The decay of 1 + states as a new probe of the structure of 0 + shape isomers

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Rosalind Parsons
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1 The decay of 1 + states as a new probe of the structure of 0 + shape isomers G. Rusev 1, R. Schwengner 1, F. Dönau 1, S. Frauendorf 1,2, L. Käubler 1, L. K. Kostov 3, S. Mallion 1,4, K. D. Schilling 1, A. Wagner 1, E. Grosse 1,5, H. von Garrel 6, U. Kneißl 6, C. Kohstall 6, M. Kreutz 6, H. H. Pitz 6, M. Scheck 6, F. Stedile 6, P. von Brentano 7, J. Jolie 7, A. Linnemann 7, N. Pietralla 7,8, V. Werner 7,9 1 Institut für Kern- und Hadronenphysik, FZ Rossendorf, Dresden 2 Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, USA 3 Institute for Nuclear Research and Nuclear Energy, BAS, 1784 Sofia, Bulgaria 4 Instituut voor Kern- & Stralingsfysica, Katholieke Universiteit Leuven, 3001 Leuven, Belgium 5 Institut für Kern- und Teilchenphysik, Technische Universität Dresden, Dresden 6 Institut für Strahlenphysik, Universität Stuttgart, Stuttgart 7 Institut für Kernphysik, Universität zu Köln, Köln 8 Nuclear Structure Laboratory, Dept. of Physics & Astronomy, SUNY, Stony Brook, NY , USA 9 Wright Nuclear Structure Laboratory, Yale University, New Haven, CT , USA Supported by the Deutsche Forschungsgemeinschaft

2 Shape coexistence The appearence of excited 0 + states in even-even nuclei is considered as the manifestation of shape coexistence. Shape coexistence may be caused by the transfer of a broken nucleon pair to orbitals driving the deformation in a different way. Mean-field models predict such configurations and their shapes. However, the coupling between them is not described. Experimental probes which are sensitive to the mixing of the coexisting configurations are desired

3 Experiments Photon-scattering experiments at the Dynamitron of the University of Stuttgart 98 Mo: target of 1998 mg, enriched to %, combined with 757 mg Al, measurements at electron energies of 3.3 and 3.8 MeV 100 Mo: target of 1620 mg, enriched to %, combined with 757 mg Al, measurements at electron energies of 3.2, 3.4 and 3.8 MeV Gamma rays were measured with three detectors of 100 % relative efficiency placed at 90, 127 and 150, respectively, with respect to the beam direction.

4 Spectrum of photons scattered from 98 Mo

5 Level scheme of 98 Mo 3.8 MeV J =1 3.3 MeV Mo

6 Spectrum of photons scattered from 100 Mo

7 Level scheme of 100 Mo 3.8 MeV J =1 3.4 MeV 3.2 MeV Mo

8 Transitions to the state Transitions from J=1 states to excited 0 + states transitions have not been quantitatively described so far because common interpretations like two-phonon mixed-symmetry states in terms of the Interacting-Boson Approximation (IBA) or the interpretation in terms of the Random-Phase Approximation (RPA) do not take shape coexistence into account. We develop a model based on 1p1h excitations, which allows us to calculate the mixing of the two 0 + shape isomers from experimental transition strengths. The model works analogously for 1 + and 1 states. Based on systematics we assume positive parity for the J=1 states.

9 Level crossing in 98 Mo γ a 15 Minimum a: Proton configuration: (fp) 2 g 4 9/2 Shape: ε 2 = 0.19, γ = 16 e / MeV ε 2 g fp g g fp g fp a f a ε 2 ( γ ) b b b f Minimum b: Proton configuration: (fp) 4 g 6 9/2 Shape: ε 2 = 0.22, γ = 0 The shape change is caused by the reoccupation of the last pair of protons from an (fp) orbital to a g 9/2 orbital.

10 Two-level mixing 0 + states in terms of the configurations a and b: = cos α a + sin α b = sin α a + cos α b (1) All 1 + states can be generated by a particular 1p1h excitation from the ground state: 1 + (c pc h ) (2) The majority of the 1 + states can be generated by 1p1h excitations where any orbitals become reoccupied except the two crossing levels reserved for the shape changing pair transfer. The M1-transition matrix-elements can be approximately factorised as: 1 + M(M1) 0 + 1,2 p M(M1) h ,2 (3) In this case, the transition is suppressed due to the orthogonality = 0.

11 Two-level mixing The observed branching to the state is related with a minor group of 1 + states where the crossing orbitals are involved in the 1p1h excitation. Such a state, including either a or b, is formed, e.g. as: (a f - Fermi level of configuration a) The transition matrix-elements for this 1 + state read: 1 + (c pc h=af ) 1 + a (1) 1 + M(M1) 0 + 1,2 p M(M1) a f a 0 + 1,2 (2) We obtain a relation between B(M1) values and mixing coefficients: B(M1, ) B(M1, ) = sin α cos α The unknown matrix elements p M(M1) a f cancel in the ratio. 2 (3)

12 Results for 98 Mo and 100 Mo 98 Mo: Experimental intensities of the and kev transitions result in B(M1, ) / B(M1, ) = 0.28(5) sin 2 α = 0.22(3); cos 2 α = 0.78(3) 100 Mo: Experimental intensities of the and kev transitions result in B(M1, ) / B(M1, ) = 0.45(13) sin 2 α = 0.31(6); cos 2 α = 0.69(6) The increase of the mixing from 98 Mo to 100 Mo is consistent with the measured growing E 0 transition strengths.

13 Summary One of the observed J=1 states in 98 Mo and 100 Mo decays to both the 0 + ground state and the first excited 0 + state. The existence of the two decay branches indicates that two coexisting configurations are mixed in the 0 + states. The calculation of the deformation-energy surface yields a triaxial shape for the ground configuration and an axially deformed prolate shape for the excited configuration. Assuming that (i) the pairing interaction is the main source of the coupling of the two configurations, (ii) the decaying J=1 state can be represented by its dominant 1p1h excitation, the ratio of the squared mixing coefficients is proportional to the branching ratio. This relation is generally valid for analogous cases of shape coexistence in other nuclides. The observation of decay branches to excited 0 + states in connection with the presented model provides a new means to investigate the structure of shape-isomeric states.

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

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 2 1 3 2 4 5 3,4 N. Botha,