. Rev. Lett. 83, 1303 (1999) • inelastic hadron scattering cross sections • measurements of the electron conversion coefficients in β decay 1 July 2016 23 Ch. Stoyanov

13. Mixed symmetry states Experiment • MS have been populated by means of many nuclear reactions as • Inelastic scattering of • Electrons • Photons • β decay • Coulomb excitation 1 July 2016 24 Ch. Stoyanov

14. Review papers • N. Pietralla, P. von Brentano, • and A. F. Lisetskiy, • Prog. Part. Nucl. Phys. 60, 225 (2008). • N Lo Iudice, V Yu Ponomarev, Ch Stoyanov, A V Sushkov, V V Voronov • J. Phys. G: Nucl. Part. Phys. 39 (2012) 043101

15. Test of the Structure In order to test the isospin nature of 2+states the following ratio is computed: • This ratio probes: • The isoscalar ((2+)<1) and • The isovector (B(2+)>1)properties of the 2+ state under consideration

16. The dependence of M1 and E2 transitions on the ratio G(2)/k0(2) in 136Ba.

17. B(2+) Structure of the first RPA phonons (only the largest components are given) and corresponding B(2+) ratios for 136Ba

18. 11 July 2015 30 Ch. Stoyanov

19. Explanation of the method used The quasi-particle Hamiltonian is diagonalized using the variational principle with a trial wave function of total spin JM Where ψ0 represents the phonon vacuum state and R, P and T are unknown amplitudes; ν labels the specific excited state.

20. B(E2; g.s.→2+) strength distributions in 94Mo.

21. B(M1;2+k →2+1 ) strength distributions in 94Mo

22. Ch. Stoyanov 96RuNew experimental information • Hennig et al. Phys. Rev. C 92 064317 (2015) Properties of the two-phohon mixed-symmetry quintuplet 2+1(sm)⃰ 2+2(ms)

23. Ch. Stoyanov Contribution of main components in the structure of low-lying QRPA 2+states in 96Ru.

24. Ch. Stoyanov 96 Ru isospin nature of 2+states JπB (2+) 2+1 0.013isoscalar (symmetric) 2+21.25isovector (mixed symmetry)

25. Ch. Stoyanov

26. Ch. Stoyanov

27. Ch. Stoyanov Distribution of two-phonon component {[2+1(sm)]QRPA ⃰ [2+2(ms)]QRPA} Jπ contribution E[MeV] 2+3 2.47% 2.16 MeV 2+4 21 % 2.98 MeV 2+5 69%3.34 MeV

28. Ch. Stoyanov Forth and fifth quadrupole excitations

29. Ch. Stoyanov 3+ excited states structure

30. Ch. Stoyanov 3+ excited states

31. Ch. Stoyanov 4+ excited states structure

32. Ch. Stoyanov 4+ excited states

33. Ch. Stoyanov 1+ excited states structure

34. Ch. Stoyanov 1+ excited states

35. Conclusions • There are two modes in the low-lying quadrupole excitations – isoscalar and isovector one. • The properties of these two modes are close to IBM-2 symmetric and mixed-symmetry states. • The coupling of the modes leads to variety of excited states. There are well pronounced regularities of E2 and M1 transitions connecting the states.

36. Thank You for Your attention!!!