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Energy Levels of the Single Excited States in the Magnesium Isoelectronic Sequence.

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Annalen der Pliysik. 7. Folge, Band 46, Heft 2 , 1989, S. 144-148
VEB J. A. Barth, Leipzig
Energy Levels of the Single Excited States
in the Magnesium lsoelectronic Sequence
By TH. M. EL-SHERBINI,
H. M. M. MANSOUR,A. A. FARAGand A. A. RAHMAN
Cairo University, Giza, Egypt
1. Introduction
The study of MgI sequence is of great astrophysical importance. It helps in interpreting
the properties of the solar atmosphere and many astrophysical phenomenon. Determination of energy levels of MgI sequence are important for abundance analysis of
various elements of the sequence in the solar corona [l].
MgI with a ground state configuration (ls22s22p63s2)
can be considered as a two
electron system (i.e. two electrons outside a closed shell), for which we expect a deviation from the one electron system, i. e. the hydrogenic case. The departure from the hydrogenic behaviour yields valuable insight into the properties of the ionic core and reveals
some of the details of the interaction between the valence electrons and the ionic
core.
2. Method of Galculation
The Hartree-Fock programme of Froese-Fisher “4 was used in calculating the average
energies of the various configurations and the method of E d l h [31 for extrapolating
level intervals in terms of Slater parameters was applied in order t o obtain the term
energies of the levels. The method of calculation was explained in detail in previous
publications [4, 51.
3. Results and Discussions
The calculated Hartree-Fock energies of the magnesium sequence relative to the
ground state ls22s22p63s2(2S)
energy are given in Tables 1-4. The use of the LS-coupling
scheme in describing the various configurations is justified by the large values of the
electrostatic interactions obtained from Slater parameters as compared with the spinorbit interactions for the same configuration.
A comparison between our results and the experimental data of Moore [6] and Ekberg [7] are given for P IV, Ar VII and K VIII in Tables 5-7. From these tables
we find a discrepancy of about 6yo,2.5% and 1.5% between our values and the experimental results for P IV, Ar VII and K VIII respectively. However, in order to improve
the accuracy of the calculated energy levels for the low 2-members of the sequence,
it is necessary to include the effect of configuration interactions in the calculations.
33 956.9
82 746.7
143826.4
216462.7
300351.9
34389.8
83530.4
144911.3
217826.4
301981.9
47 710.6
122 173.2
218 130.8
334169.5
469679.5
G34 355.9
798036.0
990633.6
47 868.0
122560.9
218 749.1
335 014.7
470748.8
626647.5
799548.7
992366.2
43871.9
110389.3
195153.9
296989.5
415396.6
550129.G
701060.6
868123.8
44168.6
111075.6
196222.2
298431.5
417 207.3
552305.3
703598.6
871022.5
ls23s22pG3sGs
3sGs ('8)
3sGs (3S)
ls22s22p~3s5s
3s5s (18)
3s5s ( 3 s )
49698.7
128353.8
230836.9
356002.4
500379.4
666630.1
853571.9
1061106.1
ls22s22p63s7s
3s7s ('8)
49608.4
128323.4
230464.9
354 490.4
499 729.1
666842.5
853647.5
1060045.7
3s7s ( 3 8 )
CI VI
Ar VII
K VIII
sv
Mg 1
Al I1
