Imagine a hypothetical universe in which the nuclear potential between two nucleons is attractive at all separations; that is, the repulsive core present in our universe is absent.
(a) Qualitatively discuss how the absence of a repulsive core would alter the minimum separation between nucleons inside a nucleus and hence the nuclear density.
(b) Assuming the nuclear force remains short-ranged and saturating in this universe, derive how the binding energy per nucleon would vary with the mass number A. State any assumptions clearly.
(c) Based on your discussion in (a) and (b), predict the likely stability of very heavy nuclei (A>200) and comment on the possibility of naturally occurring super-heavy elements in such a universe.