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Exploring the X(5) characteristic in the mass A ~ 80 region : Coulomb excitation of 78 Sr nucleus

Dipa Bandyopadhyay University of York. Exploring the X(5) characteristic in the mass A ~ 80 region : Coulomb excitation of 78 Sr nucleus. Microscopic picture in the region A ~80. Ref: Nazarewicz et al., NPA 435, (1985) 397. 40.

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Exploring the X(5) characteristic in the mass A ~ 80 region : Coulomb excitation of 78 Sr nucleus

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  1. Dipa Bandyopadhyay University of York Exploring the X(5) characteristic in the mass A ~ 80 region : Coulomb excitation of 78Sr nucleus INTC meeting, CERN

  2. Microscopic picture in the region A ~80 Ref: Nazarewicz et al., NPA 435, (1985) 397 40 At prolate shape (2~0.35) the largest gap appears for particle number 38 which corresponds to Z of Sr isotopes. At oblate shape (2 ~-0.3) the major shell gap occurs at particle number 36, which corresponds to N of 74Sr. INTC meeting, CERN

  3. Energy surfaces obtained with Woods-Saxon potential : shape change with change in neutron number Prolate : 78Sr Prolate + Oblate : 74,76Sr, 80Sr Prolate-Spherical -Oblate : 80Sr Prolate-Spherical: 82Sr Spherical : 84Sr Ref: Nazarewicz et al., NPA 435 (1985) 397 Competition between different shapes may create transitional region. INTC meeting, CERN

  4. P factor estimation : A measure of deformation driving quadrupole quadrupole force vs spherical driving pairing force. Np, N n ~ number of valence protons and neutrons. For X(5), [ E. A. McCutchan et al, PRC 70, 011304 ] N=90 82 p-drip line Z 50 78,80Zr 76,78Sr 28 28 50 82 126 N N-drip line INTC meeting, CERN

  5. Critical points in Symmetry (Casten) Triangle [F Iachello PRL 85, 3580(2000); PRL 87 052502(2001)] U(5) =0 Spherical harmonic vibrator V=V(), > 0,  independent V=V(), > 0,  = 0 X(5) E(5) SU(3) O(6)  > 0, =0  > 0, unstable Axially deformed rotor  unstable deformed rotor INTC meeting, CERN

  6. Examples of X(5) symmetry ~ N=90 isotones (152Sm) Casten & Zamfir PRL 87, 052503(2001) R 4/2 = E(41+)/E(21+) = 2.90; E(02+)/E(21+) = 5.65; Larger energy spacing in the excited band; B(E2)s of yrast transitions are in between that of vibrator and rotor; B(E2)s of non yrast transitions are smaller compared to that of yrast transitions. INTC meeting, CERN

  7. Candidate for X(5) symmetry; 78Sr D. S. Brenner et al, AIP Conference Proceedings 638, 223 (2002) INTC meeting, CERN

  8. Systematic of Sr nuclei (Z=38) : R4/2 ~ E(41+)/E(21+) 3.33 76,78Sr 2.90 2.0 INTC meeting, CERN

  9. E(41+)/E(21+) systematic; A~80 : expected value for X(5) ~ 2.90 42 2.34 2.23 2.11 40 2.86 2.56 2.34 2.22 2.02 38 2.81 2.54 2.23 2.85 2.32 2.07 Z 36 2.38 1.86 2.22 2.11 2.16 2.11 2.31 34 2.28 2.16 1.90 2.15 2.38 2.45 2.37 2.65 2.28 2.27 2.23 2.07 2.07 2.46 2.50 2.54 2.64 32 30 2.18 2.29 2.32 2.36 2.24 2.02 30 32 34 36 38 40 42 44 46 48 N INTC meeting, CERN

  10. INTC meeting, CERN R4/2 systematic and the P factor estimations are necessary but not sufficient conditions to characterize a nucleus as X(5).

  11. Many nuclei which follow the expected X(5) trend closely!!!! Clark et al PRC 68, 037301(2003) INTC meeting, CERN

  12. …Fail to follow their X(5) characteristics except : 126Ba, 130Ce & N=90 isotones from Nd (Z=60) to Er (Z=68). Clark et al PRC 68, 037301(2003) INTC meeting, CERN

  13. We must measure the transition strengths between the levels of the yrast and non yrast bands along with the level energies to confirm the X(5) assignment to 78Sr. INTC meeting, CERN

  14. Known: Yrast band energies upto 26ħ. B(E2)s of first 2 yrast transitions. Negative parity non yrast band. Tentative positive parity band. We will measure: The second 0+ band. B(E2)s of yrast states upto 8ħ. B(E2; 02+ 21+). [B(E2; 22+ 02+)]. INTC meeting, CERN

  15. Fusion-evaporation approach: 58Ni(28Si,2)78Sr Gammasphere + microball D. Rudolph et al, Phys. Rev C56,(1997)98 ??? X(5) prediction demands it to be 4+ 2+ 0+ transition INTC meeting, CERN

  16. Fusion-evaporation approach: 40Ca(40Ca,2p)78Sr , 118 and 121 MeV, Jurogam + RITU Nuclear physics group, University of York 278 keV gated -ray spectra 1200 77Rb has very similar half life and  endpoint energies compared to 78Sr. So -tagging is not very effective in this case. 77,78Rb has very similar energies [ 77Rb: 501.9 (2), Ig ~ 100% ], [ 78Rb: 278.3 (2), Ig ~ 100% and 503.2 (4), Ig ~ 80% keV ] compared to that of 78Sr [ 278.5(4), Ig ~ 100% & 503.7(4), Ig ~ 100% keV ]. Hence  gating is also not very effective. INTC meeting, CERN

