Semiclassical Perturbation Formalism Research Articles

The Feshbach Resonances Applied to the Calculation of Stark Broadening of Ionized Spectral Lines: An Example of Interdisciplinary Research

In the present paper, we revisit the determination of Feshbach resonances in the elastic and fine-structure cross-sections of the spectral lines of ionized atoms colliding with electrons. The Gailitis approximation will be recalled and used to calculate the Feshbach resonances. A historical point of view will be used, emphasizing the interest of interdisciplinary research, with a back and forth between physics and astrophysics. First, the theory of Feshbach (arising at end of the 1950s and beginning of the 1960s) resonances will be briefly recalled and applied to the calculation of the cross-sections. In the beginning of the 1970s, the insertion of Feshbach resonances in spectroscopic diagnostics calculations permitted researchers to interpret the intensities of solar coronal lines. Then, in the middle of the 1970s, this gave rise to the idea of including the Feshbach resonances in the calculation of electron impact broadening (the so-called “Stark” broadening) of isolated spectral lines of ionized atoms. Finally, in the recent example of the Stark broadening of the Mo VI 5d D5/22−5p P°3/22 line, the S-matrices will be calculated using the semi-classical perturbation formalism and will be compared to those of the more recent quantum distorted wave formalism.

Stark broadening of Fe xxv spectral lines

ABSTRACT Stark broadening parameters, full widths at half-maximum of intensity and shifts for 18 spectral lines of Fe xxv, broadened by collisions with electrons, protons, and Fe xxvii ions, have been calculated using the impact semiclassical perturbation formalism for a grid of electron densities and temperatures of interest for neutron star atmospheres and their environment.

Stark broadening of Zn II spectral lines

ABSTRACT Stark broadening parameters, full widths at half intensity maximum, and shifts for 34 multiplets of singly charged zinc ion have been calculated using the impact semiclassical perturbation formalism. Stark broadening parameters due to collisions with electrons, protons, and helium ions have been obtained for a grid of electron densities and temperatures. The obtained results have been used to demonstrate the influence of Stark broadening mechanism on spectral lines of Zn II in stellar atmospheres.

Stark broadening of B iv spectral lines

Stark broadening parameters for 157 multiplets of helium like boron (B IV) have been calculated using the impact semiclassical perturbation formalism. Obtained results have been used to investigate the regularities within spectral series. An example of the influence of Stark broadening on B IV lines in DO white dwarfs is given.

Stark broadening of B IV lines for astrophysical and laboratory plasma research

Stark broadening parameters for 36 multiplets of B IV have been calculated using the semi-classical perturbation formalism. Obtained results have been used to investigate the regularities within spectral series and temperature dependence.

Stark shifts and transition probabilities within the Kr I spectrum

On the basis of 28 experimentally determined prominent neutral krypton (Kr i) line shapes (in the 5s–5p and 5s–6p transitions), we have obtained electron (de) and ion (di) contributions to the total Stark shifts (dt). Stark shifts are also calculated using the semiclassical perturbation formalism (SCPF) for electrons, protons and helium ions as perturbers up to 50 000 K electron temperatures. Transition probabilities of spontaneous emission (Einstein’s Ak, i values) have been obtained using the relative line-intensity ratio method. The separate electron (de) and ion (di) contributions to the total Stark shifts are presented, as well as the ion-broadening parameters, which describe the influence of the ion–dynamical effect on the shift of the line shape, for neutral krypton spectral lines. We made a comparison of our measured and calculated de data and compared both of these with other available experimental and theoretical de values.

Similarities in calculated stark broadening parameters of argon spectral lines

The similarities of the calculated Stark broadening parameters of four argon spectral lines within a spectral series 3p5→3p54p have been analyzed. The Stark broadening parameters have been calculated using Sahal-Bréchot theory within the semi-classical perturbation formalism. The dependeces of the Stark width and shift versus the effective quantum number have been presented.

Semi-classical Stark broadening calculations of HeI lines in a non-ideal plasma

New semi-classical collision functions are used to compute the inelastic contribution to the impact electronic total width, by considering three interaction potentials (Coulomb Debye, Cut-off, and Ion Sphere). Numerical results are calculated for the neutral helium 6678 A ($2^{1}\rm P\degr{-}3^{1}D$) and 5876 A ($2^{3}\rm P\degr{-}3^{3}\rm D$) visible lines. The lines corresponding to these transitions are isolated, and the plasma is weakly non-ideal for all temperatures and electronic densities of interest. For electronic collisions, semi-classical perturbation theory is sufficient and the impact approximation is well satisfied. The ion effects can be treated within the quasistatic approximation, and the quasistatic ionic contribution is dominated by the polarization (or quadratic) $r_{\rm p}^{-4}$-interaction. To consider both the electron and the ion effects, the microfield distributions and the complete reduced Stark profile of isolated line are calculated using different methods. The computed total widths corresponding to the three interaction potentials are compared to the available experimental widths and then approximated by appropriate formulae. The data we obtained provide an opportunity to test various approximations included in the semi-classical perturbation formalism. They are also of interest for stellar spectroscopic diagnosis in dense atmospheres (white dwarfs for instance).

