Emission cross sections for energetic O$^+$($^4S,^2D,^2P$)-N$_2$ collisions

TL;DR

This study measures excitation cross sections for energetic O$^+$ ions in different states colliding with N$_2$, revealing state-dependent excitation behaviors, energy dependencies, and polarization effects in the process.

Contribution

It provides high-resolution measurements of excitation functions and polarization effects for O$^+$-N$_2$ collisions, highlighting the impact of metastable states on excitation cross sections and polarization.

Findings

Metastable O$^+(^{2}P)$ induces larger excitation cross sections than ground state.

Excitation cross sections increase with ion energy in dissociative charge exchange.

Metastable ions reduce the degree of polarization compared to ground state ions.

Abstract

We report measurements of excitation functions for the O$^{+}-$N$_{2}$ process with the incident beam of $1-10$ keV O$^{+}$ in the ground O$^{+}(^{4}S)$ and metastable O$^{+}(^{2}D)$ and O$^{+}(^{2}P)$ states. The measurements are performed with the sufficiently high energy resolution of 0.001 eV, which allows to distinguish the excitation channels. The excitation cross section induced by incident ions in the metastable state O$^{+}(^{2}P)$ is much larger than that for the ground O$^{+}(^{4}S)$. The excitation cross section of N$_{2}^{+}$ ion for (0,0), (0,1) and (1,2) bands system is measured and the ratio of intensities for these bands is established as $10:3:1.$ It is shown that the cross sections for the N$^{+^{\ast }}$ions excitations in the dissociative charge exchange processes increase with the increase of the incident ion energy. The energy dependence of the excitation cross section of the band (0,0) $\lambda=391.4$ nm of the first negative system of the N$_{2}^{+}$ and degree of polarization of radiation in O$^{+}-$N$_{2}$ collision are measured for the first time. An influence of an admixture of the ion metastable state on a degree of polarization is revealed. It is demonstrated that for O$^{+}-$N$_{2}$ collision system the degree of polarization by metastable O$^{+}$($^{2}P$) ions is less compared to those that are in the ground O$^{+}$($^{4}S$) state and the sign of polarization degree of excited molecular ions does not change.

Equations

$${\text{O}}^{+}+\text{Ar}\to {\text{O}}^{+}+{\text{Ar}}^{\ast }(6s).$$

$${\text{O}}^{+}{\text{(}}^{4}S\text{)}+{\text{N}}_2(X^1{\Sigma }_g^{+})(v^{\prime }$$

$${\text{O}}^{+}{\text{(}}^{2}D{+}^{2}P\text{)}+{\text{N}}_2(X^1{\Sigma }_g^{+})(v^{\prime }$$

$${\text{O}}^{+}{\text{(}}^{4}S\text{)}+{\text{N}}_2(X^1{\Sigma }_g^{+})(v^{\prime }$$

$$\downarrow$$

$$\to {\text{N}}^{{+}^{\ast }}(3d{}^3{F}^0)+\text{N}+\text{O}{(}^{3}P)$$

$$\to {\text{N}}^{{+}^{\ast }}(3p{}^{3}D)+\text{N}+\text{O}{(}^{3}P)$$

$$\to {\text{N}}^{{+}^{\ast }}(4fF)+\text{N}+\text{O}{(}^{3}P)$$

$${\text{O}}^{+}{\text{(}}^{2}D{+}^{2}P\text{)}+{\text{N}}_2(X^1{\Sigma }_g^{+})(v^{\prime }$$

$$\downarrow$$

$$\to {\text{N}}^{{+}^{\ast }}(3d{}^3{F}^0)+\text{N}+\text{O}{(}^{3}P)$$

$$\to {\text{N}}^{{+}^{\ast }}(3p{}^{3}D)+\text{N}+\text{O}{(}^{3}P)$$

$$\to {\text{N}}^{{+}^{\ast }}(4fF)+\text{N}+\text{O}{(}^{3}P)$$

$${\sigma }_{eff}(P,E)=f_0(P){\sigma }_0(E)+f_1(P){\sigma }_1(E)+f_2(P){\sigma }_2(E),$$

$$\Pi =\frac{I_{||}-I_{\perp }}{I_{||}+I_{\perp }},$$

$$\Pi =\frac{I_{||}-I_{\perp }}{I_{||}+I_{\perp }}=\frac{15\left[\sigma (m_l=0)-\sigma (m_l=\pm 1)\right]}{41\left[\sigma (m_l=0)+67\sigma (m_l=\pm 1)\right]},$$

$$I_{||}(P)=f_0(P)I_{||}{(}^{4}S)+f_2(P)I_{||}{(}^{2}P),I_{\perp }(P)=f_0(P)I_{\perp }{(}^{4}S)+f_2(P)I_{\perp }{(}^{2}P).$$

$$\Pi {(}^{4}S)=\frac{I_{||}{(}^{4}S)-I_{\perp }{(}^{4}S)}{I_{||}{(}^{4}S)+I\perp {(}^{4}S)},\Pi {(}^{2}P)=\frac{I_{||}{(}^{2}P)-I_{\perp }{(}^{2}P)}{I_{||}{(}^{2}P)+I_{\perp }{(}^{2}P)},$$

$$\Pi (P_1)$$

$$\Pi (P_3)$$

$${\sigma }_{eff}(P_1)$$

$${\sigma }_{eff}(P_3)$$

$$\Pi (P_1)$$

$$\Pi (P_3)$$

Full text

I Introduction

The oxygen and nitrogen molecules are two of the most common elements in the atmosphere and the ionosphere of the Earth. There has been considerable research in the past 20 years on both the production and loss of vibrationally excited O2 and N2 in the thermosphere and their role in ionospheric processes. Excitation and deexcitation of O2 and N2 molecules can occur through direct electron and ion impact, cascade from excited states, and chemical reactions [1]. Different constituents of the atmosphere have their characteristic airglow emissions. Atomic oxygen is a very important constituent of the upper atmosphere. It plays a crucial role in the atmospheric chemistry at the mesosphere and thermosphere altitudes. Further more excitation, dissociation and charge transfer between singly charged O*+* ions and various atmospheric molecules are relevant to the low–temperature edge plasma region of current thermonuclear fusion devices [2].

