Figure 1

(a) The Hartree-Fock ground state of a trapped Fermi gas. The curves correspond to (thick) the Hartree potential $W\left(x\right)$, (thin) the Gaussian external potential $V_{\text{ext}}\left(x\right)$, and (dashed) the combined potential $V_{\text{ext}}\left(x\right)+W\left(x\right)$. (b) A scattering one-particle excitation and (c) a bound two-particle one-hole excitation, where the energy-level occupation of the (●) spin-up and (○) spin-down particles is indicated schematically. The arrows indicate the particle rearrangement between the configurations in panels (b) and (c). (d) The ground-state energy-level occupation [see Eq. (7)] is indicated by the horizontal component of the markers $\times$. In all panels, the horizontal lines indicate (dashed) the Fermi energy $E_{\text{F}}$ and (solid) the bound Hartree-Fock energies $E_n<0$ [see Eq. (6)]. Parameters are $g=-9.55w{E}_w$, $V_0=127.32E_w$, and $E_{\text{F}}=-19.10E_w$.Reuse & Permissions

Figure 2

(a) Scattering phase shifts and (b) transmission probability for a trapped Fermi gas, calculated using the configuration-interaction method. The curves in (a) correspond to (thick) the even phase shift ${\delta }_{\text{e}}\left(k\right)$ and (thin) the odd phase shift ${\delta }_{\text{o}}\left(k\right)$. The vertical lines in (b) indicate the uncoupled resonance wave vectors $k_{rs}^t$ [see Eq. (16)]. Parameters are $g=-9.55w{E}_w$, $V_0=127.32E_w$, and $E_{\text{F}}=-19.10E_w$.Reuse & Permissions

Figure 3

(a) The BCS ground state of a trapped Fermi gas. The curves correspond to (thick) the Hartree potential $U\left(x\right)$, (dotted) the pair potential $\Delta \left(x\right)$, (thin) the Gaussian external potential $V_{\text{ext}}\left(x\right)$, and (dashed) the combined potential $\overline{V}\left(x\right)=V_{\text{ext}}\left(x\right)+U\left(x\right)$. (b) A scattering particle excitation and (c) a bound hole excitation, where the energy-level occupation of the (●) spin-up and (○) spin-down particles is indicated schematically. The arrows indicate the particle rearrangement between the configurations in panels (b) and (c). (d) The ground-state occupation of the bound states in the combined potential $\overline{V}\left(x\right)$ [see Eqs. (20, 21)] is indicated by the horizontal component of the markers $\times$. In all panels, the horizontal lines indicate (dashed) the chemical potential $\mu$ and (solid) the bound-state energies $E_n=E_{\text{b}}<0$ in the combined potential $\overline{V}\left(x\right)$. Parameters are $g=-9.55w{E}_w$, $V_0=127.32E_w$, and $\mu =-19.10E_w$.Reuse & Permissions

Figure 4

(a) Scattering phase shifts and (b) transmission probability for a trapped Fermi gas, calculated using the mean-field method. The curves in (a) correspond to (thick) the even phase shift ${\delta }_{\text{e}}\left(k\right)$ and (thin) the odd phase shift ${\delta }_{\text{o}}\left(k\right)$. The vertical lines in (b) indicate the uncoupled resonance wave vectors $k_{\text{r}}^{\text{b}}$ [see Eq. (23)]. Parameters are $g=-9.55w{E}_w$, $V_0=127.32E_w$, and $\mu =-19.10E_w$.Reuse & Permissions

Figure 5

(a) The energy-level diagram for a generic quantum system for which the energy levels near the chemical potential are highly degenerate. (b) The average energy-level population $n_{\text{b}}$ that could be expected from a BCS mean-field calculation. In both panels, the dashed horizontal line indicates the chemical potential $\mu$.Reuse & Permissions