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Experimental measurement of the deformation through the electromagnetic probe

Experimental measurement of the deformation through the electromagnetic probe Shape coexistence in exotic Kr isotopes. E. Clément CNRS/GANIL Kazimierz 2010. Shape coexistence in exotic Kr. Single particule level scheme (MeV) ‏. Shape coexistence in the proper sense only if

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Experimental measurement of the deformation through the electromagnetic probe

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  1. Experimental measurement of the deformation through the electromagnetic probe Shape coexistence in exotic Kr isotopes. E. Clément CNRS/GANIL Kazimierz 2010

  2. Shape coexistence in exotic Kr Single particule level scheme (MeV)‏ Shape coexistence in the proper sense only if (i) The energies of the states are similar, but separated by a barrier, so that mixing between the different components of the wave functions is weak and the states retain their character. (ii) The shapes involved are clearly distinguishable 74Kr

  3. Shape coexistence in n-deficient Kr : an experimentalist view What can we measure experimentally ? • Establish the shape isomer : 0+2 • Collectivity in such nuclei : level scheme and B(E2) . • Shape (oblate - prolate ?) : Q0 • Wave function mixing ? : r²(E0)

  4. Transition strenght: ²(E0).10-3 72(6) 84(18) 79(11) 47(13) Shape isomer : systematic of 0+2 states prolate oblate 6+ 6+ 6+ 6+ 791 2+ 2+ 858 824 768 4+ 0+ 918 4+ 4+ 4+ 612 1233 0+ 664 2+ 611 562 558 346 0+ 0+ 2+ 2+ 1017 2+ 770 710 671 52 455 508 456 424 0+ 0+ 0+ 0+ 72Kr 74Kr 76Kr 78Kr E. Bouchez et al. Phys. Rev. Lett., 90(2003) • Shape inversion • Maximum mixing of wave function in 74Kr

  5. Collectivity measurement : the B(E2) Recoil Distance Doppler Shift • Measure the B(E2) through the lifetime of the state ( ≈ ps ! ) Target andstopperat a distance d During the desexcitation of the nuclei, g are emitted : • In flight  Shifted by the Doppler effect • Stopped  E0

  6. Weak mixing ≈ quantum rotor Collectivity measurement : the B(E2) • The collectivity of the shape-coexisting states are highly pertubated by the mixing Strong mixing  perturbation of the collectivity 74Kr GSB

  7. Collectivity measurement : safe coulomb excitation d dRuth __ __ Pif = dif d Reorientation effect 1er order: 2nd order: 2+ 2+ a(1)‏ a(2)‏ a(1)‏ a(2)‏ 0+ 0+ Q0  B(E2)

  8. 74Kr Static quadrupole moment sensitivity minimisation du 2 : 74Kr Negative matrix element (positive quadrupole moment Q0)  prolate deformation Positive matrix element (Negative quadrupole moment Q0)  oblate Deformation

  9. Radioactive beams experiment at GANIL 78Kr 1 MeV/u • The 74,76Kr RIB are produced by fragmentation of a 78Kr beam on a thick carbon target. • Radioactive nuclei are extracted and ionized • Post-accelaration of the RIB 1 10 MeV/u 4.7 MeV/u 1.5104 pps 1 3 70 MeV/u 1012 pps 2 74Kr 6104 pps

  10. Safe Coulomb excitation g detection Pb Particle detection E. Clément et al. PRC 75, 054313 (2007)‏ Very well known technique for stable nuclei but for radioactive one … The differential Coulomb excitation cross section is sensitive to transitionnal and diagonal E2 matrix elements  GOSIA code

  11. Safe Coulomb excitation results Transition probability : describe the coupling between states Spectroscopic quadrupole moment : intrinsic properties of the nucleus 74Kr 76Kr • 13 E2 transitional matrix elements • 16 E2 transitional matrix elements In 74Kr and 76Kr, a prolate ground state coexists with an oblate excited configuration • 5 E2 diagonal matrix element • 5 E2 diagonal matrix element E. Bouchez PhD 2003 E. Clément PhD 2006 E. Clément et al. PRC 75, 054313 (2007)‏

  12. Configurations mixing Pure states Perturbed states Shape coexistence in a two-state mixing model Extract mixing and shape parameters from set of experimental matrix elements.

