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The collapse of marginally bound, inhomogeneous, pressureless (dust) matter,in spherical symmetry, is considered. The starting point is not, in this case,the integration of the Einstein equations from some suitable initialconditions. Instead, starting from the corresponding general exact solution ofthese equations, depending on two arbitrary functions of the radial coordinate,the fulfillment of the Lichnerowicz matching conditions of the interiorcollapsing metric and the exterior Schwarzschild one is tentatively assumed(the continuity of the metric and its first derivatives on the time-likehypersurface describing the evolution of the spherical 2-surface boundary ofthe collapsing cloud), and the consequences of such a tentative assumption areexplored. The whole analytical family of resulting models is obtained and someof them are picked out as physical better models on the basis of the finite andconstant value of its {\em intrinsic} energy.

Spherical symmetric parabolic dust collapse: ${\cal C}^{1}$ matching metric with zero intrinsic energy