The importance of excitation and dissociation processes of O${}^{+}-$N2 has been established from the fundamental atomic physics point of view. One important motivation to study the collision of O${}^{+}-$N2 pair is the fact that the cross section is strongly dependent on the initial electronic state of the O*+* ions [3, 4, 5] and, in particular, two low-lying excited metastable states ${}^{2}D$ and ${}^{2}P$  of O*+* have approximate lifetimes of 3.6 h and 5 s, respectively [6]. As a result of these long lifetime metastable O*+(${}^{2}D$) and O+(${}^{2}P$) states, O+* ions are available for ion – molecule reactions. The importance of the O*+(${}^{2}D$, ${}^{2}P$) metastable states for planetary science have been stressed for a long time, for instance for Earth [7, 8, 9], Venus [10], Europa [11] and Titan [12] atmospheres. In particular, charge transfer reactions of state-selected atomic oxygen ions O+(${}^{4}S$, ${}^{2}D$, ${}^{2}P$) with nitrogen and oxygen molecules, which are the major species in the atmosphere, play an important role in atmospheric chemistry. Various experimental investigations were performed for O+* collisions with H2, N2, CO, CO2, CS2 molecules and these studies are mostly related to charge transfer processes [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]. The charge transfer processes induced by O*+* collision with N2 and O2 are important in the field of aeronomy [31] since the O*+* is the dominant ion in the F region [32] of the atmosphere and both metastable species of O*+(${}^{2}D$) and O+(${}^{2}P$) have been detected here too. While the reactions of O+* ions with N2 have received a considerable attention and several experimental studies (see e.g. [33, 34]) have been conducted, there is still some uncertainty related to the magnitude of the total cross sections of charge transfer and transfer with excitation processes. Since inelastic processes at low energy strongly depend on the internal electronic structure of the colliding particles, the presence of metastable excited ions in the primary ion beam may sometimes significantly influence the observed cross sections. For example, the study of charge transfers cross sections for N*+* and O*+* ions in collisions with H2 molecules and He atoms, have found that metastable state ions indeed enhance the cross sections, sometimes by an order of magnitude [35].

The influence of the excited O*+(${}^{2}D$) state is monitored by a charge transfer reaction in O+* + Ar collisions in Ref. [28]. The large cross section for reactions involving O*+(${}^{2}D$) incident ions and small cross section for reactions of O+(${}^{4}S$) ground state ions is explained by the energy difference between the O+(${}^{4}S$) recombination energy and Ar ionization potential for forming Ar+(${}^{2}P_{1/2}$). Collisions of O+(${}^{2}D$) metastable ions with O2* leading to formation of the O${}_{2}^{+}$ ion either in the $A^{2}\Pi_{u}$ or $a^{4}\Pi_{g}$ state involves only a small energy defect and, as expected, the cross sections for such processes are found to be quite large. As to the data related to the collision with N2 molecules, the O*+(${}^{2}D$) metastable state is also in resonance with the N2*($A^{2}\Pi_{u}$) state and the cross section is expected to be large, while there is 2 eV gap between the O*+(${}^{4}S$) and the nearest N${}_{2}^{+}$( $X^{2}\Sigma_{g}^{+}$) state, resulting in a smaller cross section. Similar considerations also apply to collisions with O+(${}^{2}P$). The charge transfer performed with O+(${}^{2}P$) to N${}_{2}^{+}$($B$, $v=0$) level is near-resonant (energy defect is 0.1 eV) that causes about a two order of magnitude difference of cross sections between the metastable O+(${}^{2}P$) state and the ground O+(${}^{4}S$) state [13]. In [5] it is stated that the abundance of metastable ions is strongly dependent on the operating conditions. In particular, the abundance depends on the gas pressure in the ion source and on the energy of impacting electrons producing ions. There are many options that allow the control of metastable states and perform measurements with known species [14, 15, 16, 17, 18, 19, 20, 21, 22, 25]. Translational spectroscopy experiments have indicated that the long lifetime of ${}^{2}D$ and ${}^{2}P$ metastable states comprise a significant fraction of ions in an O+* beam [36].

The ratio of the metastable electronic states to the ground state can be varied by a careful control of the energy of the ionizing electrons in the primary ion source. It is well known (see e.g. [37] and [38]) that the use of high pressure ion sources can lead to a significant loss of metastable ions due to collisional quenching mechanisms. In [38] the loss of O*+(${}^{2}D$) and O+(${}^{2}P$) state ions was observed in the reaction O+(${}^{2}D$,${}^{2}P$) + CO. The relatively low O+(${}^{2}D$, ${}^{2}P$) metastable ion abundance was observed in [39], when a CO pressure of the order of $10^{-1}$ Torr was applied in an ion source. The beam attenuation method, to determine the fractional abundance of different states in an O+* ion beam formed by the ionization of O2, is considered in an early study [40]. In [41] an appropriate range of an ion source pressures (0.02$-$0.1 mTorr) was found for the O${}^{+}-$ N2 collision system and it was reported that the excited metastable species exhausted by about 3.5 times. As stated by the authors of [41] at a pressure higher than 2 mTorr the beam can contain either ground state O*+* ions or a mix of the ground state and excited-state ions. At a low pressure of 0.1 mTorr the ion beam is composed of a mix of ground and excited state ions. The quenching rate of O*+(${}^{2}P$) by O and N2* have been evaluated in [42]. In [43] the O*+* metastable fraction is estimated to be approximately 0.19 from an ion beam attenuation technique. Production of the O*+* ions in [44] expected to be a mix of ground state and metastable species but again at some unknown ratio. This brief survey shows that much of the difficulties in the laboratory investigation of inelastic processes is due to the fact that incident ions are typically present in both the ground ${}^{4}S$ state and in the long-lived excited metastable ${}^{2}D$ and ${}^{2}P$ states. It should be noted that metastable species are attenuated differently and that the composition of the total metastable fraction is different. Furthermore, it seems that the data related to the abundance for different targets are contradictory. This difference is also observed for the same target case. The source of this large discrepancy between an abundance of metastable state can be attributed to a different operating condition of ion sources. We can conclude that the magnitudes of cross sections for inelastic processes are largely dependent on the composition of the beam. Thus, for reactions involving chemically stable molecular targets, the experimental difficulties are primarily associated with the determination of the composition of the primary ion beam. Most of the excited-state measurements reported generally pertain to an undetermined mixture of O*+(${}^{2}D$) and O+(${}^{2}P$) ions and in the 0.2–10 keV range, the uncertainty is on the order of $\pm$35 % and it is now known that the cross sections for these two excited-state species differ [45]. Finally let us mention that the charge transfer processes of O+* with N2 for collision energies from 10 eV to 100 keV are reviewed by Lindsay and Stebbings in Ref. [45], which also gives a brief descriptions of the experimental measurement techniques. To control the metastable species in the ion beam both the precise exploration of pressure condition in the ion source and the evaluation of electrons energy used in the ion source for ionization are crucial.

