Photoabsorption of the ground state of Ne and of Ne-like Na+ , Mg2+ , Al3+ , Si4+ , P5+ , S6+ , and Cl7+ ions

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Photoabsorption of the ground state of Ne and of Ne-like Na+ , Mg2+ , Al3+ , Si4+ , P5+ , S6+ , and Cl7+ ions I. Sakho Department of Physics, UFR of Sciences and Technologies, University Assane Seck of Ziguinchor, Ziguinchor, Senegal

highlights • • • •

Accurate energies and widths of the 2p6 np 1 P1 series of Ne-like. Precise wavelengths of 2p6 . . . 2p5 nd transitions in Na+ and of 2p6 . . . 2p6 np 1 P1 transitions in Ne-like systems. New data for Ne-like Si4+ , P5+ , S6+ , and Cl7+ ions. Useful benchmarked data for the diagnostic of laboratory and astrophysical plasmas.

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Article history: Received 24 June 2015 Received in revised form 23 August 2015 Accepted 28 September 2015 Available online xxxx Keywords: Photoabsorption Photoionization Resonance energy Width Screening constant by unit nuclear charge

E-mail address: [email protected]. http://dx.doi.org/10.1016/j.adt.2015.09.003 0092-640X/© 2015 Elsevier Inc. All rights reserved.

abstract Photoabsorption of the 1s2 2s2 2p6 (1 S0 ) ground state of Ne-like ions is presented in this paper. Resonance energies and width of the 2s2p6 np 1 P1 series of Ne and Ne-like Na+ , Mg2+ , Al3+ , Si4+ , P5+ , S6+ , and Cl7+ ions are reported. Wavelengths of the 2s2 2p6 (1 S0 ) → 2s2 2p5 (2 P3/2,1/2 ) nd transitions in neon-like Na+ ion and of the 2s2 2p6 (1 S0 ) → 2s2p6 np 1 P1 transitions in Ne and in Ne-like Na+ , Mg2+ , Al3+ , Si4+ , P5+ , S6+ , and Cl7+ ions are tabulated. Analysis of the resonances investigated is done in the framework of the LS, jj and JK coupling schemes. All the calculations are made using the Screening constant by unit nuclear charge (SCUNC) formalism. Very good agreement is found between the SCUNC results and various experimental and theoretical literature values and new data for the Ne-like Si4+ , P5+ , S6+ , and Cl7+ ions are listed. © 2015 Elsevier Inc. All rights reserved.

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I. Sakho / Atomic Data and Nuclear Data Tables (

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Contents 1. 2.

3.

4.

Introduction........................................................................................................................................................................................................................ Theory ................................................................................................................................................................................................................................. 2.1. Brief description of the SCUNC formalism ........................................................................................................................................................... 2.2. Breakdown of LS coupling ..................................................................................................................................................................................... Results and discussion ....................................................................................................................................................................................................... 3.1. Energy limits of the 1s2 2s2p6 (2 S1/2 ) thresholds of neutral neon and of Ne-like (Z = 11–18) ions ................................................................ 3.2. Resonance energies of the 2s2p6 np 1 P1 series of neutral Ne atom..................................................................................................................... 3.3. Resonance energies of the doubly 2s2p4 (1 D)3s(2 D)np 1 P1 2s2p4 (3 P )3p(2 P )ns 1 P1 , and 2s2p4 (3 P )3p(2 P )nd 1 P1 excited states of neutral Ne atom................................................................................... 3.4. Resonance energies and width of the 1s2 2s2p6 (2 S1/2 )np1 P o series of Ne-like ions .......................................................................................... 3.5. Wavelengths of the 2s2 2p6 (1 S0 ) → 2s2p6 np1 P1 and 2s2 2p6 (1 S0 ) → 2s2 2p5 (2 P3/2,1/2 )nd transitions........................................................................................................................................................................ 3.5.1. Wavelengths of the 2s2 2p6 (1 S0 ) → 2s2p6 np1 P1 transitions in Ne-like ions ..................................................................................................... 3.5.2. Wavelengths of the 2s2 2p6 (1 S0 ) → 2s2 2p5 (2 P3/2,1/2 )nd transitions in Ne-like Na+ ion ................................................................................. Summary and conclusion .................................................................................................................................................................................................. Acknowledgments ............................................................................................................................................................................................................. References........................................................................................................................................................................................................................... Explanation of Tables .........................................................................................................................................................................................................

1. Introduction As well known, the transport of energy in hot dense plasmas is governed by Photoabsorption processes involving the Photoionization of the plasma ions. So, study of Photoabsorption of ionized matters is of great importance for understanding Photoionization processes playing a key role in many high-temperature plasma environments such as those in stars and nebulae [1] and those in inertial-confinement fusion experiments [2]. Neon is known to be the sixth most abundant element in the universe and then is of great importance in astrophysics in connection with the role of neon ions in the interpretation of astronomical data from stellar objects such as gaseous nebulas [3]. In addition, because of their closed-shell nature and wide applications in laboratory experiments, astrophysics and plasma physics, Ne-like ions were attractive candidate and have been the subject of several experimental [4–15] and theoretical [8, 16–23] studies. In a pioneering experiment on Ne at photon energies from 44 to 64 eV, Codling et al. [4] resolved only some of the numerous spectral features due to their limited 12 meV resolution. Using high resolution at 3 meV in the photon energy range 44–53 eV, Schulz et al. [10] resolved new relativistic features of highly excited resonances converging to different finestructure threshold 2p4 (3 P)3s 2 P and 2p4 (3 P)3p 2 P states of Ne+ . By neglecting fine-structure effects in the LS coupling scheme, Schulz et al. [10] stated that only the 2s singly 2s2p6 (2 S)np excited and five doubly excited 2p4 (3 P)3s(2 P)np, 2p4 (1 D)3s(2 D)np, 2p4 (3 P)3p(2 P)ns, 2p4 (3 P)3p(2 D)nd, and 2p4 (3 P)3p(2 P)nd Rydbergs series need to be considered below 53 eV, each of the preceding series being coupled to the final symmetry 1 Po . On the other hand, Lucatorto and Mcllrath [8] reported the first observation of ionization of dense Na vapor by using high-power tunable lasers (HPTL) source. Using a spark source, the Ne-like Na+ series 2s2 2p6 → 2s2 2p5 ns and nd, and several autoionizing resonances of the type 2s2 2p6 → 2s2p6 np have been resolved [8]. In addition, from high-voltage spark spectra (HVSS) experiments, Kastneret al. [9] observed and reported autoionizing transitions 2s2 2p6 → 2s2p6 np in Ne-like Mg III and Al IV ions and the similar transitions 3s2 3p6 → 3s3p6 np in Arlike Ca III, Sc IV, Ti V, V VI, Cr VII, and Fe IX ions. On the theoretical side, Schulz et al. [10] employed numerical calculations (NC) combining eigenchannel R-matrix method, multichannel quantum defect, and recoupling frame transformation to report energy positions and quantum defects relative to the singly 2s2p6 (2 S)np excited and to various observed doubly excited series. Besides, of great importance are also investigations focused

2 2 2 3 4 4 4 4 5 6 6 6 7 7 7 8

on heavy highly charged ions. In fact, relativistic effects, quantum electrodynamics (QED) contributions and nuclear size effects grow with higher powers of the charge state of highly charged ions as well stated by Gao et al. [22]. Experimentally, Simon et al. [13] studied the photoionization cross section of the Ne-like Ar8+ ion using an electron ion trap and synchrotron radiation (EIT-SR) and reported energy positions of the 2s2p6 (2 S1/2 )np 1 Po (n = 5–36) Rydberg series of Ar8+ converging to the 2s2p6 (2 S1/2 ) series limit in Ar9+ . Besides, Gao et al. [22] reported theoretical resonant parameters relative to the dominant 2s → np transitions in Nelike Ar8+ , Fe16+ , Kr26+ and Xe44+ ions using the Dirac atomic R-matrix codes (DARC) based on a fully relativistic R-matrix method. Very recently, Nrisimhamurty et al. [23], investigated the 2s → np autoionization resonances in the neon isoelectronic sequence from a time-dependent Dirac–Hartree–Fock (DHF) formalism and reported resonance energies, widths along with energy limits of the 2s2 2p5 (2 P3/2,1/2 ) and 2s2p6 (2 S1/2 ) thresholds of neutral neon and of several heavy highly charged Ne-like ions such as Hg70+ , and Bi73+ . The goal of the present study is to revisit the former studies on low and middle Z -Ne-like ions and to report new data for Si4+ , P5+ , S6+ , and Cl7+ ions. We apply then the SCUNC formalism [24–27] to report resonance energies and widths of the 2s2p6 np 1 P series of Ne and Ne-like Na+ , Mg2+ , Al3+ , Si4+ , P5+ , S6+ , and Cl7+ ions along with wavelengths of the 2s2 2p6 (1 S0 ) → 2s2 2p5 (2 P3/2,1/2 )nd transitions in neon-like Na+ ion and of the 2s2 2p6 (1 S0 ) → 2s2p6 np 1 P1 transitions in Ne and in Ne-like Na+ , Mg2+ , Al3+ , Si4+ , P5+ , S6+ , and Cl7+ ions. Analysis of the investigated resonances is done in the framework of the LS, jj and JK coupling. Section 2 presents the theoretical part of the work. In Section 3 we discuss and compare the results obtained with various experimental and theoretical literature values. 2. Theory 2.1. Brief description of the SCUNC formalism The starting point of the Screening constant by unit nuclear charge (SCUNC) formalism is the total energy of two electron

2S +1

systems for the Nl, nl′ Lπ doubly excited states described in the LS coupling scheme. For these states, the total energy is expressed as (in Rydberg units)



E Nl, nl′ ;



= −Z

2

2S +1 π

L



1 N2



+

1  n2

1 − β Nl, nl ;



′

2S +1 π

L ;Z

2



.

(1)

I. Sakho / Atomic Data and Nuclear Data Tables (

In this equation, the principal quantum numbers N and n are respectively for the inner and the outer electron of the heliumisoelectronic series. The β -parameters are screening constants by unit nuclear charge expanded in inverse powers of Z and given by

 β Nl nl′ ;

2S +1 π



L ;Z =

 k q  1 fk

k=1

(2)

Z

where fk = fk Nl nl′ ; 2S +1 Lπ are screening constants to be evaluated empirically. q stands for the number of terms in the expansion of the β -parameter. In general precise resonance energies are obtained for q < 5. For a given Rydberg series originating from a 2S +1 LJ state, we obtain



En = E∞ −

Z02  n2



1 − β(Z0 ,2S +1 LJ , n, s, µ, ν)

2

.

