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SUMMARY:Developments of analysis functions for $\\mu$SR time spectra which
  show intermediate shapes between Gaussian and Lorentzian
DTSTART;VALUE=DATE-TIME:20220829T164000Z
DTEND;VALUE=DATE-TIME:20220829T170000Z
DTSTAMP;VALUE=DATE-TIME:20220826T110026Z
UID:indico-contribution-3790@indico.stfc.ac.uk
DESCRIPTION:Speakers: Isao Watanabe (RIKEN)\nHow to choose analysis functi
 ons is a key matter to deduce the information in physics from the muSR res
 ults. For instance\, local magnetic fields at the muon site in the paramag
 netic state are well known to be coming from surrounding nuclear dipole mo
 ments. In this case\, the field distribution at the muon site becomes to b
 e the Gaussian distribution [1]. This Gaussian distribution typically occu
 rs when there are independent contributions from many magnetic sources wit
 h similar amount of contribution. On the other hand\, in case that\, one m
 agnetic spin\, which is located nearest to the muon\, tends to give a domi
 nant contribution\, the local field due becomes random and a different fie
 ld distribution appears at the muon site. For the dilute limit (effectivel
 y for concentrations less than 3~5 %)\, the field distribution becomes to 
 be Lorentzian [2]. \n   In our presentation\, we described the crossover f
 ield in terms of a convoluted function of Gaussian and Lorentzian. We deri
 ved the equation of the three-dimensional (3D) convolution in two ways. Th
 e first derivation uses the convolution integral starting directly in the 
 3D space. The other derivation starts from that of the one-dimensional (1D
 ) convolution and make it to be converted to the 3D form. From the latter\
 , we showed that the equation can be decomposed to a sum of three known co
 nvolutions. By applying the Fourier transform to this equation\, we achiev
 ed the correct relaxation function for the zero-field condition\, which wa
 s found to be given by a simple analytical equation. In addition\, we trie
 d to describe the intermediate analysis function under applied magnetic fi
 elds and under dynamic fluctuations based on the development of the zero-f
 ield intermediate analysis function. Finally\, we applied our developed an
 alysis function to some $\\mu$SR results to make sure its validity [3].\n\
 nhttps://indico.stfc.ac.uk/event/53/contributions/3790/
LOCATION:Science and Technology Campus\, University of Parma
URL:https://indico.stfc.ac.uk/event/53/contributions/3790/
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