Figure 1

Elastic cross section for $n-{}^{19}\mathrm{C}$ scattering vs center-of-mass energy for a $n-{}^{18}\mathrm{C}$ binding energy of 250 keV. Calculated cross section (full curve) is fitted to the resonance formula in Eq. (1) for three different values of index parameter $q$. The best fit obtained (in our view) is for parameters $E_r=1.63\mathrm{keV}$, $\Gamma =0.25\mathrm{keV}$, and $q=4.0$. The dotted line represents a Breit-Wigner fit to the calculated curve.Reuse & Permissions

Figure 2

Similar to Fig. 1 with lower binding energies of $n-{}^{18}\mathrm{C}$, showing a resonance due to the second excited Efimov state for $n-{}^{18}\mathrm{C}$ binding energy of 150 keV. The 150 keV data fit Eq. (1) with approximately the same $q$ value as for the 250 keV curve in Fig. 1.Reuse & Permissions

Figure 3

Comparison between He and ${}^{20}\mathrm{C}$ as three-body systems in atoms and nuclei. (a) The ground and first excited state (there are infinitely many) of ${\mathrm{He}}^{+}$ and the lowest bound states of He (again there are infinitely many) attached to them are shown, along with their energies below the fully dissociated limit of two electrons and the helium nucleus. Cross-hatched region is the ionization continuum of He built on the ground state of ${\mathrm{He}}^{+}$, that is, the two-electron states $1sEs$, $E$ being the energy of the continuum electron. The $2s^2$ state lies embedded in this continuum, that is, is degenerate with $1sEs$ and, therefore, mixes with it to give the quasibound resonance state. The resonance can be accessed either by ($e+{\mathrm{He}}^{+}$) scattering or by photoexcitation from the ground state as shown (because of dipole selection rules, a single photon will reach similar states of $2s2p^1{P}^0$ symmetry whereas two-photon absorption would be necessary to reach the $2s^2$). (b) Similar schematic for the nuclear system. Now ${}^{19}\mathrm{C}$ has only one bound state, its ground state ${ϵ}_2$. For an appropriate value of ${ϵ}_2$, one bound Efimov state ${ϵ}_3(1)$ and a second which just fails to be bound, ${ϵ}_3(2)$, are shown, together with the ground state of ${}^{20}\mathrm{C}$. The state ${ϵ}_3(2)$, lying embedded in the $n+{}^{19}\mathrm{C}$ continuum, manifests as a resonance in low energy elastic scattering of $n+{}^{19}\mathrm{C}$. For somewhat more negative ${ϵ}_2$, the first Efimov state ${ϵ}_3(1)$ also fails to be bound and will appear as a resonance in $n+{}^{19}\mathrm{C}$ scattering as in Fig. 1.Reuse & Permissions