(3)

In Eq. (3), ν and µ (µ > ν ) denote the principal quantum numbers of the electron in the (2S +1 LJ )nl states used to evaluate empirically the fi — screening constants, s represents the spin of the nl-electron (s = 1/2), E∞ is the energy value of the series limit, En denotes the resonance energy and Z0 stands for the atomic number. The β -parameters are screening constants by unit nuclear charge expanded in inverse powers of Z0 as in Eq. (2)

β(Z0 ,2S +1 LJ , n, s, µ, ν) =

 k q  1 fk

k =1

Z0

(4)

where fk = fk (2S +1 LJ , n, s, µ, ν) are screening constants to be evaluated empirically. In the framework of the standard quantum-defect expansion formula, the resonance energy is given by

En = E∞ −

2 RZcore

(n − δ )2

.

(5)

In this equation, R is the Rydberg constant, E∞ denotes the converging limit, Zcore represents the electric charge of the core ion, and δ means the quantum defect. In the SCUNC formalism, the f2 -parameter in Eq. (4) can be theoretically determined from the equation ∗

lim Z = Z0

n→ ∞

 1−

f2 Z0



= Zcore .

(6)

We get then f2 = Z0 – Zcore , where Zcore is directly obtained from the photoionization process of an atomic Xp+ system:Xp+ hν → X (p+1)+ + e− . We find then Zcore = p + 1. For example, for Ne and Ne-like Na+ , Mg2+ , . . . , Cl7+ , we obtain for Zcore and f2

• Ne + hν → Ne+ + e− ; Zcore = 1; f2 = 9, 0; • Na + hν → Na +

2+

+ e ; Zcore = 2; f2 = 9, 0;

• Mg + hν → Mg + e− ; Zcore = 3; f2 = 9, 0; • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..; 2+

3+

(7)

• Cl7+ + hν → Cl8+ + e− ; Zcore = 8; f2 = 9, 0. These particular results indicate clearly that f2 = 9, 0 for all the Ne-like ions. The remaining f1 -parameter is evaluated empirically using experimental data for a given (2S +1 LJ )ν l level with µ = 0 in Eq. (4).

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2.2. Breakdown of LS coupling For light atoms where relativistic effects can be ignored, resonances can be analyzed in the LS coupling scheme. So the term   ⃗ ⃗L = ⃗ ⃗ is labeled as 2S +1 LJ with ⃗J = ⃗L + S; i li , S = i s⃗i ,

⃗L =

⃗ ⃗ and s⃗i being the orbital and spin angular momentums of the i-electron. For the 2s → np [1s2 2s2 2p6 (1 S0 ) → 1s2 2s2p6 np] transitions in low Z -Ne-like ions which lead to the 1s2 2s2p6 np series, the coupling of ⃗L and S⃗ gives the terms 1 P1 and 3 P2,1,0 terms; the 2s2 2p6 (1 S0 ) → 2s2p6 np 1 P1 transitions being optically allowed (∆S = 0) whereas the 2s2 2p6 (1 S0 ) → 2s2p6 np3 P2,1,0 transitions are optically forbidden (∆S = ±1). 

i li , li

When Z increases, the coupling scheme moves progressively from LS to jj coupling which is reached when the spin–orbit interaction is predominant with respect to the Coulomb repulsion between electrons. In general, the LS and jj couplings are only approximately satisfied because at intermediate Z , the coupling differs at each Z . Subsequently, in most of the cases, the resonances are characterized by intermediate coupling. In the jj scheme  ⃗ ⃗ ⃗ (with ⃗J = i ji and ji = li + s⃗i ) reached by approximately Z = 40 [23], the fine structure splitting of the Rydberg series is well described as (jc , jo )J (where jc denotes the total angular momentum of the target state and j0 represents the total angular momentum of the outermost electron) or as (jc , jo )n in Ref. [10]. Omitting for brevity the filled 1s2 and 2p6 shells, the 1s2 2s2p6 np series can be noted as 2snp. Then for 2s jc = 1/2 and for np, j0 = l ± s = 1/2 or 3/2. So the resonances are characterized as (1/2, 1/2)J =1,0 and (1/2, 3/2)J =2,1 . For J = 1, the 1s2 2s2p6 np series are described as [{1s2 2s2p6 }1/2np1/]J =1 and [{1s2 2s2p6 }1/2np3/2]J =1 respectively [23]. In addition, a mode of coupling observed mainly in excited configurations containing two outer electrons (or an electron and a vacancy), is the jK coupling (observed in the case of rare gas Ne I, Ar I, Kr I, . . .) ⃗ , and K⃗ + described as [28] l⃗1 + s⃗1 = j⃗1 , j⃗1 + l⃗2 = K s⃗2 = ⃗J. Symbolically, the excited n1 l1 n2 l2 configurations can be labeled as {[(l1 , s1 )j1 , l2 ]K , s2 }J or abbreviated as j1 [K ]J [23] or in Ref. [10] as [jc , nl]K . For example, in the case of the doubly 3p nd [2s2p4 (3 P)3p(2 P)nd1 P] excited states of Ne, j1 = 1/2, 3/2; K = 5/2, 3/2 (for j1 = 1/2) and 7/2, 5/2, 3/2, 1/2 (for j1 = 3/2). For the 2s2p4 (3 P)3p(2 P)nd1 P resonances, we obtain in JK coupling, the notations [1/2, nd]5/2; [1/2, nd]3/2, [3/2, nd]7/2; [3/2, nd]5/2, [3/2, nd]3/2; [3/2, nd]1/2 according to the [jc , nl]K label. In general, the SCUNC method is based on the empirical determination of the β -parameter given by Eq. (2) for total energy and by Eq. (4) for resonance energy. Pure LS coupling scheme is considered since the resonances are labeled as Nlnl′ 2S +1 Lπ . However, when the LS coupling scheme moves to another one, the SCUNC formalism moves naturally in the same way so no changes in the analytical formulas (1) and (3) are necessary. This is one of the strength of the SCUNC formalism. For instance, when the 2S +1 π resonances labeled as Nlnl′ L move to the new classification of the supermultiplets labeled as N (K , T )An 2S +1 Lπ , Eq. (1) for example is just rewritten as E

−

)

 (K , T )An ; 2S +1 Lπ    2 1  1 A 2S +1 π + 1 − β ( K , T ) ; L ; Z Ryd. = −Z 2 N n 2 2



N

N

n

One just needs to evaluate empirically the β -parameter using experimental data with respect to the N (K , T )An 2S +1 Lπ classification scheme as demonstrated previously [29–31]. In this paper, some of the resonances are labeled according to the jK coupling scheme as 2 PJ nd[K ]1 . The β -parameter is then just rewritten as β[2 PJ nd[K ]1 ] and the linked screening constants as fi [2 PJ , [K ]1 ]. So, for the resonances labeled as 2 PJ nd[K ]1 , the jK coupling is used in this work.

4

I. Sakho / Atomic Data and Nuclear Data Tables (

Otherwise, the LS coupling scheme is used for the investigated resonances. Overall, in the framework of the SCUNC formalism, the choice of a given coupling scheme depends on the availability of experimental data for resonances labeled according to the LS, jj or jK coupling.

Γn =

Z02 n2

+

The energy limit of the 1s2 2s2p6 (2 S1/2 ) threshold of neutral neon and of Ne-like ions (Z = 11–18) is given by (in Rydberg units). E (2s) =

Z2

 1−

4

f1 Z

+

f1 Z0

(Z − Z0 )

+ f1 ×

Z4

×

(Z − Z0 ) Z2

+ f13 ×

+

f1 Z0

(Z − Z0 ) Z5

×

2

.

(Z − Z0 ) Z3 (8)

The screening constants in Eq. (8) are evaluated using the experimental measurements of Persson [5] on Ne (Z0 = 10) at 48.475 eV. We get f1 = 6.2249. The results obtained for Ne up to Ar8+ are quoted in Table 1 and compared with experiments [5,15], theory [16,19,21,22] and the NIST [32] and good agreements are obtained. It should be mentioned that the SCUNC results for Al3+ at 164, 943 eV and for Ar8+ at 497,513 eV compare well with the NIST [32] data respectively equal to 164, 480 eV and 497,440 eV. It should be underlined that, the time-dependent Dirac–Hartree–Fock (DHF) calculations of Nrisimhamurty et al. [23] are slightly higher than the experimental energies because electron correlations have not been included in the DHF methodology as stated by Nrisimhamurty et al. [23]. This may explain the discrepancies between the SCUNC and DHF calculations. The expected accuracy of the present results from Ne to Ar8+ is due to the fact that the fk -screening constants are evaluated empirically using experimental data incorporating relativistic and electron–electron correlation effects. It has been shown previously [27] that the fk -parameters are sensitive to relativistic and electron–electron correlation corrections when they are evaluated from experiments. 3.2. Resonance energies of the 2s2p6 np 1 P1 series of neutral Ne atom The work of Schulz et al. [10] show that photoionization of the 2s2 2p6 1 S ground state of Ne is characterized at photon energies from 44 to 53 eV, by singly excited 2s2p6 np autoionizing Rydberg series and by overlapping doubly excited 2p4 3snp and 2p4 3pnl (l = s, d) autoionizing Rydberg series. The doubly excited resonances can be photoexcited mainly through the presence of 1

electron correlations in the initial 2s2 2p6 S state. But, these series typically appear with very low intensities in the photoionization cross section. We focus then our study on the optically allowed 2s2 2p6 1 S → 2s2p6 np 1 P1 dominant transitions in the Ne-like ions investigated. The resonance energy of the 2s2p6 np 1 P1 series is given by (in Ryd) En = E∞ −

Z02 n2

 1−

f1 (1 P1 ) Z0 (n − 1)

−

f2 ( 1 P1 ) Z0

f1 ( P1 ) × (n − ν) 1

−

+

Z02 (n + ν + s + 1) × (n + ν + s) f1 (1 P1 ) × (n − ν) Z03 (n + ν − s) × (n + ν + s)

2

.

(9)

From synchrotron radiation experiments of Schulz et al. [10] on Ne (Z0 = 10), we get for the 2s2p6 3p 1 P1 level (ν = 3) E3 =

–

45.5442(50) eV with the limit E∞ = 48.475. As f2 (1 P1 ) = 9, 0, Eq. (9) gives f1 (1 P1 ) = −0.7847 ± 0.0048. Besides, the width of the 2s2p6 np 1 P1 series is expressed as follows (in Ryd)

3. Results and discussion 3.1. Energy limits of the 1s2 2s2p6 (2 S1/2 ) thresholds of neutral neon and of Ne-like (Z = 11–18) ions

)

 1−

f1′ (1 P1 ) Z0 (n − 1 )

−

f2′ (1 P1 ) Z0

f1′ (1 P1 ) × (n − ν) × (n − µ) Z02 (n − ν + s + 1) × (n − µ + s + 1)

2

.

