page_title: Perturbed angular correlation
section_title: Theory
hierarchical_section_title: Perturbed angular correlation / Theory
caption_attribution_description: Deutsch: Übergang im KernEnglish: PAC-Spectroscopy: cascade with intermediate state.
context_page_description: 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 is used.
context_section_description: The first -quantum () will be emitted isotopically. Detecting this quantum in a detector selects a subset with an orientation of the many possible directions that has a given. The second -quantum () has an anisotropic emission and shows the effect of the angle correlation. The goal is to measure the  relative probability  with the detection of  at the fixed angle  in relation to . The probability is given with the angle correlation (perturbation theory):
  For a --cascade,  is due to the preservation of parity:
  Where  is the spin of the intermediate state and  with  the multipolarity of the two transitions. For pure multipole transitions, is .
   is the anisotropy coefficient that depends on the angular momentum of the intermediate state and the multipolarities of the transition.
  The radioactive nucleus is built into the sample material and emits two -quanta upon decay. During the lifetime of the intermediate state, i.e. the time between  and , the core experiences a disturbance due to the hyperfine interaction through its electrical and magnetic environment. This disturbance changes the angular correlation to:
   is the perturbation factor. Due to the electrical and magnetic interaction, the angular momentum of the intermediate state  experiences a torque about its axis of symmetry. Quantum-mechanically, this means that the interaction leads to transitions between the M states. The second -quantum () is then sent from the intermediate level. This population change is the reason for the attenuation of the correlation.
  The interaction occurs between the magnetic core dipole moment  and the intermediate state  or/and an external magnetic field . The interaction also takes place between nuclear quadrupole moment and the off-core electric field gradient .
caption: General γ-γ-cascade with life-time 
    
      
        
          
            τ
            
              N
            
          
        
      
      {\displaystyle \tau _{N}}
    
   of the intermediate state.
exif: {}