  We have investigated the microstructure, normal-state electrical
connectivity, and critical current density of ex-situ MgB2 polycrystalline
bulks prepared by systematically varying the sintering conditions under low
pressure. Samples heated at a high temperature of ~900{\deg}C for a long period
showed an increased packing factor, a larger intergrain contact area, and a
significantly enhanced electrical connectivity, all of which indicate
solid-state self-sintering of MgB2. Sintered ex-situ MgB2 bulks from a
laboratory-made ball-milled powder exhibited a greatly enhanced connectivity of
28%, which is the highest connectivity of pressureless ex-situ MgB2 bulks,
wires, and tapes. Surprisingly, grain growth did not occur during long-duration
(~100 h) sintering in the sintered ex-situ MgB2 bulks. This is in marked
contrast to in-situ processed MgB2 samples for which significant grain growth
occurred during heat treatment at ~900{\deg}C, producing grains that are
several tens of times larger than the initial boron grains. Consequently, the
critical current density as a function of the external magnetic field at 20 K
progressively improved with sintering due to the relatively small grain size
and good intergrain connectivity. We thus conclude that solid-state
self-sintering is an effective approach for producing strongly connected, dense
ex-situ MgB2 polycrystals without grain growth.
