Figure 1

Diagrammatic equation for the full Hamiltonian corresponding to the dynamics in the $\mathcal{P}$ space, Eq. (11). Parts $H^{°}$ and $V$ on the figure indicate the one- (s.p. energies) and two-body parts of the internal Hamiltonian $H_{\mathcal{P}\mathcal{P}}$.Reuse & Permissions

Figure 2

Diagrams for two-body decays: sequential (left part) and direct (right part).Reuse & Permissions

Figure 3

Single-particle decay width as a function of resonance energy for the $p$- and $\mathit{sd}$-shell models. The solid lines represent the results of the reaction calculations based on the Woods-Saxon potential appropriate for the corresponding case (helium or oxygen) discussed in the text. One experimental point on the $p$-state line corresponds to the ground-state $3/2^{-}$ resonance in ${}^5\mathrm{He}$ ($\epsilon =0.895$ MeV and $\gamma =648$ keV). Two points for the $d_{3/2}$ state correspond to the experimentally known $3/2^{+}$ resonances in ${}^{17}\mathrm{O}$ ($\epsilon =0.941$ MeV and $\gamma =98\pm 5$ keV) and ${}^{19}\mathrm{O}$ ($\epsilon =1.540$ MeV and $\gamma =310\pm 30$ keV [55]). The near-threshold power-law fits of Eq. (51) are shown with dashed lines.Reuse & Permissions

Figure 4

CSM results for ${}^7\mathrm{He}$ isotopes. The full scattering cross section is plotted for several reactions: $n$(${}^6\mathrm{He}$, ${}^6\mathrm{He}$)$n$—elastic neutron scattering off the ground state of ${}^6\mathrm{He}$; $n$(${}^6\mathrm{He}$, $X$)—total cross section of neutron scattering by ${}^6\mathrm{He}$; and $n$(${}^6\mathrm{He}$, ${}^6\text{H}{\text{e}}^{*}$)$n$—inelastic scattering of ${}^6\mathrm{He}$ to the excited $2^{+}$state. The remaining curve shows a typical Breit-Wigner shape for elastic scattering via the single ${3/2}^{-}$ resonance.Reuse & Permissions

Figure 5

CSM calculation for oxygen isotopes with the HBUSD interaction. The states (vertical bars) are plotted as a function of energy relative to the ground state of ${}^{16}\mathrm{O}$. States shown with solid black lines are stable in our model; they are either below decay thresholds or with decays forbidden owing to the angular-momentum restrictions in the selected model space. States from yellow (color online)/lighter shade of gray (long lifetime) to red/darker gray (short lifetime) are resonance states. For some of the low-lying states the energy (in units of keV), spin and parity are given. Along with the resonance structure above thresholds, the elastic $d$-wave neutron scattering cross section, off the ground state of a daughter nucleus with $M=0$ (even mass) or $M=1/2$ (odd mass) magnetic quantum number, is plotted as a function of energy. The cross section is obtained as a part of the same CSM calculation.Reuse & Permissions

Figure 6

(Lower panel) The result of the CSM calculation of the level scheme and neutron scattering cross section from the ground state of ${}^{17}\mathrm{O}$. Marked levels corresponding to the $\mathit{sd}$-shell model states are included in the CSM calculation. All other levels result from the expanded $sd\text{−}pf$ shell calculation (see text); the configurations of this type are not coupled to continuum and corresponding (negative-parity) states do not appear in the cross-section plot. (Upper panel) The empirical level scheme in ${}^{18}\mathrm{O}$. The neutron scattering cross section on the upper panel is indirectly inferred from the ${}^{14}\text{C}(\alpha n){}^{17}$O reaction [62] and other compilations [61, 63, 64]. The parts of the cross section shown with a solid line are expected to be dominated by the positive-parity $l=0$ or $l=2$ partial waves and thus can be distantly juxtaposed to the curve on the lower plot.Reuse & Permissions