(10)

To determine the fi -parameters in Eq. (10), we use the experimental data of Codling et al. [4] on Ne (Z0 = 10) for the 2s2p6 3p 1 P1 (ν = 3) and 2s2p6 4p 1 P1 (µ = 4) levels respectively at (in meV) 13 (2) and 4.5 (1.5). From Eq. (10) we get f1′ (1 P1 ) = −0.120 ± 0.026 and f2′ (1 P1 ) = 9.967 ± 0.020. The results obtained for Ne and for Ne-like Na+ , Mg2+ , Al3+ , Si4+ , P5+ , S6+ , and Cl7+ ions are listed in Tables 2–4. In Table 2, the present SCUNC calculations of the resonance energies of the 2s2p6 np 1 P1 (n = 3–7) series of Ne are compared with the theoretical values of Schulz et al. [10], Langer et al. [18], Liang et al. [20], Stener et al. [17], Nrisimhamurty et al. [23] and with the experimental data of Schulz et al. [10], and of Codling et al. [4]. In general very good agreements are found. It should be underlined the very good agreement between the present SCUNC results for the 2s2p6 6p 1 P1 and 2 s2p6 7p 1 P1 levels respectively at 47.966 eV and 48.117 eV and the synchrotron radiation data [10] for the same levels respectively equal to 47.965 eV and 48.116 eV. Table 3 lists resonance energies and effective quantum number n∗ = n − δ of the 2s2p6 np 1 P1 (n = 3–30) series of neutral Ne atom. Comparison is done with the existing numerical calculations (NC) of Schulz et al. [10], synchrotron radiation (SR) experiments [10], and with photoabsorption (PA) experiments of Codling et al. [4] for n = 3–20. In pure LS coupling where relativistic effects can be neglected, the effective quantum number is simply n∗ = n − δ , with δ the quantum defect of the resonance. Comparison indicates a very good agreement between the SCUNC calculations and the quoted theoretical and experimental values up to n = 20. For example, for the 12p level, the SCUNC prediction at 48.3658 eV is seen to agree very well with the NC results of Schulz et al. [10] at 48.3666 eV, with the SR data [10] 48.3650 (10) eV and with the PA data of Codling et al. [4] equal to 48.365 (6) eV. For the high 20p state, the SCUNC value equal to 48.4379 eV agrees excellently with both the NC results [10] at 48.4380 eV and the SR data [10] at 48.4370 (10) eV. As shown in the work of Schulz et al. [10], electron–electron correlations are present in the 1

initial 2s2 2p6 S state of Ne. Subsequently, state-of-the art sophisticated ab initio methods are required to succeed on obtained high precise results. The very good agreement between the SCUNC calculations and both high resolution experiments [10] and numerical calculations [10] combining eigenchannel R-matrix method, multichannel quantum defect (MQDT), and recoupling frame transformation, demonstrate once again, the adequacy of the SCUNC formalism to threat the properties of atomic systems even if strong electron–electron correlations effects are present. Table 4 presents the width (Γ ) of the 2s2p6 np 1 P1 series of Ne. The agreement between theory and experiment is fairly good. It can be mentioned the good agreement between the SCUNC calculations and the experimental data [10] for n = 3–4 and the NC results of Schulz et al. [10] for n > 7 where the difference ∆Γ = |Γ SCUNC –Γ NC | between the SCUNC calculations and the numerical calculations [10] is less than 0.01 meV. 3.3. Resonance energies of the doubly 2s2p4 (1 D)3s(2 D)np 1 P1 2s2p4 (3 P )3p(2 P )ns 1 P1 , and 2s2p4 (3 P )3p(2 P )nd 1 P1 excited states of neutral Ne atom The resonance energies of the doubly 2s2p4 (1 D)3s(2 D)np 1 P1 , 2s2p4 (3 P)3p (2 P)ns 1 P1 , and 2s2p4 (3 P)3p (2 P)nd1 P1 excited states of neutral Ne atom are given by

I. Sakho / Atomic Data and Nuclear Data Tables (

• For 2s2p4 (1 D)3s(2 D)np 1 P  Z2 f1 (2 D) f2 (2 D) f1 (2 D) × (n − ν) En = E∞ − 02 1 − − − 2 n Z0 (n − 1 ) Z0 Z0 (n − ν + s)2 2 f1 (2 D) × (n − ν) − 3 . (11) Z0 (n − ν + s)2 • For 2s2p4 (3 P)3p(2 P)ns 1 P  Z2 f1 (2 P ) f2 (2 P ) En = E∞ − 02 1 − − n Z0 (n − 1 ) Z0 f1 (2 P ) × (n − ν) + 2 Z0 (n − ν + s + 1) × (n − ν + 2s + 1) 2 f1 (2 P ) × (n − ν) . + 3 Z0 (n − ν + 1) × (n − ν + s)

(12)

• For 2s2p4 (3 P)3p(2 P)nd1 P  f1 (2 P ) f2 (2 P ) f1 (2 P ) × (n − ν) Z02 En = E∞ − 2 1 − − − 2 n Z0 (n − 1 ) Z0 Z0 (n − ν + s2 )2 2 f1 (2 P ) × (n − ν) . (13) − 3 Z0 (n − ν + s2 )2 For the 2s2p4 (1 D)3s (2 D)np1 P1 , 2s2p4 (3 P)3p(2 P)ns 1 P1 , and 2s2p4 (3 P)3p (2 P)nd1 P1 Rydberg series of Ne atom (Z0 = 10), the f1 (2 L) screening constants are evaluated using synchrotron radiation (SR) energies of Schulz et al. [10] for the 2s2p4 (1 D)3s (2 D)3p 1 P1 (ν = 3), 2s2p4 (3 P)3p (2 P)4s 1 P1 (ν = 4), and 2s2p4 (3 P)3p (2 P)3d 1 P1 (ν = 3) levels respectively at (in eV) 48.9066 (15), 50.760 (5), and 51.308 (4). As far as energy limits are concerned, they are equal to (in eV) 52.114 and 53.082 respectively for the 2s2p4 (1 D)3s (2 D) and 2s2p4 (3 P)3p (2 P) thresholds. We find from Eq. (11) f1 (2 D) = −0.9132 ± 0.0010, from Eq. (12) f1 (2 P) = −1.9574 ± 0.0054 and from Eq. (13) f1 (2 P) = −0.1665 ± 0.0024. The present results obtained for resonance energies and effective quantum number n∗ = n − δ are quoted in Tables 5–7. Comparison is done with the numerical calculations (NC) of Schulz et al. [10] along with their synchrotron radiation (SR) values and with the photoabsorption (PA) data of Codling et al. [4]. For the 2s2p4 (1 D)3s (2 D)np 1 P series, the SCUNC results listed in Table 5 are seen to agree very well with both the quoted experimental and theoretical data up to n = 16. For the 16p level for example, the difference ∆E = |E SCUNC –E SR | between the SCUNC calculations at 52.0534 eV and the synchrotron radiation (SR) values [10] at 52.0542 (25) eV is equal to 0.008 eV. In general, the magnitude of ∆E between the SCUNC and the quoted experimental and theoretical values is less than 0.010 eV. Table 6 presents the resonance energies and effective quantum numbers n∗ = n − δ of the doubly 2s2p4 (3 P)3p (2 P)ns 1 P excited states of Ne. In their work, Schulz et al. [10] expected in pure LS coupling only two 2p4 (3 P)3p(2 P)nl 1 Po series (l = s, d) and showed that these resonances are characterized best in jK coupling. So, for the n > 7 members exhibiting weak observable relativistic effects, the resonances are classified according to the relativistic jK coupling as [jc , nl]K and only the prominent members observed in the spectrum of Ne (K = 3/2) are listed. Explicitly we get [3/2, 8s]3/2; [3/2, 9s]3/2; [3/2, 10s]3/2; [3/2, 11s]3/2; [3/2, 12s]3/2 for n = 8–12. Comparison shows that the SCUNC results reproduce very well the experimental data up to n = 12. However, it should be underlined that, in jj or jK coupling, the effective quantum number is not simply n∗ = n − δ . In Table 3 where the 2s2p6 np 1 P1 resonances are described in LS coupling, the effective quantum defect n∗ for example for n = 12, is equal to 11.163 for the SCUNC result, 11.182 for the NC value [10], and 11.12 (5) for the SR data [10]. Here it is seen

)

–

5

that the quantum defect δ < 1 and is equal to 0.837 (SCUNC), 0.818 (NC) and 0.880 (SR). But, in Table 6 for example, for the same level n = 12 [2s2p4 (3 P)3p(2 P)12s 1 P], the effective quantum defect n∗ is 10.574 (NC), and 10.40 (8) (SR) in jK coupling, and 10.350 in the present work where the resonance is described in LS coupling. The difference n − n∗ is equal to 1.426 (NC), 1.60 (SR) and 1.65 (SCUNC). So (n − n∗ ) > 1. This may indicate that, in JK coupling, the quantum defect is not given by the simply relation δ = n − n∗ . Schulz et al. [10] indicated that, jK and jj coupling are equally valid in their experimental spectrum because the only observable quantum numbers are the spin-angular momentum jc of the target, the angular l and principal quantum number n of a Rydberg electron. Subsequently, analysis of the quantum defect can be done in the framework of the jj coupling as δnlj = n − n∗ + (j + 1) − [(j + 1)2 − (z α)2 ]1/2 , where z is the asymptotic charge seen by the photoelectron and α is the fine-structure constant [23]. This relation may enlighten the behavior of the effective quantum number for the doubly 2s2p4 (1 D)3s (2 D)np1 P1 , 2s2p4 (3 P)3p(2 P)ns 1 P1 , and 2s2p4 (3 P)3p (2 P)nd1 P1 excited states of Ne described in the jK coupling (bearing in mind that jK and jj coupling are equally valid in the experimental spectrum). In Table 6, the n > 7 members are classified according to the relativistic jK coupling as [jc , nl]K . But, for the 2s2p4 (3 P)3p (2 P)12s 1 P level the SCUNC (n − n∗ ) value at 1.65 obtained in LS coupling scheme is seen to agree well with the corresponding (n − n∗ ) SR experimental data at 1.60 [10] with a relative error equal to 0.05. This good agreement may indicate that the n < 7 members quoted in Table 6 must not be described in pure LS coupling. In fact, as explained above, jK coupling is observed mainly in excited configurations containing two outer electrons in the case of rare gas Ne I, Ar I, Kr I,. . . Overall, the good agreement between theory and experiment indicate the adequacy of the SCUNC formalism to treat the properties of doubly excited states in Ne-like ions even if the resonances are classified according to the relativistic jj or jK coupling schemes. 3.4. Resonance energies and width of the 1s2 2s2p6 (2 S1/2 )np1 P o series of Ne-like ions The resonance energies of the 1s2 2s2p6 (2 S1/2 )np 1 Po series for the Ne-like Na+ , Mg2+ , Al3+ , Si4+ , P5+ , S6+ , and Cl7+ ions are given by (in Ryd). En = E∞ −

Z2

 1−

n2

f1 (1 P1 ) Z (n − 1)

×

Z Z0

−

f2 (1 P1 ) Z

f1 ( P1 ) × (n − ν) 1

− −

Z 2 (n + ν + s + 1) × (n + ν − s)

2

f1 (1 P1 ) × (n − ν) Z 3 (n − ν + s + 1) × (n − ν − s + 1)

.

