Subatomic Physics

574 Collective Model
(c) Use this form of EJ to fit the observed energy levels of 170 Hf by determining
the constants A and B from the two lowest levels. Then check
how well the computed energies agree with the observed ones up to
J = 20.
18.22. Consider an axially symmetric deformed core plus one valence nucleon
(Fig. 18.6). Why are J and K good quantum numbers, but not j?
18.23. Why are the states with odd J not excluded from the sequence (18.24)?
18.24. Discuss the rotational families of 249 Bk (Fig. 18.7):
(a) Check how well Eq. (18.23) fits the observed energy levels for each band.
(b) Show that K for each band can be found unambiguously from the lowest
three levels of a band by using Eq. (18.25).
18.25. Compare the term Hc in Eq. (18.21) with the classical Coriolis force.
18.26. Use the slope of the trajectories in Fig. 18.8 and Eq. (18.23) for EJ to determine
the moment of inertia as a function of J. PlotI against J for the three
families. Is stretching apparent?
18.27. Find another example for rotational families and prepare a plot similar to
Fig. 18.8.
18.28. Find the energy levels of the anharmonic oscillator, described by the potential
V = 1
2 m[ω⊥(x 2 1 + x 2 2)+ω 2 3x 2 3].
18.29. Describe the complete labeling of Nilsson levels.
18.30. Verify Eq. (18.30).
18.31. Justify that the rotational and the intrinsic motion in deformed nuclei can be
separated by finding approximate values for the time of rotation and the time
a single nucleon needs to traverse the nucleus.
18.32. ∗ Discuss the level diagram of 165 Ho[M.E.BunkerandC.W.Reich,Rev.
Mod. Phys. 43, 348 (1971)]:
(a) Find the various band heads and their rotational spectra.
(b) Plot the bands in a Regge plot (Section 15.7).
(c) Use a Nilsson diagram to find the complete quantum number assignment
for each band head.