Atoms,Molecules and Clusters
Z. Phys. D - Atoms, Moleculesand Clusters 7, 185-188 (1987)
ftir Physik D
© Springer-Verlag 1987
Hyperfine structure studies in the mixed configurations (4p z 4 d + 4s
4p 4) of arsenic*
S. Bouazza 1, j. Bauche 2, j. Dembczynski 3, and E. Stachowska 3 1 Laboratoire de SpectroscopieQuantitative, Facult6 des Scienceset Techniques, 6 Avenue Le Gorgeu, 29287 Brest Cedex, France 2 Laboratoire Airn6 Cotton, CNRS II, 91405 Orsay Cedex, France 3 Instytut Fizyki,PolitechnikaPoznan, Poland Received 13 July 1987 The magnetic hyperfine structures of some levels of the 4p 2 4d configuration which mixes strongly with the 4s 4p 4 configuration, have been measured for the first time, using the Fabry-Perot technique in the far UV range. A good agreement is observed between experimental results and theoretical evaluations. PACS: 31.30.G
1. Introduction The first studies of the fine structure [I] of the first spectrum of arsenic (Z = 33) reported that the energy levels of the 4p z 5 s and 4s 4p 4 configurations are very close. This, however, was later shown to be inaccurate [2, 3] : the 4s 4p 4 configuration mixes only very little (less than 1%) with 4p 2 5s, but very strongly (up to 40%) with 4p z 4d. Following previous hyperfine structure (hfs) studies of the 4p z 5s levels [4], the present work is an attempt to evaluate the impact of this configuration mixing. Figure 1 gives the diagram of the energy levels reached and of the lines studied. The latter were emitted by a hollow-cathode lamp containing the natural
profile and the positions of the hyperfine components of the odd 75As.
2. Results The data for the ground configuration levels have been given in a previous work [4]. Table 1 gives the observed magnetic hfs data for the 4p 2 4d levels studied.
3. Discussion 3.1. Hfs parameter coefficients in intermediate coupling
isotope 75As. The spectroscopic work was carried out by using silica Fabry-Perot etalon plates with A 1 - MgFz double layer. The thickness values were respectively 25 nm for A1 and 45 nm for MgF2, with a reflective finesse of 30 between 210 and 220 nm. The mathematical treatment of the fringe patterns has been described in a previous paper [5]. Figure 2 shows an example of a computed line * Dedicated to ProfessorSiegfriedPenselin on occasion of his 60th birthday
Configuration 4s 4p 4 is almost non existent as such. It mixes with the other even configurations, especially 4p 2 4d, to such a point that there is only one level, corresponding to experimental energy 70792 cm -1, whose major component in the mixing belongs to 4s 4p 4 [2]. The wave functions of the five levels studied are, on the basis of SL coupled functions:
t 4/~3/2) = 0.24212P3/2)p4d - - 0.631 1 4 P 3 / 2 ) p 4 d
186 Table 1. Hyperfine structure magnetic constants A of the levels of the 4p 2 4d configuration, in mK (1 mK = 10 -3 c m - ~)
ARSENIC
Level 0
4p a
A measured
4 p~'4d
4P3/2 2P3/2 2Fs/2 2F7]2
60
25 _+2 - 6.4 ___0.8 11.2 _+0.8 8.4 _+0.9 2.3 + 0.7
4/77/2
The expansions of the magnetic hfs factor A in intermediate coupling and configuration mixing are given in Table 2:
40
3.2. Monoelectronic hfs constants
20
0
a$o ~
312
Fig. 1. Energy level diagram of arsenic showing the levels [2, 3] and the lines investigated in this work (the wavelengths are in nm)
-- 0 . 3 8 8 1 4 F 3 / 2 ) p 4d + 0 . 2 6 2 [4 D3/2 )p4 a
+0.52014P3/2)sp4 - - 0 . 1 3 7 1 4 P 3 / 2 ) p 5a - - 0 . 1 0 5 14P3/2)p6s+... I 2P3/2) = 0.I 56 [2D3/2}p4 d
+ 0.104 [(*D) 2p3/2)~, 4a-- 0. I27 I'*D3/=)v 4a ....0.875 ](3p) 2p3/2) p,~a--0.325 [4F3/2) p4d --0.105 [2pa/g),v~ + O.13614 Pa/2) ~v, -0.118 ]2p3/2)vsd + ... [ 2 ~ / 2 ) = --0.227
l(1D) 2Fs/2)p4a
-- 0.871 [(3p) ZFs/z)p 4e + 0.25314Ds/z)p4a +0.27414Fs/z)p4e+0.18512Ds/z)v4e -0.09414Ps/2)~v~ +... [2ff7/2) = 0 . 5 3 0 [4D7/2) p 4d + 0.833 ] 2F~/2) v 4e
+0.13812GT/2)v~e+... t 4X~7/2)= --0.33114Dv/2)v4a+0.919 [4I~7/2)p4 d
+0.172 IZFT/z)v4e + O.11514FT/z)psa + .... The lower subscripts pnd, p 6s and sp 4 symbolize respectively 4p 2 nd, 4p 2 6s and 4s 4p 4. The eigenvectors without parent term given explicitely originate f r o m 3p.
