Nuclear excitation caused by the time-dependent long-ranged electric field acting between colliding nuclei. Theoretically, the Coulomb force between the positively charged colliding nuclei is well understood, and the interaction is exactly calculable. Coulomb excitation usually is the dominant reaction in nuclear scattering, and even occurs at low bombarding energies where the separation of the nuclei is sufficiently large that the short-ranged nuclear force does not act. See also: Coulomb's law
Coulomb excitation plays a vital role in probing the response of both shape and volume collective modes of motion as well as the interplay of single-particle degrees of freedom of the nuclear many-body system. The goal of this work is to develop better models of nuclear structure and to elucidate the underlying nuclear force.
Collective nuclear modes of motion
The residual interaction between nucleons bound in the nucleus leads to coherent collective modes of motion of the nuclear surface and volume. Such coherent motion of many nucleons in the nucleus is of considerable interest in understanding the physics of many-body quantal systems. Collective rotation and vibration of deformed shapes of the nuclear surface is a dominant and ubiquitous feature of the low-lying structure in nuclei. Quite separate from these low-lying surface collective modes are volume collective modes that lead to high-frequency giant resonances at 10–30 MeV in excitation energy. The nuclear charge of the nucleons involved in this coherent motion produces considerably enhanced electromagnetic properties for collective nuclear states. The electric multipole moments of the nuclear states are a direct and sensitive measure of nuclear deformation. For example, the electric quadrupole moments are a direct measure of quadrupole deformation, such as football-shaped deformation; the electric octupole moments are sensitive to octupole deformation, such as pear shapes; while electric hexadecapole moments are sensitive to more complicated hexadecapole-shaped deformation. See also: Giant nuclear resonances; Nuclear moments
The considerable importance of Coulomb excitation lies in the fact that it is the preeminent probe of collective-shape degrees of freedom in nuclei. That is, Coulomb excitation selectively populates modes of motion of the collective shape with cross sections that are a direct and sensitive measure of the electric moments, and these electric moments can be measured with considerable precision since the electromagnetic interaction is exactly calculable.
One-step and multistep excitation
Coulomb excitation was first observed in the 1950s and played a pivotal role in showing that many nuclei have prolate deformation like a football. The initial experiments used beams of protons or alpha particles for which the electromagnetic interaction is weak and only simple one-step excitation occurs. The introduction of high-atomic-number (high-Z) projectiles dramatically advanced exploitation of Coulomb excitation. With such projectiles, the electromagnetic excitation probability for surface modes can approach unity and multistep excitation dominates, leading to the population of excited states with up to 34 units of angular momentum. Such multistep Coulomb excitation can determine the electromagnetic properties of many low-lying collective states in a nucleus, making it a powerful probe of collective motion in nuclear structure. See also: Alpha particles; Proton
Three technical advances have greatly enhanced the power of Coulomb excitation as a probe of nuclear structure. The first is the development of heavy-ion accelerators that can provide copious beams of stable nuclear isotopes throughout the periodic table, including high-Z projectiles such as uranium (Z = 92). Also, radioactive beam facilities are being built that expand the arsenal of beams to include unstable nuclear species. The second advance is the fabrication of arrays of large intrinsic-germanium high-resolution gamma-ray detectors that surround the target. These have high detection efficiency and extremely high sensitivity for resolving the gamma rays emitted during the subsequent decay of excited states populated by multiple Coulomb excitation. In addition, large-solid-angle arrays of heavy-ion detectors are used to detect the coincident scattered ions and to determine unambiguously the nuclei excited and the scattering trajectories. The third advance is the development of a Coulomb excitation least-squares search computer code that makes it possible to extract the hundreds of electromagnetic matrix elements that couple the many states excited in multiple Coulomb excitation.
These advances allow population and study of complete sets of states for low-lying collective bands in a nucleus. Coulomb excitation has allowed detailed mapping of the collective-shape degrees of freedom in nuclei. The moments of inertia of collective rotation bands are derived from the excitation energies, while the nuclear shapes are derived from the electric moments. See also: Gamma-ray detectors; Particle accelerator
Studies of low-lying modes
Coulomb excitation has produced a wealth of information on low-lying collective-shape degrees of freedom in nuclei. It has allowed study of rotational bands up to high angular momentum in nuclei that are not easily populated by other reaction mechanisms, such as neutron-rich stable nuclei, transuranic nuclei, and radioactive neutron-rich nuclei produced at radioactive beam facilities. Such studies have shown that collective motion is richer than early theoretical models had suggested. In many nuclei, Coulomb excitation has identified complete sets of states in rotational bands that result from rotation of football shapes with axis ratios of about 1.5 to 1. These strongly deformed prolate quadrupole shapes have electric quadrupole transition strengths that are over 200 times greater than those produced by a single proton. Other collective nuclear states have been found corresponding to the rotation and vibration of nearly oblate quadrupole deformed shapes, but where all three spatial axes of the nuclear shape differ in length. Collective states attributed to both one and two units of quadrupole or octupole vibration have been discovered. More complicated motion, such as bands of states corresponding to pear-shaped octupole vibration about rotating prolate deformed shapes, have been studied. Coexistence of rotational-vibrational bands having very different deformation also has been discovered in certain nuclei. These observations are being used to refine models of nuclear structure.
Studies of giant resonances
The above studies involve Coulomb excitation of low-lying rotational and vibrational collective surface modes. Scattering of much faster heavy ions at very small scattering angles can lead to distances of closest approach that still are large enough to ensure that the interaction is dominated by the electromagnetic interaction. The shorter electromagnetic impulse in such fast Coulomb excitation makes it possible to excite the high-frequency collective volume modes, that is, giant resonances. Fast Coulomb excitation has been used to map giant resonances corresponding to both in-phase and out-of-phase vibrations of the protons and neutrons as well as double-phonon giant resonances. These studies elucidate the interplay of collective and single-particle degrees of freedom in nuclear structure. See also: Nuclear structure; Scattering experiments (nuclei)