In this paper we study the emission processes in collisions of the ground O${}^{+}(^{4}S)$ and long lifetime metastable O${}^{+}(^{2}D)$ and O${}^{+}(^{2}P)$ state ions with N2 molecule in the ion energy range 1–10 keV. The paper is organized in the following way. In Sec. II the method and procedure of measurements using an optical spectroscopy are presented. Here we introduce our approach and procedure for cross section measurements and its determination. The energy dependence of the emission cross sections and degree of linear polarization for O${}^{+}-$N2 processes induced by the incident beam of O*+* in the ground and metastable states and discussion of results of measurements are presented in Sec. III. Finally, in Sec. IV we summarize our investigations and present conclusions.

II METHOD AND PROCEDURE OF MEASUREMENTS

The experimental study of emission processes in reactions of oxygen ions in the ground and metastable state with nitrogen molecules is performed within the framework of optical spectroscopy. This approach allow us to study the emission processes induced by reliable beams of the ground O*+(${}^{4}S$) and metastable O+(${}^{2}D$) and O+(${}^{2}P$) ions in collisions with N2* molecules.

In our study we used a radio frequency (RF) discharge ion source for the investigation of the energy dependence of the emission cross section in collisions of oxygen ions with nitrogen molecules. Optical spectroscopy, used to study the energy dependence of the emission cross section, is characterized by a high energy resolution, but low luminosity, since radiation is observed only at a certain angle and for a certain spectral line. Therefore, it is necessary to study the process for a relatively large current of O*+* ions. The radio frequency source allows to obtain much higher ion currents ($\sim$ $\mu$A). Our experiments showed that, depending on the condition (pressure, power, gas mixture) of ion beam formation, the fraction of O*+* ions in different electronic states (ions in ${}^{4}S$ and metastable ${}^{2}D$, ${}^{2}P$ states) significantly changes, which significantly affects the dependence of the emission cross section on the ion impact energy. Establishing the formation mechanism of the ion beam in the RF source, one faces challenges. When the pressure inside the source changes, due to various inelastic processes (charge exchange process, excitation, quenching, recombination), the ion filtration process takes place. In this case, the degree of filtration and neutralization of ions depends on the internal electronic state of the ion. An increase in pressure decreases the free path of electrons, which participate in the formation of ions in various electronic states via the process of dissociative ionization. Consequently, the probability of formation of ions in different states changes. In order to determine the mechanism of the formation of O*+* ions, we investigated the dependence of the dissociative ionization cross section on the electron energy inside the ion source for various pressures of the working gas.

II.1 Optical Spectroscopy

Cross sections for the emission processes were measured by optical spectroscopy. We have used an experimental setup and method of measurements similar to those described in detail and used previously in [46]. To obtain the oxygen beam we used a 20 MHz RF ion source. The oxygen ions extracted from the RF ion source, are accelerated, collimated and focused, and mass-selected by a 600 magnetic sector field. Then the ion beam is directed into the collision chamber. The fluorescence emitted as a result of the excitation of colliding particles was observed at 900 with respect to the beam. In the present work, measurements are performed with sufficiently high spectral resolution, which allows to distinguish the emission channels. This method also allowed us to estimate the polarization of emission, that itself is a powerful tool for establishing the mechanism for inelastic processes. The spectroscopic analysis of the emission is performed with a monochromator incorporating a diffraction grating with a resolution of 40 nm/mm operated in the $400-800$ nm spectral region, which allows to distinguish the excitation channels. A polarizer and a mica quarter-wave phase plate are placed in front of the entrance slit of the monochromator and the linear polarization of the emission is analyzed. For cancelation of the polarizing effect of the monochromator, the phase plate is placed after the polarizer and is rigidly coupled to it. The emission is recorded by a photomultiplier with a cooled cathode and operated in current mode. The spectral sensitivity calibration is performed by a tungsten filament standard lamp, which is chosen due to the lack of reliable experimental data in the infrared region (the bright Meinel system), that could be used for the calibration of the system for registration of radiation [47]. The measurements for low energy collisions required a precise determination of the energy of the ions as well as their energy dispersion. To avoid errors in the measurements of the incident ion energy we employ the retarding potential method and use the electrostatic analyzer with a resolving power of 500. In our experiments the energy dispersion of the ions does not exceed 20 eV. The ion current in the collision chamber was of the order 1$-$5 $\mu$A. The residual gas pressure did not exceed $10^{-6}$ Torr. The working pressure in the collision chamber was about $5\times 10^{-4}$ Torr. Single collision condition was checked by a linear dependence of the intensity of spectral lines versus target gas pressure and density of the ion current. The absolute accuracy of the measurements is 25%. The accuracy of the measurements is related to the following factors: i. the accuracy of the pressure measurements in the collision chamber; ii. the precise and immediate determination of the primary beam current that produce the radiation, which is collected by optical system from the region where the collision occurs; iii. the accuracies of the relative and absolute calibration procedures. The uncertainty of the relative measurements is about 5%.

II.2 Cross section measurements and determination

One advantage of the RF source used in this experiment is that, depending on its operating mode, a certain fraction of the ions can be found in metastable states and easily identified. As it was mentioned in the introduction the probability of quenching is significantly related to the increase of the target pressure in the ion source. Hence, it is important to explore the working condition of a source by changing the pressure in it. Therefore we considered the following reaction

[TABLE]

A typical emission spectra for the intense spectral line of Ar atom ($\lambda=731.1$ nm) in O${}^{+}-$Ar collision for the process (1) at different pressures in the ion source are presented in figure 1. It was found that by increasing the O2 gas pressure in the ion source about 6 times (from $1.5\times 10^{-2}$ to $1.0\times 10^{-1}$ Torr) the intensity of this lines decreases by a factor of 1.4. This result indicates that the presence of metastable ions plays a definite role in excitation of the Ar(6$s$) state (the excitation energy is $14.85$ eV) and hence, this process is effectively realized due to the transfer of internal energy. In order to check the influence of the ion source operating parameters and to evaluate the role of metastable ions in the excitation processes we have extended this research to nitrogen molecules and to its dissociative products. For the latter we chose such energy and pressure values that the observation of a metastable state could be possible at high energy and for a single collision condition.

