Photoionization study of Ne-like K9+, Ca10+, Sc11+, Ti12+, V13+, Cr14+, Mn15+, and Fe16+ ions using the screening constant by unit nuclear charge method

Radiation Physics and Chemistry 125 (2016) 50–55

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Photoionization study of Ne-like K9 þ , Ca10 þ , Sc11 þ , Ti12 þ , V13 þ , Cr14 þ , Mn15 þ , and Fe16 þ ions using the screening constant by unit nuclear charge method Arun Goyal a, Indu Khatri a, Malick Sow b, Ibrahima Sakho c,n, Sunny Aggarwal d,e, A.K. Singh f, Man Mohan a a

Department of Physics & Astrophysics, University of Delhi, Delhi 110007, India Department of Physics, Faculty of Sciences and Technologies, University Cheikh Anta Diop, Dakar, Senegal Department of Physics, UFR of Sciences and Technologies, University Assane Seck of Ziguinchor, Ziguinchor, Senegal d Department of Physics and Astrophysics, University of Delhi, New Delhi, Delhi 110007, India e Department of Physics, Shyam Lal College, University of Delhi, New Delhi, Delhi 110032, India f Department of Physics, Deen Dayal Upadhyaya College, University of Delhi, New Delhi, Delhi 110015, India b c

H I G H L I G H T S

   

Photoionization of ground state of the Ne-like (Z¼19–29) presented. good agreements with scarce literature data. New data for Ne-like K9 þ , Sc11 þ , Ti12 þ , V13 þ , Cr14 þ , and Mn15 þ ions. Useful guidelines for application in laboratory, astrophysics, and plasma physics.

art ic l e i nf o

a b s t r a c t

Article history: Received 8 December 2015 Received in revised form 4 March 2016 Accepted 20 March 2016

Photoionization of the 2s22p6 (1S0) ground state of the Ne-like (Z ¼19–29) ions is presented in this paper. Resonance energies and total natural width of the 2s2p6np 1P series of the Ne-like K9 þ , Ca10 þ , Sc11 þ , Ti12 þ , V13 þ , Cr14 þ , Mn15 þ , and Fe16 þ are reported. All the calculations are made using the Screening constant by unit nuclear charge (SCUNC) formalism. New data for Ne-like K9 þ , Sc11 þ , Ti12 þ , V13 þ , Cr14 þ , and Mn15 þ ions are tabulated. Good agreements are found with available literature data. & 2016 Published by Elsevier Ltd.

Keywords: Photoionization Ne-like ions Resonance energies Natural widths Screening constant by unit nuclear charge (SCUNC)

1. Introduction Ne-like ions are attractive candidate since the earlier experiments of Codling et al. (1967) because of their closed-shell nature and their wide applications in laboratory experiments, astrophysics and plasma physics. Of great importance are heavy highlycharged Ne-like ions. As shown in the works of Gao et al. (2013), relativistic effects, quantum electrodynamics (QED) contributions and nuclear size effects grow with higher powers of the charge n

Corresponding author. E-mail address: [email protected] (I. Sakho).

http://dx.doi.org/10.1016/j.radphyschem.2016.03.017 0969-806X/& 2016 Published by Elsevier Ltd.

state of highly charged ions. Simon et al. (2010) reported energy positions of the 1s22s2p6 (2S1/2) np 1P° series of Ar8 þ converging to the 1s22s2p6 (2S1/2) series limit in Ar9 þ using an electron ion trap and synchrotron radiation. Gao et al. (2013) reported resonant parameters relative to the dominant 2 s-np transitions in Ne-like Ar8 þ , Fe16 þ , Kr26 þ and Xe44 þ ions using the Dirac atomic R-matrix code based on a fully relativistic R-matrix method. In addition, Liang. et al. (2013) investigated resonance structure in the photoionization of Ne-like Ca XI for ejection of a 2p or 2 s electron from the ground 2s22p6 1S0 or excited state 2s22p53s 1,3P using the Breit–Pauli R-matrix method in close-coupling and LS-coupling approximation. The Dirac– Coulomb R-matrix method in the closecoupling approximation has been used by Indu et al., (2015) to

