High-resolution study of Gamow-Teller transitions in the ${}^{48}\mathrm{Ti}({}^3\mathrm{He},t){}^{48}\mathrm{V}$ reaction

In this work we have studied $T_z=+2\to +1$, Gamow-Teller (GT) transitions in the ${}^{48}\mathrm{Ti}({}^3\mathrm{He},t){}^{48}\mathrm{V}$ charge-exchange reaction at 140 MeV/nucleon and $0^{\circ }$ at the Research Center for Nuclear Physics, Osaka. From the high-resolution facility, consisting of a high-dispersion beamline and the Grand Raiden spectrometer, the spectrum had an energy resolution of 21 keV, among the best achieved. Individual GT transitions were observed and GT strength was derived for each state populated up to an excitation energy of 12 MeV. The total sum of the $B$(GT) strength observed in discrete states was 4.0, which is 33% of the sum-rule-limit value of 12. The results were compared with the results of shell-model calculations carried out with the GXPF1J interaction. The measured $B$(GT) distribution was also compared with that obtained in the $\left({}^3\mathrm{He},t\right)$ charge-exchange reaction on ${}^{47}\mathrm{Ti}$. On the assumption of isospin symmetry the $\beta$ spectrum of the $T_z=-2$ nucleus ${}^{48}\mathrm{Fe}$ was deduced from the observed spectrum in the ${}^{48}\mathrm{Ti}({}^3\mathrm{He},t){}^{48}\mathrm{V}$ reaction and this predicted spectrum was compared with the measured one.

Figure 1

(a) The ${}^{48}\mathrm{Ti}({}^3\mathrm{He},t){}^{48}\mathrm{V}$ spectrum at $0^{\circ }$. Events with scattering angles $\mathrm{\Theta }\le 0.5^{\circ }$ are included. States prominently populated by $\mathrm{\Delta }L=0$ transitions are indicated by their excitation energies. (b) The same spectrum is shown with the scale on the $y$ axis expanded by a factor of $\approx$ 4.5. (c) The correction factor for the gradual decrease in $F(q,\omega )$ calculated using the results of DWBA calculations (see Sec. 3) as a function of energy. (d) The spectrum shown in (a) corrected for the results of the DWBA calculations shown in (c).

Figure 2

Angular distributions for selected transitions. They are labeled by the excitation energy of the level populated in the CE reaction. In this figure we have chosen a few weak transitions to show the power of the method to identify $\mathrm{\Delta }L=0$ transitions (see text). The counts at each angle are normalized to unity at $\mathrm{\Theta }=0^{\circ }$–$0.5^{\circ }$.

Figure 3

Comparison of (a) the measured $B$(GT) strength distribution and (b) shell-model calculations with the GXPF1J interaction of the $B$(GT) strength distribution for the ${}^{48}\mathrm{Ti}({}^3\mathrm{He},t){}^{48}\mathrm{V}$ reaction (see text).

Figure 4

Comparison of the accumulated experimental and theoretical (shell model) $B$(GT) distributions for both the ${}^{48}\mathrm{Ti}({}^3\mathrm{He},t){}^{48}\mathrm{V}$ reaction measured in the present work and the ${}^{47}\mathrm{Ti}({}^3\mathrm{He},t){}^{47}\mathrm{V}$ reaction measured earlier [15].

Figure 5

Schematic picture of the transitions involved in the CE reactions on ${}^{47}\mathrm{Ti}$ and ${}^{48}\mathrm{Ti}$. Full circles represent the particles in the final nucleus above $N=20$ and $Z=20$. Empty circles show the original position of the neutron before it is transformed into a proton. It provides a simple explanation of the differences in the accumulated $B$(GT) distributions seen in Fig. 4 (see text).

Figure 6

(a) Comparison of the accumulated theoretical (SM) $B$(GT) distributions for ${}^{47}\mathrm{V}$ and ${}^{48}\mathrm{V}$ shifted by 2 MeV and scaled by a factor of $5/6=0.833$. (b) Comparison of the accumulated experimental $B$(GT) distributions for ${}^{47}\mathrm{V}$ and ${}^{48}\mathrm{V}$ obtained in the same way as in (a).

Figure 7

(a) ${}^{48}\mathrm{Ti}({}^3\mathrm{He},t){}^{48}\mathrm{V}$ DWBA corrected spectrum up to 7 MeV for $\mathrm{\Theta }\le 0.5^{\circ }$, (b) The $f$ factor for the ${}^{48}\mathrm{Fe} \beta$ decay normalized to unity at $E_x=0$ MeV. (c) The modified ${}^{48}\mathrm{Ti}({}^3\mathrm{He},t){}^{48}\mathrm{V}$ spectrum obtained by multiplying the spectrum in (a) with the $f$ factor in (b). (d) The deduced $\beta$-decay spectrum ${}^{48}\mathrm{Mn}$ after correcting for the IAS strength (see text), and (e) the same spectrum shown on a scale expanded by a factor of 10.