Nuclear Charge Radii of Mg Isotopes by Laser Spectroscopy

Nuclear Charge Radii of Mg Isotopes by Laser Spectroscopy with Combined Fluorescence and β-decay Detection J. Krämer1, D.T. Yordanov2, M.L. Bissell3, K. Blaum2, M. De Rydt3, Ch. Geppert1,4, M. Hammen1, K. Kreim2, A. Krieger1, M. Kowalska5, R. Neugart1, G. Neyens3, W. Nörtershäuser1,4, R. Sanchez4, B. Sieber1, P. Vingerhoets3 1Institut für Kernchemie, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany 2Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, D-69117 Heidelberg, Germany 3Instituut voor Kern- en Stralingsfysica, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium 4GSI, D-64291 Darmstadt, Germany 5CERN, Physics Department, CH-1211 Geneva 23, Switzerland

The b detection method λ=280.36nm polarization

32Mg(Z=12, N=20) 30Mg(Z=12, N=18) 2p3/2 2p3/2 pf pf Shell Structure of Mg Isotopes - „Island of Inversion“ 1f7/2 1f7/2 20 20 1d3/2 1d3/2 2s1/2 sd 2s1/2 sd 1d5/2 1d5/2 n n 8 8 m = −0.7456(5) mN m = -0.88355(15)mN 33Mg(Z=12, N=21) 31Mg(Z=12, N=19) mTheory= -0.71mN mTheory= -0.84mN mSchmidt= -1.9mN mSchmidt= -1.9mN 2p3/2 2p3/2 pf pf 1f7/2 1f7/2 20 20 2p-2h 2p-2h 1d3/2 1d3/2 2s1/2 sd 2s1/2 sd 1d5/2 1d5/2 n n 8 8

The Island of Inversion an Island of Deformation? 14 13 34Mg 12 Z 11 34Al 33Mg 10 32Mg 9 31Na 31Mg 30Ne 30Na 23 22 29Na 21 N 28Ne Si 20 Al Mg 19 Na 18 Ne The “island of inversion” in terms of the SPHERICAL shell model. The height of the boxes represents the amount of particle-hole configurations present in the ground-state wave functions. (analogous to a figure fromP. Himpeet. al., Phys. Lett. B 658, 203 (2008).) 17 F

Does Deformation Explain the 31,33Mg spins and moments? 33Mg, Ip = 3/2(-) 1/2[330]: m = -0.76 m N 3/2[202]: m = +0.80 m N 3/2[321]: m = -0.32 m N 31Mg, Ip = 1/2+ 1/2[200]: m = -0.86 m N Esp (MeV) • QS(31Mg)=0. Quadrupole-moment measurements of 29,33Mg - not feasible; • Necessity of a common observable for all isotopes in order to detect the transition to a deformed configuration;

Isotope shifts by b detection dniAA = Ki (m-m)/(mm)+Fi dr2AA gF = 1.7 B = 0 B > 0 1 F=1 -1 0 1 mF 0 32P3/2 -1 F=2 F=0 D2 32S1/2 gF = 1.0 F=1 1 -1 0 1 mF 0 -1 F=1 32P3/2 2 gF = 1.0 1 F=2 -2 -1 0 1 2 mF 0 -1 -2 F=0 D2 32S1/2 gF = 1.0 F=1 • Influence of the guiding field on the atomic lines: • shift • broadening • One can solve numerically the rate equations and quantitatively describe these effects. • M. Keimet al., Eur. Phys. J. A 8, 31 (2000). 1 -1 0 1 mF 0 -1

Isotope shifts by b detection HFS 31Mg II, D2 Simulated spectra of 31Mg II, D2 M. Kowalskaet al., Phys. Rev. C77, 034307 (2008).

First use of b detection for isotope-shift measurments Preliminary Results on 24Mg - 32Mg from September 2009 30Mg triggered on the release 32Mg photon-ion coincidence 29Mg optical 31Mg b asym. 29Mg b asym. Proof of principle: 29Mg optical and b detection are consistent!

Charge radii of Magnesium Isotopes Isotope shifts radii from muonic data Fricke et al., Phys. Rev. C45 (1992) 80 King plot KSMS=367,3(3) GHz u electronic factor F theoretical calculation Berengut et al., Phys. Rev. A68 (2003) 022502 reference radius: rC (26Mg)=3.034(2) fm Fricke et al., Phys. Rev. C45 (1992) 80 PRELIMINARY

values for Na taken from Huber et al., Phys. Rev. C18 (1978) 2342 Otten, Treat. Heav. Ion Sci. 8 (1989) 515 PRELIMINARY Discussion: PRELIMINARY Isotope shift24Mg-26Mg: 3077(2)(9) MHz -in agreement with trap measurement: 3084.905(93) MHz Batteiger et al. Phys. Rev. A80 (2009) 022503 • radii • Mg and Na reveal similar trend • Indication for an effect at 30Na and 31Mg staggering parameter <1, well within the known systematics

Nuclear Charge Radii of Mg Isotopes by Laser Spectroscopy