Coulomb Excitation
Douglas Cline

Heavy-ion Coulomb excitation is the pre-eminent probe of collective shape degrees of freedom in nuclear structure. Our research group has exploited this technique, and made significant contributions, during the past four decades. The research has addressed three separate themes during this period.

1969-1975: Measurements were made of static E2 moments of excited states to determine triaxiality in collective motion. Initially this employed a magnetic spectrometer but then evolved to use of $\gamma $-ray detection.
1976- present: Following the advent of heavier ion accelerator facilities in the late 1970's, multiple Coulomb excitation was used to probe the spin and state dependence of the collective shape degrees of freedom in nuclei.
1995- present: The program has focussed primarily on study of rotational bands built on isomeric states and now is exploiting the burgeoning opportunities provided by the new radioactive beam facilities ATLAS/CARIBU and TRIUMF/ISACII to probe the evolution of nuclear structure in exotic nuclei that occurs moving away from the valley of stability.

Important achievements include showing that Coulomb excitation data recorded for a wide range of projectile Z values and scattering angles is sufficient to determine uniquely the complete set of electric multipole matrix elements involving the low-lying states excited [1,2]. These data, plus direct lifetime measurements, are analyzed using the least-squares Coulomb-excitation search code GOSIA [3] that was developed at Rochester. These developments make it feasible to measure an essentially complete set of phases and magnitudes of electric multipole matrix elements for the lowest 75 or more Coulomb excited states in nuclei. The precision, extent and completeness of the measured set of matrix elements add a new dimension to the study of collective motion in nuclei. In particular, it allows exploitation of the rotational-invariant technique [1,4,5,6] to project, directly from measured E2 data, the centroids and fluctuation widths of the electric quadrupole moments in the intrinsic frame without recourse to any model. These intrinsic frame observables are the significant collective shape degrees of freedom. The suite of GOSIA codes plus instruction manual were updated August 2006 and expanded to include a new version specifically for radioactive beam experiments. Cline and Hayes are members of the Gosia Steering Committee and as such are spending an appreciable fraction of effort developing, and maintaining the Gosia suite of codes as well as providing community support.

Three experimental techniques were developed that are currently in use for this research. The impact of this program can be evaluated from the publication list and the educational record.

  1. D. Cline, Ann. Rev. Nucl. Part. Sci. 36, 683 (1986).

  2. L. Hasselgren, and D. Cline, Proc. of the Int. Conf. on Interacting Bose-Fermi Systems in Nuclei, Ed. F. Iachello (Plenum Press 1981) p. 241.

  3. T. Czosnyka, D. Cline, C.Y. Wu, Bull. Amer. Phys. Soc. 28, 745 (1983); Gosia users manual UR-NSRL-305 (1991).

  4. D. Cline, Proc. Orsay Coll. on Intermediate Nuclei, Ed. Foucher, Perrin, Veneroni, 4 (1971).

  5. D. Cline and C. Flaum, Proc. of the Int. Conf. on Nuclear Structure Studies Using Electron Scattering, Sendai, Ed. Shoa, Ui, 61 (1972).

  6. K. Kumar, Phys. Rev. Lett. 28, 249 (1972).