The perturbed γ-γ angular correlation, PAC for short or PAC-Spectroscopy, is a method of nuclear solid-state physics with which magnetic and electric fields in crystal structures can be measured. In doing so, electrical field gradients and the Larmor frequency in magnetic fields as well as dynamic effects are determined. With this very sensitive method, which requires only about 10-1000 billion atoms of a radioactive isotope per measurement, material properties in the local structure, phase transitions, magnetism and diffusion can be investigated. The PAC method is related to nuclear magnetic resonance and the Mössbauer effect, but shows no signal attenuation at very high temperatures. Today only the time-differential perturbed angular correlation (TDPAC) is used.
History and development
PAC goes back to a theoretical work by Donald R. Hamilton from 1940. The first successful experiment was carried out by Brady and Deutsch in 1947. Essentially spin and parity of nuclear spins were investigated in these first PAC experiments. However, it was recognized early on that electric and magnetic fields interact with the nuclear moment, providing the basis for a new form of material investigation: nuclear solid-state spectroscopy.
Step by step the theory was developed. After Abragam and Pound published their work on the theory of PAC in 1953 including extra nuclear fields, many studies with PAC were carried out afterwards. In the 1960s and 1970s, interest in PAC experiments sharply increased, focusing mainly on magnetic and electric fields in crystals into which the probe nuclei were introduced. In the mid-1960s, ion implantation was discovered, providing new opportunities for sample preparation. The rapid electronic development of the 1970s brought significant improvements in signal processing. From the 1980s to the present, PAC has emerged as an important method for the study and characterization of materials, e.g. for the study of semiconductor materials, intermetallic compounds, surfaces and interfaces, and a number of applications have also appeared in biochemistry.
While until about 2008 PAC instruments used conventional high-frequency electronics of the 1970s, in 2008 Christian Herden and Jens Röder et al. developed the first fully digitized PAC instrument that enables extensive data analysis and parallel use of multiple probes. Replicas and further developments followed.
Measuring principle
PAC uses radioactive probes, which have an intermediate state with decay times of 2 ns to approx. 10 μs, see example 111In in the picture on the right. After electron capture (EC), indium transmutates to cadmium. Immediately thereafter, the 111cadmium nucleus is predominantly in the excited 7/2+ nuclear spin and only to a very small extent in the 11/2- nuclear spin, the latter should not be considered further. The 7/2+ excited state transitions to the 5/2+ intermediate state by emitting a 171 keV γ-quantum. The intermediate state has a lifetime of 84.5 ns and is the sensitive state for the PAC. This state in turn decays into the 1/2+ ground state by emitting a γ-quantum with 245 keV. PAC now detects both γ-quanta and evaluates the first as a start signal, the second as a stop signal.
Now one measures the time between start and stop for each event. This is called coincidence when a start and stop pair has been found. Since the intermediate state decays according to the laws of radioactive decay, one obtains an exponential curve with the lifetime of this intermediate state after plotting the frequency over time. Due to the non-spherically symmetric radiation of the second γ-quantum, the so-called anisotropy, which is an intrinsic property of the nucleus in this transition, it comes with the surrounding electrical and/or magnetic fields to a periodic disorder (hyperfine interaction). The illustration of the individual spectra on the right shows the effect of this disturbance as a wave pattern on the exponential decay of two detectors, one pair at 90° and one at 180° to each other. The waveforms to both detector pairs are shifted from each other. Very simply, one can imagine a fixed observer looking at a lighthouse whose light intensity periodically becomes lighter and darker. Correspondingly, a detector arrangement, usually four detectors in a planar 90 ° arrangement or six detectors in an octahedral arrangement, "sees" the rotation of the core on the order of magnitude of MHz to GHz.