Efimov Effect in Nuclear Three-Body Resonance Decays

We investigate the effects of the nearly fulfilled Efimov conditions on the properties of three-body resonances. Using the hyper-spheric adiabatic expansion method we compute energy distributions of fragments in a three-body decay of a nuclear resonance. As a realistic example we investigate the $1^{-}$ state in the halo nucleus ${}^{11}\mathrm{Li}$ within a three-body ${}^9\mathrm{Li}+n+n$ model. Characteristic features appear as sharp peaks in the energy distributions. Their origin, as in the Efimov effect, is in the large two-body $s$-wave scattering lengths between the pairs of fragments.

Figure 1

The lowest adiabatic potentials $W_n(\rho )$ for the ${}^{11}\mathrm{Li}(1^{-})$ halo nucleus within the three-body ${}^9\mathrm{Li}+n+n$ model with interactions from Ref. 15. The $n$-core and $n\mathrm{\text{−}}n$ scattering lengths are $a_{nc}\approx a_{nn}\approx 20\mathrm{fm}$. The inset shows the lowest hyper-radial resonance function with its large distance asymptotics—the Hankel function. The complex scaling angle $\theta =0.15$, the resonance angle ${\theta }_R=0.12$ corresponds to the resonance energy of about $0.4-0.1i\mathrm{MeV}$.

Figure 2

The energy distributions of the fragments—the core, ${}^9\mathrm{Li}$, and the neutrons—in the decay of a three-body resonance ${}^{11}\mathrm{Li}(1^{-})$ calculated in the three-body ${}^9\mathrm{Li}+n+n$ model with only $s$-wave $n$-core interactions (scattering length $a_{nc}\approx 50\mathrm{fm}$). The different curves are calculated with different ${\rho }_{\max }$ and different numbers of adiabatic channels $N$ to illustrate the convergence.

Figure 3

The same as Fig. 2 with additional $s$-wave interaction in the $n\mathrm{\text{−}}n$ subsystem ($a_{nn}\approx a_{nc}\approx 50\mathrm{fm}$).

Figure 4

The energy distributions of the fragments—the core, ${}^9\mathrm{Li}$, and the neutrons—in the decay of a three-body resonance ${}^{11}\mathrm{Li}(1^{-})$ calculated with interactions from Ref. 15 where the $n$-core and $n\mathrm{\text{−}}n$ scattering lengths are about 20 fm.