Odd resonance of a strongly repulsive symmetric double-delta potential

For $U_{0}a\gg 1$, the lowest odd scattering resonance pole lies near the first odd mode trapped between the barriers:in its real part and to leading nonzero order in its imaginary part. Writing $E={\hslash }^2{k}^2/(2m)=E_R-i\Gamma /2$, the survival probability decays as $e^{-\Gamma t/\hslash }$.