Electron Capture and Bound-State $\beta$ Decays in Ions and Plasma

We present a new theory describing the variation of electron capture and bound-state $\beta$-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 $\beta$-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.