- Email: [email protected]
Electronic g factors eleven atomic states of Zr
Volume 58A, number 1
PHYSICS LETTERS
26 July 1976
ELECTRONIC g FACTORS FOR ELEVEN ATOMIC STATES OF Zr S. BUTTGENBACH, R. DICKE and H. GEBAUER Institut flu Angewandte Physik der Universitdt Bonn, Bonn, West Germany Received 5 February 1976 Revised manuscript received 27 June 1976 The gj factors for eleven low-lying atomic levels of Zr I have been measured with the atomic-beam magneticresonance method. The agreement between the experimental gj values and theoretical predictions deduced from intermediate coupling wave functions isbetter than 0.1%.
The spectrum of the neutral Zirconium atom has been studied optically by several authors. A summary of these investigations, especially the excitation energies and the electronic g factors gj of the observed atomic levels, is given by Moore [1]. The present atomic-beam magnetic-resonance measurements were performed in order to get more precise gj values for the analysis of hyperfine-Zeeman interaction studies as well as for testing recently developed intermediate coupling wave functions. The (4d 5~)4electron scheme provides a number of low-lying closely packed levels which interact strongly with each other. Therefore eigenvectors that span the three configurations 4d2 5s2, 4d3 5 s, and 4d4 in intermediate coupling have to be used in order to understand measured properties of the states such as their excitation energies, electronic g factors, or hyperfme interaction constants. All observed levels of the three configurations and their LS designations are shown in fig. 1. Intermediate coupling wave functions +
were obtained from a three-configuration least-squares fit of the appropriate Slater, spin-orbit, and configuration interaction parameters to the experimental energy levels. Configuration interaction between the three configurations was included explicitly, and interactionwith higher configurations was taken into account by including the effective electrostatic interaction described by aL(L 1) A total of 16 parameters was varied to fit 40 energy levels; the mean deviation was ±58cm~ In this calculation four badly fitting levels were omitted from the least-squares procedure, namely the 4d3 Ss D(2 D) state and the multiplet 4d35s 3F(2F). The effect of including these levels in the calculation was a disproportional increase in the mean deviation, and the difference between calculated and observed energies was unreasonable large for these levels. Probably higher-lying configurations would have to be included explicitly to explain these deviations. Zirconium belongs to the group of highly refractory +
+ (3Q.
-
Table 1
Comparison between experimental, intermediate coupling,
and LS-coupling g
1 values (gj~and gj~Sinclude the Schwinger correction) State
25s 3F
4d
3F 2 3F3
4
‘D2 35s5F 4d 2
56
exp gj
IC
gj
gj
0.66981 (4)
0.66999
—0.00018
0.66589
1.08331 (9) 1.24987 (6) 1.50072(12) 1.26472 (5) 1.23146 (3) 1.00052 (5) 1.00081(10) 1.25021 (5) 1.35012 (4)
1.08352 1.25008 1.50110
—0.00021 —0.00021 —0.00038
1.08353 1.25058 1.50116
1.23096 1.00072 1.00155 1.25038 1.35026
0.00050 —0.00020 —0.00074 —0.00017 —0.00014
1.00000 1.00000 1.00000 1.25058 1.35081
1.39991 (4)
1.40002
—0.00011
1.40093
1.26520
exp IC (gj
—0.00048
LS
gj
1.50116
Volume 58A, number 1
conventional flop-in type atomic beam magnetic-re-
-
2~
-
sonance was atomic used tostates determine ZeemanI splitting apparatus of the eleven listed the in column -
of table 1. No measurements were performed in the 3P states 4d25s2 35s 5F0 with no resulting angular momenturn and 4d 1 possessing an electronic g factor nearly equal to zero. In order to determine the gj values the frequencies of the Zeeman transitions (m 1 = 0) -÷(m,~= 1) were measured at different magnetic fieldsH. To separate resonances belonging to very similar gj values relatively
-
20000
•~E U
1H
>-
5
SD
________
—-
(2H)
‘G (‘0)
______
w z -
26 July 1976
PHYSICS LETTERS
+
2P)
______
io,(2D)_4 _______~ ___
z
o
2
‘PC —
________~.
¶5000
________~.. __________
2
________
~i*
3P(’P)
high fields up to 1700 Oe were necessary. The resoances were recorded using an on-line computer system by scanning the resonance curves in small frequency steps [3]. Fi 2 shows such a resonance pattern for the states 4d~5s21G 35s 5F 4 and 4d 2 The difference in intensity between the two peaks indicates that the two levels have different populations. The observed transition frequency v is given by
3F(2F) 3H(2H) 3D(2D)
iii
‘S
0
—
.
