AG Hofsäss - II- Institute of Physics

Perturbed γ-γ angular correlation spectroscopy (PAC)

The application of perturbed angular correlation (PAC) has derived from nuclear solid state physics. The PAC technique is similar to Mößbauer spectroscopy (MS) and Nuclear Magnetic Resonance (NMR), where information about the microscopic structure of solids can be obtained by hyperfine interactions.

This method uses radioactive probe nuclei, implanted or diffuse in solids, which decay via a γ-γ cascade over an intermediate state. In contrast to the Mößbauer effect, where the energetic shift of the gammas depopulating the excited state is measured, one determines the variation in time of the gamma emission characteristics. A basic requirement is an anisotropic emission from the isomeric probe state to achieve a precession of the angular correlation.

At the site of a probe nucleus the hyperfine interaction arises from the surrounding electric and/or magnetic fields. A non cubic charge distribution around the probe generates an electric field gradient (EFG), which interacts with the nuclear electric quadrupole moment Q and leads to a level splitting. Because the EFG is short ranged with a 1/r3 dependence, its strength Vzz (= largest component of the diagonalized 3x3 tensor) and symmetry η = (Vxx - Vyy) / Vzz are characteristic parameters for each microscopic structure.

PAC probe nuclei

The most common used radioactive probe nuclei are 111In and 181Hf. The PAC isotope 111In has reached similar importance like 57Co for Mößbauer spectroscopy.

Radioactive isotopes must fulfil special requirements to use them for PAC spectroscopy:

  • decay by γ-&gamma, cascade with population and depopulation of an intermediate state
  • high anisotropy of angular correlation
  • existence of an intermediate state with adequate lifetime between 10 nanoseconds and 1 microsecond
  • state should feature a suitable strong quadrupole moment in terms of a detectable electric quadrupole interaction and in case of magnetic interaction a suitable strong magnetic dipole moment ?N
  • easy handling of parent nuclide

In Göttingen PAC experiments are performed with 111In as probes. This isotope decays via electron capture to the stable state 111Cd with a convenient half life of nearly three days.

Experimental Setup

In perturbed angular correlation spectroscopy one records the coincidence counting rates as a function of time between both gammas of the same cascade and not as a function of angle. So the main point of an PAC apparatus is a precise time measurement.
Standard configuration is a four detector setup in 90° symmetry. Each detector is able to register both different gammas and so gives start and also stop signals. This leads to eight 90°- and four 180°-coincidence spectra. With this start-stop-principle lifetime measurements of the intermediate state are performed, whose exponential decays are temporally modulated due to hyperfine interactions.
A common analog PAC setup is the so-called slow-fast arrangement. Each detector provides a positive ("slow") signal, which is proportional to the gamma energy but features a time uncertianty. To obtain a precise time measurement a second negative ("fast") signal with a rapid rising edge is tapped directly from the anode. Both signaltypes must be process separately from each other, as it is shown in the figure below.

A recent development is the full digital PAC spectroscopy which utilizes fast scintillation LaBr detectors, fast photomultipliers and fast digitizers, followed by a comepletly software controlled data acquisition, energy analysis and coincidence analysis.

PAC experimental setup

Schematic diagram of an analog slow-fast PAC spectrometer. Triangles symbolize amplification units and semi-circles coincidence modules.


For detailed information the reader is referred to:
H. Frauenfelder, R. M. Steffen: Alpha-, beta- and gamma-ray spectroscopy; edited by K. Siegbahn, North Holland Publishing, Vol. II, Amsterdam (1965)
R. M. Steffen, K. Alder: The electromagnetic interaction in nuclear spectroscopy; edited by W. D. Hamilton, North Holland Publishing, Amsterdam (1975)
Th. Wichert: Hyperfine interaction of Defects in Semiconductors; edited by G. Langouche, Elsevier, Amsterdam (1992)
G. Schatz, A. Weidinger: Nukleare Festkörperphysik; B. G. Teubner Verlag, 3. Auflage, Stuttgart (1997)