We performed a test experiment for the intensity of the emission of the (0,0), (0,1) and (1,2) bands of molecular N${}_{2}^{+}$ ions and of the dissociative N*+* fragment in collision of the O*+* ion with N2 molecules. The intensity of emission depends on the projectile ion energy. A typical spectrum at the energy $E=5$ keV of the primary beam and pressure $P=7\times 10^{-3}$ Torr in the ion source is shown in figure 2. As it is seen from figure 2a the ratio between the intensities of these bands is $10:3:1$, respectively. As the relative intensity has been established, we chose an intensive band (0,0) N${}_{2}^{+}$ ion ($\lambda=391.4$ nm) and performed a study with variable pressure. Such procedure allowed us to separate the ground and metastable state ions in the primary beam and to perform a systematic measurement. In the same figure 2a the emission of the satellite dissociative product for the nitrogen ionic line, $\lambda=424.2$ nm, is also presented, while in figure 2b the band (0,3) of the N${}_{2}^{+}$ ion emission, $\lambda=522.8$ nm, is shown.

The main objective of our research is the study of the emission processes in reactions of the ground O${}^{+}(^{4}S)$ and metastable O${}^{+}(^{2}D)$ and O${}^{+}(^{2}P)$ state ions with N${}_{2}(X^{1}\Sigma_{g}^{+})(v^{\prime}=0)$ molecule in a wide energy range of incident ions. In particular, in collisions of O*+* ions with nitrogen molecules the studies are carried out for the following inelastic channels with formation of the excited state $B^{2}\Sigma_{u}^{+}(v^{\prime}=0$ or $v^{\prime}=1)$ of the nitrogen molecular ion and the dissociation products of N*+*.

[TABLE]

In the reactions (4) and (8) the dissociative product N${}^{+^{\ast}}$ can be in different excited states, (5)–(7) and (9)–(11), respectively. For the molecule N2 in reactions (2)–(4) and (8) the vibrational quantum number is $v^{\prime}=0$, and for the excited molecular ion N${}_{2}^{+}$ in reaction (2) and (3) the vibrational quantum number can be either $v^{\prime}=0$ or $v^{\prime}=1$.

III RESULTS OF MEASUREMENTS AND DISCUSSION

The characteristic emission of N2 and N${}_{2}^{+}$ are generally attributed to the first-positive $(B$ ${}^{3}\Pi_{g}^{+}\rightarrow A$ ${}^{3}\Sigma_{u}^{+})$ and first-negative $B^{2}\Sigma_{u}^{+}$ $\rightarrow$ $X^{2}\Sigma_{g}^{+}$ band systems of N2 and N${}_{2}^{+}$, respectively [48]. In collisions of O*+* ions with N2, we studied the emission of the band (0,0) of the first-negative band system of the N${}_{2}^{+}$ which corresponds to the transition $B^{2}\Sigma_{u}^{+}$ $\rightarrow$ $X^{2}\Sigma_{g}^{+}$. The study is carried out with O*+* in the ground state ${}^{4}S$ and metastable states (${}^{2}D,$ ${}^{2}P$). The presence of ions in metastable states is monitored by measuring the energy dependence of the emission cross section of the (0,0) $\lambda=391.4$ nm bands of the first-negative band system of N${}_{2}^{+}$ ion for different pressure conditions of the RF source. The energy dependence of the effective emission cross section of N${}_{2}^{+}$ ion in collisions of the oxygen ion with nitrogen molecules at different pressures in the RF source, in particular, at $P_{1}=2.4\times 10^{-2}$ Torr, $P_{2}=$ $8\times 10^{-2}$ Torr, and $P_{3}=2\times 10^{-1}$ Torr, are presented in figure 3. The curves 1, 2, and 3 in figure 3 show our results for the effective cross section obtained for the corresponding pressures in the RF source. The effective emission cross section refers to the sum of terms, each of which is the product of the emission cross section of the given band by ions in the corresponding excited state and the relative weight of these ions in the primary particle beam. In general, the value of the effective cross section for O${}^{+}-$N2 collision can be written as

[TABLE]

where $\sigma_{0}(E),$ $\sigma_{1}(E)$ and $\sigma_{2}(E)$ are the corresponding emission cross sections induced by the ground O*+(${}^{4}S$) and metastable O+(${}^{2}D$) and O+(${}^{2}P$) ions of the primary O+ion beam, which depend on the energy of the beam, while $f_{0}(P)$, $f_{1}(P)$ and $f_{2}(P)$ are the corresponding relative weight of the ground O+(${}^{4}S$) and metastable O+(${}^{2}D$) and O+(${}^{2}P$) ions in the incident O+*ion beam at the given pressure in the collision chamber. The relative weights depend on the pressure in the collision chamber and at the same time $f_{0}(P)+f_{1}(P)+f_{2}(P)=1$.

It is known, that the excitation of the indicated band system by oxygen ions in the ${}^{4}S$ ground state proceeds with a significantly lower efficiency than excitation by ions in the metastable ${}^{2}D$ and ${}^{2}P$ states. The ratio of the corresponding cross sections is $1:9:300$ [13]. As can be seen from the graph in figure 3, there is the difference in the magnitudes for the effective cross sections at the different pressure, which depends on the incident energy of O*+* ions. At a fixed energy, the effective cross section decreases with increasing pressure in the RF source. The absolute emission cross section for the energy of the incident beam $E=1$ keV obtained in [13] are $\sigma_{0}=0.73\times 10^{-18}$ cm${}^{2},$ $\sigma_{1}=6.6\times 10^{-18}$ cm${}^{2},$ $\sigma_{2}=2.20\times 10^{-16}$ cm2, which correspond to ${}^{4}S$ , ${}^{2}D$ and ${}^{2}P$ states of the O*+* ions, respectively. The comparison of these results with the effective cross section $\sigma_{eff}=1.7\times 10^{-17}$cm2 that we measured at the same energy and pressure $P_{1}=2.4\times 10^{-2}$ Torr in the RF source shows, that our result is greater than the emission cross sections $\sigma_{0}$ and $\sigma_{1}$ for the oxygen ions in the ${}^{4}S$ and ${}^{2}D$ states and significantly less than for the O*+* ions in the metastable ${}^{2}P$ state obtained in [13]. This suggests that the value of the effective cross section we obtained is determined to a significant extent by oxygen ions in the metastable ${}^{2}P$ state.

