Investigation of the mixed-symmetry states in Mo by means of high-resolution electron and proton scattering*

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1 Investigation of the mixed-symmetry states in Mo by means of high-resolution electron and proton scattering* Institut für Kernphysik, Technische Universität Darmstadt Oleksiy Burda ,4 N. Botha, O. Burda, J. Carter, R.W. Fearick, S.V. Förtsch, C. Fransen, H. Fujita, M. Kuhar, A. Lenhardt, P. von Neumann-Cosel, R. Neveling, N. Pietralla, V.Yu. Ponomarev, A. Richter, E. Sideras-Haddad, R. Smit and J. Wambach Technische Universität Darmstadt - 2 University of Cape Town University of the Witwatersrand - ithemba LABS, Somerset West 5 Universität zu Köln - 6 SUNY, Stony Brook 3 4 * Supported by DFG through contracts SFB 634 and Ne 679/2-1

2 Content Motivation Experiments Results and microscopic interpretations Summary and outlook

3 Identification of Mixed-Symmetry States: Interacting Boson Model - 2 Pairing of nucleons to s-/ d-bosons F-Spin: boson: F = 1/2 0 boson: F = -1/2 0 N- N 2 F F = m a x N N 2 F = F max F<F : max : symmetric states mixed-symmetry states (ms) Q-Phonon scheme: Q= s Q Q 2 Q s Q N Q N N ) ms ms ms 1 2 Q = ) 2 Q 0

4 Identification of Mixed-Symmetry States: Q-Phonon Scheme F = F max (sym. states) F = F -1 max (ms states) ms ms 0,...,4 QQ s ms 0,2, QQ s s 2 ms Q ms 2 1 Q s 0 1

5 Identification of Mixed-Symmetry States: Q-Phonon Scheme F = F max (sym. states) F = F -1 max (ms states) ms ms 0,...,4 QQ s ms Strong E2 transitions for decay of sym. Q-phonon 0,2, QQ s s Q s M1 2 ms E2 Q ms Weak E2 transitions for decay of ms Q-phonon Strong M1 transitions for decay of ms states to sym. states

6 Why Mo? The low-energy spectrum of Mo is well studied and candidates for most one- and two-phonon states have been identified N. Pietralla et al, Phys. Rev. Lett. 83 (1999) 1303 N. Pietralla et al, Phys. Rev. Lett. 84 (2000) 3775 C. Fransen et al, Phys. Lett. B 508 (2001) 219 C. Fransen et al, Phys. Rev. C 67 (2003)

7 Why (e,e ) and (p,p ) Experiments? Study of 2 states with (e,e ) and (p,p ) sensitive to one-phonon components of the wave function test of fundamental phonon character isoscalar / isovector decomposition purity of two-phonon states

8 Identification of Mixed-Symmetry States: Experiments High resolution required to resolve all 2 states below 4 MeV Lateral dispersion matching techniques (e,e ): S-DALINAC, TU Darmstadt E = 70 MeV e = E = 30 kev (FWHM) (p,p ): SSC, ithemba LABS E = 200 MeV p = 7-26 E = 35 kev (FWHM)

9 S-DALINAC Accelerator Hall Experimental Hall 0 5 m

10 S-DALINAC Accelerator Hall Experimental Hall 0 5 m High-resolution (e,e ) experiments

11 LINTOTT Spectrometer S-DALINAC

12 Focal Plane Detector System: Si Microstrip Detectors 10 cm

13 Separated-Sector Cyclotron Facility S-DALINAC

14 to Faraday cup K600 Magnetic Spectrometer at ithemba LABS S-DALINAC 2 m beam from SSC

15 Measured Spectra S-DALINAC 3 Counts (x10 ) x kev FWHM Mo(p,p ) E p= 200 MeV = 9 0 Counts / C x kev FWHM Mo(e,e ) E e = 70 MeV = Excitation Energy (MeV)

16 3 Counts (x10 ) Measured Spectra Mo(p,p ) E p = 200 MeV = 9 2 S-DALINAC Counts / C Mo(e,e ) E e = 70 MeV = Excitation Energy (MeV)

17 Theoretical Calculation Quasi-Particle Phonon Model (QPM) full (up to 3 phonons) pure one- and two-phonon states Shell Model (SM) 88 Sr core Surface Delta Interaction (SDI)

18 Theoretical Calculation IBA-2 Model SM wave function for s and d boson pairs p and n separately transition densities: IBA WS Tassie = ( ) i s.p. col Cross Sections DWBA treatment effective nucleon-target interaction (Paris, Love-Franey)

19 Experiment vs. QPM Predictions S-DALINAC Excitation Energy (MeV) J QPM Exp. QPM Exp. QPM Exp States 3 States 4 States J J

20 One-Phonon Symmetric State (d /d ) / (d /d ) Mott Mo(e,e ) 2 1 d /d (mb/sr) Mo(p,p ) -1 q (fm ) -1 q (fm )

21 One-Phonon MS State (d /d ) / (d /d ) Mott Mo(e,e ) 2 3 d /d (mb/sr) Mo(p,p ) -1 q (fm ) -1 q (fm )

22 One-Phonon Symmetric and MS States: Momentum Transfer dependence S-DALINAC Mo(e,e ) 2 1 Model 2 QPM 0.33 (d /d ) / (d /d ) Mott 2 3 SM IBA-2 Model QPM SM IBA q (fm )

23 QPM Predictions: Wave Functions of One-Phonon Symmetric and MS States Main config. (1g 1g ) 9/2 9/2 (2d 2d ) 5/2 5/2 2 1,sym 2 3,ms QPM SM QPM SM symmetric state - isoscalar ms state - isovector

24 Two-Phonon Symmetric State (d /d ) / (d /d ) Mott Mo(e,e ) 2 2 d /d (mb/sr) Mo(p,p ) -1 q (fm ) -1 q (fm ) pure two-phonon state

25 Two-Phonon MS State (d /d ) / (d /d ) Mott Mo(e,e ) 2 5 d /d (mb/sr) Mo(p,p ) -1 q (fm ) -1 q (fm ) 7-10% one-phonon admixture two-step contributions?

26 Coupled-Channel Analysis Collective model U (r) fi = L R 0 2L1 d dr U(r), L 2 L 2 = ( d d exp ( L ( d d DWBA ( L

27 Coupled-Channel Analysis: One and Two-Phonon Symmetric States ms S-DALINAC Mo(p,p ) 2 1 sym = 1.23 = 0.0 d /d (mb/sr) Experiment CHUCK3 2 2 pure two-phonon symmetric state confirmed CHUCK q (fm )

28 Coupled-Channel Analysis: One and Two-Phonon MS States ms S-DALINAC Mo(p,p ) 2 3 sym d /d (mb/sr) Experiment CHUCK = 0.35 = admixture to two-phonon ms state confirmed CHUCK q (fm )

29 Summary Study of one- and two-phonon 2 states in Mo with high-resolution (e,e ) and (p,p ) experiments Combined analysis reveals: symmetric and ms character of one-phonon states two-phonon symmetric state extremely pure about 25% admixtures in the two-phonon ms wave function (mostly 3-phonon) quantitatively consistent results after inclusion of two-step processes in (p,p )

30 Outlook Systematic study around N=50 shell closure 92 Case of Zr: Mixed-symmetry concept seems to fail: C.Fransen et al, Phys. Rev. C 71 (2005) Experiments: (p,p ) at ithemba LABS (e,e ) at S-DALINAC Other shell closures?