  13. Configurations mixing Pure states Perturbed states Shape coexistence in a two-state mixing model Extract mixing and shape parameters from set of experimental matrix elements. 76Kr 74Kr 72Kr • Energy perturbation of 0+2 states E. Bouchez et al. Phys. Rev. Lett90 (2003) 0.48(1) 0.10(1) cos2θ0 0.73(1) • Full set of matrix elements : * 0.69(4) 0.48(2) E. Clément et al. Phys. Rev. C 75, 054313 (2007) • Excited Vampir approach: 0.5 0.6 * A. Petrovici et al., Nucl. Phys. A 665, 333 (00)‏ Model describes mixing of 0+ states well, but ambiguities remain for higher-lying states. Two-band mixing of prolate and oblate configurations is too simple.

  14. Vampir calculations A. Petrovici et al., Nucl. Phys. A 665, 333 (00)‏

  15. Beyond … Several theoretical approaches, such as shell-model methods, self-consistent triaxial mean-field models or beyond-mean-field models predict shape coexistence at low excitation energy in the light krypton isotopes. The transition from a prolate ground-state shape in 76Kr and 74Kr to oblate in 72Kr has only been reproduced in the so-called excited VAMPIR approach, This approach has only limited predictive power since the shell-model interaction is locally derived for a given mass region. On the other hand, no self-consistent mean-field (and beyond) calculation has reproduced this feature of the light krypton isotopes so far.

  16. Shape coexistence in mean-field models • In-band reduced transition probability and spectroscopic quadrupole moments GCM-HFB (Gogny-D1S) E. Clément et al., PRC 75, 054313 (2007) M. Girod et al. Physics Letters B 676 (2009) 39–43 GCM-HFB (SLy6) M. Bender, P. Bonche et P.H. Heenen, Phys. Rev. C 74, 024312 (2006)

  17. Shape coexistence in mean-field models (2) Skyrme HFB+GCM method Skyrme SLy6 force density dependent pairing interaction g Restricted to axial symmetry : no K=2 states • Inversion of oblate and prolate states • Collectivity of the prolate rotational band is correctly reproduced B(E2) values e2fm4 • Interband B(E2) are under estimated E. Clément et al., PRC 75, 054313 (2007)

  18. Shape coexistence in mean-field models (3) Gogny HFB+GCM with Gaussian overlap approximation Gogny D1S force Axial and triaxial degrees of freedom E. Clément et al., PRC 75, 054313 (2007)

  19. Shape coexistence in mean-field models (3) Gogny g g The agreement is remarkable for excitation energy and matrix elements • K=0 prolate rotational ground state band • Strong mixing of K=0 and K=2 components for 2+3 and 2+2 states • K=2 gamma vibrational band • Grouping the non-yrast states above 0+2 state in band structures is not straightforward • 2+3 oblate rotational state E. Clément et al., PRC 75, 054313 (2007)

  20. Shape coexistence in mean-field models (3) Gogny M. Girod et al. Physics Letters B 676 (2009) 39–43 Potential energy surface using the Gogny GCM+GOA appraoch

  21. Shape coexistence in mean-field models (3) Gogny M. Girod et al. Physics Letters B 676 (2009) 39–43

  22. Is the triaxiality the key ? Difference #1: effective interaction very similar single-particle energies → no big differences on the mean-field level axial quadrupole deformation q0↔triaxial quadrupole deformation q0, q2 (exact GCM formalism)Euler angles Ω=(θ1,θ2,θ3)→ 5-dimensional collective Hamiltonian (Gaussian overlap approximation) • Good agreement for in-band B(E2) • Wrong ordering of states: oblate shape from76Kr to72Kr • K=2 outside model space • Excellent agreement for Ex, B(E2), and Qs • Inversion of ground state shape from prolate in 76Kr to oblate in 72Kr • Assignment of prolate, oblate, and K=2 states • When triaxiality is “off” same results than the “old” Skyrme M. Bender and P. –H. Heenen Phys. Rev. C 78, 024309 (2008) Triaxiality seems to be the key to describe prolate-oblate shape coexistence in this region

