Isospin symmetry in the $sd$ shell: Transition strengths in the neutron-deficient $sd$ shell nucleus ${}^{33}\mathrm{Ar}$

Reduced transition strengths of the deexciting transitions from the first two excited states in ${}^{33}\mathrm{Ar}$ were measured in a relativistic Coulomb excitation experiment at the GSI Helmholtz center. The radioactive ion beam was produced by fragmentation of a primary ${}^{36}\mathrm{Ar}$ beam on a ${}^9\mathrm{Be}$ target followed by the selection of the reaction product of interest via the GSI Fragment Separator. The ${}^{33}\mathrm{Ar}$ beam hit a secondary ${}^{197}\mathrm{Au}$ target with an energy of approximately 145 MeV/nucleon. An array of high-purity germanium cluster detectors and large-volume ${\mathrm{BaF}}_2$ scintillator detectors were employed for $\gamma$-ray spectroscopy at the secondary target position. The Lund-York-Cologne Calorimeter was used to track the outgoing ions and to identify the nuclear reaction channels. For the two lowest energy excited states of ${}^{33}\mathrm{Ar}$ the reduced transition strengths have been determined. With these first results the $T_z=-3/2$ nucleus ${}^{33}\mathrm{Ar}$ is now, together with ${}^{21}\mathrm{Na} \left(T_z=-1/2\right)$, the only neutron-deficient odd-$A sd$ shell nucleus in which experimental transition strengths are available. The experimental values are compared to results of shell-model calculations which describe simultaneously mirror-energy differences and transition-strength values of mirror pairs in the $sd$ shell in a consistent way.

Figure 1

Experimental MED values ($2_1^{+}$ states) of $T_z=\pm 1\text{(black}\text{dots)}\text{and}{T}_z=\pm 2\text{(red}\text{squares)} sd$ shell nuclei with shell-model calculations employing different interactions (different lines). For details see the text.

Figure 2

$\Delta E\text{−}E$ plot of the LYCCA for $Z$ identification.

Figure 3

$\beta \text{−}E$ plot of the LYCCA, which is used for mass identification, demonstrated for ${}^{31,30}\mathrm{S}$ produced in second fragmentation of ${}^{33}\mathrm{Ar}$ (see text).

Figure 4

Background-subtracted, Doppler-corrected $\gamma$-ray spectra showing the $2_1^{+}\to 0^{+}$ transition at 1970(3) keV from ${}^{36}\mathrm{Ar}$ in the top panel, and the ${\left(\frac{3}{2}\right)}^{+}\to {\left(\frac{1}{2}\right)}^{+}$- at 1360(3) keV and the ${\left(\frac{5}{2}\right)}^{+}\to {\left(\frac{1}{2}\right)}^{+}$ transitions at 1804(6) keV from ${}^{33}\mathrm{Ar}$ in the bottom panel.

Figure 5

Experimental mirror energy differences of the first excited states of the $T=\frac{3}{2} sd$ shell mirror pairs and shell-model calculations [1]. The black dot indicates a new data point at $A=29$; a measurement that was released in Ref. [7] after the modified ${\mathrm{USD}}_{2,3}^m$ interactions were published in Ref. [1]. The experimental data, beside the $A=29$ data point, are taken from [28].

Figure 6

Experimental $B\left(E2\right)$ values (dots) and results from shell-model calculations (lines) are compared for $T_z=\pm 1,\pm 2 sd$ shell nuclei. For details see text.

Figure 7

Experimental $B\left(E2\right)$ values (dots) and shell-model calculations (lines) of $T_z=-\frac{3}{2}\text{(blue)}\text{and}+\frac{3}{2}\text{(red)} sd$ shell nuclei. The ${\left(\frac{5}{2}\right)}^{+}\to {\left(\frac{1}{2}\right)}^{+}$ transition is shown in the top panel and the ${\left(\frac{3}{2}\right)}^{+}\to {\left(\frac{1}{2}\right)}^{+}$ transition in the bottom panel.

Figure 8

Experimental and shell-model $\left(\mathrm{USD}{}_{2,3}^m\right)$ isoscalar (IS, top) and isovector (IV, bottom) $E2$ transition matrix elements in $sd$ shell nuclei. For $T=\frac{3}{2}$ only mirror pairs with odd-neutron $T_z=-T$ are considered, as the odd-proton nuclei are essentially proton unbound. The $T=\frac{3}{2}$ full and dashed lines refer to ${\left(\frac{5}{2}\right)}^{+}\to {\left(\frac{1}{2}\right)}^{+}$ and ${\left(\frac{3}{2}\right)}^{+}\to {\left(\frac{1}{2}\right)}^{+}$ transitions, respectively. For ${}^{33}\mathrm{P}$ the averages of the two experimental results are listed in Table 2, and for ${}^{22}\mathrm{Mg}$ the more precise value of Ref. [33] is used.