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SUMMARY:Inverse Laplace Transform Approaches to $\\beta$NMR Relaxation
DTSTART;VALUE=DATE-TIME:20220830T164000Z
DTEND;VALUE=DATE-TIME:20220830T170000Z
DTSTAMP;VALUE=DATE-TIME:20220826T120654Z
UID:indico-contribution-3797@indico.stfc.ac.uk
DESCRIPTION:Speakers: Andrew MacFarlane (UBC)\, Derek Fujimoto (University
  of British Columbia)\nSpin lattice relaxation is the simplest type of $\\
 beta$NMR measurement. The usual approach is to implant a pulse of hyperpol
 arized nuclei and monitor the time-resolved $\\beta$-decay asymmetry\, yie
 lding the ensemble average spin-lattice relaxation. In the simplest case\,
  the asymmetry decays exponentially with a characteristic time constant $T
 _1$\, but this ideal is rarely obtained in practice. In most data\, the re
 laxation is more complicated. This can be the result of multiple crystallo
 graphic sites for the implanted probe each having a distinct $T_1$. The sa
 mple may also be inhomogeneous due to: impurities or defects (including in
 terfaces important for thin films)\; intrinsic phase separation\; or\, if 
 it is a glass. There may also be a background signal from probe ions that 
 stop outside the sample. The general approach to this problem has been the
  *ad hoc* development of an appropriate relaxation model that avoids overp
 arametrization.\n\nGiven the prevalence of more complicated relaxation\, i
 t is crucial to develop a *systematic* approach to relaxation modelling. T
 he decomposition of a relaxing signal into exponentials is\, however\, a m
 athematically ill-posed problem$^1$. This feature is intrinsic and unavoid
 able\, but there are a number of methods to accommodate it for noisy real-
 world data\, including nuclear spin relaxation$^2$\n\nHere we demonstrate 
 regularization methods for the inverse Laplace transform adapted to the pa
 rticularities of $\\beta$NMR relaxation data\, most importantly the strong
  time dependence of the statistical uncertainty stemming from the radioact
 ive lifetime of the probe.\n\n$^1$ see Istratrov et al\, Rev. Sci. Instr.7
 0\, 1233 (1999)\n$^2$ Spencer et al\, NMR in Biomedicine 33\, e4315 (2020)
 \; Singer et al\, PRB 101\, 174508 (2020).\n\nhttps://indico.stfc.ac.uk/ev
 ent/53/contributions/3797/
LOCATION:Science and Technology Campus\, University of Parma
URL:https://indico.stfc.ac.uk/event/53/contributions/3797/
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