(14)

Using the high-power tunable lasers (HPTL) data of Lucatorto and Mcllrath [8] on Ne-like Na+ (Z0 = 11) at 69.95 ± 0.02 eV for the 2s2p6 3p 1 P1 level (ν = 3). The uncertainty in the experimental data 69.95 eV is estimated from the relation ∆E /E = ∆λ/λ. For the 2s2p6 3p 1 P1 level, λ = 17.724 ± 0.005 nm and E = 69.95 eV [8]. So we get ∆E = 0.02 eV. Using our energy limit E∞ = 80.274 eV we find f1 (1 P) = −1.2265 ± 0.0051 with f2 (1 P1 ) = 9, 0. Besides, the widths are given by

Γn =

Z2 n2

×

 1−

(Z − Z0 ) Z2

f1′ (1 P1 ) Z (n − 1)

×

Z Z0

−

f2′ (1 P1 ) Z

×

Z Z0

+

f2′ (1 P1 ) Z

f1 ( P1 ) × (n − ν) × (n − µ) ′ 1

+

Z 2 (n − ν + s + 1) × (n − µ + s + 1)

2

. (15)

6

I. Sakho / Atomic Data and Nuclear Data Tables (

The screening constants calculated for Ne (Z0 = 10) are the same in Eqs. (15) and (10), so f1′ (1 P1 ) = −0.120 ± 0.026 and f2′ (1 P1 ) = 9.967 ± 0.020. Tables 8–11 list the results obtained for the Ne-like Na+ , Mg2+ , Al3+ , Si4+ , P5+ , S6+ , and Cl7+ ions. Comparison is done with scare literature values. Table 8 quotes the present SCUNC calculations of the resonance energies of the 2s2p6 np 1 P1 series of Na+ and Mg2+ up to n = 30. Comparison is done with highpower tunable lasers (HPTL) data of Lucatorto and Mcllrath [8], high-voltage spark spectra (HVSS) results of Kastner et al. [9], and with time-dependent Dirac–Hartree–Fock (DHF) calculations of Nrisimhamurty et al. [23]. For Na+ , the present results are seen to agree with the HPTL data [8] up to n = 8 with a maximum relative energy difference at 0.22 eV. The difference between the present energy limit at 80.274 eV and the HPTL energy limit at 80.091 eV (645 977 cm−1 in Ref. [8], using for energy conversion 1 cm−1 = 0.00012398 eV) is equal to 0.18 eV ≈ 0.20 eV and may explain why the SCUNC results are about 0.20 eV greater than the experimental data [8]. This is also shown comparing the DHF calculation at 73.746 eV (with an energy limit at 83.877 eV) and the experimental data at 69.95 eV for the 2s2p6 3p 1 P1 level where the shift in energy is at 3.796 eV. This difference is seen to be in the same magnitude that the difference between the DHF and experimental energy limits (83.877 − 80.091 = 3.786 eV). For Mg2+ and Al3+ the high-voltage spark spectra (HVSS) results of Kastner et al. [9] are deduced from the formula E = hc /λ where h and c denote respectively the Planck’s constant (h = 6.63 × 10−34 J.s) and the velocity of light (c = 3 × 108 m s−1 ). For energy conversion, we use 1 Ryd = 13.60569 eV with 1 eV = 1.60 × 10−19 J. If λ is expressed in Å, we get in eV, E = 12 431.25/λ. The experimental wavelengths [9] for the 2s2 2p6 (1 S0 ) → 2s2p6 np 1 P1 transitions are quoted in Table 12. The agreements between the SCUNC results and the HVSS results [9] are seen to be good for both Mg2+ and Al3+ . For Si4+ , comparison indicates a good agreement with the multiconfiguration Dirac–Fork (MCDF) calculations of Bizau et al. [12] who mentioned in their work the R-matrix calculation of Hibbert and Scott [33] for the 2s2p6 3p 1 P1 level at 167 eV to be compared with the SCUNC result at 167.169 eV. Table 10 lists the present calculations of resonance energies of the 2s2p6 np 1 P1 series of Ne-like P5+ , S6+ , and Cl7+ ions. No literature values are found for comparison and they may be considered as benchmarked new data for future experimental and theoretical studies on their Ne-like ions. 3.5. Wavelengths of the 2s2 2p6 (1 S0 ) → 2s2p6 np1 P1 and 2s2 2p6 (1 S0 ) → 2s2 2p5 (2 P3/2,1/2 )nd transitions 3.5.1. Wavelengths of the 2s2 2p6 (1 S0 ) → 2s2p6 np1 P1 transitions in Ne-like ions The wavelength of the 2s2 2p6 (1 S0 ) → 2s2p6 np 1 P1 transitions, the wavelengths are given by

∆E = [E (2s) − En ] =

hc

λ

.

(16a)

In this equation, h and c denote respectively the Planck’s constant (h = 6.63 × 10−34 J s) and the velocity of light (c = 3 × 108 m s−1 ). For energy conversion, we use 1 Ryd = 13.60569 eV with 1 eV = 1.60 × 10−19 J. In addition, the resonance energy En of the 2s 2p6 np 1 P1 series is given by (in Ryd) En = E∞ −

×

Z2



n2

(Z − Z0 ) Z

1−

+

f1 ( 1 P1 ) Z (n − 1)

×

Z Z0

−

f2 (1 P1 ) Z

+

f12 (1 P1 )

( ) × (n − ν) × (n − µ) ( + ν − s) × (n + ν + µ − s)

f12 1 P1 Z2 n

Z

2

.

(16b)

The values of the fi -screening constants are evaluated using the experimental wavelengths of Codling et al. [4] for the

)

–

2s2 2p6 (1 S0 ) → 2s2p6 3p1 P1 (ν = 3) and 2s2 2p6 (1 S0 ) → 2s2p6 4p1 P1 (µ = 4) transitions respectively at 272.21 Å and 263.11 Å for Ne (Z0 = 10) as quoted in Kastner et al. [9]. Eq. (16) gives then f1 = −0.7684 and f2 = 8.9908. The results obtained for Ne and for the Ne-like Na+ , Mg2+ , Al3+ , Si4+ , P5+ , S6+ , and Cl7+ ions are presented in Tables 12–14 compared to the experimental data of Codling et al. [4], Esteva and Mehlman [6], Carillon et al. [7], Lucatorto and McIlrath [8] and of Kastner et al. [9]. Good agreements are found between the SCUNC calculations and the quoted experimental data for Na+ , Mg2+ , and Al3+ . The results for the Ne-like Si4+ , P5+ , S6+ , and Cl7+ ions expected to be accurate are new useful data for the physical community focusing their study on the Photoabsorption or Photoionization of the 2s2 2p6 (1 S0 ) ground state of Ne-like ions characterized by singly excited 2s2p6 np 1 P series. 3.5.2. Wavelengths of the 2s2 2p6 (1 S0 ) → 2s2 2p5 (2 P3/2,1/2 )nd transitions in Ne-like Na+ ion The wavelength of the 2s2 2p6 (1 S0 ) → 2s2 2p5 (2 P3/2,1/2 )nd transitions in Ne-like Na+ ion are given by

∆E = [E (2s) − En ] =

hc

λ

.

(17a)

As the 2s2 2p5 (2 P3/2,1/2 )nd series are described in jK coupling, the resonance energy En is given by (in Ryd) En = E∞ −

−

Z02 n2

 1−

f1 (2 PJ , [K ]1 ) Z0 (n − 1)

−

f2 (2 PJ , [K ]1 ) Z0

f1 (2 PJ , [K ]1 ) × (n − ν) × (n − µ)2 Z02 (n − ν + s + 1) × (n − µ + s + 1)

2

.

(17b)

The values of the fi (2 PJ , [K ]1 )-screening constants (J = 3/2, 1/2; K = 3/2, 1/2) are evaluated using the experimental wavelengths from Lucatorto and McIlrath [8] for the 2s2 2p6 (1 S0 ) → 2s 2 2p5 (2 P3/2,1/2 ) 5d (ν = 5) and 2s2 2p6 (1 S0 ) → 2s2 2p5 (2 P3/2,1/2 ) 6d (µ = 6) transitions in Na+ (Z0 = 11). The resonances are labeled according of the jK coupling as 2 P3/2,1/2 nd[K ]J . In the present work, the 2 P1/2 nd[3/2]1 , 2 P3/2 nd[1/2]1 , and 2 P3/2 nd[3/2]1 series are considered due the availability of the experimental data. The energy limits of the 2p5 (2 P3/2 ) and 2p5 (2 P1/2 ) are respectively equal to 381390 cm−1 and 382754 cm−1 [8]. Using for energy conversion 1 cm−1 = 0.00012398 eV, we get E∞ [2p5 (2 P3/2 )] = 47.285 eV and E∞ [2p5 (2 P3/2 )] = 47.454 eV. From Lucatorto and McIlrath [8], we get the 2 P3/2 5d [1/2]1 and 2 P3/2 5d [1/2]1 levels respectively at (in Å) 275. 22 and 271.37. So we obtain from Eq. (17) the screening constants f1 (2 P3/2 , [1/2]1 ) = 0.079 and f2 (2 P3/2 , [1/2]1 ) = 9.008. In the same way, using the data for the 2 P3/2 5d [3/2]1 and 2 P3/2 5d [3/2]1 levels respectively at (in Å) 275. 00 and 270.95 [8], Eq. (17) gives f1 (2 P3/2 , [3/2]1 ) = −0.545 and f2 (2 P3/2 , [3/2]1 ) = 9.181. Finally, using the data for the 2 P1/2 5d [3/2]1 and 2 P1/2 5d [3/2]1 levels respectively at (in Å) 274. 02 and 269.99 [8], Eq. (17) gives f1 (2 P1/2 , [3/2]1 ) = −0.533 and f2 (2 P1/2 , [3/2]1 ) = 9.175. The results obtained for Na are listed in Tables 15 and 16 compared with the experimental data of Lucatorto and McIlrath [8] and with data from unpublished thesis of Wu as quoted in [8]. The agreement between the SCUNC calculations and the quoted experimental data is very good. These agreements demonstrate again the adequacy of the SCUNC formalism to treat the properties of doubly excited states in Nelike ions where the resonances are classified according to the relativistic jK coupling.

