Odd resonance of a strongly repulsive symmetric double-delta potential
= Odd resonance of a strongly repulsive symmetric double-delta potential
For $U_0a\gg1$, the lowest odd <scattering resonance> pole lies near the first odd mode trapped between the barriers:
$$
k=\frac\pi a\left(1-\frac1{U_0a}+O((U_0a)^{-2})\right)
-i\frac{\pi^2}{U_0^2a^3}\left(1+O((U_0a)^{-1})\right)
$$
in its real part and to leading nonzero order in its imaginary part. Writing $E=\hbar^2k^2/(2m)=E_R-i\Gamma/2$, the survival probability decays as $e^{-\Gamma t/\hbar}$.