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

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