Perturbed angular correlation

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.

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.

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.

[24] 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.

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.

Very simply, one can imagine a fixed observer looking at a lighthouse whose light intensity periodically becomes lighter and darker.

In order to obtain a PAC spectrum, the 90° and 180° single spectra are calculated in such a way that the exponential functions cancel each other out and, in addition, the different detector properties shorten themselves.

, the count rate ratio, is obtained from the single spectra by using: Depending on the spin of the intermediate state, a different number of transition frequencies show up.

In crystals, due to the high regularity of the arrangement of the atoms or ions, the environments are identical or very similar, so that probes on identical lattice sites experience the same hyperfine field or magnetic field, which then becomes measurable in a PAC spectrum.

Photomultipliers convert the weak flashes of light into electrical signals generated in the scintillator by gamma radiation.

Whereas in classical instruments, "windows" limiting the respective γ-energies must be set before processing, this is not necessary for the digital PAC during the recording of the measurement.

For the observation of clear perturbation frequencies it is necessary, due to the statistical method, that a certain proportion of the probe atoms are in a similar environment and e.g. experiences the same electric field gradient.

Furthermore, during the time window between the start and stop, or approximately 5 half-lives of the intermediate state, the direction of the electric field gradient must not change.

In liquids, therefore, no interference frequency can be measured as a result of the frequent collisions, unless the probe is complexed in large molecules, such as in proteins.

In PAC measurements, this is shown by the decrease of the crystalline frequency component in a reduction of the amplitude (attenuation).

The following methods are usual: During implantation, a radioactive ion beam is generated, which is directed onto the sample material.

Due to the kinetic energy of the ions (1-500 keV) these fly into the crystal lattice and are slowed down by impacts.

The radioactive probe is applied to a hot plate or filament, where it is brought to the evaporation temperature and condensed on the opposite sample material.

The solution with the radioactive probe should be as pure as possible, since all other substances can diffuse into the sample and affect thereby the measurement results.

This method is particularly well suited if, for example, the PAC probe diffuses only poorly in the material and a higher concentration in grain boundaries is to be expected.

This method is limited to sample materials containing elements from which neutron capture PAC probes can be made.

Rarely used are direct nuclear reactions in which nuclei are converted into PAC probes by bombardment by high-energy elementary particles or protons.

Radioactive ion beams are produced at the ISOLDE by bombarding protons from the booster onto target materials (uranium carbide, liquid tin, etc.)

With the subsequent mass separation usually very pure isotope beams can be produced, which can be implanted in PAC samples.

The interaction also takes place between nuclear quadrupole moment and the off-core electric field gradient

becomes diagonalized, that: The matrix is free of traces in the main axis system (Laplace equation) Typically, the electric field gradient is defined with the largest proportion

Likewise, the high-energy transition process may cause the Auger effect, that can bring the core into higher ionization states.

From this one obtains the exponential case: For the total number of nuclei in the static state (c) follows: The initial occupation probabilities