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Laser spectroscopic hyperfine structure measurements of 51V as a test of a new parametrization of the hyperfine structure
PhysicsLettersAl59(1991)4l5—416 North-Holland
PHYSICS LETTERS A
Laser spectroscopic hyperfine structure measurements of 51V as a test of a new parametrization of the hyperfine structure H. El-Kashef Physics Department, Faculty ofScience, Tanta University, Tanta, Egypt
N. Ludwig, K. Cloppenburg and W. Ertmer Institutfür AngewandlePhysik der Universität Bonn, W-5300 Bonn, Germany Received 13 May 1991; revised manuscript received 24 July 1991; accepted for publication 20 August 1991 Communicatedby A.A. Maradudin
The hyperfine structure (HFS) ofthe fourhigh lying and metastable fine structure levels of vanadium-5 1 have been calculated. The calculations are based on the parametrization of one- and two-body interactions to the second order perturbation theory for a model space of the three configurations 3d3 +M 45M (M= 0, 1, 2). The experimental HFS data were measured using the laser spectroscopic double-resonance technique (ABMR-LIRF) with high-frequency precision.
Each hyperfine structure investigation is based on the analysis of the fine structure. It gives information about the electromagnetic interaction of the electronic shells with the atomic nucleus. The weak interaction of electronic shells with the nuclear moments (magnetic dipole moment, electric quadrupole moment, etc.) leads to a hyperfine structure splitting of fine structure levels. These interactions are described in detail using a new parametrization [1,21. All essential one- and two-body interactions of the hyperfine structure for the model space 3d~M4S2_M (M=O, 1, 2...) are formulated in a linear combination of radial parameters. The developing coefficients can be exactly calculated. The radial parameters will be determined from fitting the linear combination with the measured hyperfine splitting, This paper presents the HFS calculations according to the developed new parametrization of the hyperfine structure interaction, and tests its precision by comparing the measured experimental results with the calculated ones. The experimental results were measured using the ABMR-LIRF method (atomic beam magnetic resonance detected by the laser induced resonance fluorescence) [3]. This method has the advantage of ...,
Elsevier Science Publishers B.V.
high detection efficiency. Therefore it is especially suited to measure the hyperfine structure ofthe high lying and poorly populated metastable atomic states. The ABMR-LIRF detection scheme consists oftwo interaction regions of an atomic beam with a single mode cw-dye laser beam crossing the atomic beam twice orthogonally. In the first interaction region one of the HFS levels is depleted by optical pumping. In the second interaction region the residual population of this depleted level is probed by the laser induced fluorescence signal. If the rf loop is stopped between the two regions, the rf transitions are induced from a neighbouring HFS level. This leads to an increase in the population ofthe depleted level, which can be detected very efficiently. It should be mentioned that the line width of the rf resonance signal is independent of the spectral width of the laser beam. The line width is mainly determined as in conventional ABMR-measurements by the time of flight ofthe atoms through the rf interaction region. The apparatus used is explained in detail in ref. [4]. Therefore its description is omitted. Table 1 shows the spectral lines used in this experiment which are extracted from refs. [5,6]. Table 2 illustrates the experimental A and B factors, the J off-diagonal corrections ~A, ~B, and the corrected A 41 5
Volume 159, number 8,9
PHYSICS LETTERS A
28 October 1991
Table 1 The spectral lines used extracted from refs. [5,6]. Levels 44s)2H 44p)2G~, (3d 44s)2H~, 912 —.(3d44p)2G~,2 (3d34s2)2D 2—.(3d34s4p)2P~, 2 (3d34s2)2D512 —.(3d 34s4p)2P?, 2 (3d 312 -.(3d 2
AE (cm~)
i-vacuum (nm)
Frequency (MHz)
18151.21 18216.52 18219.05 18210.11
550.9275 548.9523 548.8760 549.1455
544159620 546126600 546193450 545925440
Table 2 The experimental A and B factors, the J off-diagonal corrections ~A, z~.Band the corrected A and B factors: A (corrected) =A B(corrected) = B— ~B. Level 2H 2H, 912 2D 2 2D512 312
—
AA.
J
A (MHz)
B (MHz)
AA (MHz)
AB (MHz)
A (corrected)
B (corrected)
9/2 11/2 5/2 3/2
398.8739 160.9550 259.4827 341.5336
—2.8402 —17.3358 7.737 0.1726
—0.017 —0.028 0 —0.001
1.511 —4.417 —0.005 0.042
398.8909 160.983 259.4827 341.5346
—4.3512 —12.9188 7.742 0.1306
Table 3 The theoretically calculated A and B factors using the new parametrization.
interaction, shows a deviation from the experimentally measured A factor from 5 to a maximum of 10%.
_______________________________________________
On the other hand, the B factors give large relevant deviation. Therefore, the current new experimentally measured A and B factors must be taken into account in the analysis ofthe model space parameter.
Level
J
A (MHZ)
B (MHz)
9/2 11/2 5/2 3/2
421.082 153.344 279.790 309.240
—6.318 —7.282 5.891 2.080
2l~i 912
2D 2D 5,2 372
References and B factors. Table 3 shows the theoretically evaluated A and B factors using the model space parameters 1 and 2. On comparison of the theoretical and experimental data in tables 2 and 3 it is clear that the calculated hyperfine splitting factor A, according to the model space parameters of the magnetic dipole
416
[I] J. Dembczynski et al., Z. Phys. A 321(1985) 1. [2] P. Unkel, Dissertation, Universität Bonn (1985). [3]W.Ertmeretal.,Z.Phys.A 276 (1976) 9. [4] H. El-Kashef etal., to be published in Physica B. [5] J. Sugaret al., J. Phys. Chem. Ref. Data 7 (1978) 1191. [6] W.F. Meggers et al., Tables of spectral-line intensities (U.S. Government Printing Office, Washington, 1961).
