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Huang, W.J., Audi, G., Wang, M., Kondev, F.G., Naimi, S. and Xu, X. (2017) The Ame2016 Atomic Mass Evaluation, (I). Evaluation of Input Data; and Adjustment Procedures. Chinese Physics C, 41, Article ID: 030002.

has been cited by the following article:

• TITLE: Integral Equations in Neutrino Mass Searches from Beta Decay

  AUTHORS: Thomas M. Semkow, Xin Li

  KEYWORDS: Fredholm Equation, Abel Equation, Heaviside Function, Heavy Neutrino

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.7 No.1, January 10, 2019

  ABSTRACT: A new mathematical model for elucidating neutrino mass from beta decay is proposed. It is based upon the solutions of transformed Fredholm and Abel integral equations. In principle, theoretical beta-particle spectra can consist of several neutrino-mass eigenstates. Integration of the beta spectrum with a normalized instrumental response function results in the Fredholm integral equation of the first kind. This equation is then transformed to yield a solution in a form of superposition of Heaviside step-functions, one for each neutrino mass eigenstate. A series expansion leading to matrix linear equations is then derived to solve the transformed Fredholm equation. Another approach is derived when the theoretical beta spectrum is obtained by a separate deconvolution of the observed spectrum. It is then proven that the transformed Fredholm equation reduces to the Abel integral equation. The Abel equation has a general integral solution, which is proven in this work by using a specific equation for the beta spectrum. Several examples of numerical solutions of the Abel equation are provided, which show a fractional sensitivity of about 10-3for subtle neutrino eigenstate searches and can distinguish from the beta-spectrum discrepancies, such as minute shape and energy nonlinearities.