I. Sakho / Atomic Data and Nuclear Data Tables (

4. Summary and conclusion Photoabsorption from the 1s2 2s2 2p6 (1 S0 ) ground state of Ne-like ions have been investigated in this paper using the Screening constant by unit nuclear charge (SCUNC) method. Resonance energies and widths of the 2s2p6 np 1 P1 series of Nelike (Z = 10–17) along with wavelengths of the 2s2 2p6 (1 S0 ) → 2s 2 2p5 (2 P3/2,1/2 )nd transitions in neon-like Na+ ion and of the 2s2 2p6 (1 S0 ) → 2s2p6 np1 P1 transitions in Ne and in Ne-like Na+ , Mg2+ , Al3+ , Si4+ , P5+ , S6+ , and Cl7+ ions are tabulated. Overall, the SCUNC results agree very well with various experimental and theoretical literature data. It should be mentioned the adequacy of the SCUNC formalism to treat the properties of doubly excited states in Ne-like ions when the resonances are classified according to the relativistic jK coupling. New data for the Ne-like Si4+ , P5+ , S6+ , and Cl7+ ions are tabulated and they may be useful benchmarked data for future studies on the Photoionization of the 2s2p6 np1 P1 series of Ne-like Si4+ , P5+ , S6+ , and Cl7+ ions on the both sides of theory and experiment.

[4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]

Acknowledgments [24]

The author would like to thank Prof. S.T Masson at the Department of Physics and Astronomy, Georgia State University, Atlanta, Georgia 30303, USA for useful support. References [1] J.N. Bregman, J.P. Harrington, Astrophys. J. 309 (1986) 833. [2] I. Hofmann, Laser Part. Beams. 8 (1990) 527. [3] M. Faye, B. Diop, M. Guèye, I. Sakho, A.S Ndao, M. Biaye, A. Wagué, Rad. Phys. Chem. 85 (2013) 1.

[25] [26] [27] [28] [29] [30] [31] [32] [33]

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K. Codling, R.P. Madden, D.L. Ederer, Phys. Rev. 155 (1967) 26. W. Persson, Phys. Scr. 3 (1971) 133. J.M. Esteva, G. Mehlman, Astrophys. J. 193 (1974) 747. A. Carillon, G. Jarnelot, A. Sureau, P. Jaegle, Phys. Lett. 38A (1972) 91. T.B. Lucatorto, T.J. Mcllrath, Phys. Rev. Lett. 37 (1976) 428. S.O. Kastner, A.M. Crooker, W.E. Behring, Leonard Cohen, Phys. Rev. A 16 (1977) 577. K. Schulz, M. Domke, R. Püttner, A. Gutiérrez, G. Kaindl, G. Miecznik, C.H. Greene, Phys. Rev. A 54 (1996) 3095. H.S. Chakraborty, A. Gray, J.T. Costello, P.C. Deshmukh, G.N. Haque, E.T. Kennedy, S.T. Manson, J.-P. Mosnier, Phys. Rev. Lett. 83 (1999) 2151. J.-M. Bizau, J.-P. Mosnier, E.T. Kennedy, D. Cubaynes, F.J. Wuilleumier, C. Blancard, J.-P. Champeaux, F. Folkmann, Phys. Rev. A 79 (2009) 033407. J.S. Hildum, J. Cooper, J. Quant. Spectros. Radiat. Transfer 12 (1972) 1453. L. Liang, W. Gao, C. Zhou, Phys. Scr. 87 (2012) 015301. M.C. Simon, et al., J. Phys. B 43 (2010) 065003. W.C. Martin, R. Zalubas, J. Phys. Chem. Ref. Data 10 (1981) 153. M. Stener, P. Decleva, A. Lisini, J. Phys. B 28 (1995) 4973. B. Langer, N. Berrah, R. Wehlitz, T.W. Gorczyca, J. Bozek, A. Farhat, J. Phys. B 30 (1997) 593. A.K.S. Jha, P. Jha, S. Tyagi, M. Mohan, Eur. Phys. J. D 39 (2006) 391. L. Liang, Y.C. Wang, C. Zhou, Phys. Lett. A 360 (2007) 599. L. Liang, Z. Chao, Z.-X. Xie, Opt. Commun. 282 (2009) 558. C. Gao, D.H. Zhang, L.Y. Xie, J.G. Wang, Y.L. Shi, C.Z. Dong, J. Phys. B 46 (2013) 175402. M. Nrisimhamurty, G. Aravind, P.C. Deshmukh, S.T. Manson, Phys. Rev. A 91 (2015) 013404. I. Sakho, B. Diop, M. Faye, A. Sène, M. Guèye, A.S. Ndao, M. Biaye, A. Wagué, At. Data Nucl. Data Tables 99 (2013) 447. I. Sakho, At. Data Nucl. Data Tables 100 (2014) 297. I Sakho, M. Sow, A. Wagué, Rad. Phys. Chem. 82 (2015) 110. I Sakho, M. Sow, A. Wagué, Phys. Scr. 90 (2015) 045401. E. Biémont, Spectroscopie atomique, COURS, Editions De Boeck Université, Bruxelles, 2006. I. Sakho, A. Konte, A.S. Ndao, M. Biaye, A. Wague, Phys. Scr. 77 (2008) 055303. I. Sakho, Eur. Phys. J. D 59 (2010) 171–177. I. Sakho, Eur. Phys. J. D 61 (2011) 267–283. A.E. Kramida, Yu. Ralchenko, J. Reader, NIST ASD Team (2014), NIST Atomic Spectra Database, version 5.2, http://physics.nist.gov/asd. A. Hibbert, M.P. Scott, J. Phys. B 27 (1994) 1315.

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I. Sakho / Atomic Data and Nuclear Data Tables (

)

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Explanation of Tables Table 1. Table 2. Table 3. Table 4. Table 5. Table 6. Table 7. Table 8. Table 9. Table 10. Table 11. Table 12. Table 13. Table 14. Table 15. Table 16.

Energy limit (E, in eV) of the 1s2 2s2p6 (2 S1/2 ) threshold of neutral neon and of Ne-like ions (Z = 11–18). Resonance energies (E, eV) and quantum defect (δ ) of the 2s2p6 np 1 P1 series of Ne. Resonance energies (E, eV) and effective quantum number n∗ = n − δ of the 2s2p6 np 1 P1 series of neutral Ne atom. Width (Γ , meV) of the 2s2p6 np 1 P1 series of Ne. Resonance energies (E, eV), and effective quantum number n∗ = n − δ of the doubly 2s2p4 (1 D)3s (2 D)np1 P excited states of Ne. Resonance energies (E, eV), and effective quantum number n∗ = n − δ of the doubly 2s2p4 (3 P)3p (2 P)ns1 P excited states of Ne. Resonance energies (E, eV), and effective quantum number n∗ = n − δ of the doubly 2s2p4 (3 P)3p(2 P)nd1 P excited states of Ne. Resonance energies (E, eV) of the 2s2p6 np 1 P1 series of Na+ and Mg2+ . Resonance energies (E, eV) of the 2s2p6 np 1 P1 series of Ne-like Al3+ and Si4+ ions. Present screening constant by unit nuclear charge (SCUNC) calculations of resonance energies (E, eV) and quantum defect (δ ) of the 2s2p6 np 1 P1 series of Ne-like, P5+ , S6+ , and Cl7+ ions. Width (Γ , meV) of the 1s2 2s2p6 np 1 P1 series of Ne-like ions (Z = 11–14). Wavelengths (λ, in Å) of the 2s 2 2p6 (1 S0 ) → 2s2p6 np 1 P1 transitions in Ne and in Ne-like Na+ and Mg2+ ions. Wavelengths (λ, in Å) of the 2s 2 2p6 (1 S0 ) → 2s2p6 np 1 P1 transitions in Ne-like Al3+ and Si4+ ions. Present screening constant by unit nuclear charge (SCUNC) calculations of wavelengths (λ, in Å) of the 2s2 2p6 (1 S0 ) → 2s 2p6 np 1 P1 transitions in Ne-like S6+ , Cl7+ and Ar8+ ions. Wavelengths (λ, in Å) of the 2s 2 2p6 (1 S0 ) → 2s 2 2p5 (2 P3/2 )nd transitions in neon-like Na+ ion. Wavelengths (λ, in Å) of the 2s 2 2p6 (1 S0 ) → 2s 2 2p5 (2 P1/2 )nd transitions in neon-like Na+ ion.

I. Sakho / Atomic Data and Nuclear Data Tables (

)

–

9

Table 1 Energy limit (E, in eV) of the 1s2 2s2p6 (2 S1/2 ) threshold of neutral neon and of Ne-like ions (Z = 11–18). System

Ea

Eb

Ne Na+ Mg2+ Al3+ Si4+ P5 + S6 + Cl7+ Ar8+

48.475 80.274 119.126 164.943 217.683 277.323 343.848 417.247 497.513

52.677 83.877 122.356 167.931 220.526 280.106 — — 500.675

a b c d e f g h i

Ec

Others 48.029d 80.073e

164.480

167.047f

497.44

497.80 (80)g , 497.39h , 501.92i

Screening constant by unit nuclear charge (SCUNC) present results. Time-dependent Dirac–Hartree–Fock (DHF) calculations of Nrisimhamurty et al. [23]. NIST, http://physics.nist.gov/asd [32]. Hollow-cathode discharge (HCD) measurements of Persson [5]. Energy value from compilations of Martin and Zalubas [16]. Relativistic R-matrix close-coupling (RCC) calculations of Jha et al. [19]. Electron ion trap and synchrotron radiation (EIT-SR) measurements of Simon et al. [15]. R-matrix calculations of Liang et al. [21]. Dirac atomic R-matrix codes (DARC) computations of Gao et al. [22].

