I build a toy model in the frame of the jittering jets explosion mechanism (JJEM) of core collapse supernovae that incorporates both the stochastically varying angular momentum component of the material that the newly born neutron star (NS) accretes and the constant angular momentum component, and show that the JJEM can account for the ≃2.5–5M⊙ mass gap between NSs and black holes (BHs). The random component of the angular momentum results from pre-collapse core convection fluctuations that are amplified by post-collapse instabilities. The fixed angular momentum component results from pre-collapse core rotation. For slowly rotating pre-collapse cores the stochastic angular momentum fluctuations form intermittent accretion disks (or belts) around the NS with varying angular momentum axes in all directions. The intermittent accretion disk/belt launches jets in all directions that expel the core material in all directions early on, hence leaving an NS remnant. Rapidly rotating pre-collapse cores form an accretion disk with angular momentum axis that is about the same as the pre-collapse core rotation. The NS launches jets along this axis and hence the jets avoid the equatorial plane region. Inflowing core material continues to feed the central object from the equatorial plane increasing the NS mass to form a BH. The narrow transition from slow to rapid pre-collapse core rotation, i.e., from an efficient to inefficient jet feedback mechanism, accounts for the sparsely populated mass gap.