One density is per volume unit, the other per radius unit.
Multiplying a small radius increment by the sphere's area at that volume, you get a volume increment. This tells that the density per radius unit is zero even though the spherical orbitals have non-zero density per volume unit at the nucleus, and also that the both maximums don't need to coincide, as the r
2 factor can shift the maximum towards bigger radii.
It is the same kind of computation, in the k
xk
yk
z space of wave vectors, for the density of eigenstates per unit of |k|
2 (hence per unit of E), knowing the density per unit of k
x×k
y×k
z "volume" of wave vectors, for acoustics, electromagnetism, semiconductors.
Only spherical orbitals can (and do) have non-zero density per volume unit at the nucleus. The orbital angular momentum being (with some constants) the number of phase turns of the wave function (or better, its part without e
iωt) over a geometric turn around the nucleus, all orbitals with non-zero angular momentum have several phases at the nucleus, which only the number zero fits. As opposed, spherical orbitals have one single phase at the nucleus, and can be non-zero there.
Electron capture (a radioactive decay mode) needs some electron density at the nucleus, so only electrons from spherical orbitals are candidates, 1s more so than 2s 3s... In the case of
7Be, chemical bonds influence the electronic density at the nucleus (from molecular orbitals resulting from 2s) hence the decay half-time
https://en.wikipedia.org/wiki/Electron_capture#Reaction_details