Effect of Woods-Saxon Wave Functions on the Calculation of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>A</mml:mi><mml:mo>=</mml:mo><mml:mn>18</mml:mn><mml:mo>,</mml:mo><mml:mi> </mml:mi><mml:mn>2</mml:mn><mml:mn>0</mml:mn><mml:mn>6</mml:mn><mml:mo>,</mml:mo><mml:mi> </mml:mi><mml:mn>210</mml:mn></mml:math>Spectra with a Realistic Interaction

The spectra of the nuclei ${\mathrm{O}}^{18}$, ${\mathrm{F}}^{18}$, ${\mathrm{Pb}}^{206}$, ${\mathrm{Pb}}^{210}$ are calculated using realistic forces and a Woods-Saxon form for the shell-model average field. The substitution of Woods-Saxon for harmonic-oscillator single-particle wave functions leads to appreciable upward shifts in the calculated positions for many low-lying levels in the $A=18$ nuclei. In particular the $T=0$, $J={1}^{+}$ and $T=1$, $J={0}^{+}$ binding energies are decreased by 0.6-1.7 MeV. In the heavier nuclei, one finds significant changes in observed energy levels perhaps only for the ground states. Nevertheless, the introduction of the more realistic single-particle average field in the Pb isotopes and in neighboring nuclei permits one to improve the conceptual basis upon which this field is erected.

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