10

I. Sakho / Atomic Data and Nuclear Data Tables (

)

–

Table 2 Present SCUNC calculations of resonance energies (E, eV) of the 2s2p6 np 1 P1 series of Ne compared with various literature data. States

Theory

n

δa

Eb

Eb

Ec

Ed

Ee

Ef

Eg

Eh

3 4 5 6 7

0.845 0.838 0.834 0.832 0.832

45.544 47.114 47.691 47.966 48.117

45.534 47.111 47.692 47.967 48.119

45.557 47.111 47.687

45.565 47.129 47.697 47.969

46.253 47.397 47.814

49.725 51.318 51.894

45.544 47.119 47.695 47.965 48.116

45.546 47.121 47.692

a b c d e f g h

Experiment

Screening constant by unit nuclear charge (SCUNC), present results. Numerical calculations (NC) of Schulz et al. [10]. R-matrix calculations of Langer et al. [18]. R-matrix calculations of Liang et al. [20]. Density functional-time-dependent local density approximation (TDLDA) calculations of Stener et al. [17]. Time-dependent Dirac–Hartree–Fock (DHF) calculations of Nrisimhamurty et al. [23]. Synchrotron radiation (SR) measurements of Schulz et al. [10]. Photoabsorption (PA) measurements of Codling et al. [4].

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Table 3 Resonance energies (E, eV) and effective quantum number n∗ = n − δ of the 2s2p6 np 1 P1 series of neutral Ne atom. n

Theory

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

... ∞

Experiment

Ea

Eb

n∗ a

n∗ b

Ec

Ed

n∗ c

45.5443 47.1141 47.6911 47.9655 48.1173 48.2101 48.2710 48.3130 48.3433 48.3658 48.3830 48.3964 48.4071 48.4158 48.4229 48.4288 48.4337 48.4379 48.4415 48.4446 48.4473 48.4496 48.4517 48.4535 48.4551 48.4565 48.4578 48.4590

45.5340 47.1109 47.6918 47.9671 48.1186 48.2111 48.2717 48.3136 48.3437 48.3662 48.3833 48.3967 48.4073 48.4160 48.4230 48.4289 48.4338 48.4380

2.155 3.162 4.166 5.168 6.168 7.167 8.166 9.165 10.164 11.163 12.162 13.160 14.159 15.158 16.157 17.156 18.156 19.155 20.154 21.153 22.152 23.152 24.151 25.150 26.150 27.149 28.149 29.148

2.151 3.158 4.168 5.176 6.178 7.181 8.181 9.181 10.182 11.182 12.182 13.182 14.182 15.182 16.182 17.182 18.181 19.181

45.5442 (50) 47.1193 (50) 47.6952 (15) 47.9650 (30) 48.1168 (20) 48.2093 (20) 48.2693 (20) 48.3124 (10) 48.3424 (10) 48.3650 (10) 48.3820 (10) 48.3954 (10) 48.4060 (10) 48.4147 (10) 48.4220 (10) 48.4280 (10) 48.4326 (10) 48.4370 (10)

45.547 (9) 47.123 (6) 47.694 (6) 47.967 (6) 48.116 (6) 48.207 (6) 48.271 (6) 48.312 (6) 48.344 (6) 48.365 (6)

2.155 (2) 3.168 (6) 4.177(4) 5.17(2) 6.16(2) 7.16(3) 8.13(4) 9.15(3) 10.13(4) 11.12(5) 12.10 (7) 13.07 (8) 14.04 (10) 15.02 (12) 16.02 (15) 17.01 (18) 17.91 (21) 18.92 (25)

...

...

48.4750 a b c d

Screening constant by unit nuclear charge (SCUNC) calculations, present results. Numerical calculations (NC) of Schulz et al. [10]. Synchrotron radiation (SR) measurements of Schulz et al. [10]. Photoabsorption (PA) measurements of Codling et al. [4].

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Table 4 Width (Γ , meV) of the 2s2p6 np 1 P1 series of Ne. States

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 ...

Theory

Experiment

Γa

Γb

Γc

Γd

Γe

Γf

Γ g ,h

Γi

13.08 4.53 1.98 1.04 0.62 0.40 0.28 0.20 0.15 0.12 0.09 0.08 0.06 0.05 0.04 0.04 0.03 0.03 0.03 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.01 ...

34.9 6.65 2.47 1.28 0.70 0.46 0.31 0.22 0.16 0.12 0.09 0.07 0.06 0.05 0.04 0.03 0.03 0.02

18.6 4.3 1.8

11.4 5.28 2.61 1.44

13.9 3.86 1.62

13 7 3 1.58

16 (2)f 5.7 (2)g 3.6 (1.8)g

13 (2) 4.5 (1.5) 2 (1)

∞p a b c d e f g h i

Screening constant by unit nuclear charge (SCUNC), present results. Numerical calculations (NC) of Schulz et al. [10]. R-matrix calculations of Langer et al. [18]. R-matrix calculations of Liang et al. [20]. Density functional-time-dependent local density approximation (TDLDA) calculations of Stener et al. [17]. Time-dependent Dirac–Hartree–Fock (DHF) calculations of Nrisimhamurty et al. [23]. Synchrotron radiation (SR) data of Schulz et al. [10]. angle-resolved photoelectron spectroscopy (ARPS) measurements of Langer et al. [18]. Photoabsorption (PA) measurements of Codling et al. [4].

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Table 5 Resonance energies (E, eV), and effective quantum number n∗ = n − δ of the doubly 2s2p4 (1 D)3s (2 D)np 1 P excited states of Ne. n

Theory

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

... ∞

Experiment

Ea

Eb

n∗ a

n∗ b

Ec

Ed

n∗ c

48.9066 50.5664 51.2494 51.5632 51.7326 51.8343 51.9001 51.9452 51.9773 52.0011 52.0192 52.0332 52.0444 52.0534 52.0607 52.0668 52.0719 52.0762 52.0799 52.0831 52.0858 52.0882 52.0903 52.0922 52.0938 52.0953 52.0966 52.0978

48.9063 50.6496 51.3049 51.5865 51.7450 51.8419 51.9047 51.9479 51.9789 52.0017 52.0186 52.0299

2.060 2.965 3.967 4.970 5.972 6.974 7.976 8.977 9.978 10.979 11.979 12.980 13.980 14.981 15.981 16.981 17.982 18.982 19.982 20.982 21.982 22.983 23.983 24.983 25.983 26.983 27.983 28.983

2.060 3.049 4.102 5.082 6.078 7.080 8.075 9.069 10.039 11.039 11.985 12.771

48.9066 (15) 50.5600 (70) 51.2620 (50) 51.5610 (30) 51.7320 (30) 51.8332 (15) 51.8975 (15) — 51.9792 (25) 52.0032 (25) 52.0208 (25) 52.0348 (25) 52.0452 (25) 52.0542 (25)

48.907 (7) 50.565 (20) 51.276 (20) 51.563 (7) 51.736 (7) 51.842 (7) 51.898 (7)

2.0597 (5) 2.963 (7) 3.997(12) 4.961(13) 5.970 (23) 6.964 (19) 7.933 (28) — 10.058 (93) 11.10 (13) 12.10 (16) 13.13 (21) 14.09 (26) 15.12 (32)

...

...

52.1140 a b c d

Screening constant by unit nuclear charge (SCUNC) calculations, present results. Numerical calculations (NC) of Schulz et al. [10]. Synchrotron radiation (SR) measurements of Schulz et al. [10]. Photoabsorption (PA) measurements of Codling et al. [4].

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Table 6 Resonance energies (E, eV), and effective quantum number n∗ = n − δ of the doubly 2s2p4 (3 P)3p (2 P)ns 1 P excited states of Ne. n

Theory

4 5 6 7 8* 9* 10* 11* 12* 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

... ∞

Experiment

Ea

Eb

n∗ a

n∗ b

Ec

Ed

n∗ c

50.7600 51.9271 52.3847 52.6157 52.7485 52.8319 52.8876 52.9266 52.9550 52.9763 52.9926 53.0055 53.0157 53.0241 53.0309 53.0366 53.0414 53.0455 53.0490 53.0520 53.0547 53.0569 53.0590 53.0607 53.0623 53.0637 53.0650

51.1834 52.0367 52.4303 52.6400 52.7623 52.8394 52.8916 52.9282 52.9549

2.421 3.432 4.417 5.401 6.388 7.376 8.366 9.357 10.350 11.344 12.338 13.333 14.329 15.325 16.322 17.318 18.316 19.313 20.311 21.309 22.307 23.305 24.303 25.301 26.300 27.298 28.297

2.676 3.606 4.567 5.544 6.580 7.578 8.576 9.576 10.574

50.760 (5) 51.926 (4) 52.388 (4) 52.618 (4) 52.7493 (15) 52.8320 (15) 52.8863 (15) 52.9243 (15) 52.9513 (20)

50.749 (7) 51.928 (7) 52.387 (7) — 52.737 (20) 52.827 (20)

2.423(3) 3.438 (6) 4.444 (13) 5.446 (24) 6.443 (15) 7.452 (23) 8.447 (33) 9.44 (5) 10.40 (8)

...

...

53.082 a

Screening constant by unit nuclear charge (SCUNC) calculations, present results. Numerical calculations (NC) of Schulz et al. [10]. c Synchrotron radiation (SR) experiments of Schulz et al. [10]. d Photoabsorption (PA) experiments of Codling et al. [4]. * The n > 7 members are classified according to the relativistic jK coupling as [jc , nl]K in Ref. [10] and only the prominent members observed in the spectrum of Ne (K = 3/2) are listed. Explicitly we get [3/2, 8s]3/2; [3/2, 9s]3/2; [3/2, 10s]3/2; [3/2, 11s]3/2; [3/2, 12s]3/2 for n = 8–12. b

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Table 7 Resonance energies (E, eV), and effective quantum number n∗ = n − δ of the doubly 2s2p4 (3 P)3p(2 P)nd 1 P excited states of Ne. n

Theory

3 4 5 6 7* 8* 9* 10* 11* 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

... ∞

Experiment

Ea

Eb

n∗ a

n∗ b

Ec

Ed

n∗ c

51.3081 52.1135 52.4833 52.6744 52.7864 52.8577 52.9060 52.9402 52.9653 52.9843 52.9990 53.0106 53.0199 53.0275 53.0338 53.0391 53.0435 53.0473 53.0506 53.0534 53.0558 53.0580 53.0599 53.0616 53.0631 53.0644 53.0656 53.0667

51.5042 52.1587 52.4994 52.6829 52.7885 52.8570 52.9036 52.9369 52.9614

2.769 3.748 4.767 5.778 6.784 7.789 8.792 9.795 10.797 11.799 12.800 13.801 14.802 15.803 16.804 17.805 18.805 19.806 20.806 21.807 22.807 23.807 24.808 25.808 26.808 27.809 28.809 29.809

2.936 3.837 4.829 5.834 6.872 7.872 8.870 9.869 10.867

51.308 (4) 52.110 (4) 52.474 (4) 52.676 (15) 52.7767 (15) 52.8493 (15) 52.8977 (15) 52.9333 (15) 52.9587 (15)

51.309 (7) 52.112 (7) 52.478 (7) 52.658 (20)

2.773(3) 3.751(8) 4.750 (16) 5.71 (10) 6.731 (17) 7.730 (25) 8.71 (4) 9.73 (5) 10.72 (7)

...

