Molecular structures in $T=1$ states of ${}^{10}$B

Background: Multicenter (molecular) structures can play an important role in light nuclei. The highly deformed rotational band in ${}^{10}$Be with a bandhead at 6.179 MeV has been observed recently and suggested to have an exotic $\alpha$:$2n$:$\alpha$ configuration.

Purpose: Search for states with $\alpha$:$pn$:$\alpha$ two-center molecular configurations in ${}^{10}$B that are analogous to the states with $\alpha$:$2n$:$\alpha$ structure in ${}^{10}$Be.

Methods: The $T=1$ isobaric analog states in ${}^{10}$B were studied in the energy range of $E_x=8.7\text{--}12.1$ MeV using the reaction ${}^1$H(${}^9$Be,$\alpha$)${}^6$Li*($T=1$, 0${}^{+}$, 3.56 MeV). An $R$-matrix analysis was used to extract parameters for the states observed in the ($p$,$\alpha$) excitation function.

Results: Five $T=1$ states in ${}^{10}$B have been identified. The known 2${}^{+}$ and 3${}^{-}$ states at 8.9 MeV have been observed and their partial widths have been measured. The spin parities and partial widths for three higher-lying states were determined.

Conclusions: Our data support theoretical predictions that the 2${}^{+}$ state at 8.9 MeV (isobaric analog of the 7.54-MeV state in ${}^{10}$Be) is a highly clustered state and can be identified as a member of the $\alpha$:$np$:$\alpha$ rotational band. The next member of this band, the 4${}^{+}$ state, has not been found. A very broad 0${}^{+}$ state at 11 MeV that corresponds to pure $\alpha +{}^6\mathrm{Li}$(0${}^{+}$, $T=1$) configuration is suggested and it might be related to similar structures found in ${}^{12}$C, ${}^{18}$O, and ${}^{20}$Ne.

Figure 1

Experimental setup to measure the excitation function for ${}^1$H(${}^9$Be,$\alpha$)${}^6$Li reactions. The position-sensitive $\Delta E-E$ telescope (with gas ionization chamber as $\Delta E$) was used to identify the ${}^6$Li recoils. $\alpha$ particles were measured in an array of Si pin-diode detectors. A Faraday cup was installed at the back of the chamber to measure the beam current.

Figure 2

Typical $\Delta E-E$ spectrum measured in the telescope with an example of the cut that was used to select the ${}^6$Li recoils (solid red contour). The band above the ${}^6$Li corresponds to the ${}^9$Be and below is the $\alpha$ band.

Figure 3

Angle-energy correlation plot for ${}^6$Li recoils measured at $E_{\mathrm{c}.\mathrm{m}.}=4.68$ MeV by position-sensitive $\Delta E-E$ telescope. The inner arch corresponds to the ${}^1$H(${}^9$Be,$\alpha$) reaction that leaves ${}^6$Li in the 3.56-MeV $T=1$ $0^{+}$ excited state. The outer arch corresponds to the population of the ${}^6$Li ground state. The two branches for each arch are attributable to forward and backward scattering in the c.m.

Figure 4

${}^1$H(${}^9$Be,$\alpha$)${}^6$Li*($T=1$, 0${}^{+}$, 3.56 MeV) excitation function at ${55}^{\circ }$ in c.m. The solid (red) curve is the best $R$-matrix fit. The $R$-matrix parameters for this fit are listed in Table . The dashed (blue) curve is the cross section owing to direct ($p$,$\alpha$) process calculated using the DWBA code fresco assuming unity for the overlap integral (spectroscopic factor) between ${}^9$Be(g.s.) and the ${}^6\mathrm{Li}\left(0^{+}\right)\times {}^3\mathrm{H}$ configuration.

Figure 5

Angular distributions of the 2${}^{+}/$3${}^{-}$ doublet at $E_{\mathrm{c}.\mathrm{m}.}=2.3$ MeV ($E_x=8.9$ MeV). The three energies are 20 keV below the maximum cross section (top), near the maximum of the cross section (center), and 14 keV above the maximum of the cross section (bottom). The solid (red) line is the best $R$-matrix fit and the dashed (blue) line is the $R$-matrix calculation with small (25 eV) partial $\alpha$ width in the 3${}^{-}$ state.

Figure 6

The angular distribution at $E_{\mathrm{c}.\mathrm{m}.}=4.4$ MeV ($E_x=11$ MeV). The contribution of the $0^{+}$ state alone is shown by the dotted (black) line. The angular distribution produced by DWBA calculations at this energy is shown by the dash-dotted (green) line. The dashed (blue) line is the best $R$-matrix fit with parameters given in the Table . The solid (red) curve is the best $R$-matrix fit with an additional $2^{+}$ resonance at higher excitation energy (13 MeV), which was found to improve the overall fit.

Figure 7

Effect of the broad $0^{+}$ state at 11 MeV and narrow $2^{+}$ resonance at 10.7 MeV. The solid (red) line is the best $R$-matrix fit that includes the $0^{+}$ and $2^{+}$ states, the dashed (blue) line is the same fit but excluding the $0^{+}$ state, and the dot-dash (green) line is the best fit with the $2^{+}$ state removed.

Figure 8

Angular distribution at $E_{\mathrm{c}.\mathrm{m}.}=5.0$ MeV with four different $R$-matrix fits. Three of the fits have a different state at 5 MeV. The $4^{+}$ (dotted, black) and $3^{-}$ (dash-dotted, green) spin-parity assignments show obvious disagreement with the data at large angles. The solid (red) and dashed (blue) fits have a $1^{-}$ resonance at 5 MeV. The solid (red) curve describes the data best and includes a higher-lying $2^{+}$ state that lifts the cross section at the larger angles.

Figure 9

Excitation functions with three different $R$-matrix fits that correspond to three spin-parity assignments for the state at 5 MeV. The best fit corresponds to $1^{-}$ spin-parity assignment, as shown by the solid (red) line, the fit with a $4^{+}$ spin-parity assignment is shown by the dashed (blue) line, and the 3${}^{-}$ fit is shown by the dash-dotted (green) line. All three fits agree with the data relatively well at lower angles, but only the fit with a $1^{-}$ spin-parity assignment agrees well with larger angle data.

Figure 10

Energy level diagram of select ${}^{10}$Be states and $T=1$ states of ${}^{10}$B. The states observed in this experiment are shown in red. Suggested isobaric analogs are connected by dashed lines. The energy levels generated by the $\alpha +\mathrm{core}$ potential model are shown in bold blue (see text for details).