A. Goyal et al. / Radiation Physics and Chemistry 125 (2016) 50–55

perform photoionization cross section calculation for the ground state 1s22s22p6 1S (J ¼0) of Ne-like W64 þ ions and resonance energy positions of prominent Rydberg series 2s2p6(2S)np1P0 for WLXV ion have been reported. Nrisimhamurty et al. (2015) studied the 2 s-np autoionization resonances in the neon isoelectronic sequence using relativistic multichannel quantum-defect theory and reported energy resonance, linewidths along with energy limits of the 1s22s22p5 (2P3/2, 1/2) 1s22s2p6 (2S1/2) threshold of neutral neon and of several heavy highly-charged Ne-like ions such as Bi73 þ . Using the Screening constant by unit nuclear charge (SCUNC) method (Sakho et al., 2015a; Sakho et al., 2015b), Sakho (2016) reported very recently, resonance energies and width of the 2s2p6np 1P1 series of Ne and Ne-like Na þ , Mg2 þ , Al3 þ , Si4 þ , P5 þ , S6 þ , and Cl7 þ . For Ne-like Z¼ 19–26 ions, only the results of Liang et al., on Ca10 þ exist in the literature up to our knowledge. As heavy Ne-like ions are very challenging for astrophysical interest, we extend in this paper the previous calculations (Sakho, 2016) on the highly-charged Ne-like K9 þ , Ca10 þ , Sc11 þ , Ti12 þ , V13 þ , Cr14 þ , Mn15 þ , and Fe16 þ ions focusing our study on the 2s2p6np 1P1 series in the LS coupling scheme. Section 2 presents the theoretical part of the work. In Section 3 we discuss and compare the results obtained with available literature values.

The relationship between Z* and

Z* =

Zcore

(1 − ) δ n

δ is in the form

. (5)

According to this equation, each Rydberg series must satisfy the following conditions

⎧ Z * ≥ Zcore if δ ≥ 0 ⎪ ⎨ Z * ≤ Zcore if δ ≤ 0 . ⎪ ⎩ lim Z *n →∞ = Zcore

(6)

Besides, the f2-parameter in Eq. (2) can be theoretically determined from the equation

⎛ f ⎞ lim Z * = Z 0 ⎜ 1 − 2 ⎟ = Zcore Z0 ⎠ ⎝

(7)

n→ ∞

We get then f2 ¼ Z0 – Zcore, where Zcore is directly obtain by the photoionization process from an atomic Xp þ system Xp þ þhν -X(p þ 1) þ þe  . We find then Zcore ¼p þ1. According to that f2 ¼9,0 for all the Ne-like ions, only the remaining f1-paramerter is to be evaluated empirically using experimental data for a given (2S þ 1LJ) ml level with ν ¼0 in Eq. (1) as shown previously (Sakho, 2016). 2.2. Energy limits of the 1s22s2p6 (2S1/2) thresholds of Ne-like (Z ¼ 18–26) ions

2. Theory 2.1. Brief description of the SCUNC formalism In the framework of the SCUNC formalism, the resonance energy of a given Rydberg series originating from a-2S þ 1LJ state, is given by (Sakho et al., 2015a, 2015b)

En = E∞ −

51

Z 02 n2

The energy limit (of the 1s22s2p6 (2S1/2) threshold of the Nelike ions (Z¼18–26) is given by (in Rydberg units).

E (2s ) =

f (s ) f (s ) (Z − Z 0 ) f (s ) (Z − Z 0 ) Z2 ⎧ ⎨1 − 1 + 1 × + 1 × 4⎩ Z Z0 Z0 Z2 Z3

2

{ 1 − β (Z0, 2S + 1L J , n, s, μ, ν) }

−

(1)

The β-parameters in Eq. (1) are screening constants by unit nuclear charge expanded in inverse powers of Z0 and given by

⎛ 1 ⎞k β (Z 0, 2S + 1L J , n, s , μ , ν ) = ∑ fk ⎜ ⎟ . ⎝ Z0 ⎠ k=1

+

f 12 (s ) Z0 f13 (s ) Z0

×

(Z − Z0 ) Z

4

+

f 12 (s ) Z0

×

(Z − Z 0 ) Z5

2

×

(Z − Z0 )2 ⎫ ⎬ . ⎪ Z6 ⎭ ⎪

(8)

q

(2)

where fk = fk (2S + 1L J , n, s, μ, ν ) are screening constants to be evaluated empirically. In Eqs. (1) and (2), ν and m (m 4 ν) denote the principal quantum numbers of the (2S þ 1LJ) nl Rydberg series used in the empirical determination of the fk-screening constants, s represents the spin of the nl- electron (s ¼½), E1 is the energy value of the series limit, En denotes the resonance energy and Z0 stands for the atomic number. In addition in Eq. (2), q stands for the number of terms in the expansion of the β–parameter. Generally, precise resonance energies are obtained for qo5. In general, resonance energies are analyzed from the standard quantum-defect expansion formula

En = E∞ −

2 RZcore

(n − δ )2

.

