Semi-Empirical Oscillator Strengths and Lifetimes for the P IV Spectrum

In this work numerical codes carried out in a multiconfiguration Hartree-Fock relativistic (HFR) approach for the P IV ion are used to obtain the oscillator strengths of each transition as well as the lifetimes of each energy level. With the existing data from several authors that contributed to the spectrum using different light sources, and optimizing the electrostatic parameters by a least-squares procedure when replacing the theoretical values by the experimental ones in the energy matrices, one obtains closer values and according to the observations for the intensities, and also of the lifetimes closer to those that would be obtained experimentally.


Introduction
P IV spectrum is a member of the Mg-like isoelectronic sequence with a complete core plus a double-electron valence shell giving singlets and triplets terms.This sequence has several terms of perturbations, a numerous spin-forbidden lines, and also configuration interactions.Some transitions can be explained by a mixing of one or both involved terms with a perturbing term, indicating that each of them possesses a large portion of the wave function of the other ones.
The first analysis of P IV was made by Bowen and Millikan [1] (1925), who identified 23 lines connecting 14 levels belonging to 8 terms.Wavelengths above 2000 Å, were taken from Geuter [2] (1907).The observations in the vacuum ultraviolet region were made by using a vacuum spark between electrodes of magnesium or silicon containing compounds of phosphorus.Another recording of A. J. Mania DOI: 10.4236/sar.2017.5400551 Spectral Analysis Reviews adjusted from a least-squares procedure.In this adjustment, the code fits experimental levels by varying the electrostatic parameters.This procedure improves the values of the wavelengths σ in, 0 8π 3 with S being the electric dipole line strength.Also the quantities, that measure the total strength of the spectral line in were improved in this new fitting.Considering that, ( ) ( ) as the probability per unit time of an atom in a specific state γJ to make a spontaneous transition to any state with lower energy being ( ) , A J J γ γ′ ′ the Eins- tein spontaneous emission transition probability rate related to the natural lifetime ( ) J τ γ of a state by, These equations must to be applied to an isolated atom.Matter or radiation interaction will tend to reduce their values.In this way, the values for gf and lifetime given in this work were calculated according to previous equations.
For to convert the wavelengths vac air n λ λ = given by the code, were used the relation [15], 2406030.0 15997.01.0 8342.13 10 130.0 10 38. 9 10 for the index of refraction (dry air containing 0.03 CO 2 by volume at normal pressure and T = 15˚C).

Methodology of Calculation
The theoretical predictions for the energy level values were obtained diagonalizing the energy matrices with appropriate Hartree-Fock relativistic (HFR) values for the electrostatic parameters.In these computations all strong configuration interactions were included and HFR method is used to give a better accuracy in many cases.For this purpose, the computer code developed by Cowan [16] was employed.The main purpose is to reach a fitting to the experimental energy levels, minimizing the uncertainties as much as possible, using the least-squares method for each parity.The standard deviation is less than one percent of the energy range covered by the energy levels.The accuracy is related in the computation of the gf and lifetimes values.The propagated experimental uncertainties of the input data, in the optimization of the energy levels, does not influence the process, being small values when are compared to the uncertanties coming from the fitting.The radial integrals E AV , F k , G k and R k are considered simply as ad-A.J. Mania DOI: 10.4236/sar.2017.5400552 Spectral Analysis Reviews justable parameters, whose values are to be determined empirically so as to give the best possible fitting between the calculated eigenvalues and the observed energy levels.The values for the optimized electrostatic parameters substitute their corresponding theoretical values, and the are used again to calculate energy matrices.

Results and Discussion
The P IV spectrum is characterized by strong interactions among their configurations yelding a mixture of levels that difficult a severe analysis.These effects of perturbations are stronger on the singlet levels, namely in 3p 2 , 3s3d, 3s4d, 3s5g, 3s6s, 3p4p and 3d 2 .He same effect appears in the 3p3d, 3s4f, 3p4s, 3s5p, 3s5f, 3p4d and 3s8f configurations.There are many examples of spin-forbidden lines caused by near coincidence of singlet and triplet levels with the same J-value.
Also, configuration interactions are numerous.Apparent two-electron transitions, such as 3s5p l P -3p4p 1 P, 3s4d 3 D -3p4s 3 P or 3p 2 1 D -3snf 1 F, 3s6s 3 S -3p4p 3 S, can be explained by a mixing of one or both of the involved terms with a perturbing term.The term 3p 2l D combines just like 3s3d 1 D, indicating that each of them possesses a large portion of the wavefunction of the other one.The perturbation of 3s7p 3 P by the inverted 3p4d 3 P term is also evident.The energy levels used in our fitting method are from spectral analyses [11], even though the code has exchanged values making it difficult to adjust the electrostatic parameters.The fittings were achieved by considering some simplifications such as keeping fixed those singlet energy levels that exchanged their values due to mutual interactions, -3p3d 1 F ( fitted 290 3268; experimental 314 4237), 3s4f 1 F (fitted 314 4251 -experimental 290 3277), 3p4s 1 P (fitted 316 8828 -experimental 327 8735), 3s5p 1 P ( fitted 321 0106 -experimental 316 8888), 3s8f 1 F ( fitted 385 9827 -experimental 388 1242), 3p4d 1 F ( fitted 388 1209 -experimental 385 9800), -and where there was no success in reproducing the observed structure these levels were not included in the calculations of gf and lifetimes, however, we retain the percentage compositions with the values indicated by the adjustment.
Standard deviation reached for each parity as 10 cm −1 and 17 cm −1 , for even and odd configurations, respectively, were satisfactory for the aims of this work [16].The leading eigenvector percentages are in accordance with those provided by the numerical code [16].
In Table 1 (for the vacuum region) and Table 2 (in the air), are shown the results for the oscillator strengths.A comparison with the observed wavelegenths values derived from previous works, as well as their nomenclatures of intensities adopted are also shown.trum of the ion P IV are presented by the method of attempting to reproduce as much as possible the observed values and extracting information about the values of gf and lifetimes that are closer to the experimental ones.Phosphorus is an astrophysically important element.The present work is part of an ongoing program, whose goal is to obtain oscillator strength and lifetimes for elements of astrophysical importance.Phosphorus occupies the fifteenth place with respect to cosmic distribution [17].

Table 1 .
P IV wavelengths and semi-empirical oscillator strengths calculated in the region vacuum-ultraviolet.

Table 2 .
PIV semi-empirical oscillator strengths calculated in the region above 2000 Å.

Table 3 .
P IV energy levels and lifetimes for the even configurations.
1Percentage composition lower than 3% were omitted.N.I.: Level no identified.*As suggested by the fitting.

Table 4 .
P IV energy levels and lifetimes for the odd configurations.
1Percentage composition lower than 3% were omitted.N.I.: Level no identified.*As suggested by the fitting.