Fine Structure Calculations of Atomic Data for Ar XVI

Fine structure energy levels, wavelengths, log gf and allowed transition probabilities (E1) have been calculated for Lithium-like Ar XVI. The optimized electrostatic parameters by a least square approach, have been used in the calculation to include the configuration interaction and relativistic effects. A total number of 69 Ar XVI levels having total angular momenta, 1/2 ≤ J ≤ 9/2 of even and odd parities, orbital angular momenta 2 ≤ l ≤ 4, with 546 E1 transitions for 6 ≤ n ≤ 10 are considered using the relativistic effect in the Breit-Pauli method, where n is the principal quantum number. A comparison is made with the available results in literature.


INTRODUCTION
Many of the emission lines observed in laboratory and astrophysical plasmas are formed by electron-impact excitation of multiply charged atomic ions.Interpreting and modeling the observed spectra of such plasmas requires an accurate knowledge of a large number of rate coefficients.Theoretical calculations can provide the needed rate coefficients, but experimental benchmark values are needed for the comparison.The most important rate coefficients for electron collisions which are the electron-neutral ionization and the electron impact excitation have been calculated for some states.The plasma parameters of electron are significant factors for computing the rate coefficients, namely, the electron temperature (Te) and the electron density (Ne).Further study has been made for the heavier elements like Argon [Sapirstein and Cheng (2011); Saloman (2010); Mu-Hong and Zhi-Wen (2009); Natarajan and Natarajan (2007); Nahar (2002)].Inner-shell excitation energy and autoionization rates for Li-, Be-, B-like ions with Z = 6-54 were calculated using the 1/Z perturbation theory method.Relativistic corrections were taken into account in the frame of the Breit operators [Safronova and Shlyaptseva (1996)].Relativistic many-body calculations of dielectronic satellite spectra created by autoionizing 1s2l2l' states in Li-like ions including the Breit interaction, is used to evaluate energy levels, radiative matrix elements and autoionization rates [Safronova et al. (2010)].Relative intensities of dielectronic satellite lines, determined by radiative transition probabilities and autoionization rates, were calculated for Li-like ions with high values of n by using the perturbation theory method [Safronova et al.(1997)].Effective collision strengths, for electron-impact excitation of Al 10+ are evaluated in the close-coupling approximation using the multichannel Rmatrix method [Stancalie et al. (2005)].
The ion Ar XVI studied in this work, is found to be the heaviest ion allowing a rapid recombination scheme to develop a VUV or soft X-ray laser.
Radiative transition probabilities, for allowed and forbidden transitions including relativistic effects in Breit-Pauli approximation, have been calculated using the Cowan code [Cowan and Griffin (1976); Cowan (1981)].These radiative transition rates have been used in the calculations of the ionization and excitation rate coefficients, i.e., the calculations have been carried out using the coupled rate simultaneous equations where the monopole and the quadrupole transitions have been included in the calculations in addition to the dipole transitions.Neither experimental nor theoretical data have been found in the literature for the rate coefficients for comparison.
A theoretical population model has been developed, to study the influence of the different processes contributing to the population of the different levels for the plasma parameters.The level populations, for these 24 different levels, have then been derived from these rate coefficients for Ar XVI.The calculations have been performed at the electron temperatures equal to both fourth of the ionization potential (in eV) and also to half its value.

Rate coefficients
The electronic p n and p i  transitions in an atom are considered, where p and n are the (effective) principal quantum numbers of initial and final states p and n, and i denotes the ion ground state [Vriens (1980)].Epi denotes the ionization energy while Epn = En -Ep represents the excitation energy (for En  Ep) or de-excitation energy (for En  Ep) energies.The incident electron energy and the energy transfer to the atomare given by Ee and E, respectively.

