Ch. Stoyanov Two-Phonon Mixed-Symmetry States in the Domain N=52 Nuclear structure calculations in a large domain of excitation energies Two-Phonon Mixed-Symmetry States in the Domain N=52 Ch. Stoyanov Institute for Nuclear Research and Nuclear Energy Sofia, Bulgaria

Nuclear structure calculations in a large domain of excitation energies 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)

U(5) limit of IBM-2 1 July 2016 Ch. Stoyanov

E2 and M1transitions connecting one phonon states 1 July 2016 Ch. Stoyanov

M1 Transitions conneting two-phonon states 1 July 2016 Ch. Stoyanov

General view 11 July 2015 Ch. Stoyanov

Nuclear structure calculations in a large domain of excitation energies The model Hamiltonian

Quasiparticle RPA (collective effects) Nuclear structure calculations in a large domain of excitation energies Quasiparticle RPA (collective effects)

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

Quasiparticle RPA (3) (collective effects) Nuclear structure calculations in a large domain of excitation energies Nuclear structure calculations in a large domain of excitation energies Quasiparticle RPA (3) (collective effects) 14

mixed-symmetry states Nuclear structure calculations in a large domain of excitation energies Applications Even-even nuclei mixed-symmetry states

Mixed symmetry states Experiment Nuclear structure calculations in a large domain of excitation energies 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 Ch. Stoyanov 23

Mixed symmetry states Experiment Nuclear structure calculations in a large domain of excitation energies 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 Ch. Stoyanov 24

Nuclear structure calculations in a large domain of excitation energies 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

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

Nuclear structure calculations in a large domain of excitation energies The dependence of M1 and E2 transitions on the ratio G(2)/k0(2) in 136Ba.

Nuclear structure calculations in a large domain of excitation energies Structure of the first RPA phonons (only the largest components are given) and corresponding B(2+) ratios for 136Ba B(2+)

Nuclear structure calculations in a large domain of excitation energies 11 July 2015 Ch. Stoyanov 30

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.

B(E2; g.s.→ 2+) strength distributions in 94Mo. Nuclear structure calculations in a large domain of excitation energies B(E2; g.s.→ 2+) strength distributions in 94Mo.

B(M1;2+k →2+1 ) strength distributions in 94Mo Nuclear structure calculations in a large domain of excitation energies B(M1;2+k →2+1 ) strength distributions in 94Mo

96Ru New 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) Ch. Stoyanov

Contribution of main components in the structure of low-lying QRPA 2+ states in 96Ru. Jπ E(MeV) Structure B(E2,g.st.→2+) (W.u.) B(M1) ( μ2N) 2+2→2+1 2+ 1 0.999 0.79(2d5/2)2n + 1.1(1g9/2)2p 96   2+ 2 2.276 - 1.19(2d5/2)2n + 0.75(1g9/2)2p 3.8 1.37 Ch. Stoyanov

96 Ru isospin nature of 2+ states Jπ B (2+) 2+1 0.013 isoscalar (symmetric) 2+2 1.25 isovector (mixed symmetry) Ch. Stoyanov

State Jπ E(MeV) EXP. QPM Structure,% 2+1 2+2 2+3   2+1 0.832 0.775 88%[2+1]QRPA +5%{[2+1]QRPA ⃰ [2+1]QRPA} + … 2+2 1.932 1.826 80% {[2+1]QRPA ⃰ [2+1]QRPA} + …. 2+3 2.283 2.164 90% [2+2 ]QRPA + .. Ch. Stoyanov

State E (MeV) Transition E2 [Wu] M1 [μN] strength Jπ EXP. QPM Nuclear structure calculations in a large domain of excitation energies State E (MeV) Transition E2 [Wu] M1 [μN] strength   Jπ EXP. QPM Jπi → Jπf σλ B(σλ)exp B(σλ)QPM g e f f = 0.8 g f ree B(σλ)IBM 2+1 0.832 0.775 2+1 →0+1 18.1(5) 16 18.4 2+2 1.932 1.826 2+2 →2+1 2+2 →0+1 0.05(2) …….. 28(9) 0.11 0.77 30 24 2+3 2.283 2.164 2+3 →2+1 2+3 →0+1 0.69(14) 1.36(19) 0.63 0.75 0.69 2.53 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 Ch. Stoyanov

Forth and fifth quadrupole excitations Jπ State E (MeV) Transition   strength EXP. QPM Jπi → Jπf σλ B(σλ)exp B(σλ)QPM g e f f = 0.8 g free B(σλ)IBM 2+4 2.980 2+4→0+1 2+4→2+1 2+4→2+2 E2 M1 0.01 2.9 0.06 2+5 2.740 3.338 2+5 →0+1 2+5 →2+1 2+5 →2+2 0.006(12) 0.58(15) 0.17(3) 0.16 1.1 0.15 1.92 0.17 Ch. Stoyanov

3+ excited states structure Jπ E(MeV) EXP. QPM Structure,%   3+1 2.852 2.644 9% {[2+1]QRPA ⃰ [2+2]QRPA} + …. 3+2 2.898 3.164 76% {[2+1]QRPA ⃰ [2+2]QRPA} + …. Ch. Stoyanov

3+ excited states Jπ State E (MeV) Transition strength EXP. QPM   strength EXP. QPM Jπi → Jπf σλ B(σλ)exp B(σλ)QPM g e f f = 0.8 g free B(σλ)IBM 3+1 2.852 2.644 3+1→2+1 3+1→2+2 E2 M1 < 0.01 0.008(1) < 5.58 0.09 0.016 0.009 14.7 3+2 2.898 3.164 3+2→2+1 3+2→2+2 < 0.28 0.02(4) 0.078(14) 0.66 0.07 0.27 3.17 0.56 Ch. Stoyanov

4+ excited states structure Jπ E(MeV) EXP. QPM Structure,%   4+1 1.518 1.585 63% {[2+1]QRPA ⃰ [2+1]QRPA} + …. 4+2 2.462 2.207 61%[4+1]QRPA +13%{[2+1]QRPA ⃰ [2+1]QRPA} + 2.3% {[2+1]QRPA ⃰ [2+2]QRPA} +… 4+5 3.300 86% {[2+1]QRPA ⃰ [2+2]QRPA} + …. Ch. Stoyanov

4+ excited states Jπ State E (MeV) Transition strength EXP. QPM   strength EXP. QPM Jπi → Jπf σλ B(σλ)exp B(σλ)QPM g e f f = 0.8 g f ree B(σλ)IBM 4+1 1.518 1.585 4+1→2+1 E2 22.6(17) 15 25.6 4+2 2.462 2.207 4+2→4+1 4+2→2+1 M1 0.90(18) 1.52(19) 0.07 5.5 1.13 1.44 4+5 3.300 1.6 1.8 Ch. Stoyanov

1+ excited states structure Jπ E(MeV) EXP. QPM Structure,%   1+1 3.154 3.118 93%{[2+1]QRPA ⃰ [2+2]QRPA} + .. Ch. Stoyanov

1+ excited states Jπ State E (MeV) Transition strength EXP. QPM   strength EXP. QPM Jπi → Jπf σλ B(σλ)exp B(σλ)QPM g e f f = 0.8 g f ree B(σλ)IBM 1+1 3.154 3.192 1+1 →0+1 M1 0.17(6) 0.13 Ch. Stoyanov

Nuclear structure calculations in a large domain of excitation energies 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.

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