(3)

In this equation, R is the Rydberg constant, E1 denotes the converging limit, Zcore represents the electric charge of the core ion, and δ means the quantum defect. In addition, theoretical and measured energy positions can be analyzed by calculating the Z*-effective charge in the framework of the SCUNC-procedure

En = E∞ −

Z *2 R. n2

In this equation, Z*= Z0 { 1 − F [fi (2S + 1L ) ; n, ν, μ, s, Z0 ] }

(4)

The f1-screening constant in Eq. (8) is determined using the NIST (Kramida et al., 2014; Biémont et al., 1999) data for Ar8 þ at 497.44 eV. So, we get from Eq. (8) with Z0 ¼18, f1(s)¼ 5.90683. The results for the Ne-like K9 þ , Ca10 þ , Sc11 þ , Ti12 þ , V13 þ , Cr14 þ , Mn15 þ , and Fe16 þ ions investigated are listed in Table 1. 2.3. Resonance energies of the 1s22s2p6 (2S1/2)np 1P0 Rydberg series For the 1s22s2p6 (2S1/2)np 1P° levels of the Ne-like Ar8 þ ions, Table 1 Energy limits (E1, in eV) of the 1 s22 s2p6 (2S1/2) threshold and quantum defect δ of the 2s2p6np 1P1 series of the Ne-like ions (Z¼ 18–26). Ion

9þ

K Ca10 þ Sc11 þ Ti12 þ V13 þ Cr14 þ Mn15 þ Fe16 þ

δ

E1 SCUNC

DHF

585.686 680.800 782.758 891.543 1007.146 1129.556 1258.769 1394.780

588.158 682.642 – – 1008.297 1130.993 – 1397.766

NIST

1394.71

DARC

SCUNC

DHF

DARC

1394.166

0.27 0.25 0.23 0.22 0.21 0.20 0.19 0.18

∼0.17

0.176

SCUNC, Screening constant by unit nuclear charge, present results. DHF, time-dependent Dirac-Hartree-Fock calculations of Nrisimhamurty et al. (2015). NIST (Kramida et al., 2014; Biémont et al., 1999). DARC, Dirac atomic R-matrix code calculations of Gao et al. (2013).

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A. Goyal et al. / Radiation Physics and Chemistry 125 (2016) 50–55

Table 2 Present SCUNC calculations of resonance energies (E, eV) and widths (Γ, meV) of the 2s2p6np 1P1 series of the Ne like Ar8 þ , K9 þ , and Ca10 þ ions. np

6p 7p 8p 9p 10p 11p 12p 13p 14p 15p 16p 17p 18p 19p 20p 21p 22p 23p 24p 25p 26p 27p 28p 29p 30p …. 1p

Ar8 þ

K9 þ

Ca10 þ

E

Γ

δ

E

Γ

δ

E

Γ

δ

463.54 472.93 478.89 482.91 485.75 487.83 489.41 490.62 491.58 492.35 492.98 493.50 493.93 494.29 494.60 494.87 495.10 495.30 495.48 495.64 495.77 495.90 496.01 496.10 496.19 … 497.440

12.253 6.340 3.747 2.420 1.666 1.203 0.902 0.697 0.552 0.447 0.368 0.307 0.260 0.222 0.192 0.168 0.147 0.130 0.116 0.104 0.094 0.085 0.077 0.070 0.064 …

0.298 0.295 0.292 0.291 0.290 0.289 0.288 0.287 0.287 0.287 0.286 0.286 0.286 0.286 0.285 0.285 0.285 0.285 0.285 0.285 0.285 0.285 0.285 0.285 0.284 …

544.18 555.62 562.91 567.83 571.32 573.87 575.80 577.29 578.47 579.42 580.19 580.83 581.36 581.81 582.19 582.52 582.81 583.05 583.27 583.46 583.63 583.78 583.92 584.04 584.15 … 585.686

13.153 6.844 4.064 2.634 1.819 1.317 0.990 0.767 0.609 0.493 0.406 0.340 0.288 0.247 0.214 0.186 0.164 0.145 0.129 0.116 0.105 0.095 0.086 0.079 0.072 …

0.275 0.273 0.271 0.270 0.269 0.268 0.268 0.268 0.267 0.267 0.267 0.267 0.267 0.266 0.266 0.266 0.266 0.266 0.266 0.266 0.266 0.266 0.266 0.266 0.266 …

630.92 644.62 653.37 659.29 663.48 666.55 668.87 670.67 672.09 673.23 674.16 674.93 675.57 676.12 676.58 676.98 677.32 677.62 677.88 678.11 678.32 678.50 678.66 678.81 678.94 … 680.800

14.003 7.330 4.372 2.845 1.971 1.431 1.079 0.837 0.666 0.540 0.446 0.374 0.317 0.272 0.235 0.206 0.181 0.161 0.143 0.129 0.116 0.105 0.096 0.087 0.080 …

