Why are higher magic numbers not accurately predicted if nuclear potential is assumed to be a central potential? Nuclei with magic numbers have a higher stability that those without. If we think of the nuclear potential as a central potential though these magic numbers aren't predicted accurately. Why is this so?
 A: 
If we think of the nuclear potential as a central ...

One should not think that N-N potential is only a central attractive one.
The test of the potential form and nature has been done when one tries to 
reproduce two nucleon binding energy and other properties of deuteron ground 
state.
The initial trial is done with central potential like a square well but later to explain the quadrupole moment of deuteron non-central terms do come into play. A small D-state contribution is observed.
Moreover, the Nuclear forces are spin-dependent (As amply shown by the scattering results of  Nucleon with Ortho and para-Hydrogen molecule ).
Therefore for a realistic potential, the spin-orbit interaction also comes into play.
Therefore the Shell model was attempted with potentials of the form of a square well as well as the harmonic oscillator form but they failed to reproduce the higher magic number.(they could  show only 2, 8, 20 as the completely filled shells)
With the inclusion of spin-orbit term of the type  -f(r). (l.s) 
the shell  model reproduces the experimental  magic  numbers namely
2, 8, 20, 28, 50, 82 ,126 ,184

ref.https://ocw.mit.edu/courses/nuclear-engineering/22-02-introduction-to-applied-nuclear-physics-spring-2012/lecture-notes/MIT22_02S12_lec_ch5.pdf

