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Electromagnetic Properties of Nuclear Chiral Partners

Electromagnetic Properties of Nuclear Chiral Partners. For triaxial odd-odd nuclei Chirality = Nilsson model + irrotational flow moment of inertia. E [MeV]. b. The Master Equation. Valence nucleons behave as gyroscopes.

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Electromagnetic Properties of Nuclear Chiral Partners

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  1. Electromagnetic Properties of Nuclear Chiral Partners

  2. For triaxial odd-odd nuclei Chirality = Nilsson model + irrotational flow moment of inertia E [MeV] b The Master Equation

  3. Valence nucleons behave as gyroscopes. • Pairing interactions couple single particle states to Cooper pairs with no net angular momentum. • Valence odd nucleons are unpaired. • The properties of valence nucleons can be derived from the Nilsson model

  4. Nuclear single-particle shell model states. HSM = V(r) +VLS (r) L  S 112 126 N=5 70 h11/2   82 N=4 40 50 N=3 20 20 N=2 8 8 N=1 2 2 N=0   Spher. Harm. Oscillator +L  S +L2

  5. HSM = Unique parity h11/2 state in quadrupole-deformed triaxial potential. H= HSM+ Hdef Triaxial shape for b = 0.3, g = 30º. Hdef= kb [ cos(g)Y20(q,f)+ 1/2sin (g){Y22(q,f)+ Y2-2(q,f)}] • js =0.00  s =1.36 • ji =0.00  i =2.01  jl =5.46  l =0.30 • js =5.46  s =0.30 • ji =0.00  i =2.01  jl =0.00  l =1.36

  6. j2=jx2+jy2+jz2 E - EF=k( jx2 - jy2) E < EF E > EF Semi classical analysis for single-particle Nilsson hamiltonian in a triaxial nucleus.

  7. irrotational liquid rigid body laboratory intrinsic Collective nuclear rotation resembles that of irrotational liquid but is different than that of a rigid body. In particular moments of inertia differ significantly.

  8. J[ħ2/MeV] Angular momentum for rotating triaxial body with irrotational flow moment of inertia aligns along intermediate axis.

  9. Triaxial odd-odd nuclei result in three perpendicular angular momenta for particle-hole configurations built on high-j orbitals .

  10. Results of the Gammasphere GS2K009 experiment. band 2 band 1 134Pr ph11/2 nh11/2

  11. Systematics of partner bands in odd-odd A~130 nuclei. 138Eu Energy [MeV] 136Pm 134Pr 132Pr 132La 130La 134La Energy [MeV] 130Cs 128Cs 132Cs Spin [ħ] Spin [ħ]

  12. Chirality is a general phenomenon in triaxial nuclei: • two mass regions identified up to date, • partner bands in odd-odd and odd-A nuclei.

  13. jn jn jp long long short I+2 R Int R Int I+1 I General electromagnetic properties of chiral partners.

  14. General particle plus triaxial rotor model H = Vsp + Hrot Vsp (b,g,q,f) Hrot Moment of inertia: k =1,2,3 Model for odd-odd nuclei follows the model developed for odd-A nuclei by J. Meyer-ter-Vehn in Nucl. Phys. A249 (1975) 111

  15. For irrotational flow moment of inertia there are two special cases for which two out of three moments are equal: axial symmetry for g=0º(prolate shapes) Js=Ji=J0 Jl=0 for g=60º(oblate shapes) Jl=Ji=J0 Js=0 triaxiality forg=30º(triaxial shapes) Jl=Js=J0 Ji=4J0. J[ħ2/MeV] A useful limit of the particle rotor model for triaxial nuclei

  16. g=90 g=30 2 2 3 1 1 3 Symmetric rotor with a triaxial shape at g=90 o • l2<l3<l1, but J1=J2=1/4J3 , Q20=0, Q22 =Q2-2 ~b at g=90o • Intermediate axis is an effective symmetry axis of the core, • a good choice for the quantization axis. • Core rotation orients along the intermediate axis to minimize • the rotational energy.