-
________
3 -
10000
‘F(’F) 5P(’P)
________~-
v(p~/h).gJ.H+~Sv
-
where p~is Bohr’s magneton and h is Planck’s con-
stant. is the frequency shift due to the Zeeman interaction between the state under investigation and other atomic states. The shifts were calculated by second order perturbation theory and the gj factors were evaluated from the corrected frequencies. Table 1 compares these experimental gj values with theoretical values derived from the intermediate coupling wave functions. Land~values in pure LS-coupling are listed in the last colunm of table 1. The
________
~i’
45
5000
2
—
________~
5F(’F)
________ _________
________
agreement found between experimental and theo4 --
3F<_______
0
3 2
-
<
_____________________
4d25s2
ELECTRON
£d35s
4d’
CONFIGURATION
5F 2
CD
in -
10
Fig. 1. Schematic diagram of the known levels of the Zr I configurations 4d25s’, 4d35s, and 4d4. For states of 4d35s the parent terms are given in parenthesis. elements. A detailed description of the evaporation method applied is given elsewhere [2]. At the evaporation temperature of about 3000 K all levels with an excitation energy up to 8000 cm—1 were sufficiently populated to observe rf transitions in 90Zr, which has zero nuclear spin and a natural abundance of 51%. A
-
r f F REQ U EN C Y
Fig. 2. Zeeman transitions in the 4d2 ~s~‘G 1) 4 (8057 cm and 4d35s 5F 90Zr at 1700 Oe. The curve required about 10 mm of data collection. The distance 2 (5023 cm_i)ievels of between the frequency steps is 25 kHz.
57
Volume 58A, number 1
PHYSICS LETTERS
retical values is very good. Even for the most per3P 1D turbed2,states for which the deviation the L-S cou2 and 2 of thefrom configuration 4~j23s pling gj values is most severe, one gets a residual of less than 0.1%. Judd and Lindgren [4] have given the expression (J + 1) g 1 (.1 1 )gj.~= ~2 + b —
—
to be satisfied by the g1 values of the members of an LS multiplet. The relation includes the Schwinger, relativistic, diamagnetic, and second-order spin-orbit 3 5s corrections toopportunity the Landé values. 4d If 5F offers the to testThe thismultiplet relationship. one evaluates the constants a and b from the gj values of the J = 2, 3, 4 states one can predict gj(5 F 5) = 1.40024(15). This prediction is nearly consistent with the experimental value.
58
26
July 1976
The authors would like to thank W.J. Childs, puter program for the energy level ThethecalculaArgonne National Laboratory, whofitting. supplied corn-
tions were performed with the computer system IBM 370/168 of the Regionales Hochschulrechenzentrum der Universität Bonn. Thanks are also due to the Deutsche Forschungsgemeinschaft for financial support.
References [1] C.E. Moore, Atomic Energy Levels, Washington D.C., U.S. Government Printing Office (1971). [2] S. Bllttgenbach, et al., Z. Physik 230 (1970) 329.
[3] Buttgenbach G. Meisel, Z. Physik 244 (1971)149. [4] S. B.R. Judd and I.and Lindgren, Phys. 122 (1961) 1802.
PHYSICS LETTERS
26 July 1976
ELECTRONIC g FACTORS FOR ELEVEN ATOMIC STATES OF Zr S. BUTTGENBACH, R. DICKE and H. GEBAUER Institut flu Angewandte Physik der Universitdt Bonn, Bonn, West Germany Received 5 February 1976 Revised manuscript received 27 June 1976 The gj factors for eleven low-lying atomic levels of Zr I have been measured with the atomic-beam magneticresonance method. The agreement between the experimental gj values and theoretical predictions deduced from intermediate coupling wave functions isbetter than 0.1%.
The spectrum of the neutral Zirconium atom has been studied optically by several authors. A summary of these investigations, especially the excitation energies and the electronic g factors gj of the observed atomic levels, is given by Moore [1]. The present atomic-beam magnetic-resonance measurements were performed in order to get more precise gj values for the analysis of hyperfine-Zeeman interaction studies as well as for testing recently developed intermediate coupling wave functions. The (4d 5~)4electron scheme provides a number of low-lying closely packed levels which interact strongly with each other. Therefore eigenvectors that span the three configurations 4d2 5s2, 4d3 5 s, and 4d4 in intermediate coupling have to be used in order to understand measured properties of the states such as their excitation energies, electronic g factors, or hyperfme interaction constants. All observed levels of the three configurations and their LS designations are shown in fig. 1. Intermediate coupling wave functions +
were obtained from a three-configuration least-squares fit of the appropriate Slater, spin-orbit, and configuration interaction parameters to the experimental energy levels. Configuration interaction between the three configurations was included explicitly, and interactionwith higher configurations was taken into account by including the effective electrostatic interaction described by aL(L 1) A total of 16 parameters was varied to fit 40 energy levels; the mean deviation was ±58cm~ In this calculation four badly fitting levels were omitted from the least-squares procedure, namely the 4d3 Ss D(2 D) state and the multiplet 4d35s 3F(2F). The effect of including these levels in the calculation was a disproportional increase in the mean deviation, and the difference between calculated and observed energies was unreasonable large for these levels. Probably higher-lying configurations would have to be included explicitly to explain these deviations. Zirconium belongs to the group of highly refractory +
+ (3Q.