...

53.082 a

Screening constant by unit nuclear charge (SCUNC) calculations, present results. Numerical calculations (NC) of Schulz et al. [10]. c Synchrotron radiation (SR) experiments of Schulz et al. [10]. d Photoabsorption (PA) experiments of Codling et al. [4]. * The n > 7 members are classified according to the relativistic jK coupling as [jc , nl]K in Ref. [10] and only the prominent members observed in the spectrum of Ne (K = 3/2) are listed. Explicitly we get [3/2, 7d]3/2; [3/2, 8d]3/2; [3/2, 9d]3/2; [3/2, 10d]3/2; [3/2, 11d]3/2. b

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Table 8 Resonance energies (E, eV) quantum defect (δ ) of the 2s2p6 np 1 P1 series of Na+ and Mg2+ . States

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

... ∞p

Na+ Ea

Eb

Ec

δa

Ea

Ec

Ed

0.704 0.685 0.675 0.669 0.666 0.664 0.662 0.662 0.661 0.661 0.661 0.661 0.661 0.662 0.662 0.662 0.662 0.663 0.663 0.663 0.663 0.664 0.664 0.664 0.664 0.664 0.665 0.665

69.950 75.320 77.365 78.359 78.918 79.263 79.491 79.650 79.765 79.851 79.917 79.968 80.009 80.043 80.070 80.093 80.112 80.128 80.142 80.154 80.165 80.174 80.182 80.189 80.196 80.201 80.206 80.211

69.95 75.18 77.17 78.14 78.70 79.04

73.746

0.547 0.522 0.508 0.500 0.495 0.491 0.489 0.487 0.486 0.485 0.484 0.483 0.483 0.482 0.482 0.482 0.482 0.482 0.481 0.481 0.481 0.481 0.481 0.481 0.481 0.481 0.481 0.481 ...

101.525

98.278 108.722 112.888 — 116.126

80.274

80.091

83.877

98.776 109.004 113.057 115.078 116.232 116.954 117.436 117.773 118.018 118.203 118.344 118.456 118.545 118.617 118.677 118.727 118.769 118.805 118.835 118.862 118.885 118.905 118.922 118.938 118.952 118.964 118.975 118.985 ... 119.126

122.356

118.766

...

a b c d

Mg2+

δa

...

Screening constant by unit nuclear charge (SCUNC) calculations, present results. High-power tunable lasers (HPTL) data of Lucatorto and Mcllrath [8]. Time-dependent Dirac–Hartree–Fock (DHF) calculations of Nrisimhamurty et al. [23]. High-voltage spark spectra (HVSS) results of Kastner et al. [9].

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Table 9 Resonance energies (E, eV) and quantum defect (δ ) of the 2s2p6 np 1 P1 series of Ne-like Al3+ and Si4+ ions. States

Al3+ SCUNC

HVSS

Si4+ SCUNC

MCDF

n

δa

Ea

Eb

δa

Ea

Ec

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

0.460 0.434 0.420 0.411 0.406 0.402 0.399 0.397 0.396 0.395 0.394 0.393 0.392 0.392 0.391 0.391 0.390 0.390 0.390 0.390 0.390 0.389 0.389 0.389 0.389 0.389 0.389 0.389

131.196 147.824 154.566 157.973 159.937 161.172 162.000 162.582 163.007 163.327 163.573 163.767 163.923 164.049 164.154 164.241 164.314 164.377 164.431 164.477 164.517 164.552 164.584 164.611 164.636 164.657 164.677 164.695

130.088 147.325 154.272 157.777 — 161.068

0.405 0.379 0.365 0.357 0.352 0.348 0.345 0.343 0.341 0.340 0.339 0.338 0.337 0.337 0.336 0.336 0.335 0.335 0.335 0.334 0.334 0.334 0.334 0.334 0.334 0.333 0.333 0.333

167.169 191.739 201.848 207.001 209.988 211.874 213.142 214.036 214.689 215.181 215.561 215.861 216.101 216.297 216.458 216.593 216.707 216.803 216.887 216.958 217.021 217.076 217.124 217.167 217.205 217.239 217.269 217.297

166.36 191.60

164.943

164.473

... ∞p

...

a b c

...

...

Screening constant by unit nuclear charge (SCUNC) calculations, present results. High-power tunable lasers (HPTL) data of Kastner et al. [9]. Multiconfiguration Dirac–Fork (MCDF) calculations of Bizau et al. [12].

...

217.683

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Table 10 Present screening constant by unit nuclear charge (SCUNC) calculations of resonance energies (E, eV) and quantum defect (δ ) of the 2s2p6 np 1 P1 series of Ne-like, P5+ , S6+ , and Cl7+ ions. States

P 5+

Cl7+

S6 +

n

δ

E

δ

E

δ

E

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

0.367 0.342 0.328 0.320 0.315 0.311 0.309 0.307 0.305 0.304 0.303 0.302 0.302 0.301 0.301 0.301 0.301 0.301 0.301 0.301 0.301 0.301 0.302 0.302 0.302 0.303 0.304 0.304

206.673 240.724 254.880 262.140 266.363 269.038 270.839 272.111 273.041 273.743 274.285 274.713 275.056 275.336 275.567 275.760 275.923 276.061 276.180 276.283 276.373 276.451 276.520 276.582 276.636 276.685 276.729 276.768

0.339 0.314 0.302 0.294 0.289 0.285 0.282 0.280 0.278 0.277 0.276 0.275 0.274 0.274 0.273 0.273 0.272 0.272 0.272 0.271 0.271 0.271 0.271 0.270 0.270 0.270 0.270 0.270

249.691 294.766 313.648 323.374 329.047 332.648 335.076 336.791 338.048 338.997 339.730 340.309 340.774 341.152 341.465 341.727 341.947 342.135 342.296 342.436 342.557 342.664 342.758 342.841 342.915 342.981 343.040 343.094

0.318 0.294 0.281 0.274 0.269 0.265 0.262 0.260 0.259 0.257 0.256 0.256 0.255 0.254 0.254 0.253 0.253 0.252 0.252 0.252 0.251 0.251 0.251 0.251 0.251 0.250 0.250 0.250

296.213 353.852 378.140 390.692 398.030 402.693 405.841 408.068 409.700 410.932 411.885 412.638 413.242 413.735 414.142 414.482 414.769 415.014 415.224 415.406 415.564 415.703 415.825 415.934 416.030 416.116 416.194 416.263

... ∞p

...

...

277.323

...

...

343.848

...

...

417.247

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Table 11 Width (Γ , meV) of the 1s2 2s2p6 np 1 P1 series of Ne-like ions (Z = 11–14). Na+ 6

1

2s2p np P 6

1

2s2p 3p P 2s2p6 4p1 P 2s2p6 5p 1 P 2s2p6 6p 1 P 2s2p6 7p 1 P 2s2p6 8p 1 P 2s2p6 9p 1 P 2s2p6 10p 1 P 2s2p6 11p1 P 2s2p6 12p 1 P 2s2p6 13p 1 P 2s2p6 14p 1 P 2s2p6 15p1 P a b

Γ

a

51.56 22.50 12.11 7.50 5.09 3.67 2.77 2.17 1.74 1.42 1.19 1.01 0.86

Mg2+

Γ

b

60

Γ

a

94.51 43.44 24.40 15.58 10.80 7.92 6.06 4.78 3.87 3.20 2.68 2.29 1.97

Screening constant by unit nuclear charge (SCUNC) calculations, present results. Time-dependent Dirac–Hartree–Fock (DHF) calculations of Nrisimhamurty et al. [23].

Γ

b

90

Al3+

Si4+

Γ

Γa

a

134.09 62.83 35.87 23.15 16.17 11.94 9.17 7.27 5.90 4.88 4.11 3.51 3.03

168.25 79.42 45.66 29.62 20.76 15.36 11.83 9.38 7.63 6.32 5.33 4.55 3.93

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Table 12 Wavelengths (λ, in Å) of the 2s2 2p6 (1 S0 ) → 2s2p6 np 1 P1 transitions in Ne and in Ne-like Na+ and Mg2+ ions. Na+

Mg2+

Transition

Ne

2p6 (1 S0 ) → np 1 P1

λa

λb

λa

λc

λa

λd

λe

272.20 263.14 259.98 258.50 257.69 257.19 256.87 256.65 256.48 256.36 256.27 256.20 256.14 256.09 256.06 256.02 256.00 255.97 255.95 255.94 255.92 255.91 255.90 ... 255.77

272.21 263.11 259.96 258.48 257.68 257.19

175.25 164.44 160.49 158.59 157.52 156.85 156.41 156.10 155.88 155.71 155.58 155.48 155.40 155.33 155.28 155.23 155.19 155.16 155.13 155.11 155.09 155.07 155.05 ... 154.84

177.24 164.92 160.66 158.67 157.55 156.88

125.74 114.21 110.12 108.16 107.07 106.39 105.94 105.62 105.39 105.22 105.09 104.98 104.90 104.83 104.78 104.73 104.69 104.66 104.63 104.60 104.58 104.56 104.55 ... 104.39

126.50 114.32 110.16 108.08 106.92 106.30

126.49 114.34 110.12

...