Excitation rate
An empirical formula representing the numerical rate coefficients for the excitation rate with energy transfer pn is given by:   = 1.6 × 10 −7 (  )

Population densities
The level population can be calculated by solving the steady-state rate equations [Feldman et al. (1986); Seaton (1987)] where   is the population of level , ji A is the spontaneous decay rate from level  to level  (transition probabilities) and    is the electron collisional excitation rate coefficient.   is the collisional de-excitation rate coefficient, given by [Vriens (1980)] where Γ np and Δ np are obtained from Γ pn and Δ pn by interchanging p and n and where   and   are the statistical weights of level p and n.
The population of the  th level is obtained from the following identity: where   is the total number density of all the levels of the ion under consideration and   is the total number density of all ionization stages.Since the populations calculated from Eq. ( 3) are normalized such that [Feldman et al. (1986); Seaton (1987)] where n=24 is the number of all levels of the ion under consideration, the quantity actually obtained from the steadystate rate equation (3) is the fractional or reduced population . The population densities have been calculated at different electron temperatures and various electron densities by solving a set of 24 coupled rate equations (Eq.( 3)) [Feldman et al., 1983;1984;1985;1986;Seaton (1987)].

Ionization and excitation rate coefficients
The fine structure energy levels and transition probabilities have been calculated using the Cowan code [Cowan (1981)].The electron impact ionization and excitation rate coefficients have been evaluated for excited atomic states in Ar XVI according to Vriens [Vriens (1980)] given by Eq. ( 1).The calculations have been carried out using a computer program (CRMO code) [Allam] and including all the forbidden and allowed transitions necessary for calculations.Thus, the monopole and quadrupole transitions have been introduced in addition to the dipole transitions.
The ionization rates for all the levels at the different temperatures are listed in table 1. Fig. 1 shows the relation between the electron temperature (kTe) versus ionization rates for Ar XVI ion.The curve shows the usual behavior for the ionization trend.
Fig. 2 shows that as the principal quantum number "n" decreases, the coupling between the electrons and the nucleus increases.By increasing the temperature and for n = 2 the behavior of the energy states shows saturation.This phenomenon may be explained that as the temperature is increased the electrons from these ionization states are expelled.
Excitation rate coefficients have been calculated as a function of electron temperature by using Eq. ( 2).Fig. 3 for the 1s 2 ns ( 2 S1/2) -1s 2 np ( 2 P1/2) allowed radiative transitions for Ar XVI shows that the curves are divided into groups according to n, that is by increasing n, the coupling between the electrons and the nucleus becomes weaker.It can also be shown that by increasing the temperature the excitation rate coefficients are decreasing when n increases due to the fact that they are far from the nucleus.There is no data available in the literature to be compared with.The ionization rates for the levels 1s 2 ns ( 2 S1/2) and 1s 2 np ( 2 P1/2), where n = 2-5 are drawn versus the electron temperature (kTe) as shown in Fig. 2 for Ar XVI ion.

CONCLUSION
The ionization and excitation rates have been calculated for 24 levels up to n = 5 in Ar XVI ion.Atomic data have been used to evaluate the rate coefficients and the reduced population densities for the ground and excited levels of Ar XVI.Simultaneous coupled rate equations for the 24 levels, under consideration, have been solved.At low electron densities, the population density is directly proportional to the electron density, where the excitation in the excited states is immediately followed by a radiative decay, and where the collisional mixing of the excited levels may be ignored.At high electron densities (Ne≥ 10 23 cm -3 ), the radiative decay to all the levels will be negligible compared to the collisional depopulations and all the level populations become independent of electron density and are approximately equal.No data, theoretical or experimental, have been found in the literature for comparison.

Fig. 6 .
Fig.6.Reduced population for selected levels of Ar XVI ion at the electron temperature equals to fourth the ionization potential.

Fig. 7 .
Fig. 7. Reduced population for selected levels of Ar XVI ion at the electron temperature equals to half the ionization potential.

Table 1 .
Electron temperature and ionization rates for ground and excited atomic states in Ar XVI.

Table 1 . continue
Ionization rate coefficients of all levels for Ar XVI.