At the next step we investigated the presence of the metastable ${}^{2}D$ state in the oxygen ions beam, by examining the emission of the Meinel bands (3,0) $\lambda=687.4$ nm and (4,1) $\lambda=703.7$ nm, which correspond to the transition $A^{2}\Pi_{u}-X^{2}\Sigma_{g}^{+}$ of the N${}_{2}^{+}$ ion in O${}^{+}-$N2 collisions. The experiments showed that, despite the quasiresonant character of these processes (energy defect $\Delta E=0.06$ eV) the Meinel bands are excited with a low probability, which is probably due to the absence of the oxygen ions in metastable ${}^{2}D$ state in the primary particle beam. The small fraction of these ions in the primary particle beam in comparison with O*+(${}^{2}P$) ions is due to a peculiarity of the mechanism of formation of these ions during the dissociative ionization in collisions of electrons with oxygen molecules in the RF ion source. An analysis of the energy terms of the oxygen molecule and the oxygen molecular ion shows that the most efficient mechanism of formation of dissociation products in various states is a decay of highly excited states of the O${}_{2}^{+}$ ion in the region of internuclear distances corresponding to the Franck–Condon transitions. The same result follows from Ref. [49]. In this paper is shown that during electron impact dissociative ionization of O2* molecules mainly ions in the ground O*+(${}^{4}S$) state and metastable O+(${}^{2}P$) state are created. It means that the probability for formation of O+(${}^{2}P$) is higher compared to O+*(${}^{2}D$).

As our measurement shows, as well as its follows from [13], the formation of the metastable O*+(${}^{2}D$) ions has low probability. Hence we can infer that in Eq. (12) term $f_{1}(P)\sigma_{1}(E)\approx 0$ and, therefore, $\sigma_{eff}=f_{0}(P)\sigma_{0}(E)+f_{2}(P)\sigma_{2}(E),$* where now $f_{0}(P)+f_{2}(P)=1$. Using these equations one can estimate the value of $f_{0}(P)$ and $f_{2}(P)$ for the given $\sigma_{0}(E)$ and $\sigma_{2}(E)$ and the different pressure conditions. Let us estimate the value of $f_{0}(P)$ and $f_{2}(P)$ at a fixed energy, $E=1$ keV, and for the different pressure conditions. Using the values of the effective cross sections $\sigma_{eff}$ measured at $E=1$ keV and different pressures, and the values of the $\sigma_{0}=0.73\times 10^{-18}$ cm2 and $\sigma_{2}=2.2\times 10^{-16}$ cm2 at $E=1$ keV from [13], by solving the above mentioned equations one obtains: $f_{0}=0.926$ and $f_{2}=0.074$ for $P_{1}=2.4\times 10^{-2}$ Torr, $f_{0}=0.966$ and $f_{2}=0.034,$ for $P_{2}=8.0\times 10^{-2}$ Torr, and $f_{0}=0.986$ and $f_{2}=0.014$ for $P_{3}=20.0\times 10^{-2}$ Torr. Thus, the portion of metastable ions $f_{2}$ decreases, while the portion $f_{0}$ of ground state ions increases with increasing pressure in the ion source. It should be noted that a main reason for the attenuation of the ion beam is caused by charge exchange processes in the ion source. If we assume, that the relative weights $f_{0}$ and $f_{2}$ are functions of pressure and do not depend on the energy, then it is possible to determine the emission cross section for different energies of incident ions being in the ground O${}^{+}(^{4}S)$ and metastable O${}^{+}(^{2}P)$ states. This assumption is true because the energy of emerging ions from the high frequency ion source is the same (extraction potential of the ions and potential of a plasma in the discharge area is a constant) and energy of ions is defined in a focusing area e.g. outside of ion source. It should be mentioned, that the relative weight of metastable O${}^{+}(^{2}P)$ ions, in effective cross section, is significant at relatively small energies and increases for the ground state O${}^{+}(^{4}S)$ ions with the increase of energy.

Since the relation between the relative weight for different pressure conditions is established, we can use this ratio of relative weight for the effective cross section at a different energy. For a particular incident energy we can write a simple system of equation by solving of which one can restore the energy dependence of the absolute emission cross section as for the ground O${}^{+}(^{4}S)$ state and metastable O${}^{+}(^{2}P)$ state as well. The results of this reconstruction are shown in figure 4.

