Data on Stark Broadening of N V Spectral Lines

Abstract

A data set on Stark broadening parameters defining the Lorentzian line profile (spectral line widths and shifts) for 31 multiplets of four-times-charged nitrogen ion (N V), with lines broadened by impacts with electrons (e), protons (p), He II ions, $\alpha$ particles (He III), and B III, B IV, B V, and B VI ions, is given. The above-mentioned data have been calculated within the frame of the semiclassical perturbation theory, for temperatures from 50,000 K to 1,000,000 K, and densities of perturbers from 10¹⁵ cm⁻³ up to 10²¹ cm⁻³. These data are, first of all, of interest for diagnostics and modeling of laser-driven plasma in experiments and investigations of proton–boron fusion, especially when the target is boron nitride (BN). Data on Stark broadening by collisions with e, p, He II ions, and $\alpha$ particles are useful for the investigation of stellar plasma, in particular for white dwarf atmospheres and subphotospheric layer modeling.

Dataset: Supplementary Files

Dataset License: CC-BY 4.0

1. Introduction

Knowledge about profiles of spectral lines broadened by collisions with charged particles in their surroundings (Stark broadening) may be useful in many different research topics. First of all, it may be useful for diagnostics, analysis, and modeling of stellar atmospheres and spectra, laser-produced plasmas, plasmas in laboratory, technology, and investigation of plasma in fusion experiments.

Among investigations of thermonuclear fusion, of particular interest is the proton–boron fusion [1], since it is aneutronic, producing three alpha particles during the fusion of a proton and a boron atom nucleus into a carbon nucleus. Since there are no neutrons, the process does not induce radioactivity in the environment. One of the targets used in such experiments is boron nitride (BN) [2]. We note that for optimization of the fusion yield, one needs diagnostics of plasma [3], so that Stark broadening parameters for spectral lines of four-times-charged nitrogen ion (N V) are useful. Since in the corresponding plasma, boron ions in different ionization stages like B IV, B V, and B VI have been found [4], the broadening of N V spectral lines by boron ions in various ionization stages is useful.

Spectral lines of N V have been found in the spectra of a number of stars [5,6,7,8,9,10,11,12], confirming the need for their Stark broadening parameters. They can be used for their atmosphere modeling, interpretation, and synthesis of stellar spectra, for calculation of the line absorption coefficients and a number of quantities where they enter.

With the help of the semiclassical perturbation theory [13,14], Stark widths and shifts, for 31 multiplets of four-times-charged nitrogen ion (N V), broadened by impacts with important charged particles in proton–boron fusion plasma, $\alpha$ particles, B III, B IV, B V, and B VI ions, are calculated for a set of temperatures and perturber densities.

Earlier, we published [15]; Stark widths and shifts for these 31 N V multiplets, for spectral lines broadened by collisions with electrons, protons, and ionized helium (He II). There, only values for four temperatures have been given (50,000 K, 100,000 K, 200,000 K, and 500,000 K), because of the request of an anonymous reviewer to minimize the data set. Since this is neither enough for a good interpolation, especially for the shift, nor for the purposes of proton–boron fusion, we calculated here the additional data for temperatures 80,000 K (for better interpolation) and 1,000,000 K (for proton–boron fusion), and added the data from Ref. [15], including the results calculated here for two additional temperatures, to the present data set of N V Stark broadening parameters for collisions with $\alpha$ particles, B III, B IV, B V, and B VI ions.

Here, all these data are given online, in computer-readable form.

We want to draw attention here that for proton–boron fusion with BN target are of interest and Refs. [16,17], where the broadening of N V by collisions with N III, N IV, N V, N VI, and N VII ions, has been reported for 3s²S - 3p²P^o transition.

2. The Semiclassical Perturbation Method

The semiclassical perturbation theory [13,14], used here for the calculation of Stark full widths at half-intensity maximum (FWHM) and shifts, has been reviewed many times, so only basic formulas will be presented to explain how Stark broadening parameters have been calculated. FWHM (W) and shift (d) of an isolated spectral line of a non-hydrogenic ion are expressed as

$$\begin{array}{c}\hfill W=N\int vf\left(v\right)dv\left(\sum _{i^{\prime }\ne i}{\sigma }_{i{i}^{\prime }}\left(v\right)+\sum _{f^{\prime }\ne f}{\sigma }_{f{f}^{\prime }}\left(v\right)+{\sigma }_{el}\right)\end{array}$$

$$\begin{array}{c}\hfill d=N\int vf\left(v\right)dv{\int }_{R_3}^{R_D}2\pi \rho d\rho sin\left(2{\phi }_p\right).\end{array}$$

(1)

With i and f are denoted the initial and final levels of the considered transition, $i^{\prime }$ and $f^{\prime }$ are the corresponding perturbing levels, $N$ is the perturber density, $\upsilon$ velocity of the perturber, $f\left(\upsilon \right)$ the Maxwellian velocity distribution, and $\rho$ is the impact parameter of the perturbing charged particle.

