Spectroscopy of ${}^{13}\mathrm{B}$ via the ${}^{13}\mathrm{C}(t,{}^3\mathrm{He})$ reaction at $115A$ MeV

Gamow-Teller and dipole transitions to final states in ${}^{13}\mathrm{B}$ were studied via the ${}^{13}\mathrm{C}(t,{}^3\mathrm{He})$ reaction at $E_t=115A$ MeV. In addition to the strong Gamow-Teller transition to the ${}^{13}\mathrm{B}$ ground state, a weaker Gamow-Teller transition to a state at 3.6 MeV was found. This state was assigned a spin-parity of $3/2^{-}$ by comparison with shell-model calculations using the WBP and WBT interactions which were modified to allow for mixing between $n\hslash \omega$ and $(n+2)\hslash \omega$ configurations. This assignment agrees with a recent result from a lifetime measurement of excited states in ${}^{13}\mathrm{B}$. The shell-model calculations also explained the relatively large spectroscopic strength measured for a low-lying $1/2^{+}$ state at 4.83 MeV in ${}^{13}\mathrm{B}$. The cross sections for dipole transitions up to $E_x$$({}^{13}\mathrm{B})=20$ MeV excited via the ${}^{13}\mathrm{C}(t,{}^3\mathrm{He})$ reaction were also compared with the shell-model calculations. The theoretical cross sections exceeded the data by a factor of about 1.8, which might indicate that the dipole excitations are “quenched”. Uncertainties in the reaction calculations complicate that interpretation.

Figure 1

(a) Excitation-energy spectrum in ${}^{13}\mathrm{B}$, measured via the ${}^{13}\mathrm{C}(t,{}^3\mathrm{He})$ reaction at $115A$ MeV. (b) Differential cross section for the transition to the ${}^{13}\mathrm{B}$(g.s.) and the decomposition in $\Delta L=0$ (dashed line) and $\Delta L=2$ (dotted line) components. The solid line is the sum of the two components. The data points are placed at the center of $0.{72}^{°}$-wide c.m. scattering angle bins (the c.m. angular resolution was $0.6^{°})$. (c) Differential cross section for the peak in the ${}^{13}\mathrm{B}$ spectrum at 3.6 MeV and the decomposition into $\Delta L=0$ (dashed) and $\Delta L=1$ (dotted) components. The solid line is the sum of the two components. (d) Differential cross section for the peak in the ${}^{13}\mathrm{B}$ spectrum at 5.2 MeV. The data is well described by a pure dipole transition. The theoretical cross sections in (b), (c), and (d) were calculated in DWBA and scaled to match the data as discussed in the text.

Figure 2

Decomposition of differential cross section measured for excitation energies in ${}^{13}\mathrm{B}$ between 5 and 20 MeV. The decomposition into a dipole and isotropic component is performed for 1-MeV bins in excitation energy. The isotropic component represents the continuum and small contributions from transitions with $\Delta L>1$. For details, see text.

Figure 3

Excitation energy spectrum measured for $3.0^{°}<{\theta }_{\mathrm{c}.\mathrm{m}.}<3.5^{°}$. The isotropic contribution due to quasifree processes for each 1-MeV bin above 5 MeV is indicated by solid markers. The hatched band is the assumed contribution of the quasifree processes in the further analysis of the spectrum. The width of the band indicates the estimated uncertainty in these contributions.

Figure 4

Comparison between the experimental Gamow-Teller strengths of Table and the theoretical values calculation with the CKII interaction ($0\hslash \omega$) and WBP interaction $(0+2)\hslash \omega$. Dashed lines indicate $1/2^{-}$ states and solid lines correspond to $3/2^{-}$ states. The theoretical values have been scaled by a factor of 0.677 to account for “quenching” as discussed in detail in the text.

Figure 5

(a) Contribution of dipole transitions to the experimental excitation-energy spectrum in ${}^{13}\mathrm{B}$ for $3.0^{°}<{\theta }_{\mathrm{c}.\mathrm{m}.}<3.5^{°}$. This spectrum was obtained by subtracting the estimated contributions from quasifree processes for excitation energies above 5 MeV from the full spectrum (see Fig. 3). For the peak at 3.6 MeV, the dipole contribution was determined from the decomposition shown in Fig. 1c. (b) Theoretical prediction of the dipole cross section for $3.0^{°}<{\theta }_{\mathrm{c}.\mathrm{m}.}<3.5^{°}$. The calculation is based on shell-model results that employ the adjusted WBP interaction with mixed $(1+3)\hslash \omega$ configurations and that were input for the DWBA calculation as detailed in the text. The theoretical spectrum has been folded with the experimental energy resolution. (c) Idem, but the contributions from dipole transitions to $J^{\pi }=1/2^{+},3/2^{+},5/2^{+}$ states in ${}^{13}\mathrm{B}$ are separately indicated.

Figure 6

Cumulative cross sections as a function of excitation energy for dipole transitions excited via ${}^{13}\mathrm{C}(t,{}^3\mathrm{He})$. The thick solid line represents the experimental result, with the thin solid line indicating the error. The dashed line represents the result from the theoretical calculations in DWBA with input from the shell-model calculation that uses the adjusted WBP interaction with mixed $(1+3)\hslash \omega$ configurations. The dotted line represents the same calculation but scaled by a factor 0.56 for reasons discussed in the text.