The assumption regarding the fact that the ratio of a portion for metastable and ground state ions does not depend on the collision energy can be confirmed from our results shown on figure 3. The analyses of the results shows that by increasing the pressure the portion of metastable ion beam decreases, hence the effective emission cross section decreases as well. At the same time, we know that $\sigma_{2}\gg\sigma_{1}\gg\sigma_{0}$. Here $\sigma_{0},$ $\sigma_{1},$ and $\sigma_{2}$. stands for ${}^{4}S,$ ${}^{2}D$ and ${}^{2}P$ cross sections, respectively. So, if we take the difference between cross section for two different pressure condition 1) $\sigma_{eff}(P_{1},E)-\sigma_{eff}(P_{2},E)$ and $\sigma_{eff}(P_{1},E)-\sigma_{eff}(P_{3},E)$ and for a different collision energy and normalized them to each other we will get the energy dependence of the emission cross section for metastable states in arbitrary units. The results can be calibrated on the absolute cross section from [13] and we will get a curve which within the error bar (10%) coincides with the results shown in Fig. 4. For example, our estimation shows, that the difference between the effective emission cross section for $P_{1}$ and $P_{3}$ pressure $\sigma_{eff}(P_{1},E)-\sigma_{eff}(P_{3},E)$ as shown in figure 4, in the energy interval $1-10$ keV makes 6 $\%$ of total cross section of metastable particles. This value is in good agreement with our previous estimation (7.4%) for the total metastable portion which we did for the energy $E=1$ keV. From this result also follows, that the remaining 1.4%  ($7.4\%-6\%$) in the case of pressure condition $P_{3}=2.0\times 10^{-1}$ Torr in the ion source, is still related to the presence of metastable states in ion current. Taking this result into consideration we can obtain the energy dependence of the absolute emission cross section for the ground ${}^{4}S$ state ion. This also justified by the fact that when the pressure in the ion source is $P_{3}=2.0\times 10^{-1}$ Torr the weight of the metastable ion is about 1.4 % in total ion beam, in all energy interval. It should be mentioned, that an accuracy of absolute cross section, in low energy is about 30% and the accuracy does not exceed 15 % for high energy. Using the data from [13], we can estimate from our results the fraction of oxygen ions in the ${}^{4}S$ ground state and in the metastable ${}^{2}P$ state in the primary particle beam for different values of the pressure of the working gas in the RF source. Simple calculations show that the fraction of O*+(${}^{2}P$) ions in the primary particle beam for the pressures of $2.4\times 10^{-2}$ Torr, $8\times 10^{-2}$ Torr and $2\times 10^{-1}$ Torr in the RF source is 7.4%, 3.4% and 1.4%, respectively. As we mentioned our measurements show that the O+(${}^{2}P$) ions make a substantial contribution to the effective cross section. Therefore, the decrease in the effective cross section resulting by the increase of the pressure inside the RF source is entirely due to the decrease of the fraction of these ions in the primary beam. The contribution of the metastable ions to the effective cross section also depends substantially on their energy — it decreases as their energy increases. After determining the relative weight of metastable ions in the primary beam, it is easy to reconstruct the dependence of the cross section of emission of the (0,0) $\lambda=391.4$ nm band by O+* ions in the ${}^{4}S$ ground state and in the metastable ${}^{2}P$ state from the energy dependence of the effective emission cross section by solving some simple algebraic equations. The results of this reconstruction are shown in figure 4. It can be seen that the cross section for emission of the given band by O*+(${}^{2}P$) and O+(${}^{4}S$) ions behave differently. The emission cross section for the incident O+* ion in ${}^{2}P$ state slightly increases in the energy range $1-5$ keV and is almost constant in the energy range $5-10$ keV. The emission cross section for the ground state incident O*+* ion ${}^{4}S,$ sharply increases in the entire energy range of the incident beam, and at higher ion energies the contribution of the ions found in the ${}^{4}S$ ground state to the excitation becomes decisive. However, the magnitude of this cross section is still more than one order of magnitude smaller than the one for O${}^{+}(^{2}P)$ ions at the energy 10 keV.

In order to check the influence of the ion source operating parameters and evaluate the role of metastable ions in emission processes we have made measurements for the first negative band system of the N${}_{2}^{+}$ ion under different pressure conditions. The dependence of the effective cross section for the band (0,0) $\lambda=391.4$ nm of N${}_{2}^{+}$ on the pressure in the ion source are presented in figure 5. The analysis of figure 5 shows that the intensity of the emission from the decays of the excited band (0,0) ($\lambda=391.4$ nm) sharply decreases with increasing pressure in the RF ion source and reaches saturation at $P>$10*-1* Torr. In this region the percentage ratio of the metastable and ground states ions does not change. The abrupt decrease of intensity indicates a decrease of the relative weight of metastable ions in the ion source. Therefore, in collisions mainly ions of O*+* in the ground ${}^{4}S$ state participate.

To confirm this observation let us consider the dependence of the emission cross section of the band (0,0) $\lambda=391.4$ nm on the inverted velocity of the incident ion. This dependence is presented in figure 6. The observed linear dependence of the cross section on a semilogarithmic scale (linear decrease with increase of $1/v$) is nicely described by the relation $\sigma=Ae^{-a/v},$ where $A$ and $a$ are constants. As it is well known [50] such a dependence is a peculiar characteristic of inelastic processes realized in an adiabatic area. From this dependence one can conclude that the excitation process takes place in one inelastic channel and a definite portion in it is related solely to the ground state O*+(${}^{4}S$) ions. Thus, we can conclude that it is possible to vary the O+* ion beam content with different internal electronic states (ground and metastable) by changing the working condition in the ion source.

In our study of O${}^{+}-$N2 collisions, in addition to molecular bands, we also observed lines related to the N${}^{+^{\ast}}$ ion emissions, which are formed in the process of dissociative charge exchange processes (4) and (8). The most clearly identified lines for the dissociative product N${}^{+^{\ast}}$, which have sufficient intensity in the considered energy interval, are $\lambda=424.2$ nm, $\lambda=500.5$ nm, and $\lambda=567.9$ nm and they are presented in figure 2. The dissociation of the N${}_{2}(X^{2}\Sigma_{g}^{+})$ molecule in O${}^{+}-$N2 collisions leads to the production of N${}^{+^{\ast}}$ions in different excited states. The results of measurements of the dependence of the emission cross section on the energy of O*+* ions for the wavelength $\lambda=500.5$ nm, $\lambda=567.9$ nm and $\lambda=424.2$ nm are presented in figure 7. The emission cross sections for the dissociative product N${}^{+^{\ast}}$ increase with increasing the incident ion energy and show almost a linear dependence on the energy. The cross sections are measured at a pressure of $2.4\times 10^{-2}$ Torr in the ion source. With increasing pressure inside the source, the ion current at the outlet from the source drops sharply and, therefore, decreases also in the collision chamber. As a result the accuracy of the measurements decreases and, therefore, the sensitivity of the measurement of the emission cross section is significantly reduced. In particular, with a change in pressure inside the source by an order of magnitude from $P=2.4\times 10^{-2}$ Torr to $P=2.0\times 10^{-1}$ Torr, the change in the emission cross section of dissociation products in the low energy range of $1-2.5$ keV does not exceed 30% and in the high energy range of $5-10$ keV $10-15$%, and the latter one is within the accuracy of experimental measurements. The analyses of the cross sections for the 3$d$ ${}^{3}F^{0}\rightarrow$3$p$ ${}^{3}D$ (the line, NII $500.5$ nm) and 3$p$ ${}^{3}D\rightarrow 3s$ ${}^{3}P$ (the line NII $567.9$ nm) transitions shows that while the cross sections are of the same order of magnitude, the increment of the cross section for the 3$d$ ${}^{3}F^{0}\rightarrow$3$p$ ${}^{3}D$ transition is slightly larger than the one for the 3$p^{3}D\rightarrow 3s^{3}P$ transition. Moreover, these cross sections are significantly ($\sim$15 times) greater than the emission cross section for the $4fF\rightarrow$3$d$ ${}^{3}D$ (the line NII $424.2$ nm) transition. The similarity of the cross sections for NII $500.5$ nm and NII $567.9$ nm is probably due to the cascade population of the $3p$ ${}^{3}D$ state by the 3$d$ ${}^{3}F^{0}\rightarrow 3p$ ${}^{3}D$ transition.