  17. Requirement Pure intense radioactive beam of 78Sr. Problem 78Rb will be produced with several magnitude higher (~109) compared to 78Sr (~106) Solution Electron beam ion source (EBIS) Successfully used to produce light Sr nuclei at CERN-ISOLDE Nucl. Phys. 763A, 45 (2005) Procedure CF4 gas is introduced in the ion source to form SrF+. No high-rate contaminants not specially RbF+ is expected. INTC meeting, CERN

  18. Coulomb excitation of 78Sr : Target selection 3.0 MeV/A 78Sr on 1 mg/cm258Ni target; MINIBALL efficiency : 10%; CD detector angle – 150 – 500 in laboratory frame. 58Ni Higher Z gives higher yield but looses in kinematic focusing!!! INTC meeting, CERN

  19. Coulomb excitation of 78Sr : yield estimate 3.0 MeV/A 5x104 ions/sec 78Sr on 1 mg/cm2 58Ni target; MINIBALL efficiency : 10%; CD detector angle – 150 – 500 in laboratory frame. 106 105 104 103 Yield / 10 days 102 101 100 21+ 41+ 61+ 02+ 22+ 81+ 42+ Aim : E(02+), E(22+) and E(42+) , B(E2; 81+  61+), B(E2; 61+  41+), B(E2; 02+  21+), [B(E2; 22+  02+)] INTC meeting, CERN

  20. Coulomb excitation of 78Sr Requesting Beam : 78Sr [ T½ ~ 2.5 min ] Energy : 3.0 MeV/A Beam time : 10 days [Considering the challenges related to maintain a stable high intensity beam, we agree to accept 10 days beam time separated in different time slots] Ion source : EBIS with CF4 gas [ Beam with Rb contamination is not acceptable] Beam intensity : > 5 x 104 s-1 (Assumed 3 out of 12 pulses from the PSB to ISOLDE and total 2% transmission efficiency) Primary target : Nb metal powder of thickness 50 gm/cm2 Secondary target : 58Ni of thickness 1 mg/cm2 Detectors : MINIBALL + CD INTC meeting, CERN

  21. Collaboration D. Bandyopadhyay University of York, UK Spokesperson C. J. Barton University of York, UK J. E. Butterworth University of York, UK R. Wadsworth University of York, UK B. S. Nara Singh University of York, UK D. Jenkins University of York, UK M. Bentley University of York, UK S. Fox University of York, UK P. E. Garrett University of Guelph, Canada C. E. Svensson University of Guelph, Canada E. Clement CEA-Saclay, France Contactperson N. Pietralla Technische Universitaet Darmstadt, Germany L. M. Fraile CERN, Switzerland P. Delahaye CERN, Switzerland F. Wenander CERN, Switzerland N. Warr University of Koln,Germany J. Cederkall Lund University, Sweden A. Ekstrom Lund University, Sweden R. Krucken TU Munich, Germany T. Kroll TU Munich, Germany R. Gernhauser TU Munich, Germany The MINIBALL and REX-ISOLDE collaboration. INTC meeting, CERN

  22. INTC meeting, CERN ADDENDUM

  23. The CD detector at 150 – 500 detects most of the scattered particles INTC meeting, CERN

  24. Rutherford X-section estimate CD detector angle INTC meeting, CERN

  25. INTC meeting, CERN

  26. INTC meeting, CERN

  27. Systematic of N=40 nuclei : R4/2 ~ E(41+)/E(21+) 3.33 78Sr 80Zr 2.90 2.0 INTC meeting, CERN

  28. Systematic of N=40 nuclei : B(E2; 21+ 01+) 78Sr INTC meeting, CERN

  29. INTC meeting, CERN Bohr Hamiltonian : H= - ħ2/2B[(1/4)(4/)/1/(2sin3) (sin3//–Q2k/sin2V] k This Hamiltonian lives in 5-dimensional space with two intrinsic variables ,  and three Euler angles  i(i=1,2,3) If potential depends only on , V(,) = U(), one can write separating the variables, H = (,  i) + Eƒ(  ) The second part of the Hamiltonian is exactly solvable in a five- dimensional infinite potential well corresponding to E(5) symmetry, U() = 0,  w , u() = ,  >  w. >> phase transitions in coordinate.

  30. INTC meeting, CERN X(5) symmetry : connecting U(5) and SU(3) Situation is much more complex compared to E(5). Bohr Hamiltonian does not support any other exact solution like E(5). However, there is an approximate solution to Bohr Hamiltonian, which describes many of the properties of the X(5). Consider the potential at = 00 Q2k/sin2=4/3 (Q12+Q22+Q32)+Q32 [(1/sin2  And look for solution like, (,, i) =LK(,) DL M,K ( i) Separate the potential (approximately) in  and with a square well potential for  and harmonic oscillator potential for  U(,) = u() + u() The equation can be solved now and the corresponding symmetry is known as X(5) symmetry.

  31. INTC meeting, CERN Property E(5) X(5) U(5) O(6) SU(3) Initial excitations R = (E41 – E01)/ (E21 – E01) 2.20 2.90 2.00 2.50 3.33 Second excitation : R = (E02 – E01)/ (E21 – E01) 3.03 5.65 Importance of E02+ state in case of transitional nuclei:

  32. Systematic of Sr isotopes (Z=38) : B(E2; 21+ 01+) Collective 98Sr 78Sr Sharp change in observable : signature of shape transition INTC meeting, CERN

  33. INTC meeting, CERN

  34. Isotope chart 2.2 x106 2.4 x109 INTC meeting, CERN

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