0.255 0.254 0.253 0.252 0.252 0.251 0.251 0.251 0.250 0.250 0.250 0.250 0.250 0,250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 …

Table 3 Present SCUNC calculations of resonance energies (E, eV) and widths (Γ, meV) of the 2s2p6np 1P1 series of the Ne like Sc11 þ , Ti12 þ , and V13 þ ions. np

6p 7p 8p 9p 10p 11p 12p 13p 14p 15p 16p 17p 18p 19p 20p 21p 22p 23p 24p 25p 26p 27p 28p 29p 30p … 1p

Sc11 þ

Ti12 þ

V13 þ

E

Γ

δ

E

Γ

δ

E

Γ

δ

723.75 739.91 750.25 757.25 762.21 765.85 768.60 770.73 772.42 773.77 774.87 775.79 776.55 777.19 777.74 778.21 778.62 778.98 779.29 779.56 779.81 780.02 780.22 780.39 780.55 … 782.758

14.816 7.803 4.676 3.054 2.123 1.546 1.168 0.908 0.724 0.588 0.486 0.408 0.347 0.298 0.258 0.226 0.199 0.176 0.158 0.141 0.128 0.116 0.105 0.096 0.088 …

0.238 0.238 0.237 0.237 0.236 0.236 0.236 0.236 0.236 0.235 0.235 0.235 0.235 0.235 0.235 0.235 0.235 0.235 0.235 0.235 0.235 0.235 0.235 0.235 0.235 …

822.64 841.47 853.52 861.69 867.49 871.75 874.97 877.46 879.43 881.01 882.31 883.37 884.27 885.02 885.66 886.22 886.69 887.11 887.48 887.80 888.08 888.34 888.56 888.77 888.95 … 891.543

15.605 8.268 4.978 3.264 2.276 1.662 1.258 0.981 0.783 0.637 0.528 0.443 0.377 0.324 0.281 0.246 0.217 0.193 0.172 0.155 0.140 0.127 0.116 0.106 0.097 …

0.223 0.224 0.223 0.223 0.223 0.223 0.223 0.223 0.223 0.222 0.223 0.223 0.223 0.223 0.223 0.223 0.223 0.223 0.223 0.223 0.223 0.223 0.223 0.223 0.223 …

927.60 949.29 963.19 972.62 979.32 984.24 987.96 990.84 993.12 994.95 996.45 997.69 998.72 999.59 1000.34 1000.98 1001.53 1002.01 1002.43 1002.81 1003.14 1003.43 1003.69 1003.93 1004.14 … 1007.146

16.378 8.730 5.280 3.475 2.430 1.779 1.350 1.055 0.843 0.688 0.570 0.480 0.408 0.351 0.305 0.268 0.236 0.210 0.188 0.169 0.152 0.138 0.126 0.115 0.106 …

0.210 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.212 0.212 …

A. Goyal et al. / Radiation Physics and Chemistry 125 (2016) 50–55

53

Table 4 Present SCUNC calculations of resonance energies (E, eV) and widths (Γ, meV) of the 2s2p6np 1P1 series of the Ne like Cr14 þ , Mn15 þ , and Fe16 þ ions. Cr14 þ

np

6p 7p 8p 9p 10p 11p 12p 13p 14p 15p 16p 17p 18p 19p 20p 21p 22p 23p 24p 25p 26p 27p 28p 29p 30p … 1p

Mn15 þ

Fe16 þ

E

Γ

δ

E

Γ

δ

E

Γ

δ

1038.60 1063.35 1079.24 1090.02 1097.68 1103.31 1107.57 1110.87 1113.48 1115.58 1117.29 1118.71 1119.89 1120.89 1121.75 1122.48 1123.11 1123.67 1124.15 1124.58 1124.96 1125.29 1125.59 1125.86 1126.11 … 1129.556

17.143 9.192 5.585 3.689 2.587 1.899 1.444 1.130 0.905 0.739 0.614 0.517 0.441 0.380 0.330 0.290 0.256 0.228 0.204 0.183 0.166 0.150 0.137 0.126 0.115 …

0.199 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.201 0.201 0.201 0.201 0.201 0.201 0.201 0.201 0.201 0.201 0.201 0.201 0.201 0.201 0.201 0.201 …

1155.64 1183.66 1201.66 1213.89 1222.57 1228.96 1233.79 1237.54 1240.50 1242.89 1244.83 1246.44 1247.79 1248.92 1249.89 1250.72 1251.45 1252.07 1252.62 1253.11 1253.54 1253.92 1254.26 1254.57 1254.85 … 1258.769

