Although the concept of random close packing with an almost universal packingfraction of ~ 0.64 for hard spheres was introduced more than half a centuryago, there are still ongoing debates. The main difficulty in searching thedensest packing is that states with packing fractions beyond the glasstransition at ~ 0.58 are inherently non-equilibrium systems, where the dynamicsslows down with a structural relaxation time diverging with density; hence, therandom close packing is inaccessible. Here we perform simulations ofself-propelled hard spheres, and we find that with increasing activity therelaxation dynamics can be sped up by orders of magnitude. The glass transitionshifts to higher packing fractions upon increasing the activity, allowing thestudy of sphere packings with fluid-like dynamics at packing fractions close torandom close packing. Our study opens new possibilities of investigating densepackings and the glass transition in systems of hard particles.
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