Gamow-Teller strengths in ${}^{24}\mathrm{Na}$ using the ${}^{24}\mathrm{Mg}(t,{}^3\mathrm{He})$ reaction at $115A$ MeV

Gamow-Teller transitions from ${}^{24}\mathrm{Mg}$ to ${}^{24}\mathrm{Na}$ were studied via the ($t,{}^3\mathrm{He}$) reaction at $115A$ MeV using a secondary triton beam produced via fast fragmentation of $150A$ MeV ${}^{16}\mathrm{O}$ ions. Compared to previous ($t,{}^3\mathrm{He}$) experiments at this energy that employed a primary $\alpha$ beam, the secondary beam intensity is improved by about a factor of five. Despite the large emittance of the secondary beam, an excitation-energy resolution of $~200$ keV is achieved. A good correspondence is found between the extracted Gamow-Teller strength distribution and those available from other charge-exchange probes. Theoretical calculations using the newly developed USDA and USDB $\mathit{sd}$-shell model interactions reproduce the data well.

Figure 1

Excitation-energy spectra in ${}^{24}\mathrm{Na}$, measured via the ${}^{24}\mathrm{Mg}(t,{}^3\mathrm{He})$ reaction at $115A$ MeV, integrated over the full acceptance and at forward scattering angles, as labeled. The energy regions in which significant GT components in the spectra were measured are indicated and numbered 1–4.

Figure 2

Angular distributions for each of the four excitation-energy regions labeled in Fig. 1. The results of the MDA (solid line) and the constituent $\Delta L=0$ (long-dashed lines) and $\Delta L\ne 0$ angular distributions (short-dashed lines) are superimposed (see text).

Figure 3

(a) Extracted GT strength distribution from the present ${}^{24}\mathrm{Mg}(t,{}^3\mathrm{He})$ experiment and the comparison with shell-model calculations using the USDA and USDB interactions. The experimental excitation energies of the lowest two GT transitions were fixed to the values known from Ref. [21]. The two data points at higher energies are known to consist of two GT transitions (see text) and the horizontal bars indicate the energy intervals used in the analysis. (b) The same as (a), but now for the cumulative strength. In addition, results from existing data using the ${}^{24}\mathrm{Mg}(d,{}^{2)}\mathrm{He}$ reaction [15] and the ${}^{24}\mathrm{Mg}({}^3\mathrm{He}$, $t)$ reaction [16] are included.