The monoelectronic hfs constants of p electrons in the 4p z 4d, 4p 2 5d and 4p 2 6s configurations will be evaluated from the results of the 4p 3 configuration radial integrals. The latter, computed [6] through the optimized Hartree-Fock-Slater (O.H.F.S.) method are listed in Table 3, in which the value (r_-3\1o /p deduced fi'om the experimental result for the 4S3/2 level [7] is included, because this value takes into account the spin polarisation contribution. As in previous work [4] and in keeping with Freeman et al. [8] for d electrons it is assumed that the polarizing effect per unpaired electron remains the same whatever the number of the 4p electrons, the complete shells (here: ls z 2s 2 3s 2 4s 2) being the same for the 4p 3, 4p 2 4d, 4p 2 5d and 4p 2 6s configurations. However for the 4s 4p 4 configuration, where the complete shells are only three (1 s 2 2s 2 3s 2) the spin polarisation contribution cannot be evaluated; only the relativistic one is accordingly taken into account. Using Table 3 and ~v(4p 3) = 1485 cm- 1 [9] yields the monoelectronic constants given in Table 4 (in mK). Arsenic is a light element, so that the relativistic effects are small. Using Sandars and Beck's method [10] for the d electrons gives: Ol = ~-~ 1 [12F~(ds/2, Zeff) + 12Fr(d3/2, Neff) a,a
+ Gr(d, Neff)] a,e a2 = ~s [-- 72 F~(d5/2, Zeff) + 168 F~(d3/2 Zeff) and --21 Gr(d, Zoff)] a,a
10= ~ [ 3 and
f~(dsj2, Zoff)- 2F,,.(d3/2, Zof0
-Gr(d, Zeff)] a,dKopfermann's tables [11], give:
F~(ds/2, 22) = 1.0044, G,. = (d, 22) = 1.0034
Fr(d3/2, 22)= 1.0102,
187
ii
\
I
X\\\ /
\
/
k\
\\Xx
i
cq
u~ Fig. 2. Computed profile of the 175.8 nm line, through a 500.43 m K free spectral range. The full curves stand for the initial signals, as originated by the photomultiplier, whereas the broken curves account for the processed
? O
I "200~
I
i
-Io0,
-150.
"7
I
I
I
-50.
I
50.
O,
tO0o
I I50o
I 200.
mK
Table 2. Monoelectronic constant coefficients in intermediate coupling
apol
Level
4p3/2 -0.1511
2p3/2
ap12
aplO
aOl
a~2
a~O
0.0504
0.238
0.606
0.188
0.0011
0.010
0.014
0.004
0.003
-0.2186
-0.0141
0.276
0.952
0.052
-0.077
2/75/2
0.3516
-0.0011 0.0065
0.004 --0.050
0.016 0.718
~0
ap12
aplo
aslo
-0.006
-0.0040
0.0031
apol
0.0727
-0.0819
0.129
0.06922
0.0030
-0.0031
0.006
0.0023
4p 2 4d 4s 4p 4 4p 2 5d 4p 2 6s
0.0123
-0.0009
0.020
-0.00240
4p 2 4d 4s 4p 4
0.0070
-0.0006
0.003
0.001
4p 2 6s
0.0035
0.0005
0.004
0.00177
4s 4p 4
4p 2 5d
~0
0.043
Corresponding to the configuration
--0.032
4p 2 4d
2Fv/2
0.2415
0.0624
0.205
0.539
-0.044
0.013
4p 2 4d
~FT/2
0.1872 0.0031
--0.0985 --0.0006
0.136 0.002
0.547 0.007
--0.042 N0
0.116 0.001
4p 2 4d 4p 2 5d
Table 3. Computed and experimental radial integrals in the 4p 3 configuration (in a.u.)
O.H.F.S. Experiment
which, in turn, gives:
( r - 3 > °1
( r - 3 ) 12
( r 3)1o
a o 1 = 1 . 0 0 7 aa
(1)
8.464
9.553
- 0.411
a~ z = 1 . 0 1 8 aa
(2)
a~ 0 = _ 0 . 0 0 0 0 9 4 aa.
(3)
- 0.77
188 Table 4. Computed monoelectronic constants of the 4p 2 4d, 4p 2 5d, 4p 2 6s and 4s 4p 4 configurations in mK Configuration
~p(cm-1) [2]
a°p1
a~z
a~°
4p 2 4d 4p 2 5d 4p 2 6s 4s 4p 4
1599 1667 1642 1578
27.74 28.92 28.49 27.38
31.31 32.64 32.15 30.90
-2.52 2.63 -2.59 - 1.33
T h e r a d i a l i n t e g r a l ( r - 3 ) a can be c o m p u t e d [12] by:
G ( r - 3)d = R~o ~2 a 3 ZeffHr(d ' Neff) a n d with
H~(d, 2 2 ) = 1.0035 [11] Roo = 109737 c m - 1 ao = 1 (a.u.)
