Revisiting electron-capture decay for Galactic cosmic-ray data

TL;DR

This paper reevaluates electron-capture decay in Galactic cosmic rays using a multi-level electron-attachment transport framework within diffusion and leaky-box models. It provides analytical and semi-analytical solutions for EC decay across multiple attached-electron states, compares diffusion-based and leaky-box approaches, and assesses sensitivities to attachment/stripping cross-sections. The study finds that, after accounting for energy losses and cross-section uncertainties, EC decay has at most percent-level effects on current IS/TOA fluxes, with the two-level approximation generally sufficient except for a few high-$Z$, intermediate-lived isotopes. It also analyzes the detectability of EC decay in existing data from Voyager, ACE-CRIS, AMS-02, CALET, and TIGER-inspired missions, identifying $^{51}$Cr, $^{55}$Fe, and $^{57}$Co as the most promising candidates. The work highlights the need for improved low-energy cross-sections, inclusion of energy losses, and expanded high-$Z$ measurements to exploit EC clocks as probes of Galactic CR transport and nucleosynthesis history.”

Abstract

Electron-capture (EC) unstable species in Galactic cosmic rays constrain the time elapsed between nucleosynthesis and acceleration. They have also been advocated as tracers of reacceleration or gas inhomogeneities during their transport. The number of EC-unstable species grows with mass, with an expected EC-decay impact more important for larger atomic number and lower energy. We revisit the modelling of EC decay and its detectability in the context of recent unmodulated low-energy (Voyager) and high-precision data for heavy (AMS-02) and very-heavy nuclei (ACE-CRIS, CALET and Super-TIGER). We solve the transport equation for a multi-level configuration (up to any number of electrons attached) in the diffusion and leaky-box models. Their decayed fractions are found to be qualitatively similar but with very different absolute fluxes. We check that the standard two-level approximation, wherein the cosmic-ray nucleus is fully ionised or with one electron attached, is sufficient for most situations. We find that the impact of EC-decay is negligible in current data, except possibly for fluxes or ratios involving $^{51}$Cr, $^{55}$Fe, and Co. These conclusions are robust against significant uncertainties in the attachment and stripping cross-sections. This first analysis calls for further investigation, as several forthcoming projects (e.g., TIGERISS) are targeting $Z>30$ cosmic rays.

Figures (7)

• Figure 1: Timescales for the processes listed in Table \ref{['tab:timescales']}, as a function of the atomic number $Z$, for three energies (from left to right). The attachment time (pink dotted line) is broken down into the radiative (thin-dotted grey line) and non-radiative (thick-dotted grey line) contributions, see \ref{['app:sig_att']}. The black dots represent the effective decay time ($\gamma\,\tau_{\rm EC}$) for each EC-unstable isotopes reported in Table \ref{['tab:EC clocks']} (highlighted species are compared to CR data in Sect. \ref{['sec:sensibility_data']}).
• Figure 2: Colour-coded EC-decayed fraction, Eq. \ref{['eq:dec_frac']}, in the $t_{1/2}$--$Z$ plan for the 1D-DM (top) and LBM (middle), for three IS energies. The two near-vertical lines separate short-lived, intermediate-lived, and long-lived isotopes (see text for details). Symbols indicate existing EC-unstable isotopes (see Table \ref{['tab:EC clocks']}), highlighting the names of those for which CR data exist (see Sect. \ref{['sec:sensibility_data']}).
• Figure 3: Same axes and configuration as in Fig. \ref{['fig:dec_frac_IS']}, but now the colour scale shows the ratio of the LBM to the 1D-DM calculation, defined in Eq. \ref{['eq:def_ratio']}. The size of the circles encodes the decayed fraction $f$ of the EC-unstable isotopes.
• Figure 4: Same as bottom panel of Fig. \ref{['fig:dec_frac_IS']}, but for the ratio ${\cal R}^{\sigma_{\rm new}}$, see Eq. \ref{['eq:def_ratio_err']}, when halving the attachment (top) and doubling the stripping cross-sections (bottom).
• Figure 5: Same as in previous figures, but showing $n$ at which convergence is reached (top row), and the relative difference between the literature approximation $n=2$ and the converged solution (bottom row); both calculations are for the 1D-DM.