  We consider the $L^2$-supercritical nonlinear Schr\"{o}dinger equation with a
repulsive Dirac delta potential in one dimensional space. In a previous work,
we clarified the global dynamics of even solutions with the same action as the
high-frequency ground state standing wave solutions. In that case, there are
obvious non-scattering global solutions, i.e., the standing waves. In this
paper, we show a scattering and blow-up dichotomy for threshold even solutions
in the low-frequency case. We emphasize that this dichotomy still holds at the
critical frequency between high and low.
