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

Scattering and Blow-up for threshold even solutions to the nonlinear Schr\"{o}dinger equation with repulsive delta potential at low frequencies