Mg II 448.1 nm Spectral Line Stark Broadening Parameters

The Stark width (W) and shift (d) of the singly ionized magnesium (Mg II) 448.1 nm spectral line in 3d2D5/2–4f2F7/20 transition have been measured at a 16 900 K electron temperature and 1.35×1023 m-3 electron density in nitrogen plasma generated in an optically thin linear, low-pressure, pulsed arc discharge. They represent the first experimental results obtained at an electron temperature higher than 12 000 K. Magnesium atoms, as impurities in the driving gas, have been introduced by erosion from the pure magnesium bands fixed on the discharge electrodes providing conditions free of self-absorption. Our W and d have been compared to existing experimental and theoretical data. A good agreement was found between the results calculated by semiclassical perturbation formalism and our data, particulary in the case of the Stark shift.

Mg II spectral line broadening in helium, oxygen and argon-helium plasmas

Stark widths (W) and shifts (d) of the astrophysically very important six (279.0777, 279.5528, 279.7998, 280.2705, 292.8633 and 293.6510 nm) singly ionized magnesium (Mg II) spectral lines in helium, oxygen and argon-helium plasmas have been measured at electron temperatures between 30 000 and 52 300 K and electron densities between 1.2 × 10 23 and 1.65 × 10 23 m −3 . They are the first experimental results obtained at electron temperatures higher than 20 000 K. A linear, low-pressure, pulsed arc has been used as an optically thin plasma source. The magnesium atoms, as impurities in the driving gases, have been introduced by erosion from the pure magnesium bands fixed on the discharge electrodes. Our measured Stark width and shift values have been compared to the existing experimental and theoretical data. We have found a good agreement with W and d values calculated by the semiclassical perturbation formalism (SCPF).

Electron and ion contributions to the Ne I spectral line broadening

On the basis of the experimentally determined 26 prominent neutral neon (Ne I) line shapes (in the 3s–3p, 3s–3p′, 3s′–3p′, 3s′–3p and 3p–3d transitions) we have obtained electron (We) and ion (Wi) contributions to the total Stark width (Wt). Stark widths are also calculated using the semiclassical perturbation formalism for electrons and protons as perturbers up to 50 000 K electron temperatures. We made comparison of our measured and calculated We data and compared both of them with available experimental and theoretical We values.

Stark broadening parameters in singly and doubly ionized fluorine spectra

Stark widths (W) and shifts (d) of 5 singly ionized fluorine (F II) spectral lines within the 3s−3p, 3s � −3pand 3d−4f transitions and 5 doubly ionized fluorine (F III) spectral lines within the 3s−3p transition have been measured in a linear, low- pressure, pulsed arc discharge created in SF6 plasma at 30 400−33 600 K electron temperatures and at (2.75−2.80) × 10 23 m −3 electron densities. For Stark parameters of two F II and five F III lines there are no other experimental data. The widths and shifts have also been calculated using the semiclassical perturbation formalism (SCPF) (taking into account the impurity of energy levels, i.e. that the atomic energy levels are expressed as a mix of different configurations due to the configuration interaction). Calculations have been performed for temperatures between 5000 K and 100 000 K for the F II spectral lines and between 10 000 K and 300 000 K for the F III spectral lines for electrons, protons and helium ions as perturbers. Our measured and theoretical Stark parameters are compared with existing experimental and theoretical data. Tolerable agreement was found among them.

Mg II h and k lines Stark parameters

Stark widths (W) and shifts (d) of the astrophysically very important singly ionized magnesium (Mg II) resonance h and k (279.5528 and 280.2705 nm) spectral lines in the 3s–3p transition have been measured at a 26,000 K electron temperature and 1.1×1023 m−3 electron density in helium–oxygen plasma created in an optically thin linear, low-pressure, pulsed arc discharge. The magnesium atoms, as impurities in the driving gas, have been introduced by erosion from the pure magnesium bands fixed on the discharge electrodes providing conditions free of the self-absorption in the resonance h and k lines. Besides, the W and d values of the 279.0777 nm and 279.7998 nm Mg II lines in the 3p–3d transition have also been measured. Our W and d have been compared to the existing experimental and theoretical data. Good agreement was found with the results calculated by the semiclassical perturbation formalism, especially in the case of the Stark widths.