-
Table 1
Comparison between experimental, intermediate coupling,
and LS-coupling g
1 values (gj~and gj~Sinclude the Schwinger correction) State
25s 3F
4d
3F 2 3F3
4
‘D2 35s5F 4d 2
56
exp gj
IC
gj
gj
0.66981 (4)
0.66999
—0.00018
0.66589
1.08331 (9) 1.24987 (6) 1.50072(12) 1.26472 (5) 1.23146 (3) 1.00052 (5) 1.00081(10) 1.25021 (5) 1.35012 (4)
1.08352 1.25008 1.50110
—0.00021 —0.00021 —0.00038
1.08353 1.25058 1.50116
1.23096 1.00072 1.00155 1.25038 1.35026
0.00050 —0.00020 —0.00074 —0.00017 —0.00014
1.00000 1.00000 1.00000 1.25058 1.35081
1.39991 (4)
1.40002
—0.00011
1.40093
1.26520
exp IC (gj
—0.00048
LS
gj
1.50116
Volume 58A, number 1
conventional flop-in type atomic beam magnetic-re-
-
2~
-
sonance was atomic used tostates determine ZeemanI splitting apparatus of the eleven listed the in column -
of table 1. No measurements were performed in the 3P states 4d25s2 35s 5F0 with no resulting angular momenturn and 4d 1 possessing an electronic g factor nearly equal to zero. In order to determine the gj values the frequencies of the Zeeman transitions (m 1 = 0) -÷(m,~= 1) were measured at different magnetic fieldsH. To separate resonances belonging to very similar gj values relatively
-
20000
•~E U
1H
>-
5
SD
________
—-
(2H)
‘G (‘0)
______
w z -
26 July 1976
PHYSICS LETTERS
+
2P)
______
io,(2D)_4 _______~ ___
z
o
2
‘PC —
________~.
¶5000
________~.. __________
2
________
~i*
3P(’P)
high fields up to 1700 Oe were necessary. The resoances were recorded using an on-line computer system by scanning the resonance curves in small frequency steps [3]. Fi 2 shows such a resonance pattern for the states 4d~5s21G 35s 5F 4 and 4d 2 The difference in intensity between the two peaks indicates that the two levels have different populations. The observed transition frequency v is given by
3F(2F) 3H(2H) 3D(2D)
iii
‘S
0
—
.
-
________
3 -
10000
‘F(’F) 5P(’P)
________~-
v(p~/h).gJ.H+~Sv
-
where p~is Bohr’s magneton and h is Planck’s con-
stant. is the frequency shift due to the Zeeman interaction between the state under investigation and other atomic states. The shifts were calculated by second order perturbation theory and the gj factors were evaluated from the corrected frequencies. Table 1 compares these experimental gj values with theoretical values derived from the intermediate coupling wave functions. Land~values in pure LS-coupling are listed in the last colunm of table 1. The
________
~i’
45
5000
2
—
________~
5F(’F)
________ _________
________
agreement found between experimental and theo4 --
3F<_______
0
3 2
-
<
_____________________
4d25s2
ELECTRON
£d35s
4d’
CONFIGURATION
5F 2
CD
in -
10
Fig. 1. Schematic diagram of the known levels of the Zr I configurations 4d25s’, 4d35s, and 4d4. For states of 4d35s the parent terms are given in parenthesis. elements. A detailed description of the evaporation method applied is given elsewhere [2]. At the evaporation temperature of about 3000 K all levels with an excitation energy up to 8000 cm—1 were sufficiently populated to observe rf transitions in 90Zr, which has zero nuclear spin and a natural abundance of 51%. A
-
r f F REQ U EN C Y
Fig. 2. Zeeman transitions in the 4d2 ~s~‘G 1) 4 (8057 cm and 4d35s 5F 90Zr at 1700 Oe. The curve required about 10 mm of data collection. The distance 2 (5023 cm_i)ievels of between the frequency steps is 25 kHz.
57
Volume 58A, number 1
PHYSICS LETTERS
retical values is very good. Even for the most per3P 1D turbed2,states for which the deviation the L-S cou2 and 2 of thefrom configuration 4~j23s pling gj values is most severe, one gets a residual of less than 0.1%. Judd and Lindgren [4] have given the expression (J + 1) g 1 (.1 1 )gj.~= ~2 + b —
—
to be satisfied by the g1 values of the members of an LS multiplet. The relation includes the Schwinger, relativistic, diamagnetic, and second-order spin-orbit 3 5s corrections toopportunity the Landé values. 4d If 5F offers the to testThe thismultiplet relationship. one evaluates the constants a and b from the gj values of the J = 2, 3, 4 states one can predict gj(5 F 5) = 1.40024(15). This prediction is nearly consistent with the experimental value.
58
26
July 1976
The authors would like to thank W.J. Childs, puter program for the energy level ThethecalculaArgonne National Laboratory, whofitting. supplied corn-
tions were performed with the computer system IBM 370/168 of the Regionales Hochschulrechenzentrum der Universität Bonn. Thanks are also due to the Deutsche Forschungsgemeinschaft for financial support.
References [1] C.E. Moore, Atomic Energy Levels, Washington D.C., U.S. Government Printing Office (1971). [2] S. Bllttgenbach, et al., Z. Physik 230 (1970) 329.
[3] Buttgenbach G. Meisel, Z. Physik 244 (1971)149. [4] S. B.R. Judd and I.and Lindgren, Phys. 122 (1961) 1802.