  23. Do the GCM (+GOA) approachand the triaxialitykeyworkeverywhere ?

  24. In the n-rich side ? • The n-rich Sr (Z=38), Zr (Z=40) isotopes present one of the most impressive deformation change in the nuclear chart • Systematic of the 2+ energy (Raman’s formula : b2~0.17  0.4) • Low lying 0+ states were observed 2+1  + 2n 0+2 + 2n E(0+) [keV]

  25. Shape transition at N=60 HFB Gogny D1S E [MeV] b2 Both deformations should coexist at low energy • Shape coexistence between highly deformed and quasi-spherical shapes

  26. Shape transition at N=60 C. Y. Wu et al. PRC 70 (2004) W. Urban et al Nucl. Phys. A 689 (2001) N=58 N=60

  27. Shape transition at N=60 : Coulomb excitation B(E2↓) < 625 e²fm4 • The Electric spectroscopic Q0 is null as its B(E2) is rather large  Quasi vibrator character ??. • No quadrupole ? but it doesn’t exclude octupole or something else ?? • The large B(E2) might indicate a large contribution of the protons < 152 e²fm4 399 ( -39 67) e²fm4 < 22 e²fm4 Qs = -6 (9) efm² 462 (11) e²fm4 E. Clément et al., IS451 collaboration

  28. Gogny calculations 100Sr 96Sr 98Sr 94Sr • Qualitatively good agreement • The abrupt change not reproduced • Very low energy of the 0+2 state is not reproduced •  overestimate the mixing ? • Highly dominated by K=2 configuration

  29. Conclusion • We have studied the shape coexistence in the n-deficient Kr isotopes • Beyond the mean field calculations reproduce the experimental results when the triaxiality degree of freedom is available • Same calculations seem to not reproduce the shape transition at N=60. What is missing ?

  30. P. Möller et al Phys. Rev. Lett 103, 212501 (2009)

  31. Shape transition at N=60 40 1g7/2 ll • Beyond N=60, the tensor force participates to the lowering 0+2 state and to the high collectivity of 2+1 state. 3s1/2 ll 1g7/2 2d5/2 ll 1g ll ll 2d5/2 50 50 0+2 1g9/2 2p1/2 40 2p 1f5/2 ll ll ll 0+1 ll ll • But in the current valence space, need higher effective charge to reproduce the known B(E2) 2p3/2 1f 28 p n K. Sieja et al PRC 79, 064310 (2009)

  32. Shape coexistence in mean-field models (3) Gogny

  33. 2+ 4+ Coulomb excitation analysis : GOSIA* *D. Cline, C.Y. Wu, T. Czosnyka; Univ. of Rochester Lifetimes are the most important constraint because directly connected to the transitional matrix element  B(E2) 74Kr 5 lifetime known from the literature Lifetime incompatible with our coulex data

  34. 2+ 4+ Lifetime measurement A. Görgen, E. Clément et al., EPJA 26 (2005)

  35. Shape coexistence in Se isotopes Similar j(1) in 68Se & 70Se : • 70Se oblate near ground state • Prolate at higher spin G. Rainovski et al., J.Phys.G 28, 2617 (2002)

  36. Shape coexistence in mean-field models (6) Gogny Qs from Gogny configuration mixing calculation Good agreement of B(E2) Shape change in the GSB in 70,72Se 70,72Se behaviors differ from neighboring Kr and Ge Isotopes 68Se more “classical” compare to Kr and Ge

  37. h11/2 g9/2 from core g7/2 • 9/2+ isomer identified  ng9/2[404]  extruder neutron orbital from 78Ni core • Create the N=60 deformed gap • pg9/2 <-> nh11/2 influence ? • Neutron excitation from d5/2 to h11/2  Octupole correlation ? 2d5/2 • Clear evidence for neutron orbital playing an important role in the shape transition • Established sign for extruder or intruder orbital • Search for isomer in odd neutron Sr and Zr A. Jokinen WOG workshop Leuven 2009 W. Urban, Eur. Phys. J. A 22, 241-252 (2004)

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