Experimental and calculated Stark widths within the Kr I spectrum

On the basis of the precisely recorded 20 neutral krypton (Kr I) line shapes (in the 5s-5p and 5s-6p transitions), we have obtained the basic plasma parameters, i.e., electron temperature (T) and electron density (N) using our line deconvolution procedure in a plasma created in a linear, low-pressure, pulsed arc discharge operated in krypton. The mentioned plasma parameters have also been measured using independent experimental diagnostics techniques. Agreement has been found among the two sets of the obtained parameters. This recommends our deconvolution procedure for plasma diagnostical purposes, especially in astrophysics where direct measurements of the main plasma parameters (T and N) are not possible. On the basis of the observed asymmetry of the Stark broadened line profile, we have obtained not only its ion broadening parameter (A) which is caused by influence of the ion-microfield over the line broadening mechanism but also the influence of the ion-dynamic effect (D) over the line shape. The separate electron (W(e)) and ion (W(i)) contributions to the total Stark width, which have not been measured so far, have also been obtained. Stark widths are calculated using the semiclassical perturbation formalism for electrons, protons, and helium ions as perturbers.

Stark broadening parameters in the S III spectrum

Stark widths and shifts of astrophysically important 10 doubly ionized sulfur (S III) spectral lines (within the 3d-4p and 4s-4p transitions) have been measured in a SF 6 plasma created in the linear, low-pressure, pulsedarc discharge at about 35 000 K electron temperature and about 2.8 x 10 2 3 m - 3 electron density. The widths and shifts have been calculated using the semiclassical perturbation formalism (SCPF) (taking into account the impurity of energy levels, i.e. that the atomic energy levels are expressed as a mix of different configurations due to the configuration interaction), modified semiempirical (SEM) approximation, simplified semiclassical theory (G) and its modification (GM) taking into account new energy level values. Calculations have been performed for electron temperatures between 10000 K and 150000 K for electrons, protons and helium ions as perturbers. The measured and calculated S III shifts present the first published data in this field.

Stark shifts and transition probabilities in Si III and Si IV spectra

Stark shifts of nine doubly charged (Si III)and six triply charged (Si IV) siliconion spectral lines have been measured in a linear, low-pressure, pulsed arc operated in O2 and SF6 discharges. Si III Stark shift values have been also calculated using the semiclassical perturbation formalism (SCPF) for electrons, protons and helium ions as perturbers. Transition probabilities of the spontaneous emission (Einstein's A values) of nine Si III transitions have been obtained using the relative line intensity ratio (RLIR) method, not applied before in Si III spectrum, and, also, calculated using the Coulomb approximation method. The measured Si IV shift and some calculated Si III shift values present the first published data in this field.

Stark shifts and transition probabilities in the Ne spectrum

Stark shifts $(d)$ and transition probabilities of the spontaneous emission (Einstein's A values) of forty two singly charged neon ($\ion{Ne}{ii}$) ion spectral lines have been measured in a linear, low pressure, pulsed arc at 35 300 K electron temperature and 1.83 $\times$ 10 23 m -3 electron density. Transition probabilities have been obtained using the relative line intensity ratio (RLIR) method. Stark shift values have also been calculated, using the semiclassical perturbation formalism (SCPF). The measured and calculated shift values and the measured A values have been compared to the existing data taken from available data sources.

Stark Widths of the Neii, Neiii, and NeivSpectral Lines

Stark widths of 42 single (Ne II), 10 double (Ne III), and five triple-charged (Ne IV) neon ion spectral lines, interesting for astrophysics, have been measured in a linear low-pressure pulsed arc at electron temperatures of 31,000 and 34,500 K and electron densities of 0.95 ? 1023 and 1.83 ? 1023 m-3 . The measured width values have been compared with the theoretical data calculated by us using semiclassical perturbation formalism. Our measured and calculated Stark width values have also been compared with existing experimental and theoretical data.

Stark broadening in O III spectrum

The Stark widths and shifts of 7 doubly ionized oxygen (O III) spectral lines, in five multiplets, have been measured at electron densities between 1.66 10 23 m -3 and 2.80 10 23 m -3 and electron temperatures between 17 000 K and 54 000 K in a linear pulsed-arc discharge in N 2 + O 2 and CO 2 plasmas. The above mentioned species have been calculated using the semiclassical perturbation formalism. Our measured and calculated Stark width and shift values have been compared to the existing calculated and experimental data.

Stark broadening parameter tables for Au I and Au II

Using the semiclassical perturbation formalism, we have calculated electron-, proton-, and ionized helium-impact line widths and shifts for six Au I lines as a function of temperature and perturber density. Electron-impact broadening parameters for eight Au II transitions have been calculated within the modified semiempirical approach.