We relate the pre-explosion binding energy of the ejecta of core-collapse supernovae ( CCSNe ) of stars with masses in the lower range of CCSNe and the location of the convection zones in the pre-collapse core of these stars , to explosion properties in the frame of the jittering jets explosion mechanism . Our main conclusion is that in the frame of the jittering jets explosion mechanism the remnant of a pulsar in these low energy CCSNe has some significance , in that the launching of jets by the newly born neutron star ( NS ) spins-up the NS and create a pulsar . We crudely estimated the period of the pulsars to be tens of milliseconds in these cases . The convective zones seed perturbations that lead to accretion of stochastic angular momenזtum that in turn is assumed to launch jittering jets in this explosion mechanism . We calculate the binding energy and the location of the convective zones with the stellar evolution code mesa . For the lowest stellar masses , we study , M _ { ZAMS } \simeq 8.5 - 11 M _ { \odot } , the binding energy above the convective zones is low , and so is the expected explosion energy in the jittering jets explosion mechanism that works in a negative feedback cycle . The expected mass of the NS remnant is M _ { NS } \approx 1.25 M _ { \odot } -1.6 M _ { \odot } , even for these low energy CCSNe .