Subatomic Physics

572 Collective Model
18.4. Quadrupole moments can also be determined by using nuclear quadrupole resonance
and the Mössbauer effect. Answer the questions posed in Problem 18.2
for these two methods.
18.5. Verify Eq. (18.2).
18.6. ∗ The giant dipole resonance has a very different shape in spherical nuclei
and in strongly deformed nuclei. Sketch typical resonances for the two cases.
Explain the reason for the appearance of two peaks in deformed nuclei. How
can the ground-state quadrupole moment be deduced from the positions of
the two peaks? How are the relevant experiments performed? [F. W. K. Firk,
Annu. Rev. Nucl. Sci. 20, 39 (1970).]
18.7. How can the deformation of a nucleus be observed in an electron scattering experiment?
[See, for instance, F. J. Uhrhane, J. S. McCarthy, and M. R. Yearian,
Phys. Rev. Lett. 26, 578 (1971).]
18.8. Prepare a Z − N plot and indicate on this plot the regions where you expect
spherical nuclei and where you expect large deformations. Plot the position
of a few typical nuclides. [E. Marshalek, L. W. Person, and R. K. Sheline,
Rev. Mod. Phys. 35, 108 (1963).]
18.9. Verify Eq. (18.7).
18.10. Show that the expectation value of the quadrupole operator in states with
spins 0 and 1
2 vanishes.
18.11. Discuss the transition rates for electric quadrupole transitions in strongly
deformed nuclei:
(a) Find a particular example and compare the observed half-life with the
one predicted by a single-particle estimate.
(b) How can the observed discrepancy be explained?
18.12. Coulomb excitation. Discuss:
(a) The physical process of Coulomb excitation, and
(b) The experimental approach.
(c) What information can be extracted from Coulomb excitation?
(d) Sketch the information that supports the assumption of collective states
in strongly deformed nuclei. [K. Alder and A. Winther, Coulomb Excitation,
Academic Press, New York, 1966; K. Alder et al., Rev. Mod.
Phys. 28, 432 (1956).]