Nillson Potential We define a Hamiltonian to derive Nilsson potential, $$\hat{H}=-\frac{\mathbf{\hat{p}}^2}{2m}+
\frac{1}{2}m\left[\omega_\bot^2(\hat{x}^2+\hat{y}^2)+\omega_z^2\hat{z}^2\right]$$
Nilsson model is a famous model, but I didn't find the potential pertaining to it, so I wrote the Hamiltonian and Asked that , is there any way to get the Nilsson potential from the Hamiltonian.
EDIT: according to Thomas
So are you trying to say that, when symmetric potential is  broken, that is the Nilsson potential? 
if someone ask me to write down the potential, then I can not write that down, because it is very subtle amount? 
What are the failures of collective model that Nilsson potential introduced? I mean what are the difference between these model?
 A: The shell model is based on the idea that the nucleus is approximately described by non-interacting nucleons moving in a mean-field potential. This potential, as well as the residual interaction between nucleons, should be derived from the underlying microscopic nucleon-nucleon interaction. For example, I could try to derive the mean potential using the Hartree-Fock approximation. As an even simpler model one may try to guess the potential. The simplest of all possible choices is a Harmonic oscillator potential, which has the virtue that one can write down the states analytically. In the standard shell model we write down a spherically symmetric potential, but in the case of a deformed nucleus we expect the mean field potential to be deformed as well. This is the Nilson model mentioned in the question (We should note that the notion of a deformed potential is somewhat subtle. The wave function of a spin zero nucleus is always spherically symmetric. What we really mean is that the nucleus has rotational bands, so that the density in some suitably defined intrinsic frame is deformed.).  
