The Nilsson orbital can be decomposed into series of orbitals of 3D-harmonic oscillator, such that

with eigen energy and

Since the Nilsson orbital is normalized

Since the number of orbital for fixed is , thus using an inverse transformation from spherical orbital to Nilsson orbital, we have,

I cannot prove it, but

Thus, the single-particle energy fro Nilsson orbital is as same as the spherical orbital !!!

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