Si 111
P IV
36 095.5
61824.5
85 540.9
108395.9
130 790.9
152938.4
174973.3
196991.9
15303.2
29350.7
43 701.7
58163.4
72 714.9
87373.7
102 163.2
117 116.2
ls22s22p63s3p
3s3p ('P)
3 ~ 3 p('P)
42332.2
99654.6
169302.6
250559.3
343126.9
446 867.8
561 718.7
687 655.6
39942.1
96 143.5
164997.2
245 580.6
337527.7
440 672.8
554939.2
680296.5
ls22s~2p~3s4p
3s4p ('P)
3~4-p('P)
46935.8
117 056.9
205641.2
311434.3
433898.5
572 768.5
727905.8
899239.9
46081.0
115805.9
204112.5
309668.9
431 912.9
570569.2
725495.1
896618.2
ls22s22p63s5p
3 ~ 5 p('P)
3 ~ 5 p( 3 P )
49180.0
125510.1
223 510.9
341 712.4
479448.3
636 420.2
812447.0
1007 436.9
48770.8
124907.9
222 773.2
340858.6
478485.8
635351.6
811273.3
1006157.9
ls22s~2p~3sGp
3sGp ('P)
3sGp ('P)
50426.9
130234.3
233 596.2
358924.3
505523.9
673042.9
861 290.6
1070163.4
(3P)
50198.2
129895.5
233179.6
358440.9
504977.7
672435.3
860621.9
1069433.7
ls22s22p63s7p
3s7p ('P)
3s7p
Table 2. Hartree-Fock excitation energy values (in cm-l) for the singlet and triplet 1s22s22p63mplevles of the magnesium isoelectronic sequence
K VIII
Ar VII
CI VI
sv
Mg 1
A1 I1
Si I11
P IV
(3,s)
3s4s
ls""S2p63s4s
3s4s ('8)
Table 1 Hartree-Fock excitation energy values (in cm-l) for the signlet and triplet ls22s22p63snslevels of the magnesium isoelectronic sequence
m
c,5
T
9
FE
46179.2
111869.1
191017.8
282 113.4
384537.2
498 052.3
622582.6
758121.2
49 029.9
12379.8
217 247.8
327813.9
454 987.6
598551.4
758393.9
934458.4
48791.6
122839.5
215962.7
326481.4
453691.1
597280.4
757 107.8
933 112.2
46629.3
113947.8
194 118.6
285573.8
388058.0
501558.0
626098.1
761 708.0
40542.2
87 393.0
134054.8
179882.6
224869.2
269177.3
313 003.7
356533.9
41471.2
93 680.4
146857.6
198307.6
247 926.9
296 129.7
343340.2
389903.6
50201.9
128 682.4
350010.9
350010.9
490395.3
650000.1
1026261.7
50241.5
129201.2
229860.2
350679.2
491035.6
650628.7
1026949.2
ls22s22pG3sGd
3s6d (lo) 3s6d (3D)
51764.2
132472.9
237445.7
364373.8
512574.3
681706.4
871583.7
1082103.9
51611.8
132 158
237053.2
363986.9
512 205.9
681 343.4
871207.8
1081698.4
ls=2s"p63s7d
3s7d ('D) 3s7d ( 3 D )
519 090.7
649970.4
792220.7
c1 VI
Ar VII
K VIII
46497.9
114139.4
196600.6
292 068.8
399 710.6
Mg I
A1 I1
Si I11
P IV
SV
ls22s22p63s4f
3s4f ('F)
515678.0
645332.9
786286.2
46489.1
113980.1
195997.6
290731.9
397415.1
3s4f ( 3 F )
607581.9
770444.6
949629.9
48 965.3
123997.1
218 750.81
331412.6
461 162.8
ls22s22p63s5f
3s5f ('F)
605 786.3
768131.0
946 805.4
48 958.4
123883.5
218358.6
330610.6
459879.1
3s5f (3F)
655821.2
836166.95
1035647.1
50305.3
129349.4
230785.7
352814.4
494629.8
ls22s22p63s6f
3s6f ('F)
654803.9
834887.9
1034018.6
50300.5
129274.7
230 539.7
352 330.9
493881.4
3s6f (3F)
68446.9
137883.1
ls22s22p63s7f
337f (IF)
58196.3
127603.7
3s7f ( 3 F )
Table 4. Hartree-Fock excitation energy values (in cm-1) for the signlet and triplet 1s28s22p63sn
f levels of the magnesium isoelectronic sequence
c1 VI
Ar VII
K VIII
sv
Mg I
A1 I1
Si 111
P IV
ls22s22pG3s4d
ls22s22pG3s5d
3s4d (lD) 3s4d (30)3s5d (ID) 3s5d (3D)
ls22s22p"s3d
3s3d ('D) 3s3s (3D)
Table 3. Hartree-Fock excitation energy values (in cm-l) for the singlet and triplet ls22s22p63sndlevels of the magnesium isoelectronic sequence
CL
r
3
2.