17.906 9.656 5.892 3.906 2.747 2.021 1.541 1.208 0.969 0.792 0.659 0.555 0.474 0.409 0.356 0.312 0.276 0.246 0.220 0.198 0.179 0.163 0.149 0.136 0.125 …

0.188 0.190 0.190 0.191 0.191 0.191 0.191 0.191 0.191 0.191 0.191 0.191 0.191 0.192 0.192 0.192 0.192 0.192 0.192 0.192 0.192 0.192 0.192 0.192 0.192 …

1278.73 1310.22 1330.46 1344.21 1353.99 1361.18 1366.63 1370.85 1374.18 1376.87 1379.06 1380.88 1382.39 1383.67 1384.77 1385.71 1386.52 1387.23 1387.85 1388.40 1388.88 1389.31 1389.70 1390.04 1390.36 … 1394.780

18.670 10.125 6.205 4.126 2.911 2.147 1.639 1.287 1.034 0.847 0.705 0.595 0.508 0.439 0.382 0.336 0.297 0.265 0.237 0.214 0.193 0.176 0.160 0.147 0.135 …

0.179 0.181 0.182 0.182 0.182 0.182 0.182 0.182 0.183 0.183 0.183 0.183 0.183 0.183 0.183 0.183 0.183 0.183 0.184 0.184 0.184 0.184 0.184 0.184 0.184 …

Table 5 Resonance energies (E, in eV) and widths (Γ, in meV) of the 1s2 2s 2p6 (2S1/2) np 1P° Rydberg series of the Ne-like Ca10 þ , and Fe16 þ . The results of Liang et al., (2013) published in Ryd are converted in eV using 1 Ryd ¼ 13.60569 eV. np

Ca10 þ

Fe16 þ

SCUNC

6 7 8 9 10 11 12 13 14 15

B-P R-matrix

SCUNC

DARC

Γ

E

Γ

E

Γ

E

Γ

630.92 644.62 653.37 659.29 663.48 666.55 668.87 670.67 672.09 673.23

14.00 7.33 4.37 2.84 1.97 1.43 1.08 0.84 0.67 0.54

630.26 643.82 652.48 658.35 662.51 665.57 667.87 669.66 671.08 672.21

10.62 6.70 4.45 3.09 2.22 1.65 1.33 1.04 0.83 0.67

1278.73 1310.22 1330.46 1344.21 1353.99 1361.18 1366.63 1370.85 1374.18 1376.87

18.67 10.12 6.20 4.13 2.91 2.15 1.64 1.29 1.03 0.85

1278.30 1309.78 1329.97 1343.69 1353.44 1360.62 1366.20 1371.24

4.70 3.00 2.30 1.80 1.40 1.10 0.80 0.70

SCUNC, screening constant by unit nuclear charge calculations, present results. DARC, Dirac atomic R-matrix code calculations of Gao et al. (2013). B-P R-matrix, Breit–Pauli R-matrix method in close-coupling and LS-coupling approximation, Liang et al. (2012).

the resonance energies have been previously (Sakho et al., 2015a), expressed as follows (in Rydberg units). 2

f1 (p) × (n − ν ) f1 (p) f (p) Z 02 ⎧ ⎨1 − − 2 + 2 Z 0 (n − 1) Z0 Z 0 (n − s − 1) × (n + s + 1) n2 ⎩

2 3 ⎪ f (p) × (n − ν ) ⎫ ⎬ . − 1 ⎪ Z 03 (n − ν + s)2 ⎭

Ar8 þ

np

E

E n = E∞ −

Table 6 Widths (Γ, in meV) of the 1 s2 2 s 2p6 (2S1/2) np 1P° Rydberg series of the Ne-like Ar8 þ , Ca10 þ , Fe16 þ , and Cu29 þ . The widths for Cu29 þ obtained from Eq. (11) are added to enlighten discrepancies between the data listed in Table 5 for Fe16 þ .

5 6 7 8 9 10 11 12 13 14 15

Fe16 þ

Cu29 þ

SCUNC

DARC

SCUNC

R-matrix

SCUNC

DARC

SCUNC

R-matrix

29.725 12.253 6.340 3.747 2.420 1.666 1.203 0.902 0.697 0.552 0.447

25.80 14.10 8.40 5.40 3.60 2.60

33.430 14.003 7.330 4.372 2.845 1.971 1.431 1.079 0.837 0.666 0.540

19.41 10.62 6.70 4.45 3.09 2.22 1.65 1.33 1.04 0.83 0.67

– 18.670 10.125 6.205 4.126 2.911 2.147 1.639 1.287 1.034 0.847

– 4.70 3.00 2.30 1.80 1.40 1.10 0.80 0.70

– 21.012 11.575 7.177 4.817 3.424 2.541 1.951 1.539 1.242 1.021

– – 13.31 9.36 6.76 4.97 3.73

SCUNC, screening constant by unit nuclear charge calculations, present results. DARC, Dirac atomic R-matrix code calculations of Gao et al. (2013). R-matrix calculations of Liang et al. (2012).

