Inverse Laplace Transform Approaches to βNMR Relaxation

Abstract Spin lattice relaxation is the simplest type of β NMR measurement. The usual approach to implant a pulse hyperpolarized nuclei and monitor time-resolved β-decay asymmetry, yielding ensemble average spin-lattice relaxation. In case, asymmetry decays exponentially with characteristic time constant T 1 , but this ideal rarely obtained in practice. most data, more complicated. This can be result multiple crystallographic sites for implanted probe each having distinct . sample may also inhomogeneous due to: impurities or defects (including interfaces that are particularly important thin films), intrinsic phase separation, or, if it glass. There background signal from ions stop outside sample. general problem has been ad hoc development an appropriate model avoids overparametrization. Given prevalence complicated relaxation, crucial develop systematic modelling. decomposition relaxing into exponentials is, however, mathematically ill-posed problem[1]. feature unavoidable, there number methods accommodate noisy real-world including nuclear spin relaxation[2, 3, 4]. Here we demonstrate one best commonly used methods, Tikhonov regularization inverse Laplace transform, implemented particular features importantly strong dependence statistical uncertainty stemming radioactive lifetime probe.