F7
P
$
G
ip
a
TH. M. EL-SHERBINI
et al., Energy Levels in Magnesium Isoelectronic Sequence
147
Table 5. A comparison between our Hartree-Fock energy calculations of P IV and the experimental
results by Moore [6]
Level
This work
Ref. [6]
Level
This work
Ref. [6]
217826.4
216462.7
298431.7
296989.5
334169.5
108396.9
2506d9.3
245680.6
311434.3
233995.0
226888.6
316627.0
309102.4
346672
105189.9
257520.2
256751.3
320063.5
3s5p
309668.9
341712.4
179882.6
285573.8
282113.4
327813.9
386481.4
290731.9
330 610.6
320126.0
352125
189389.0
296767.8
293246.6
341004.8
339642.1
303350
343590
(3P)
3s6p ('P)
3s3d
(30)
3s4a ( 1 0 )
3s6d (ID)
(30)
3s4f
3s5f
(3F)
(3P)
Table 6. -4comparison between our Hartree-Fock energy calculations of Ar VII and the experimental
results by Moore [6]
Level
This work
Ref. [6]
3s3p ('P)
174973.3
554939.2
313003.7
622582.6
757107.8
654332.9
170720
566362
324184
634697
772355
660092
3s4p ('P)
3s3d (30)
3s4d (30)
3s5d ( 3 0 )
3s4f (3F)
Table 7. A comparison between our Hartree-Fock energy calculations of K V I I I and the experimental results by Moore [6]and Jan Olof Ekberg [7]
Level
This
Ref. [6]
Ref. [7]
Level
work
868123
883774
871022 893057
990633 1006186
3sGs (35)
3s3p ('P)
19G991
192537 192540.2
3941,(T) 687655 G9637G
3s5p ('P)
899239
912975
1007436 1022558
3sGp ('P)
1070163 1097914
3s7p ( I P )
3s3d ( 3 0 )
356533
36703% 368004
3s3d ('0)
389903
419100 399117.4
3s4d ( 3 0 )
758121
769271 770165
3s5s (38)
('8)
This
Ref. [6]
Ref. [7]
work
334a ( 1 0 )
3s5d ( 3 0 )
761708
7 ~ ~ 4 4
933112 947204
(
'
0
) 934458
947117
3s6d (30)1026949
104179
3s7d (30) 1081698 1097977
3s4f (3F)
786286 800376 801511
('P)
792220 809388
3s5f ($F) 946805 962505
('F)
949629
966616
3s6f ( 3 P ) 1034018 1060169
3s7f ( 3 P ) 1035547 1103948
Isoelectronic sequence regularities in the MgI sequence was studied using the charge
expansion theory of Layzer [ 8 ] . Fig. 1 shows E/Z2 (in a.u.) versus l/Z behaviour for
the lP terni of ls22s22p63s3p configuration, 3P term of 1s22s22p63s3p configuration,
3 0 terni of ls22s22p63s3dconfiguration and the IS terni of ls22s22p63s4sconfiguration.
A systematic behaviour appears from the curves but a linear relationship was not obtained since the single configuration energy level calculations are not the most adequate
148
Ann. Physik Leipzig 46 (1989) 2
methods for describing a two elect.ron system such as in the case of MgI sequence:
Multiconfiguration energy calculations which take into account correlation effects
between the two outer electrons woulcl be more suitable. Such a treatment for the MgI
sequence will appear in a future publication.
Fig. 1. Hartree-Fock excitation energies (in a.u.) for ls%22p63s3p(lP, 3P), ls22s22p~3s4s('S) and
lsZ2s22p633s3d(3D)
states of MgI sequence as a function of nuclear charge
References
[l] LAMBERT,
D. L.; WAARNER,
B.: Mon. Not. Roy. Astron. Soc. 140 (1968) 197.
121 FROESE-FISHER,
C.: Comput. Phys. Commun. 4 (1972) 107.
[3] E D L ~ N
B.:, Handbuch der Physik (S. FLUGGE
ed.). Vol. 27, p. 80, Berlin: Springer-Verlag 1964.
[41 EL-SHERBINI,
TH.M.; ALLAM,S. H.: Ann. Physik 39 (1983) 107.
[a] EL-SHERBINI,
TH. M.; RAHMAN,
A. A.: Ann. Physik 39 (1982) 333.
[GI MOORE,C. E.: Atomic Energy Levels NBS Circular, No. 467, Vol. 1(1949).
[7] EKBERG,
J. 0.:Physica Scripta 4 (1971) 101.
181 LAYZER,
D.: Ann. Phys. 8 (1959) 271; Monthly Not. Roy. Astron. SOC.114 (1964) 69.'.
Bei der Red<iktioneingegangen am 24. September 1986.
Anschr. d. Vctrf.: TH. M. ZL-SNERBINI, H. M. M.MANSOUR,
A. A. FARAG
and A. A. RAHMAN
Physics Department
Faculty of Science
Cairo University
Giza, Egypt
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