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Fine-structure splittings of 2F states of singly ionized strontium
Volume 66A, number I
PHYSICS LETTERS
17 April 1978
FINE-STRUCTURE SPLITTINGS OF 2F STATES OF SINGLY IONIZED STRONTIUM W. PERSSON and K. PIRA Department of Physics, Lund Institute of Technology, S-220 07 Lund, Sweden Received 1 February 1978
We have studied the 4d—nf and 5d—nf (n = 4—8) transitions of singly ionized strontium using high-resolution optical spectroscopy. The 2F fine structure is inverted in all the states observed and decreases from —1.06 cm1 in 4f to —0.26 cm~ in 8f.
The fine-structure intervals in the D, F, G and H terms of neutral alkali atoms have recently been the subject of several investigations using high-resolution techniques such as Doppler-free two-photon spectroscopy [1—4] and step-wise excitation by tunable dye lasers in conjunction with radio-frequency [SI and microwave [61resonance methods, level-crossing techniques [71or quantum-beat spectroscopy [8]. In particular, these methods have yielded very accurate values of the fine-structure splittings of the F states of atomic sodium [4,6] and rubidium [5]. However, none of the laser methods has hitherto been applied to the study of fine structures in ionized atoms isoelectronic with the alkali atoms. We report the first measurement of the fine-structure intervals of 2F states of singly ionized strontium for principal quantum numbers 4—8. The measurement was performed by use of high-resolution optical spectroscopy. The main reference for the Sr Ii spectrum is the report bySaunders et al. [9]. In their analysis, the fine structure of the F states was not resolved. Interferometric determination of wavelengths in the Sr II spectrum by Sullivan [101 did not involve any transitions to F states. The most recent report on wavelength determinations in Sr II is by Newsom et al. [11] who, in an investigation of the spectrum of neutral strontium, measured the wavelengths of 16 Sr II lines in the 8000—18 000 A range, among them several combinations involving 4f and Sf states. Our work was initiated by the observation that in the sliding-spark spectrograms recorded for analyzing 22
the spectrum emitted by two to four times ionized strontium [12,13] the 4f—Sg combination in Sr II at 9647 A was clearly resolved into two components. The excitation method was, however, not adequate for an accurate determination of the 2F fine-structure interval. In the present work, the strontium spectrum was excited in a water-cooled hollow-cathode discharge tube, designed for use at large current densities [14]. Argon at a pressure of 0.1 Torr served as carrier gas and at the same time furnished the reference spectrum. With a lump of metallic strontium placed inside the cathode, a well-developed Sr II spectrum was observed at 0.5 A discharge current. A schematic Sr~energy level diagram with the relevant transitions indicated is shown in fig. 1. The 4d—4f combinations at around 2160 A and the 4d—5f combinations at around 1770 A were photographed in the first diffraction order of a 3 m normal incidence spectrograph having a plate factor of 2.77 A/mm [15]. The 5d—nf(n = 5—8) transitions give rise to lines in the 5700—3400 A range. These were recorded using a 5 m Czerny—Turner spectrograph which was built some years ago but got its final adjustment and was brought into operation for the first time in the course of the present work. It is equipped with a plane grating having 300 grooves/mm, a ruled area of 206 X 128 mm2 and a blaze angle of 63°26’ (which corresponds to about 60000 A in the first diffraction order). In the present investigation, the instrument was used in the 11th to the 17th diffraction orders, which means a plate factor of about 0.1 7 A/mm.
Volume 66A, number 1
!—
PHYSICS LETTERS
states, i.e., those which combine with Sd in the wavelength range studied, the intervals quoted are weighted means of the results obtained by the two methods just
~
// :ilr— ~ 5d
__J ff//
—~-
I
/II~
“~—~-
_~J
5/2 ~-7/2 U
5/2 3/2
__________________
4d Fig. 1. Schematic term diagram of Sr~showing the terms and transitions studied in the present work. The inset shows the fine-structure components in an nd—nf transition and the resuiting spectrum.