The inelastic cross-sections ${\sigma }_{k{k}^{\prime }}\left(\upsilon \right)$, $k=i,f$ are calculated with the help of an integral of the transition probability $P_{k{k}^{\prime }}(\rho ,\upsilon )$, over the impact parameter $\rho$:

$$\sum _{k^{\prime }\ne k}{\sigma }_{k{k}^{\prime }}\left(\upsilon \right)={\displaystyle \frac{1}{2}}\pi R_1^2+{\int }_{R_1}^{R_D}2\pi \rho d\rho \sum _{k^{\prime }\ne k}{P}_{k{k}^{\prime }}(\rho ,\upsilon ).$$

(2)

The expression for elastic collisions (${\sigma }_{el}$) and resonances (${\sigma }_r$—[18]) is

$$\begin{array}{c}\hfill {\sigma }_{el}=2\pi R_2^2+{\int }_{R_2}^{R_D}2\pi \rho d\rho {sin}^2\delta +{\sigma }_r,\end{array}$$

$$\delta ={({\phi }_p^2+{\phi }_q^2)}^{{\displaystyle \frac{1}{2}}}.$$

(3)

Here, ${\phi }_p$ ($r^{-4}$) and ${\phi }_q$ ($r^{-3}$), are phase shifts due to the polarization and quadrupolar potential [13]. The cut-offs $R_1$, $R_2$, $R_3$, and $R_D$ are described in [14]. We note as well that, for positively charged particles, trajectories are different, since the Coulomb force is repulsive.

3. Data Description

A data set containing Stark widths and shifts of 31 multiplets of four-times-charged nitrogen ion (N V), with spectral lines broadened by impacts with $\alpha$ particles, B III, B IV, B V, and B VI ions, has been calculated by using the semiclassical perturbation theory [13,14]. Calculations have been performed for the following temperatures T: 50,000 K, 80,000 K, 100,000 K, 200,000 K, 500,000 K, and 1,000,000 K, and perturber densities from 10¹⁵ cm⁻³ up to 10²¹ cm⁻³. The data set presented here is of importance for proton–boron fusion investigations, first of all when the boron nitride (BN) target is irradiated by a laser.

We have previously calculated [15] Stark widths and shifts for these 31 N V multiplets, for spectral lines broadened by impacts with e, p, and ionized helium. In this article, calculations have been performed for 50,000 K, 100,000 K, 200,000 K, and 500,000 K, having in view atmospheres of white dwarfs and the modeling of subphotospheric layers. However, electrons and protons are very important and, for proton–boron fusion, temperatures higher than 500,000 K are also useful. Consequently we have recalculated these data for temperatures up to 1,000,000 K and added them to the present data set of N V Stark broadening parameters for collisions with $\alpha$ particles, B III, B IV, B V, and B VI ions.

The atomic energy levels of N V, which we used for calculations of Stark broadening parameters, have been taken from the NIST database [19].

In the tables that are in the Supplementary Material, the quantity C [20], which is useful to examine the validity of the isolated line approximation, has been provided. If divided by the spectral line width (FWHM − W), we obtain the maximal perturber density where the isolated line approximation is valid.

4. User Notes

We want to draw attention to the fact that the wavelengths, which are listed in the Supplementary Material, have been calculated from atomic energy levels, which are used as input data for the calculation of Stark widths and shifts. Consequently, they may differ from the wavelengths that are presented in the NIST database. If one needs to replace wavelength from the tables in the Supplementary material, for example, for the wavelength of a particular line within the multiplet, or from the NIST database, the following formula can be used for the width (and the analogous one for the shift):

$$W_{cor}={\left({\displaystyle \frac{{\lambda }_{new}}{\lambda }}\right)}^{2}W.$$

(4)

Here, $W_{cor}$ is the corrected width, ${\lambda }_{new}$ is the wavelength, e.g., from NIST, while $\lambda$ and W are the calculated wavelength and width (FWHM) from the tables in the Supplementary material.

Stark width (FWHM) and shift determine the Lorentzian profile $F\left(\omega \right)$, where $\omega$ is the angular frequency:

$$\begin{array}{c}\hfill F\left(\omega \right)={\displaystyle \frac{W/\left(2\pi \right)}{{(\omega -{\omega }_{if}-d)}^2+{(W/2)}^2}}.\end{array}$$

(5)

Here

$$\begin{array}{c}\hfill {\omega }_{if}={\displaystyle \frac{E_i-E_f}{\hslash }}\end{array}$$

and $E_i$ and $E_f$ are the energies of the initial and final atomic energy levels.

5. Conclusions

We provide here a computer-readable data set, which is online as the Supplementary Material, containing Stark full widths at half-intensity maximum and shifts for 31 multiplets of N V, calculated by using the semiclassical perturbation method [13,14]. The obtained results for N V multiplets with lines broadened by collisions with e, p, He II, He III, B III, B IV, B V, and B VI ions are presented as a function of temperatures and densities of the above-mentioned perturbing particles.

The results presented in this article may be useful for proton–boron fusion experiments, especially when a boron nitride (BN) target, irradiated by a laser, is used. The data on broadening by collisions with electrons, protons, and He II and He III ions (alpha particles) may be useful for investigations of dense and hot stars, as for example white and pre-white dwarfs, since these data may be of interest for abundance determination, as well as for radiative transfer and opacity investigations and stellar atmosphere modeling, for identification of stellar spectral lines, and also for analysis and synthesis of stellar spectra.