PHYSICS LETTERS A
Laser spectroscopic hyperfine structure measurements of 51V as a test of a new parametrization of the hyperfine structure H. El-Kashef Physics Department, Faculty ofScience, Tanta University, Tanta, Egypt
N. Ludwig, K. Cloppenburg and W. Ertmer Institutfür AngewandlePhysik der Universität Bonn, W-5300 Bonn, Germany Received 13 May 1991; revised manuscript received 24 July 1991; accepted for publication 20 August 1991 Communicatedby A.A. Maradudin
The hyperfine structure (HFS) ofthe fourhigh lying and metastable fine structure levels of vanadium-5 1 have been calculated. The calculations are based on the parametrization of one- and two-body interactions to the second order perturbation theory for a model space of the three configurations 3d3 +M 45M (M= 0, 1, 2). The experimental HFS data were measured using the laser spectroscopic double-resonance technique (ABMR-LIRF) with high-frequency precision.
Each hyperfine structure investigation is based on the analysis of the fine structure. It gives information about the electromagnetic interaction of the electronic shells with the atomic nucleus. The weak interaction of electronic shells with the nuclear moments (magnetic dipole moment, electric quadrupole moment, etc.) leads to a hyperfine structure splitting of fine structure levels. These interactions are described in detail using a new parametrization [1,21. All essential one- and two-body interactions of the hyperfine structure for the model space 3d~M4S2_M (M=O, 1, 2...) are formulated in a linear combination of radial parameters. The developing coefficients can be exactly calculated. The radial parameters will be determined from fitting the linear combination with the measured hyperfine splitting, This paper presents the HFS calculations according to the developed new parametrization of the hyperfine structure interaction, and tests its precision by comparing the measured experimental results with the calculated ones. The experimental results were measured using the ABMR-LIRF method (atomic beam magnetic resonance detected by the laser induced resonance fluorescence) [3]. This method has the advantage of ...,
Elsevier Science Publishers B.V.
high detection efficiency. Therefore it is especially suited to measure the hyperfine structure ofthe high lying and poorly populated metastable atomic states. The ABMR-LIRF detection scheme consists oftwo interaction regions of an atomic beam with a single mode cw-dye laser beam crossing the atomic beam twice orthogonally. In the first interaction region one of the HFS levels is depleted by optical pumping. In the second interaction region the residual population of this depleted level is probed by the laser induced fluorescence signal. If the rf loop is stopped between the two regions, the rf transitions are induced from a neighbouring HFS level. This leads to an increase in the population ofthe depleted level, which can be detected very efficiently. It should be mentioned that the line width of the rf resonance signal is independent of the spectral width of the laser beam. The line width is mainly determined as in conventional ABMR-measurements by the time of flight ofthe atoms through the rf interaction region. The apparatus used is explained in detail in ref. [4]. Therefore its description is omitted. Table 1 shows the spectral lines used in this experiment which are extracted from refs. [5,6]. Table 2 illustrates the experimental A and B factors, the J off-diagonal corrections ~A, ~B, and the corrected A 41 5
Volume 159, number 8,9
PHYSICS LETTERS A
28 October 1991
Table 1 The spectral lines used extracted from refs. [5,6]. Levels 44s)2H 44p)2G~, (3d 44s)2H~, 912 —.(3d44p)2G~,2 (3d34s2)2D 2—.(3d34s4p)2P~, 2 (3d34s2)2D512 —.(3d 34s4p)2P?, 2 (3d 312 -.(3d 2
AE (cm~)
i-vacuum (nm)
Frequency (MHz)
18151.21 18216.52 18219.05 18210.11
550.9275 548.9523 548.8760 549.1455
544159620 546126600 546193450 545925440
Table 2 The experimental A and B factors, the J off-diagonal corrections ~A, z~.Band the corrected A and B factors: A (corrected) =A B(corrected) = B— ~B. Level 2H 2H, 912 2D 2 2D512 312
—
AA.
J
A (MHz)
B (MHz)
AA (MHz)
AB (MHz)
A (corrected)
B (corrected)
9/2 11/2 5/2 3/2
398.8739 160.9550 259.4827 341.5336
—2.8402 —17.3358 7.737 0.1726
—0.017 —0.028 0 —0.001
1.511 —4.417 —0.005 0.042
398.8909 160.983 259.4827 341.5346
—4.3512 —12.9188 7.742 0.1306
Table 3 The theoretically calculated A and B factors using the new parametrization.
interaction, shows a deviation from the experimentally measured A factor from 5 to a maximum of 10%.
_______________________________________________
On the other hand, the B factors give large relevant deviation. Therefore, the current new experimentally measured A and B factors must be taken into account in the analysis ofthe model space parameter.
Level
J
A (MHZ)
B (MHz)
9/2 11/2 5/2 3/2
421.082 153.344 279.790 309.240
—6.318 —7.282 5.891 2.080
2l~i 912
2D 2D 5,2 372
References and B factors. Table 3 shows the theoretically evaluated A and B factors using the model space parameters 1 and 2. On comparison of the theoretical and experimental data in tables 2 and 3 it is clear that the calculated hyperfine splitting factor A, according to the model space parameters of the magnetic dipole
416
[I] J. Dembczynski et al., Z. Phys. A 321(1985) 1. [2] P. Unkel, Dissertation, Universität Bonn (1985). [3]W.Ertmeretal.,Z.Phys.A 276 (1976) 9. [4] H. El-Kashef etal., to be published in Physica B. [5] J. Sugaret al., J. Phys. Chem. Ref. Data 7 (1978) 1191. [6] W.F. Meggers et al., Tables of spectral-line intensities (U.S. Government Printing Office, Washington, 1961).