Electron Capture and Bound-State $β$ Decays in Ions and Plasma

TL;DR

The paper develops a general two-component framework to predict in-plasma beta-decay rates by separating atomic configuration effects from plasma ionization dynamics. It extends the Takahashi–Yokoi model by replacing electron radial wavefunctions with Coulomb amplitudes and adding correction factors, then combines configuration-dependent rates $\lambda^{*}(ij)$ with charge-state/level probabilities $p_{ij}$ to obtain $\lambda^{*}=\sum_{ij} p_{ij}\lambda^{*}(ij)$. The method is validated against storage-ring data for isotopes such as $^{163}$Dy, $^{140}$Pr and $^{142}$Pm and yields plausible solar-core enhancements for $^{7}$Be (e.g., $\lambda^{*}_{tot}/\lambda^{*}_{fc}\approx 1.26$); in laboratory magnetoplasmas like PANDORA, orbital EC is strongly suppressed at higher $kT_{e}$, with IPD and radiation fields further modulating $\lambda^{*}$. This framework enables robust predictions of in-plasma decay rates across stellar and laboratory environments and supports experimental benchmarking of fundamental plasma-nuclear coupling physics.

Abstract

We present a new theory describing the variation of electron capture and bound-state $β$-decays in atomic ions and (non) local thermodynamic equilibrium ((N)LTE) plasmas. We adopt the Takahashi-Yokoi nuclear model with added corrections to first calculate the decay rate for each atomic configuration of the isotope, and then evaluate the in-plasma decay rate by combining them with the charge state distribution (CSD) consistent with plasma density and temperature. Our approach expands the thermodynamic parameter space in which in-plasma $β$-decays can be studied, opening the possibility to validate the model in low-density laboratory magnetoplasmas before application to stellar nucleosynthesis. The model is explained using $^{7}$Be, and then applied to higher mass isotopes such as $^{140}$Pr$^{0+,57+,58+}$, $^{142}$Pm$^{0+,59+,60+}$ and $^{163}$Dy$^{66+}$. Our model is therefore amenable to isotopes in a wide range of masses, in both single charge state or in a plasma-generated CSD.

Figures (9)

• Figure 1: $^{7}$Be$\rightarrow^{7}$Li EC decay scheme, taken from ENSDF Tilley2002.
• Figure 2: $\Delta\epsilon^{ij,x}$ for different $j$ and $x=1s_{1/2},2s_{1/2}$ in (a) $^{7}\mathrm{Be}^{0,1+}$ and (b) $^{7}\mathrm{Be}^{2+,3+}$. No plot is shown for fully-ionised $^{7}\mathrm{Be}$ because it is void of electrons for capture. For sake of brevity, only a few levels in each ionisation stage are shown, but important levels are marked in the plots.
• Figure 3: Percentage change in decay rate with respect to neutral, ground state $^{7}$Be as a function of configuration $(ij)$ for (a) $i=0^{+},1^{+}$ and (b) $i=2^{+},3^{+}$. As in Fig. \ref{['Fig3']}, only a few levels per ionisation stage are shown for brevity, but important levels are marked. The split at $\mathrm{hy}1$ is due to different contributions from $m=1$ to the total capture rate depending on whether the electron is in lower or upper hyperfine level. The red diamond in (a) refers to $\delta\lambda^{*}(ij)$ of the true ground state of $^{7}$Be - $1s^{2}2s^{2}$ configuration.
• Figure 4: $^{7}$Be configuration-dependent $\lambda^{*}(ij)$ calculated using our model and DHF Taioli2022Simonucci2013Morresi2018.
• Figure 5: $\langle Z\rangle$ of $^{7}$Be as a function of $kT_{e}$ for $n_{e}=10^{12}\,\mathrm{cm^{-3}}$ (blue markers) and $n_{e}=10^{24}\,\mathrm{cm^{-3}}$ (red markers). The crossed, continuous black line represents a high-density plasma with no IPD correction.