High precision analytical description of the allowed β spectrum shape

Leendert Hayen, Nathal Severijns, Kazimierz Bodek, Dagmara Rozpedzik, and Xavier Mougeot
Rev. Mod. Phys. 90, 015008 – Published 23 March 2018
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Abstract

A fully analytical description of the allowed β spectrum shape is given in view of ongoing and planned measurements. Its study forms an invaluable tool in the search for physics beyond the standard electroweak model and the weak magnetism recoil term. Contributions stemming from finite size corrections, mass effects, and radiative corrections are reviewed. Particular focus is placed on atomic and chemical effects, where the existing description is extended and analytically provided. The effects of QCD-induced recoil terms are discussed, and cross-checks were performed for different theoretical formalisms. Special attention was given to a comparison of the treatment of nuclear structure effects in different formalisms. Corrections were derived for both Fermi and Gamow-Teller transitions, and methods of analytical evaluation thoroughly discussed. In its integrated form, calculated f values were in agreement with the most precise numerical results within the aimed for precision. The need for an accurate evaluation of weak magnetism contributions was stressed, and the possible significance of the oft-neglected induced pseudoscalar interaction was noted. Together with improved atomic corrections, an analytical description was presented of the allowed β spectrum shape accurate to a few parts in 104 down to 1 keV for low to medium Z nuclei, thereby extending the work by previous authors by nearly an order of magnitude.

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  • Received 1 February 2017

DOI:https://doi.org/10.1103/RevModPhys.90.015008

© 2018 American Physical Society

Physics Subject Headings (PhySH)

Nuclear Physics

Authors & Affiliations

Leendert Hayen* and Nathal Severijns

  • Instituut voor Kern-en Stralingsfysica, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium

Kazimierz Bodek and Dagmara Rozpedzik

  • Marian Smoluchowski Institute of Physics, Jagiellonian University, 30-348 Cracow, Poland

Xavier Mougeot

  • CEA, LIST, Laboratoire National Henri Becquerel, F-91191 Gif-sur-Yvette, France

  • *leendert.hayen@kuleuven.be

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Issue

Vol. 90, Iss. 1 — January - March 2018

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