Coupling to two target-state bands in the study of the $n+{}^{22}\mathrm{Ne}$ system at low energy

One theoretical method for studying nuclear scattering and resonances is via the multichannel algebraic scattering (MCAS) formalism. Studies to date with this method have used a simple collective-rotor prescription to model target states with which a nucleon couples. While generally these target states all belong to the same rotational band, for certain systems it is necessary to include coupling to states outside of that main band. Here, we extend MCAS to allow coupling of different strengths between such states and the rotor band. This is an essential consideration in studying the example examined herein, the scattering of neutrons from ${}^{22}\mathrm{Ne}$.

Figure 1

The low-energy experimental ${}^{22}\mathrm{Ne}$ spectrum [24]. Thick, solid lines denote states of the ground-state band, thick dashed lines denote the other states used in this paper. Letters correspond to usage in specific calculations in Figs. 2, 5, and 6.

Figure 2

The experimental ${}^{23}\mathrm{Ne}$ spectrum [35] and that calculated from MCAS evaluation of the $n{+}^{22}\mathrm{Ne}$, with target state set (a): $0_1^{+}$, $2_1^{+}$, $4_1^{+}$, $\overline{2_2^{+}}$. The bar denotes the use of reduced coupling for channels involving this state.

Figure 3

MCAS evaluation of $n{+}^{22}\mathrm{Ne}$ compound states with scaling of ${\beta }_2$ of ${}^{22}\mathrm{Ne}$ $2_2^{+}$ coupling. States shown by thin (red) lines are from coupling to the $2_2^{+}$ state.

Figure 4

Detail of Fig. 3, showing subthreshold MCAS evaluation of the energy centroids of $n{+}^{22}\mathrm{Ne}$ resonances as ${\beta }_2$ of ${}^{22}\mathrm{Ne}$ $2_2^{+}$ coupling is scaled with respect to other couplings. The dashed line indicates value obtained from theory in Sec. 4a.

Figure 5

Experimental data compared to MCAS ${}^{23}\mathrm{Ne}$ spectra using (a) $0_1^{+}$, $2_1^{+}$, $4_1^{+}$, $\overline{2_2^{+}}$ (as per Fig. 2); and (b) $0_1^{+}$, $2_1^{+}$, $4_1^{+}$, $\overline{2_2^{+}}$, ${\left(6\right)}_1^{+}$. The bar in $\overline{2_2^{+}}$ denotes the use of reduced coupling for channels involving this state.

Figure 6

Experimental data compared to MCAS ${}^{23}\mathrm{Ne}$ spectra using (a) $0_1^{+}$, $2_1^{+}$, $4_1^{+}$, $\overline{2_2^{+}}$ (as per Fig. 2); (c) $0_1^{+}$, $2_1^{+}$, $4_1^{+}$, $\overline{2_2^{+}}$, ${\left(4\right)}_2^{+}$ (as per Ref. [4]); and (d) $0_1^{+}$, $2_1^{+}$, $4_1^{+}$, $\overline{2_2^{+}}$, $\overline{{\left(4\right)}_2^{+}}$. The bar denotes the use of reduced coupling for channels involving this state. Best result presented in the solid blue box.

Figure 7

The MCAS $n{+}^{22}\mathrm{Ne}$ elastic cross section: (i) 0–4.4 MeV, three calculations; (ii) 0–1 MeV, $0_1^{+}$, $2_1^{+}$, $4_1^{+}$ calculation; (iii) 0–1 MeV, $0_1^{+}$, $2_1^{+}$, $4_1^{+}$, $\overline{2_2^{+}}$ calculation [corresponding to (a) in Figs. 2, 5, and 6]; and (iv) 0–1 MeV, $0_1^{+}$, $2_1^{+}$, $4_1^{+}$, $\overline{2_2^{+}}$, $\overline{{\left(4\right)}_2^{+}}$ calculation [corresponding to (d) in Fig. 6]. (Red) squares from Ref. [37], black circles from Ref. [38], $J^{\pi }$ assignments from Ref. [35].