File:Shape deformations 9.jpg

Summary

Neutron one-particle levels in a spheroidal Woods-Saxon plus spin-orbit potential, of which the radius \(R\) and the depth \(V_{WS}\) are adjusted approximately to those of \(_{70}^{175}\)Yb\(_{105}\). The parameters of the potential at \(\beta\)=0 are taken from p.239 of Ref. #BM69, except the strength of the spin-orbit potential that is about 20 percent stronger here. The neutron numbers, 82, 104 and 126, which are obtained by filling in all lower-lying levels, are indicated with circles. It is seen that in the deformation region of \(0.15<\beta<0.36\) the 105\(_{th}\) neutron occupies the {[}514 7/2{]} level, in agreement with the observed ground-state configuration of \(^{175}\)Yb. Moreover, the observed sequence of intrinsic states shown in Figure 8 is seen to be consistent with the single-particle spectrum in the present figure at \(\beta\approx0.28\). Namely, above the {[}514 7/2{]} level we find the {[}624 9/2{]}, {[}510 1/2{]}, {[}503 7/2{]}, {[}512 3/2{]} and {[}651 1/2{]} levels, while below the {[}514 7/2{]} level we have the {[}512 5/2{]}, {[}633 7/2{]} and {[}521 1/2{]} levels. In the figure only the one-particle levels, which lie in the neighborhood of the {[}514 7/2{]} level at \(\beta\)=0.28, are marked by respective asymptotic quantum numbers {[}\(Nn_{z}\Lambda\Omega\){]}.

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