Calculation of the rate of nuclear excitation by electron transition in an ${}^{84m}\mathbf{Rb}$ plasma under the hypothesis of local thermodynamic equilibrium using a multiconfiguration Dirac-Fock approach

One promising candidate for the first detection of nuclear excitation in plasma is the 463-keV, 20.26-min-lifetime isomeric state in ${}^{84}\mathrm{Rb}$, which can be excited via a 3.5-keV transition to a higher lying state. According to our preliminary calculations, under specific plasma conditions, nuclear excitation by electron transition (NEET) may be its strongest excitation process. Evaluating a reliable NEET rate requires, in particular, a thorough examination of all atomic transitions contributing to the rate under plasma conditions. We report the results of a detailed evaluation of the NEET rate based on multiconfiguration Dirac Fock (MCDF) atomic calculations, in a rubidium plasma at local thermodynamic equilibrium with a temperature of 400 eV and a density of ${10}^{-2}\mathrm{g}/{\mathrm{cm}}^3$ and based on a more precise energy measurement of the nuclear transition involved in the excitation.

Figure 1

Partial level scheme of ${}^{84}\mathrm{Rb}$ [9].

Figure 2

Typical spectrum recorded during the ELSA experiment. Europium and barium sources were counted together with the rubidium sample.

Figure 3

Typical spectrum recorded during the Orsay experiment. The line at 248 keV is the $3^{-}\to 2^{-}$ transition to the ground state of ${}^{84}\mathrm{Rb}$. Inset: Zoom-in centered on the $5^{-}\to 3^{-}\gamma$ line of interest.

Figure 4

NEET rate for the $6^{-}\to 5^{-}$ transition calculated with ISOMEX as a function of the plasma temperature for the $M1$ and $E2$ components. The plasma density is ${10}^{-2}\mathrm{g}/{\mathrm{cm}}^3$.

Figure 5

ISOMEX total excitation rate (including photoexcitation, nuclear excitation by electron capture, and inelastic electron scattering) and NEET rate as functions of the average charge state in an ${}^{84m}\mathrm{Rb}$ plasma at a density of ${10}^{-2}\mathrm{g}/{\mathrm{cm}}^3$.

Figure 6

Charge state distribution of an ${}^{84}\mathrm{Rb}$ plasma at $T=400$ eV and $\rho ={10}^{-2}\mathrm{g}/{\mathrm{cm}}^3$ calculated with the FLYCHK code under the LTE hypothesis [44].

Figure 7

NEET rate as a function of the plasma temperature for different values of the maximal principal quantum number used in the configuration description. The plasma density is ${10}^{-2}\mathrm{g}/{\mathrm{cm}}^3$.

Figure 8

$M1$ NEET rate as a function of the uncertainty $\mathrm{\Delta }$. Calculations with the MCDF and ISOMEX codes for a Rb plasma at $T=400$ eV and $\rho ={10}^{-2}\mathrm{g}/{\mathrm{cm}}^3$. Transitions between shells $n\in \left[\right[4,8\left]\right]$ to $n=2$ for charge states ranging from $Q={29}^{+}$ to $Q={34}^{+}$ are considered.

Figure 9

$M1$ NEET rate as a function of the energy uncertainty $\mathrm{\Delta }$ for an ${}^{84m}\mathrm{Rb}$ plasma at $T=400$ eV and $\rho ={10}^{-2}\mathrm{g}/{\mathrm{cm}}^3$. The NEET rate of charge states (a) $Q={30}^{+}$, (b) $Q={31}^{+}$, and (c) $Q={32}^{+}$ and the total NEET rate (for $Q={29}^{+}$ to $Q={34}^{+}$) are plotted.

Figure 10

$M1$ NEET rate for charge states (a) $Q={30}^{+}$, (b) $Q={31}^{+}$, and (c) $Q={32}^{+}$ as a function of the energy uncertainty $\mathrm{\Delta }$ for an ${}^{84m}\mathrm{Rb}$ plasma at $T=400$ eV and $\rho ={10}^{-2}\mathrm{g}/{\mathrm{cm}}^3$. The transitions which contribute the most to the total NEET rate for each charge state are indicated.