Electron density diagnostic for hot plasmas in coronal regime by using B-like ions

Line ratio of $3d-2p$ transition lines in boron-like spectra of Si X, S XII, Ar XIV and Fe XXII has been investigated. Collisional-radiative model calculations reveal that the line ratio is sensitive to the electron density in ranges of $n_{\rm e}=4.0\times10^7-3.0\times10^{10}$ cm$^{-3}$, $4.0\times10^8-3.0\times10^{11}$ cm$^{-3}$, $3.0\times10^9-4.0\times10^{12}$ cm$^{-3}$ and $2.0\times10^{12}-3.0\times10^{15}$ cm$^{-3}$, respectively. This complements the K-shell diagnostics of helium-like ions. By comparison between the prediction and the measured values, effective electron densities in the electron beam ion trap (EBIT) plasmas performed by Lepson and collaborators at Lawrence Livermore EBIT, are estimated to be $n_{\rm e}=3.4^{+0.8}_{-0.6}\times10^{10}$ cm$^{-3}$ and $5.6^{+1.0}_{-1.1}\times10^{10}$ cm$^{-3}$ for sulphur and argon plasmas. In case of argon, a good agreement is shown with the actual electron density derived from N VI K-shell spectrum. We further explore the $3d-2p$ transition lines of Si X and S XII in the stellar coronal spectra measured with the Low Energy Transmission Grating Spectrometer combined with High Resolution Camera on board the {\it Chandra X-ray Observatory}. The constrained electron densities show a good agreement with the those determined from C V and O VII K-shell spectra.