  17. B1 B2 A1 A2 Calculated Level Scheme

  18. Energy vs Spin: two pairs of degenerate bands

  19. Calculated B(M1) and B(E2)

  20. Core Single proton-particle in j (=h11/2 ) shell Single neutron-particle in j (=h11/2 ) shell Particle-rotor Hamiltonian for triaxial odd-odd nuclei

  21. Quantum Number A: invariance properties of H=Hrot+V p+V n • D2 symmetry → R3 = 0,±2,±4,±6,….. • Invariant under the operation A consisting of • Rotation or • R3(p/2) [1→2,2→-1,3→3], R3(3p/2) [1→-2,2→-1,3→3] • Exchange symmetry between valence proton and neutron • C: p↔n C= +1 symmetric C= -1 anti-symmetric

  22. Quantum number A and selection rules for transition rates B(E2;Ii→If )≠0 for Ai≠ Af Core contribution only ⇔ ΔC=0 Q20=0 for γ=90º [B(M1;Ii→If ) with Ai≠Af ] >> [B(M1;Ii→If ) with Ai=Af ] |ΔR3 |≤1 B(M1;Ii→If ) ≈0 for Ci=Cf due to the isovector character of M1 operator gl+gR =0.5(-0.5) gseff-gR=2.848(-2.792) for p(n) [H,A]=0 A2=1 Quantum number A=±1 A=+1 R3=0,±4,±8,… & C=+1 R3=±2,±6,±10 …& C=-1 A=-1 R3=0,±4,±8,… & C=-1 R3=±2,±6,±10 …& C=+1

  23. +1 -1 I+4 -1 +1 I+3 -1 +1 I+2 where +1 -1 I+1 +1 -1 I Electromagnetic properties of chiral partners with A symmetry

  24. Chiral fingerprints in triaxial odd-odd nuclei: • near degenerate doublet D I=1 bands for a range of spin I ; • S(I)=[E(I)-E(I-1)]/2I independent of spin I; • chiral symmetry restoration selection rules for M1 and E2 transitions vs. spin resulting in staggering of the absolute and relative transition strengths.

  25. Based on the above fingerprints 104Rh provides the best example of chiral bands observed up to date. • doubling of states • S(I) independent of I • B(M1),B(E2) staggering C. Vaman et al. PRL 92(2004)032501

  26. Electromagnetic properties – pronounced staggering in experimental B(M1)/B(E2) and B(M1)in / B(M1)out ratios as a function of spin [T.Koike et al. PRC 67 (2003) 044319 ].

  27. Electromagnetic properties – unexpected B(M1)/B(E2) behavior for 134Pr and heavier N=75 isotones.

  28. Absolute transition rates measurements in A~130 nuclei J. Srebrny et al, Acta Phys. Polonica B46(2005)1063 E. Grodner et al, Int. J. Mod. Phys. E14(2005) 347

  29. Conclusions and future • Electromagnetic properties of nuclear chiral partners in triaxial odd-odd nuclei have been identified from a symmetry of a particle-rotor Hamiltonian. • A simple ( but limited ) model has been developed which describes uniquely triaxial features with a new quantum number A: • Chiral doublet bands, • Selection rules for electromagnetic transitions, • Chiral wobbling mode. • Model predictions are not consistent with the experimental absolute transition rate measurements reported in the mass 130 region. • Absolute lifetime measurements are of crucial importance for chiral partner identification and investigation of doublet bands in odd-odd nuclei.

  30. Credits T. Koike Tohoku University, Sendai, Japan I. Hamamoto LTH, University of Lund, Sweden and NBI, Copenhagen, Denmark C.Vaman National Superconducting Cyclotron Laboratory Michigan State University, USA for 128Cs and 130La DSAM results E. Groedner, J. Srebrny et. al. Institute of Experimental Physics Warsaw University, Poland

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