Eq. (9) for the Ne-like K9 þ , Ca10 þ , Sc11 þ , Ti12 þ , V13 þ , Cr14 þ , Mn15 þ , and Fe16 þ ions as follows

En = E∞ − − (9)

As f2 ¼ 9.0, the value of f1 has been evaluated from EBIT experiments of Simon et al., (2010) for the 1s22p6 (2S1/2)5p, E5 ¼447.71 (ν ¼ 5). Eq. (9) gives then f1 (p) ¼  2.236. We extend

Ca10 þ

−

f 12 (p) × (n − ν ) f1 (p) f (p) Z2 ⎧ ⎨1 − − 2 + 2 2 Z (n − 1) Z n ⎩ Z (n − s − 1) × (n + s + 1)

f13 (p) × (n − ν ) Z 3 (n − ν + s )2 f1 (p) × (Z − Z 0 ) × (n − ν )

Z2 (n + v − s − 2) × (n − ν + s )

−

2 f1 (p) × (Z − Z 0 ) × (n − ν ) ⎫ ⎬ Z 3 (n − v + s ) × (n − ν + 1) ⎭

In this equation f1 (p)¼  2.236, Z0 ¼18 for Ar8 þ and Z stands for

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A. Goyal et al. / Radiation Physics and Chemistry 125 (2016) 50–55

Table 7 Present SCUNC calculations of effective charge (Z*) and quantum defects for the 2s2p6np 1P1 series of the Ne like (Z ¼19–22) ions. The value of the electric core charge (Zcore) deduced from the Xp þ þhν-X(p þ 1) þ e  (Zcore ¼p þ 1) photoionization process of a given Ne-like Xp þ 1 ion is indicated in last line of the table in the column relative to Z*. For example: K9 þ þ hν-K10 þ þ e  (Zcore ¼10.000). np

6p 7p 8p 9p 10p 11p 12p 13p 14p 15p 16p 17p 18p 19p 20p 21p 22p 23p 24p 25p 26p 27p 28p 29p 30p … 1

K9 þ

Ca10 þ

Sc11 þ

Z*

δ

Z*

δ

Z*

δ

Z*

δ

10.480 10.405 10.351 10.309 10.277 10.250 10.228 10.210 10.195 10.181 10.170 10.159 10.150 10.142 10.135 10.128 10.122 10.117 10.112 10.108 10.103 10.099 10.096 10.093 10.089 … 10.000

0.275 0.273 0.271 0.270 0.269 0.268 0.268 0.268 0.267 0.267 0.267 0.267 0.267 0.266 0.266 0.266 0.266 0.266 0.266 0.266 0.266 0.266 0.266 0.266 0.266 …

11.488 11.414 11.359 11.317 11.284 11.257 11.235 11.216 11.200 11.187 11.175 11.164 11.155 11.147 11.139 11.132 11.126 11.121 11.116 11.111 11.107 11.103 11.099 11.096 11.092 … 11.000

0.255 0.254 0.253 0.252 0.252 0.251 0.251 0.251 0.250 0.250 0.250 0.250 0.250 0,250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 …

12.496 12.422 12.367 12.324 12.290 12.263 12.241 12.222 12.205 12.191 12.179 12.169 12.159 12.151 12.143 12.136 12.130 12.124 12.119 12.114 12.110 12.106 12.102 12.098 12.095 … 12.000

0.238 0.238 0.237 0.237 0.236 0.236 0.236 0.236 0.236 0.235 0.235 0.235 0.235 0.235 0.235 0.235 0.235 0.235 0.235 0.235 0.235 0.235 0.235 0.235 0.235 …

13.502 13.429 13.373 13.330 13.296 13.269 13.246 13.226 13.210 13.196 13.183 13.172 13.163 13.154 13.146 13.139 13.133 13.127 13.122 13.117 13.112 13.108 13.104 13.101 13.097 … 13.000

0.223 0.224 0.223 0.223 0.223 0.223 0.223 0.223 0.223 0.222 0.223 0.223 0.223 0.223 0.223 0.223 0.223 0.223 0.223 0.223 0.223 0.223 0.223 0.223 0.223 …

6p 7p 8p 9p 10p 11p 12p 13p 14p 15p 16p 17p 18p 19p 20p 21p 22p 23p 24p 25p 26p 27p 28p 29p 30p … 1