Ar I and Ar II lines emitted from the same light source as the Sr lines and recorded in the same diffraction order served as reference lines. The wavelengths of the Ar lines were taken from Norlén’s lists [16], which are based on interferometric measurements. In the vacuum ultraviolet, Ar II wavelengths determined by Minnhagen [17] served as auxiliary standards, Table I shows the fine-structure intervals determined for the nf2F (n = 4—8) states. Since the 4d—4f transitions appear in the short-wavelength region, where the energy resolution is considerably poorer, the 4f2F splitting could not be measured directly as the wavenumber separation between the strongest and weakest components in the multiplet (fig. 1), but has been determined by adding the wavenumbers of the two stronger lines to the interferometrically determined 4d2D level values [10]. For the remaining nf Table 1 Experimental values of fine-structure intervals in the nf2F states of Sr~. fl
E(~F
outlined. As in Cs 1118], the inverted intervals tend to scale roughly as (n*)_3 for large n values. The observed behaviour of the fine-structure intervats of the nf2F states in the Rb I isoelectronic sequence bears a close resemblance to that of the nd2D states in the Na I sequence. In the latter sequence (ref. [5], fig. 6), the observed 2D interval is small and negative for all n values in Na I and remains so in MgI! and Al III. In Si IV the interval goes through zero and becomes positive as n increases, while in P V the interval is positive for all n values. In the Rb I sequence, the 2F interval is small and negative in Rb I [5] and Sr II, passes through zero between n = 4 and n = 5 in Y III .
[19] and is positive for all n values in Zr IV [20]. A comparison with the behaviour of the 2F intervals in the Cs I sequence is of limited value, since from Ba II onwards the members of this sequence are lanthanidelike in the sense that the nf orbitals are beginning to be penetrating. In conclusion, we hope that our observations will stimulate theoretical calculations of the fine-structure intervals in the nf series of Sr~’,particularly as this series turns out to have the largest negative splittings of any nf series in alkali-like spectra. We are pleased to acknowledge the generous support by Professor L. Minnhagen. References [11 T.W. Hänsch, K.C. Harvey, G. Meisel and A.L.Schawlow, Opt. Commun. 11(1974)50. [2] Y. Kato and B.P. Stoicheff, J. Opt. Soc. Am. 66 (1976) 490. [3] C.D. Harper and M.D. Levenson, Phys. Lett. 56A (1976) 361. [4] P.F. Liao and J.E. Bjorkholm, Phys. Rev. Lett. 36 (1976) 1543.
2F 7i2)— E(
4 5 6 7 8
17 April 1978
512)
(cm’)
(MHz)
—1.06 ±0.03 —0.862 ±0.005 —0.569 ±0.005 —0.368 ±0.010 —0.256 ±0.010
—31800±900 —25840 ±150 —17060 ±150 —11030 ±300 — 7670 ±300
[5] J. Farley and R. Gupta, Phys. Rev. A15 (1977) 1952. [6] T.F. Gallagher, W.E. Cooke, S.A. Edelstein and R.M. Hill, Phys. Rev. A16 (1977) 273. [7] K. Fredriksson and S. Svanberg, Phys. Lett. 53A (1975) 61. [8] 5. Haroche, M. Gross and M.P. Silverman, Phys. Rev. Lett. 33 (1974) 1063. [9] F.A. Saunders, E.G. Schneider and E. Buckingham, Proc. Nat. Acad. Sci. 20 (1934) 291. [10] F.J. Sullivan,Univ.Pittsburgh Bull. 35 (1938)1.
23
Volume 66A, number 1 [II] [121 [13] [14] [15]
24
PHYSICS LETTERS
G.H. Newsom, S. O’Connor and R.C.M. Learner, J. Phys. B6 (1973) 2162. W. Persson and S. Valind, Phys. Scripta 5 (1972) 187. J.E. Hansen and W. Persson, Phys. Scripta 13 (1976) 166. W. Persson and L. Minnhagen, Ark. Fys. 37 (1968) 273. L. Minnhagen, Phys. Scripta 11(1975) 38.
17 April 1978
[16] G. Norlén, Phys. Scripta 8(1973) 249. ]17]LL. Minnhagen, Ark. Fys. 14 (1958) 483. [18] K.B.S. Eriksson and 1. Wenhker, Phys. Scripta 1(1970) 21. [19] G.L. Epstein and I. Reader, J. Opt. Soc. Am. 65 (1975) 310. [20] C.C. Kiess, J. Res. Nat. Bur. St. 56 (1956) 167.