To study the effect of different electronic states of ions O*+* on the magnitude of cross section for O${}^{+}-$N2 collision, one can conduct a study of molecular orientation by measuring the degree of linear polarization for the emission of excited molecular ion and explore the mechanism of inelastic processes realized in this collisions. In addition, the polarization measurements can be also used to separate a pure ground state O*+(${}^{4}S$) ion from the mixture of ${}^{4}S$ and ${}^{2}P$ states of the incident beam of O+* ion with high accuracy. The details of this procedure is given in the Appendix. The energy dependence of the degree of linear polarization for O${}^{+}-$N2 and He${}^{+}-$N2 collision systems is presented in figure 8. The data of figure 8a show the result for O${}^{+}-$N2 collision system and represent the polarization of the emission for the excited N${}_{2}^{+}$ ions obtained for the beam of O*+* ions in the ground ${}^{4}S$ state (curve 1) and 1.4% and 7.4% admixture of the metastable O*+(${}^{2}P$) state (curves 2 and 3, respectively). In figure 8b a comparison between the polarization for the emission for the same excited N${}_{2}^{+}$ ions (curve 1) obtained for He${}^{+}-$N2* collision is shown, while curve 2 represents the degree of linear polarization for the emission of the excited ${}^{3}P$ state of He atom. The comparison of the results in figure 8 (a) and (b) shows that with increasing energy of the incident ions the degree of linear polarization for the first negative band system of N${}_{2}^{+}$ molecular ion decreases, reaches saturation at high energy and is always positive. In addition, it is seen that the larger the metastable ${}^{2}P$ fraction in the ion beam the smaller the value of polarization. In spite of that, the portion of the metastable ${}^{2}P$ state in the total beam does not exceed 7.4 % (Fig.8a, curve 3), their contribution into the cross section is determinative. This fact is not surprising because it is known that the process of charge exchange by oxygen ions in the ${}^{2}P$ metastable states proceeds with a significantly higher (about two order) efficiency than by ions when it is in the ${}^{4}S$ ground state. This also means, that the process of charge exchange take place at a relatively large internuclear distance and an influence of the ion electric field on the electron cloud of the molecule is less pronounced. A relatively small degree of polarization corresponds to a small electron cloud orientation in space.

To explain the mechanism of population for excited N${}_{2}^{+}$ molecular ions let us consider the results presented in figure 8b. First of all, we have to mention that when an emission is polarized then it is anisotropic. This means that the electronic cloud of excited atomic or molecular particles should be oriented mainly either perpendicular or parallel to the direction of the incident ion beam. As seen from figure 8(b) one can observe a strong correlation between the degree of polarization for the emission of excited molecular ions (curve 1) and the emission of excited atomic line $\lambda=389.9$ nm of He(${}^{3}P$) (curve 2). In both cases the sign of the linear polarization changes at $2-3$ keV and at the energy range of $2-10$ keV the polarization degree of emission for the excited N${}_{2}^{+}$ ion reaches saturation and the sign is positive. The polarization of emission for the excited He(${}^{3}P$) atom it also has saturated character but its sign is negative. The fact, that the sign of the degree of polarization for the band of molecular N${}_{2}^{+}$ ion is positive (opposite to the excited He atomic line) indicates, that the electronic cloud of excited molecular ion of N${}_{2}^{+}$ is preferably oriented parallel to the direction of the incident beam and hence a molecular axis is oriented also parallel with respect to the direction of the incident ion beam. Of course, for a complete understanding of the excitation mechanism, it would be better to measure the degree of polarization (or circular polarization) for excited oxygen atomic line, realized in charge exchange processes O*+* $+$N2 $\rightarrow$ O${}^{\ast}+$ …. and apply some theoretical approach for more clarity. However, in our experiment the value of the cross section for excited oxygen atomic line was less compared to the band of molecular ion of N${}_{2}^{+}$, and the accuracy of the measurements does not permit to obtain reliable results. As an alternative way, we checked this opportunity for the excited He atomic line obtained in collision of He*+* $+$N2 $\rightarrow$ He${}^{\ast}+$ … hoping that an obtained opposite result will serve for establishing the excitation mechanism of N${}_{2}^{+}$ molecular ion.

IV CONCLUSIONS

Optical spectroscopy, in combination with an intense RF ion source, was applied to perform emission measurements for molecular N${}_{2}^{+}$ and atomic N*+* ions in collisions of O*+* (${}^{4}S$, ${}^{2}D,^{2}P$) with N2 molecules. The measurements are performed with the sufficiently high spectral resolution, which allows to distinguish the emission channels. The emission cross section of N${}_{2}^{+}$ ion for the (0,0), (0,1) and (1,2) bands systems in collision of mixed states of O*+* ions beam with nitrogen molecules have been measured. The ratio of the intensities for these bands was established  as $10:3:1$. The exact edge of the pressure condition in the RF source was revealed which enabled us to distinguish ground state and metastable states ions in the primary beam. The presence of ions in the metastable states of ${}^{2}P$ and ${}^{2}D$ was monitored by measurement of the energy dependence of  the emission cross section of the first negative band system (0, 0) $\lambda=391.4$ nm of N${}_{2}^{+}$ ion for different pressure condition in the RF source. An influence of the pressure condition in the RF source on the formation of certain O${}^{+}(^{2}P)$ states was established. Its percentage value for a pressure in the RF source of $P=2.4\times 10^{-2}$, $8\times 10^{-2}$ and $2\times 10^{-1}$ Torr was determined to be 7.4%, 3.4% and 1.4%, respectively. A small fraction of metastable ${}^{2}D$ ions in the ion source compare to ${}^{2}P$ and ${}^{4}S$ states was identified by measurements of the Meinel band system (3,0) $\lambda=687.4$ nm and (4,1) $\lambda=703.7$ nm.

The absolute emission cross section for (0,0) $\lambda=391.4$ nm band of the first-negative band system of the N${}_{2}^{+}$ by O*+* ions in the ground ${}^{4}S$ and metastable ${}^{2}P$ state was obtained in the energy interval $1-10$ keV. The influence of ions, having different electronic states (ground and metastable) on the magnitude of the cross section was established. It was found that metastable ${}^{2}P$ state ions indeed enhance the excitation cross section compared to those measured for the ground O${}^{+}(^{4}S)$ state ions. While the emission cross section obtained for the O${}^{+}(^{4}S)$ state ions sharply increases in all energy interval, the emission cross section for the incident O*+* ions in ${}^{2}P$ state is larger by two orders of magnitude at 1 keV and 10 time larger at 10 keV than that one for the O${}^{+}(^{4}S)$ incident ions.