V13 þ

Cr14 þ

2.4. Widths of the 1s22p6 (2S1/2)np 1P0 Rydberg series For Ne, the widths of the 1s22p6 (2S1/2)np 1P0 series were given by (Sakho, 2016),

Ti12 þ

Γn =

⎪ f1′ (1P °) f ′ (1P °) f1′ (1P °) × (n − ν ) × (n − μ) Z 02 ⎧ ⎨1 − + − 2 2⎪ Z 0 (n − 1) Z0 Z 0 (n − μ + ν ) × (n − μ + ν − s ) n ⎩

+

⎫2 ⎪ ⎬ . Z 02 (n − μ + ν − 2s ) × (n − μ + ν − s ) ⎪ ⎭ f1′ (1P °) × (n − ν ) × (n − μ)

(10)

The fi-parameters have been evaluated using the experimental data of Codling et al. (1967) on Ne (Z0 ¼10) for the 2s2p63p 1P1 (m ¼3) and 2s2p64p 1P1 (ν ¼4) levels respectively at (in meV) 13 (2) and 4.5 (1.5). So Eq. (10) provided f1’ ¼0.120 70.026 and f2’ ¼9.96770.020. In this paper, this equation is extended to the Nelike K9 þ , Ca10 þ , Sc11 þ , Ti12 þ , V13 þ , Cr14 þ , Mn15 þ , and Fe16 þ ions as follows

Γn =

⎧ ⎛ Z⎞ f ′ (1P °) f ′ (1P °) ⎛ Z ⎞ Z2 ⎪ ⎨1 − 1 ×⎜ ⎟ ×⎜ ⎟− 2 2⎪ ⎝ Z0 ⎠ Z (n − 1) ⎝ Z 0 ⎠ Z n ⎩ +

f1′ (1P °) × (n − ν ) × (n − μ) 2

Z (n − μ + ν − 2s ) × (n − μ + ν − s )

×

⎫2 ⎛ Z⎞ f ′ (1P °) × (Z − Z0 ) ⎪ ⎬ . ⎜ ⎟+ 3 2 ⎝ Z0 ⎠ Z (n + μ − ν − 2s − 1) ⎪ ⎭ (11)

Table 8 Same as in Table 7 for Ne-like (Z¼ 23–26). np

the atomic number of the Ne-like K9 þ , Ca10 þ , Sc11 þ , Ti12 þ , V13 þ , Cr14 þ , Mn15 þ , and Fe16 þ .

3. Results and discussions M15 þ

Fe16 þ

Z*

δ

Z*

δ

Z*

δ

Z*

δ

14.508 14.435 14.379 14.336 14.302 14.274 14.250 14.231 14.214 14.200 14.187 14.176 14.166 14.157 14.149 14.142 14.136 14.130 14.124 14.119 14.115 14.111 14.107 14.103 14.099 … 14.000

0.210 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.211 0.212 0.212 …

15.514 15.441 15.385 15.341 15.306 15.278 15.255 15.235 15.218 15.203 15.190 15.179 15.169 15.160 15.152 15.145 15.138 15.132 15.127 15.122 15.117 15.113 15.109 15.105 15.101 … 15.000

0.199 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.201 0.201 0.201 0.201 0.201 0.201 0.201 0.201 0.201 0.201 0.201 0.201 0.201 0.201 0.201 0.201 …

16.519 16.446 16.390 16.346 16.311 16.282 16.259 16.239 16.221 16.207 16.194 16.182 16.172 16.163 16.155 16.147 16.141 16.135 16.129 16.124 16.119 16.115 16.111 16.107 16.103 … 16.000

0.188 0.190 0.190 0.191 0.191 0.191 0.191 0.191 0.191 0.191 0.191 0.191 0.191 0.192 0.192 0.192 0.192 0.192 0.192 0.192 0.192 0.192 0.192 0.192 0.192 …

17.523 17.451 17.395 17.350 17.315 17.286 17.262 17.242 17.225 17.210 17.196 17.185 17.175 17.165 17.157 17.150 17.143 17.137 17.131 17.126 17.121 17.116 17.112 17.108 17.105 … 17.000

0.179 0.181 0.182 0.182 0.182 0.182 0.182 0.182 0.183 0.183 0.183 0.183 0.183 0.183 0.183 0.183 0.183 0.183 0.184 0.184 0.184 0.184 0.184 0.184 0.184 …

