Spectroscopy of ${}^{13}\mathrm{C}$ above the $\alpha$ threshold with $\alpha +{}^9\mathrm{Be}$ reactions at low energies

In this work we reinvestigate the spectroscopy of ${}^{13}\mathrm{C}$ at excitation energies larger than the $\alpha$ emission threshold ($E_x>10.648\mathrm{MeV}$) by means of a comprehensive $R$-matrix fit of experimental data concerning $\alpha +{}^9\mathrm{Be}$ collisions at low energies. Owing to the analysis of many reaction channels in a broad energy range, we improved the current knowledge on the level scheme of ${}^{13}\mathrm{C}$, by contributing to remove uncertain $J^{\pi }$ assignments for several states. Some tentative speculations on the existence of molecular bands associated to cluster structures in this nucleus are also discussed.

Figure 1

Ejectile energy spectrum observed in $\alpha +{}^9\mathrm{Be}$ collisions at $E_{\alpha }=9.24\mathrm{MeV}$ and ${\theta }_{\text{lab}}={70}^{\circ }$. The small peaks at high energies are due to contaminants in the target. The group of peaks at 1.5–4 MeV is attributed to the inelastic scattering channels ${\alpha }_1$ (${}^9\mathrm{Be}$ at $E_x=1.684\mathrm{MeV}$, blue line), ${\alpha }_2$ (${}^9\mathrm{Be}$ at $E_x=2.429\mathrm{MeV}$, green line), and ${\alpha }_4$ (${}^9\mathrm{Be}$ at $E_x=3.049\mathrm{MeV}$, black dashed line). The yellow line represents the assumed background. The red solid line shows the fit of inelastic peaks.

Figure 2

${}^9\mathrm{Be}(\alpha ,{\alpha }_0){}^9\mathrm{Be}$ DCS at laboratory angles of ${160}^{\circ }$, ${150}^{\circ }$, ${135}^{\circ }$, and ${110}^{\circ }$. Data are taken from Ref. [47]. The energy scale shown here represents the center of mass energy calculated starting from the $\alpha$-particle bombarding energy. Effects of finite target thickness have been taken into account in the $R$-matrix fit. Red lines represent the results of the simultaneous multichannel $R$-matrix best-fit on the whole data set here investigated. Green dashed line: $R$-matrix best-fit without the $3/2^{-}$ state at 15.27 MeV. Blue dotted line: $R$-matrix best-fit without the $5/2^{-}$ state at 16.27 MeV. Magenta dash-dot line: $R$-matrix best-fit without the $5/2^{-}$ state at 16.64 MeV.

Figure 3

Low-energy ${}^9\mathrm{Be}(\alpha ,{\alpha }_0){}^9\mathrm{Be}$ DCS at center of mass angles ${160}^{\circ }$ and ${150}^{\circ }$. Data are taken from Ref. [33]. Red lines are the results of the $R$-matrix best-fit on the whole data set here investigated.

Figure 4

Excitation functions of ${}^9\mathrm{Be}(\alpha ,{\mathrm{n}}_0){}^{12}\mathrm{C}_{GS}$ and ${}^9\mathrm{Be}(\alpha ,{\mathrm{n}}_1){}^{12}\mathrm{C}_{4.44}$ angle-integrated cross section. Black dots, data from Ref. [52]; blue stars, data from Refs. [53, 54]. Average uncertainties of 15% have been used for both data sets. Red lines are the results of the simultaneous multichannel $R$-matrix fit on the whole data set here investigated.

Figure 5

(Upper panel) Zoom of ${}^9\mathrm{Be}(\alpha ,{\mathrm{n}}_0){}^{12}\mathrm{C}$ integrated cross-section data (see Fig. 4). Green dashed line: $R$-matrix best-fit without the inclusion of the $1/2^{+}$ state at 12.33 MeV. Red solid line: $R$-matrix best-fit with all the parameters of Table 1. (Lower panel) The same of upper panel, but for the ${}^9\mathrm{Be}(\alpha ,{\alpha }_0){}^9\mathrm{Be}$ DCS at ${\theta }_{\text{cm}}={160}^{\circ }$.

Figure 6

(Upper panel) Zoom of ${}^9\mathrm{Be}(\alpha ,{\alpha }_0){}^9\mathrm{Be}$ DCS data at ${\theta }_{\text{lab}}={160}^{\circ }$ (see Fig. 2). Blue dashed line: $R$-matrix best-fit where we changed the $J^{\pi }$ value of the 13.41 MeV state from $9/2^{-}$ to $7/2^{+}$. Total and partial widths values used in the case of a $7/2^{+}$ assignment for the 13.41 MeV state are the same of those reported in Table 1 for the 13.41 MeV $9/2^{-}$ state. Red solid line: $R$-matrix best-fit with all the parameters of Table 1. (lower panel) The same of upper panel, but for the ${}^9\mathrm{Be}(\alpha ,{\alpha }_0){}^9\mathrm{Be}$ DCS at ${\theta }_{\text{cm}}=137.9^{\circ }$. Data are taken from Ref. [32] and normalized as discussed in the text.

Figure 7

${}^9\mathrm{Be}(\alpha ,{\alpha }_1){}^9\mathrm{Be}_{1.68}$ DCS data at ${\theta }_{\text{lab}}={70}^{\circ }$. The red line represents the $R$-matrix best-fit on the whole data set here investigated. The brown dotted line is the $R$-matrix best-fit without the inclusion of the $3/2^{+}$ state at 16.09 MeV. The azure dashed line is the $R$-matrix best-fit without the inclusion of the $5/2^{-}$ state at 16.27 MeV. The blue dotted line is the $R$-matrix best-fit without the inclusion of the $5/2^{+}$ state at 16.40 MeV, responsible of the wing at $E_{\text{cm}}\simeq 5.8\mathrm{MeV}$. The green dashed line is the $R$-matrix best-fit without the inclusion of the $9/2^{+}$ state at 16.89 MeV. Finally, the magenta dash-dot line is the $R$-matrix best-fit without the inclusion of the $3/2^{-}$ state at 17.24 MeV.

Figure 8

${}^9\mathrm{Be}(\alpha ,{\alpha }_0){}^9\mathrm{Be}$ DCS at laboratory angles of ${160}^{\circ }$, ${150}^{\circ }$, ${135}^{\circ }$, and ${110}^{\circ }$, as in Fig. 2. Red lines are the results of $R$-matrix best-fit. Green dashed lines represent the $R$-matrix best-fit without the inclusion of both the $5/2^{-}$ broad states at 16.27 and 16.64 MeV.

Figure 9

States that could be involved in ${}^{13}\mathrm{C}$ molecular bands. Black open stars: theoretical calculation of the negative parity band of ${}^{13}\mathrm{C}$ built on the $3/2_2^{-}$ state, from Ref. [29]; the vertical scale has been transformed into excitation energy. Blue open circles: low-energy negative parity states suggested to belong to the $K^{\pi }=3/2^{-}$ molecular band by Ref. [24]. Blue full circles: negative parity states seen in the present experiment and naively associated to the $K^{\pi }=3/2^{-}$ molecular band. Blue dashed line: linear best fit of the four negative parity states. Red full squares: positive parity states that could naively belong to the $K^{\pi }=3/2^{+}$ molecular band. The red dotted line has the same slope of the blue one, but it is shifted by $E_x=0.95\mathrm{MeV}$; it is intended only to guide the eye.