Self-consistent calculations for atomic electron capture

Abstract

We present a comprehensive investigation of electron capture (EC) ratios spanning a broad range of atomic numbers. The study employs a self-consistent computational method that incorporates electron screening, electron correlations, overlap and exchange corrections, as well as shake-up and shake-off atomic effects. The electronic wave functions are computed with the Dirac-Hartree-Fock-Slater (DHFS) method, chosen following a systematic comparison of binding energies, atomic relaxation energies and Coulomb amplitudes against other existing methods and experimental data. A novel feature in the calculations is the use of an energy balance employing atomic masses, which avoids approximating the electron total binding energy and allows a more precise determination of the neutrino energy. This leads to a better agreement of our predictions for capture ratios in comparison with the experimental ones, especially for low-energy transitions. We expand the assessment of EC observables uncertainties by incorporating atomic relaxation energy uncertainties, in contrast to previous studies focusing only on Q-value and nuclear level energies. Detailed results are presented for nuclei of practical interest in both nuclear medicine and exotic physics searches involving liquid Xenon detectors (${}^{67}\mathrm{Ga}$, ${}^{111}\mathrm{In}$, ${}^{123}\mathrm{I}$, ${}^{125}\mathrm{I}$ and ${}^{125}\mathrm{Xe}$). Our study can be relevant for astrophysical, nuclear, and medical applications.

arXiv comment16 pages, 9 figures, 4 tables

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• Low-Mass Dark Matter Search with the DarkSide-50 Experiment
• DARWIN: towards the ultimate dark matter detector
• Projected WIMP sensitivity of the LUX-ZEPLIN (LZ) dark matter experiment
• Projected WIMP Sensitivity of the XENONnT Dark Matter Experiment
• PandaX-II Constraints on Spin-Dependent WIMP-Nucleon Effective Interactions
• Electron capture in stars
• Light WIMP search in XMASS
• Double-Weak Decays of ${}^{124}$Xe and ${}^{136}$Xe in the XENON1T and XENONnT Experiments
• Development of holmium-163 electron-capture spectroscopy with transition-edge sensors
• Extending light WIMP searches to single scintillation photons in LUX
• Search for inelastic scattering of WIMP dark matter in XENON1T
• Exchange correction for allowed $\beta$-decay

Cited by in corpus (3)

• Theoretical analysis and predictions for the double electron capture of ${}^{124}$Xe
• High-precision measurements of the atomic mass and electron-capture decay $Q$ value of ${}^{95}$Tc
• High-precision direct decay energy measurements of the electron-capture decay of ${}^{97}$Tc