Table 1 lists the energy limits of the 1s22s2p6 (2S1/2) threshold and quantum defect δ of the 2s2p6np 1P1 series of the Ne-like ions (Z¼18–26). Comparison is done with the Dirac atomic R-matrix code (DARC) calculations of Gao et al. (2013), with the time dependent Dirac-Hartree-Fock (DHF) calculations, Nrisimhamurty et al. (2015) and with NIST (Kramida et al., 2014; Biémont et al., 1999). Overall, good agreements are obtained It should be underlined the very good agreement between the SCUNC result at 1394.78 eV and the NIST data at 1394.71 eV for Fe16 þ . The SCUNC value is greater than the NIST data by only 0.07 eV. Besides, one can observe that DHF (Nrisimhamurty et al., 2015) are slightly higher than the present, the NIST and the DARC data for Fe16 þ because electron correlations have not been included in the DHF methodology. This may explain the discrepancies between the SCUNC and DHF calculations for the data from K9 þ to Fe16 þ .The present SCUNC calculations of resonance energies and widths of the 2s2p6np 1P1 series of the Ne like Ar8 þ up to the Nelike Fe16 þ ions are quoted in Tables 2–4. Table 5 shows a comparison of the present SCUNC resonance energies and widths of the 1 s2 2 s 2p6 (2S1/2) np 1P° series of Ne-like Ca10 þ , and of Ne-like Fe16 þ ions with the Dirac atomic R-matrix code (DARC) calculations of Gao et al. (2013) and with the results from the Breit–Pauli R-matrix (B-P R-matrix) method in close-coupling and LS-coupling approximation obtained by Liang. et al. (2013). In general, the SCUNC results agree well with both the DARC and B-P R-matrix calculations for resonance energies. For widths, the present SCUCN

A. Goyal et al. / Radiation Physics and Chemistry 125 (2016) 50–55

results for Ca10 þ agree fairly with the B-P R-matrix results (Liang. et al., 2013). But great discrepancies are observed comparing the SCUNC and DARC widths for Fe16 þ . To enlighten these discrepancies, let us add the data for Cu29 þ obtained from Eq. (11) compared with the R-matrix calculations (Liang et al., 2012). The results obtained are listed in Table 6. From this Table, it is clearly seen that width increases with increasing Z. For example, for the same 7p level, the SCUNC data (in meV) are at 6.340 (Ar8 þ ); 7.330 (Ca10 þ ); 10.125 (Fe16 þ ); and 11.575 (Cu29 þ ). For this same level, the R-matrix data (Liang et al., 2012) (in meV) are at 6.70 (Ca10 þ ); and 13.31 (Cu29 þ ). But, for the 7p-DARC (Gao et al., 2013) level, one find (in meV) 8.40 (Ar8 þ ); and 3.00 (Fe16 þ ). Here width decreases with increasing Z in contrast with the present SCUNC and R-matrix (Liang et al., 2012) predictions. Then, the DARC (2013). widths for Fe16 þ may be probably inaccurate and our data may be preferable. Tables 7–8 quotes the present SCUNC calculations of effective charge (Z*) and quantum defects for the 2s2p6np 1P1 series of the Ne like (Z¼19–26) ions. Here; one can see that the SCUNC conditions analysis (6) are thoroughly satisfied. In addition, the quantum defect decreases with increasing Z in agreement with the predictions of theory.

4. Summary and conclusion The Screening constant by unit nuclear charge (SCUNC) formalism has been used to study the Photoionization of the 2s22p6

55

(1S0) ground state of the Ne-like (Z¼ 19–29) ions. Resonance energy and widths of the Ne-like K9 þ , Ca10 þ , Sc11 þ , Ti12 þ , V13 þ , Cr14 þ , Mn15 þ , and Fe16 þ are tabulated. The present study has provided new data for Ne-like K9 þ , Sc11 þ , Ti12 þ , V13 þ , Cr14 þ , and Mn15 þ ions. These data may useful guidelines for investigators focusing their challenge on Ne-like heavy charged ions due to their wide application in laboratory, astrophysics, and plasma physics.

References Biémont, et al., 1999. . Data Nucl. Data Tables. 71, 117. Codling, K., Madden, R.P., Ederer, D.L., 1967. Phys. Rev. 155, 26. Gao, C., et al., 2013. J. Phys. B 46, 175402. Kramida, et al., and NIST ASD Team (2014), NIST Atomic Spectra Database, version 5.2, 〈http://physics.nist.gov/asd〉. Liang., L., et al., 2013. Phys. Scr. 87, 015301. Liang, L., et al., 2012. Journal. Quant. Spectrosc. Radiat. Transf. 113, 2018. Nrisimhamurty, M., et al., 2015. Phys. Rev. A 91, 013404. Simon, M.C., et al., 2010. J. Phys. B 43, 065003. Sakho, I., et al., 2015a. Rad. Phys. Chem. 82, 110. Sakho, I., et al., 2015b. Phys. Scr. 90, 045401. Sakho, I., 2016. . Data Nucl. Data Tables. 57, 108.