PHYSICS LETTERS
17 April 1978
FINE-STRUCTURE SPLITTINGS OF 2F STATES OF SINGLY IONIZED STRONTIUM W. PERSSON and K. PIRA Department of Physics, Lund Institute of Technology, S-220 07 Lund, Sweden Received 1 February 1978
We have studied the 4d—nf and 5d—nf (n = 4—8) transitions of singly ionized strontium using high-resolution optical spectroscopy. The 2F fine structure is inverted in all the states observed and decreases from —1.06 cm1 in 4f to —0.26 cm~ in 8f.
The fine-structure intervals in the D, F, G and H terms of neutral alkali atoms have recently been the subject of several investigations using high-resolution techniques such as Doppler-free two-photon spectroscopy [1—4] and step-wise excitation by tunable dye lasers in conjunction with radio-frequency [SI and microwave [61resonance methods, level-crossing techniques [71or quantum-beat spectroscopy [8]. In particular, these methods have yielded very accurate values of the fine-structure splittings of the F states of atomic sodium [4,6] and rubidium [5]. However, none of the laser methods has hitherto been applied to the study of fine structures in ionized atoms isoelectronic with the alkali atoms. We report the first measurement of the fine-structure intervals of 2F states of singly ionized strontium for principal quantum numbers 4—8. The measurement was performed by use of high-resolution optical spectroscopy. The main reference for the Sr Ii spectrum is the report bySaunders et al. [9]. In their analysis, the fine structure of the F states was not resolved. Interferometric determination of wavelengths in the Sr II spectrum by Sullivan [101 did not involve any transitions to F states. The most recent report on wavelength determinations in Sr II is by Newsom et al. [11] who, in an investigation of the spectrum of neutral strontium, measured the wavelengths of 16 Sr II lines in the 8000—18 000 A range, among them several combinations involving 4f and Sf states. Our work was initiated by the observation that in the sliding-spark spectrograms recorded for analyzing 22
the spectrum emitted by two to four times ionized strontium [12,13] the 4f—Sg combination in Sr II at 9647 A was clearly resolved into two components. The excitation method was, however, not adequate for an accurate determination of the 2F fine-structure interval. In the present work, the strontium spectrum was excited in a water-cooled hollow-cathode discharge tube, designed for use at large current densities [14]. Argon at a pressure of 0.1 Torr served as carrier gas and at the same time furnished the reference spectrum. With a lump of metallic strontium placed inside the cathode, a well-developed Sr II spectrum was observed at 0.5 A discharge current. A schematic Sr~energy level diagram with the relevant transitions indicated is shown in fig. 1. The 4d—4f combinations at around 2160 A and the 4d—5f combinations at around 1770 A were photographed in the first diffraction order of a 3 m normal incidence spectrograph having a plate factor of 2.77 A/mm [15]. The 5d—nf(n = 5—8) transitions give rise to lines in the 5700—3400 A range. These were recorded using a 5 m Czerny—Turner spectrograph which was built some years ago but got its final adjustment and was brought into operation for the first time in the course of the present work. It is equipped with a plane grating having 300 grooves/mm, a ruled area of 206 X 128 mm2 and a blaze angle of 63°26’ (which corresponds to about 60000 A in the first diffraction order). In the present investigation, the instrument was used in the 11th to the 17th diffraction orders, which means a plate factor of about 0.1 7 A/mm.
Volume 66A, number 1
!—
PHYSICS LETTERS
states, i.e., those which combine with Sd in the wavelength range studied, the intervals quoted are weighted means of the results obtained by the two methods just
~
// :ilr— ~ 5d
__J ff//
—~-
I
/II~
“~—~-
_~J
5/2 ~-7/2 U
5/2 3/2
__________________
4d Fig. 1. Schematic term diagram of Sr~showing the terms and transitions studied in the present work. The inset shows the fine-structure components in an nd—nf transition and the resuiting spectrum.