In the case of collisions of O*+* with nitrogen molecules in the incident beam in emission processes, we used a filtration chamber, as in the earlier works, to assess the role of the metastable state O${}^{+}(^{2}D$, ${}^{2}P$). However, the originality of our work lies in the fact that ion filtration occurs in the RF ion source. The latter allows us to change the pressure and the mixture of gases inside the source, the power deposited inside the discharge, and other conditions which have an influence on formation of the incident ions beam.

The cross sections for the N${}^{+^{\ast}}$ions emissions in the dissociative charge exchange processes increase with increasing incident ion energy and show almost a linear dependence on the energy. The cross sections for the 3$d$ ${}^{3}F^{0}\rightarrow$3$p$ ${}^{3}D$ and 3$p$ ${}^{3}D\rightarrow 3s$ ${}^{3}P$ transitions are of same order of magnitude but significantly greater than the emission cross section for the $4fF\rightarrow$3$d$ ${}^{3}D$ transition. The similarity of the cross sections for the 3$d$ ${}^{3}F^{0}\rightarrow$3$p$ ${}^{3}D$ and 3$p$ ${}^{3}D\rightarrow 3s$ ${}^{3}P$ transitions is probably due to the cascade population of the $3p$ ${}^{3}D$ state by the 3$d$ ${}^{3}F^{0}\rightarrow 3p$ ${}^{3}D$ transition.

The mechanism of the processes realized during collisions of ground and metastable oxygen ions on molecular nitrogen have been established by the study of molecular orientation effect and measurement the degree of linear polarization for emission of excited molecular ions. It was demonstrated that for the O${}^{+}-$N2 collision system the degree of linear polarization by the metastable O${}^{+}(^{2}P)$ ions is less compared to those that are in the ground O${}^{+}(^{4}S)$ state and the sign of the degree of linear polarization of excited molecular ions does not change.

This is the first measurements of the energy dependence of the emission cross section of the band (0,0) $\lambda=391.4$ nm of the first-negative band system of the N${}_{2}^{+}$ in a wide energy range of $1-10$ keV of the incident O${}^{+}(^{4}S)$ and O${}^{+}(^{2}P)$ ions, as well as the degree of linear polarization of emission was measured for the first time.

Appendix A Polarization

The polarization of radiation can be written as:

[TABLE]

where $I_{||}$ and $I_{\perp}$ intensities of emission along and perpendicular to the ion beam, respectively.

Polarization of the emission emerging from excited ${}^{3}P$ state of helium is connected to the relative populations of m${}_{l}=0$ and m${}_{l}=\pm 1$ sublevels. The m${}_{l}=0$ correspond to the redistribution of electron cloud to the direction of ion beam and m${}_{l}=\pm 1$ to the perpendicular, respectively. Expression for the first Stock’s parameter has been derived on the basis of general approach developed by Macek and Jaecks in [51]. Here is presented only the final formula for the linear polarization:

[TABLE]

Taking into account that experimentally observed value of $\Pi$ is 20% (sign is negative), one obtains from (14) that $\sigma(m_{l}=\pm 1)/\sigma(m_{l}=0)\approx 15$. Such a great value of this ratio indicates that $m_{l}=\pm 1$ sublevels of the excited helium atom line are preferably populated. This means that the electron density formed in He*∗* during the collision is oriented perpendicularly with respect to the incident beam direction.

In this respect, it should be bear in mind that the ion current is two-component ions in the ground ${}^{4}S$ and metastable ${}^{2}P$ states, respectively. We have already determined their relative contribution in the total current, which depends on the pressure in the ion source. To perform the calculations, we considered the data for two different pressures $P_{1}=2.4\times 10^{-2}$ Torr and $P_{3}=20.0\times 10^{-2}$ Torr in the RF ion source. Our calculations above show that for these pressures $f_{0}=0.926$   and $f_{2}=0.074,$ and $f_{0}=0.986$ and $f_{2}=0.014,$ respectively.

For a given $P$ pressure, equations for $I_{||}$ and $I\perp$ components of the intensities can be written as

[TABLE]

The magnitude of the polarization is determined for the given energy and for the given state of the ions. It will be recorded as follows:

[TABLE]

While the experimental value is determine by Eq. (13)

[TABLE]

In the given equations, we can convert the effective cross section for the fixed energy and the different pressure $P_{1}$ and $P_{3}$ in the ion source. It is clear that the intensity of emission (standardized ion current and pressure in the collision chamber) measured in the experiment differs from the effective cross section with a constant coefficient $a$. That is,

[TABLE]

where $a$ is the constant of the absolute calibration in our conditions. Similarly $\sigma_{eff}=a\left[I_{||}(^{4}S)+I_{\perp}(^{4}S)\right]$ and $\sigma_{eff}=a\left[I_{||}(^{2}P)+I_{\perp}(^{2}P)\right]$ represent the absolute values of the effective cross section for the given $E$ energy for the ground ${}^{4}S$ and metastable ${}^{2}P$ states, respectively.

Finally we have a system of equations:

[TABLE]

where $x=a\left[I_{||}(^{4}S)-I_{\perp}(^{4}S)\right]$ and $y=a\left[I_{||}(^{2}P)-I_{\perp}(^{2}P)\right]$.

We solve the system of equations and find the values of $x$ and $y$. Then one can determine the polarization as $\Pi(^{4}S)=\frac{x}{\sigma_{0}(E)}$ and $\Pi(^{2}P)=\frac{y}{\sigma_{2}(E)}$, where $\sigma_{0}(E)$ and $\sigma_{2}(E)$ are the absolute emission cross sections for the processes induced by O${}^{+}(^{4}S$) and O${}^{+}(^{2}P$) ions, respectively, at the energy $E$. We performed this procedure at all energies and determined the energy dependence of the degree of linear polarization of the nitrogen molecular ion emission. In figure 8a curve 1 shows the results for the pure ${}^{4}S$ state only. The polarization measurement accuracy for the ${}^{2}P$ is much less than for ${}^{4}S$.