(where the s e c o n d m e m b e r c o r r e s p o n d s t o Aexp(4p3/2)) 1o in the e x p r e s s i o n s of b e c a u s e the coefficients of a4s A(2P3/2) and A(2Fs/2) a r e e x t r e m e l y s m a l l ( T a b l e 2) which results in large uncertainties. This value is close to H a r t r e e - F o c k e v a l u a t i o n , a~ ° = 366 i n K .
4. Conclusion This w o r k shows t h a t the levels of the 4 p 2 4 d configur a t i o n m a y exhibit high values for the m a g n e t i c factor A, d u e to its m i x i n g with 4 s 4p4; the hyperfine structure m e a s u r e m e n t o f the 4P3/2 level, s t u d i e d a b o v e , lo p a r a m e t e r . gives access to fairly a c c u r a t e v a l u e o f a4s This was n o t p o s s i b l e in the s t u d y of 4 p 2 5s [4]. A p r e v i o u s w o r k [15] also gives all the p a r a m e t e r s for c a l c u l a t i n g the hyperfine factors of the t w e n t y levels of 4 p 2 4 d listed in [2]. O n c e again, it is f o u n d t h a t a s t u d y of hfs r e m a i n s an useful test to check the v a l i d i t y of wave functions of fine s t r u c t u r e - as exemplified in the w o r k m e n t i o n e d in [2].
= 7.2975- 1 0 - 3 ~a(4p 2 4 d ) = 4 0 c m - 1 [2]
References
~a(4p 2 5 d ) = 1 5 c m
1. Moore, C.E.: Atomic energy levels, Circ. 467. Natl. Bur. Standards (1952) 2: Dembczynski, J., Stachowska, E., Arcimowicz, B., Bancewicz, M.: Physica 142C, 111 119 (1986) 3. Howard, L.E., Andrew, K.L.: J.O.S.A. B2, 7, 1032 (1985) 4. Bouazza, S., Bauche, J., Guern, Y., Abjean, R.: Z. Phys. D Atoms, Molecules and Clusters 7, 33 (1987) 5. Bouazza, S., Guern, Y., Bauche, J.: J. Phys. B19, 1881 (1986) 6. Lindgren, I., Rosen, A.: Case Stud. At. Phys. 4, 197 (1974) 7. Pendlebury, P.J.M., Smith, K.F.: Proc. Phys. Soc. 84, 849 (t964) 8. Freeman, A.J., Bagus, P., Watson, R.E.: La structure hyperfine des atomes et des mol6cules. Moser, C., Lef+vre, R. (eds.). Paris: C.N.R.S. 1967 9. Arcimowicz, B.: Inst. Phys., Nicholas Copernicus University, Torun, Poland, Preprint Nr 321 (1975) and Private Communication 10. Sandars, P.G.H., Beck, J.: Proc. R. Soc. London Ser. A289, 97 (1965) 11. Kopfermann, H.: Nuclear moments. New York: Academic Press 1958 12. Bordarier, Y, Judd, B.R., Ktapisch, M.: Proc. R. Soc. London Ser. A289, 81 (1965) 13. Fuller, G.H., Cohen, V.W.: Nuclear data tables. K. Way (e&) New York: Academic Press 1969 14. Kuhn, H.G.: Atomic spectra. London: Longmans 1969 15. Bouazza, S.: Thesis, Brest 1987
~ [2].
T h e results are: (r-3)4e=0.310
(a.u)
and
(r-3)sa=0.116
(a.u)
which gives, k n o w i n g t h a t # N = 1 . 4 3 5 n.m a n d I = 3 [133. U s i n g (1) to (3): a4col = 0 . 9 5 i n K ,
a4a12= 0.96 m K
and
a 1°4d~ 0
ol = 0 . 3 5 a5d
a~ 2 = 0 . 3 6 m K
and
lo NO. asa
mK,
U s i n g F e r m i - S e g r 6 - G o u d s m i t f o r m u l a [14] gives [4] as~l°= 3 9 . 9 2 inK. K n o w i n g t h a t na (4P 2 5s)" 1.9811 10 a n d na ( 4 p 2 6 s ) = 3 . 0 0 4 9 [2] also gives" a6s = 11.44 m K . A p a r a m e t r i c s t u d y c a n be p e r f o r m e d with o n l y 10 o n e p a r a m e t e r : a4s. lo = 11.44 rnK, c a l c u l a t e d U s i n g T a b l e s 2 to 4, a6~ a b o v e a n d A~xp(4p3/2)=(25+_2)mK (Table 1) gives lO = (408.4 + 28.9) inK. O n l y one e q u a t i o n was used ags