... 104.39

6

2p 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 ... 2p6

( S0 ) → 3p P1 (1 S0 ) → 4p 1 P1 (1 S0 ) → 5p 1 P1 (1 S0 ) → 6p 1 P1 (1 S0 ) → 7p 1 P1 (1 S0 ) → 8p 1 P1 (1 S0 ) → 9p 1 P1 (1 S0 ) → 10p 1 P1 (1 S0 ) → 11p 1 P1 (1 S0 ) → 12p 1 P1 (1 S0 ) → 13p 1 P1 (1 S0 ) → 14p 1 P1 (1 S0 ) → 15p 1 P1 (1 S0 ) → 16p 1 P1 (1 S0 ) → 17p 1 P1 (1 S0 ) → 18p 1 P1 (1 S0 ) → 19p 1 P1 (1 S0 ) → 20p 1 P1 (1 S0 ) → 21p 1 P1 (1 S0 ) → 22p 1 P1 (1 S0 ) → 23p 1 P1 (1 S0 ) → 24p 1 P1 (1 S0 ) → 25p 1 P1 1

1

(1 S0 ) → ∞p1 P1 a b c d e

... 255.77

Screening constant by unit nuclear charge (SCUNC) calculations, present results. Photoabsorption (PA) measurements of Codling et al. [4]. High-power tunable lasers (HPTL) measurements of Lucatorto and Mcllrath [8]. Absorption spectrum measurements of Esteva and Mehlman [6]. High-voltage spark spectra (HVSS) measurements of Kastner et al. [9].

... 154.84

107.05

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Table 13 Wavelengths (λ, in Å) of the 2s 2 2p6 (1 S0 ) → 2s2p6 np 1 P1 transitions in Ne-like Al3+ and Si4+ ions. Transition

Al3+

Si4+

P5+

2p6 (1 S0 ) → np 1 P1

λa

λb

λc

λa

λa

( S0 ) → 3p P1 (1 S0 ) → 4p 1 P1 (1 S0 ) → 5p 1 P1 (1 S0 ) → 6p 1 P1 (1 S0 ) → 7p 1 P1 (1 S0 ) → 8p 1 P1 (1 S0 ) → 9p 1 P1 (1 S0 ) → 10p 1 P1 (1 S0 ) → 11p 1 P1 (1 S0 ) → 12p 1 P1 (1 S0 ) → 13p 1 P1 (1 S0 ) → 14p 1 P1 (1 S0 ) → 15p 1 P1 (1 S0 ) → 16p 1 P1 (1 S0 ) → 17p 1 P1 (1 S0 ) → 18p 1 P1 (1 S0 ) → 19p 1 P1 (1 S0 ) → 20p 1 P1 (1 S0 ) → 21p 1 P1 (1 S0 ) → 22p 1 P1 (1 S0 ) → 23p 1 P1 (1 S0 ) → 24p 1 P1 (1 S0 ) → 25p 1 P1

95.49 84.50 80.69 78.88 77.87 77.24 76.82 76.53 76.32 76.16 76.04 75.95 75.87 75.81 75.76 75.71 75.68 75.65 75.62 75.60 75.58 75.56 75.54

95.56 84.38 80.58 78.79 (77.79) 77.18

94.48 84.14

...

...

61.62 52.19 49.07 47.61 46.80 46.31 45.98 45.75 45.58 45.46 45.36 45.28 45.22 45.17 45.13 45.10 45.07 45.05 45.03 45.01 44.99 44.98 44.97

2p6 (1 S0 ) → ∞p1 P1

...

75.57 65.34 61.88 60.25 59.34 58.78 58.41 58.15 57.96 57.82 57.71 57.62 57.56 57.50 57.45 57.42 57.38 57.36 57.33 57.31 57.30 57.28 57.27

73.37

73.38

57.11

44.83

6

2p 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6

...

1

a b c

1

Screening constant by unit nuclear charge (SCUNC) calculations, present results. High-voltage spark spectra (HVSS) measurements of Kastner et al. [9]. Absorption measurements of Carillon et al. [7].

...

...

22

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Table 14 Present screening constant by unit nuclear charge (SCUNC) calculations of wavelengths (λ, in Å) of the 2s2 2p6 (1 S0 ) → 2s 2p6 np 1 P1 transitions in Ne-like S6+ , Cl7+ and Ar8+ ions. Transition 6

2p 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 2p6 ... 2p6

( S0 ) → 4p P1 (1 S0 ) → 5p1 P1 (1 S0 ) → 6p1 P1 (1 S0 ) → 7p1 P1 (1 S0 ) → 8p1 P1 (1 S0 ) → 9p 1 P1 (1 S0 ) → 10p 1 P1 (1 S0 ) → 11p 1 P1 (1 S0 ) → 12p 1 P1 (1 S0 ) → 13p 1 P1 (1 S0 ) → 14p 1 P1 (1 S0 ) → 15p 1 P1 (1 S0 ) → 16p 1 P1 (1 S0 ) → 17p 1 P1 (1 S0 ) → 18p1 P1 (1 S0 ) → 19p 1 P1 (1 S0 ) → 20p1 P1 (1 S0 ) → 21p 1 P1 (1 S0 ) → 22p 1 P1 (1 S0 ) → 23p 1 P1 (1 S0 ) → 24p 1 P1 (1 S0 ) → 25p 1 P1 1

1

(1 S0 ) → ∞p1 P1

S6+

Cl7+

Ar8+

42.72 39.92 38.62 37.90 37.46 37.17 36.97 36.82 36.71 36.62 36.56 36.50 36.46 36.42 36.39 36.37 36.35 36.33 36.31 36.30 36.29 36.28 ... 36.15

35.67 33.15 31.99 31.35 30.95 30.69 30.51 30.38 30.28 30.21 30.15 30.10 30.06 30.03 30.01 29.98 29.97 29.95 29.93 29.92 29.91 29.90 ... 29.79

— 27.98 26.94 26.37 26.02 25.79 25.63 25.51 25.42 25.36 25.30 25.26 25.23 25.20 25.18 25.16 25.14 25.12 25.11 25.10 25.09 25.08 ... 24.99

I. Sakho / Atomic Data and Nuclear Data Tables (

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Table 15 Wavelengths (λ, in Å) of the 2s 2 2p6 (1 S0 ) → 2s 2 2p5 (2 P3/2 )nd transitions in neon-like Na+ ion. 2

P3/2 nd[1/2]1

P3/2 5 d[1/2]1 2 P3/2 6 d[1/2]1 2 P3/2 7 d[1/2]1 2 P3/2 8d[1/2]1 2 P3/2 9d[1/2]1 2 P3/2 10d[1/2]1 2 P3/2 11d[1/2]1 2 P3/2 12d[1/2]1 2 P3/2 13d[1/2]1 2 P3/2 14d[1/2]1 2 P3/2 15d[1/2]1 2 P3/2 16d[1/2]1 2 P3/2 17d[1/2]1 2 P3/2 18d[1/2]1 2 P3/2 19d[1/2]1 2 P3/2 20d[1/2]1 2 P3/2 21d[1/2]1 2 P3/2 22d[1/2]1 2 P3/2 23d[1/2]1 2 P3/2 24d[1/2]1 2 P3/2 25d[1/2]1 ... 2

a

λa

λb

2

275.22 271.37 269.08 267.59 266.58 265.86 265.33 264.93 264.61 264.37 264.17 264.01 263.87 263.76 263.67 263.59 263.52 263.46 263.41 263.36 263.32 ...

275.22 271.37

P3/2 5d[3/2]1 2 P3/2 6d[3/2]1 2 P3/2 7d[3/2]1 2 P3/2 8d[3/2]1 2 P3/2 9d[3/2]1 2 P3/2 10d[3/2]1 2 P3/2 11d[3/2]1 2 P3/2 12d[3/2]1 2 P3/2 13d[3/2]1 2 P3/2 14d[3/2]1 2 P3/2 15d[3/2]1 2 P3/2 16d[3/2]1 2 P3/2 17d[3/2]1 2 P3/2 18d[3/2]1 2 P3/2 19d[3/2]1 2 P3/2 20d[3/2]1 2 P3/2 21d[3/2]1 2 P3/2 22d[3/2]1 2 P3/2 23d[3/2]1 2 P3/2 24d[3/2]1 2 P3/2 25d[3/2]1 ...

...

2

P3/2 nd[3/2]1

λa

λb

λc

275.00 270.95 268.59 267.05 266.01 265.29 264.77 264.38 264.09 263.86 263.69 263.55 263.43 263.34 263.27 263.21 263.16 263.12 263.08 263.05 263.03

275.00 270.95

275.01* 270.96 268.88 267.06 266.06* — 264.76 264.34*

Screening constant by unit nuclear charge (SCUNC) calculations, present results. Experimental data from unpublished thesis of Wu as quoted in Ref. [8]. c High-power tunable lasers (HPTL) measurements of Lucatorto and Mcllrath [8]. * Unresolved lines (275.01 for both 2 P3/2 5d[3/2]1 and 2 P3/2 6s[3/2]1 levels; 266.06 for both 2 P3/2 9d[3/2]1 and 2 P1/2 8d[3/2]1 levels; 264.34 for both 2 P3/2 12d[3/2]1 and 2 P1/2 10d[3/2]1 levels. b

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I. Sakho / Atomic Data and Nuclear Data Tables (

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Table 16 Wavelengths (λ, in Å) of the 2s 2 2p6 (1 S0 ) → 2s 2 2p5 (2 P1/2 )nd transitions in neon-like Na+ ion. 2

P1/2 nd[3/2]1

2

P1/2 2 P1/2 2 P1/2 2 P1/2 2 P1/2 2 P1/2 2 P1/2 2 P1/2 2 P1/2 2 P1/2 2 P1/2 2 P1/2 2 P1/2 2 P1/2 2 P1/2 2 P1/2 2 P1/2 2 P1/2 2 P1/2 2 P1/2 2 P1/2 ... a b c *

5d[3/2]1 6d[3/2]1 7d[3/2]1 8d[3/2]1 9d[3/2]1 10d[3/2]1 11d[3/2]1 12d[3/2]1 13d[3/2]1 14d[3/2]1 15d[3/2]1 16d[3/2]1 17d[3/2]1 18d[3/2]1 19d[3/2]1 20d[3/2]1 21d[3/2]1 22d[3/2]1 23d[3/2]1 24d[3/2]1 25d[3/2]1

λa

λb

λc

274.02 269.99 267.63 266.11 265.08 264.35 263.83 263.45 263.16 262.93 262.76 262.62 262.51 262.41 262.34 262.28 262.23 262.19 262.15 262.12 262.10 ...

274.02 269.99

274.02* 269.97 267.61 266.06 — 264.34* 263.81 263.39 263.06

Screening constant by unit nuclear charge (SCUNC) calculations, present results. Experimental data from unpublished thesis of Wu as quoted in Ref. [8]. High-power tunable lasers (HPTL) measurements of Lucatorto and Mcllrath [8]. Unresolved lines (274.02 for both 2 P1/2 5d[3/2]1 and 2 P1/2 6s[3/2]1 levels; 264.34 for both 2 P3/2 12d[3/2]1 and 2 P1/2 10d[3/2]1 levels.