Ar I and Ar II lines emitted from the same light source as the Sr lines and recorded in the same diffraction order served as reference lines. The wavelengths of the Ar lines were taken from Norlén’s lists [16], which are based on interferometric measurements. In the vacuum ultraviolet, Ar II wavelengths determined by Minnhagen [17] served as auxiliary standards, Table I shows the fine-structure intervals determined for the nf2F (n = 4—8) states. Since the 4d—4f transitions appear in the short-wavelength region, where the energy resolution is considerably poorer, the 4f2F splitting could not be measured directly as the wavenumber separation between the strongest and weakest components in the multiplet (fig. 1), but has been determined by adding the wavenumbers of the two stronger lines to the interferometrically determined 4d2D level values [10]. For the remaining nf Table 1 Experimental values of fine-structure intervals in the nf2F states of Sr~. fl
E(~F
outlined. As in Cs 1118], the inverted intervals tend to scale roughly as (n*)_3 for large n values. The observed behaviour of the fine-structure intervats of the nf2F states in the Rb I isoelectronic sequence bears a close resemblance to that of the nd2D states in the Na I sequence. In the latter sequence (ref. [5], fig. 6), the observed 2D interval is small and negative for all n values in Na I and remains so in MgI! and Al III. In Si IV the interval goes through zero and becomes positive as n increases, while in P V the interval is positive for all n values. In the Rb I sequence, the 2F interval is small and negative in Rb I [5] and Sr II, passes through zero between n = 4 and n = 5 in Y III .
[19] and is positive for all n values in Zr IV [20]. A comparison with the behaviour of the 2F intervals in the Cs I sequence is of limited value, since from Ba II onwards the members of this sequence are lanthanidelike in the sense that the nf orbitals are beginning to be penetrating. In conclusion, we hope that our observations will stimulate theoretical calculations of the fine-structure intervals in the nf series of Sr~’,particularly as this series turns out to have the largest negative splittings of any nf series in alkali-like spectra. We are pleased to acknowledge the generous support by Professor L. Minnhagen. References [11 T.W. Hänsch, K.C. Harvey, G. Meisel and A.L.Schawlow, Opt. Commun. 11(1974)50. [2] Y. Kato and B.P. Stoicheff, J. Opt. Soc. Am. 66 (1976) 490. [3] C.D. Harper and M.D. Levenson, Phys. Lett. 56A (1976) 361. [4] P.F. Liao and J.E. Bjorkholm, Phys. Rev. Lett. 36 (1976) 1543.
2F 7i2)— E(
4 5 6 7 8
17 April 1978
512)
(cm’)
(MHz)
—1.06 ±0.03 —0.862 ±0.005 —0.569 ±0.005 —0.368 ±0.010 —0.256 ±0.010
—31800±900 —25840 ±150 —17060 ±150 —11030 ±300 — 7670 ±300
[5] J. Farley and R. Gupta, Phys. Rev. A15 (1977) 1952. [6] T.F. Gallagher, W.E. Cooke, S.A. Edelstein and R.M. Hill, Phys. Rev. A16 (1977) 273. [7] K. Fredriksson and S. Svanberg, Phys. Lett. 53A (1975) 61. [8] 5. Haroche, M. Gross and M.P. Silverman, Phys. Rev. Lett. 33 (1974) 1063. [9] F.A. Saunders, E.G. Schneider and E. Buckingham, Proc. Nat. Acad. Sci. 20 (1934) 291. [10] F.J. Sullivan,Univ.Pittsburgh Bull. 35 (1938)1.
23
Volume 66A, number 1 [II] [121 [13] [14] [15]
24
PHYSICS LETTERS
G.H. Newsom, S. O’Connor and R.C.M. Learner, J. Phys. B6 (1973) 2162. W. Persson and S. Valind, Phys. Scripta 5 (1972) 187. J.E. Hansen and W. Persson, Phys. Scripta 13 (1976) 166. W. Persson and L. Minnhagen, Ark. Fys. 37 (1968) 273. L. Minnhagen, Phys. Scripta 11(1975) 38.
17 April 1978
[16] G. Norlén, Phys. Scripta 8(1973) 249. ]17]LL. Minnhagen, Ark. Fys. 14 (1958) 483. [18] K.B.S. Eriksson and 1. Wenhker, Phys. Scripta 1(1970) 21. [19] G.L. Epstein and I. Reader, J. Opt. Soc. Am. 65 (1975) 310. [20] C.C. Kiess, J. Res. Nat. Bur. St. 56 (1956) 167.