Eur. Phys. J. A (2023) 59: 198
https://doi.org/10.1140/epja/s10050-023-01111-7

Regular Article - Experimental Physics

Photo-response of the $N=Z$ nucleus ${}^{24}$Mg

¹ School of Computing, Engineering, and Physical Sciences, University of the West of Scotland, PA1 2BE, Paisley, UK
² SUPA, Scottish Universities Physics Alliance, Aberdeen, UK
³ Helmholtz-Zentrum Dresden-Rossendorf, 01328, Dresden, Germany
⁴ Technische Universität Dresden, Institut für Kern- und Teilchenphysik, 01062, Dresden, Germany
⁵ School of Physics, University of the Witwatersrand, 2050, Johannesburg, South Africa
⁶ iThemba Laboratory for Accelerator Based Sciences, 7129, Somerset West, South Africa
⁷ Department of Physics, Karamanoglu Mehmetbey University, Karaman, Turkey
⁸ INFN, Sezione di Milano, 20133, Milan, Italy
⁹ Department of Physics, Milano University, 2-133, Milano, Italy
¹⁰ Department of Physics, University of Surrey, GU2 7XH, Guildford, UK
¹¹ Triangle Universities Nuclear Laboratory, 27708-0308, Durham, NC, USA
¹² Department of Physics and Astronomy, University of North Carolina at Chapel Hill, 27599, Chapel Hill, NC, USA
¹³ Department of Physics, Oliver Lodge Laboratory, University of Liverpool, L69 7ZE, Liverpool, UK
¹⁴ Institut für Kernphysik, Technische Universität Darmstadt, 64289, Darmstadt, Germany
¹⁵ GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291, Darmstadt, Germany
¹⁶ Departments of Chemistry and Physics and Astronomy, University of Kentucky, 40506-0055, Lexington, KY, USA
¹⁷ Faculty of Physics, St. Kliment Ohridski University of Sofia, 1164, Sofia, Bulgaria
¹⁸ Department of Physics, Florida State University, 32306, Tallahassee, FL, USA
¹⁹ Ludwig–Maximilians–Universität München, 85748, Garching, Germany
²⁰ Department of Physics and Astronomy, University of the Western Cape, 7535, Bellville, South Africa
²¹ Department of Physics, Duke University, 27708-0308, Durham, NC, USA
²² Institute of Physics, Slovak Academy of Sciences, 84511, Bratislava, Slovakia
²³ Institut für Kernphysik, Universität zu Köln, 50937, Köln, Germany

^b marcus.scheck@uws.ac.uk

Received: 22 March 2023
Accepted: 18 August 2023
Published online: 7 September 2023

Abstract

The electric E1 and magnetic M1 dipole responses of the $N=Z$ nucleus ${}^{24}$Mg were investigated in an inelastic photon scattering experiment. The 13.0 MeV electrons, which were used to produce the unpolarised bremsstrahlung in the entrance channel of the ${}^{24}$Mg($\gamma ,{\gamma }^{\prime }$) reaction, were delivered by the ELBE accelerator of the Helmholtz-Zentrum Dresden-Rossendorf. The collimated bremsstrahlung photons excited one $J^{\pi }=1^{-}$, four $J^{\pi }=1^{+}$, and six $J^{\pi }=2^{+}$ states in ${}^{24}$Mg. De-excitation $\gamma$ rays were detected using the four high-purity germanium detectors of the $\gamma$ELBE setup, which is dedicated to nuclear resonance fluorescence experiments. In the energy region up to 13.0 MeV a total $B(M1)\uparrow =2.7(3){\mu }_N^2$ is observed, but this $N=Z$ nucleus exhibits only marginal E1 strength of less than $\sum B(E1)\uparrow \le 0.61\times {10}^{-3}$ e${}^2$fm${}^2$. The $B(\Pi 1,1_i^{\pi }\to 2_1^{+})/B(\Pi 1,1_i^{\pi }\to 0_{\mathit{gs}}^{+})$ branching ratios in combination with the expected results from the Alaga rules demonstrate that K is a good approximative quantum number for ${}^{24}$Mg. The use of the known ${\rho }^2(E0,0_2^{+}\to 0_{\mathit{gs}}^{+})$ strength and the measured $B(M1,1^{+}\to 0_2^{+})/B(M1,1^{+}\to 0_{\mathit{gs}}^{+})$ branching ratio of the 10.712 MeV $1^{+}$ level allows, in a two-state mixing model, an extraction of the difference $\Delta {\beta }_2^2$ between the prolate ground-state structure and shape-coexisting superdeformed structure built upon the 6432-keV $0_2^{+}$ level.