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Investigations of the Zeeman effect of some 142Nd ionic levels, using collinear laser ion beam spectroscopy
Author's Accepted Manuscript
Investigations of the Zeeman effect of some 142 Nd ionic levels, using collinear laser ion beam spectroscopy S. Werbowy, H. Hühnermann, J. Kwela, L. Windholz
www.elsevier.com/locate/jqsrt
PII: DOI: Reference:
S0022-4073(15)00261-7 http://dx.doi.org/10.1016/j.jqsrt.2015.07.012 JQSRT5037
To appear in:
Journal of Quantitative Spectroscopy & Radiative Transfer
Received date: 7 May 2015 Revised date: 20 July 2015 Accepted date: 21 July 2015 Cite this article as: S. Werbowy, H. Hühnermann, J. Kwela, L. Windholz, Investigations of the Zeeman effect of some 142Nd ionic levels, using collinear laser ion beam spectroscopy, Journal of Quantitative Spectroscopy & Radiative Transfer, http://dx.doi.org/10.1016/j.jqsrt.2015.07.012 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Investigations of the Zeeman effect of some 142Nd ionic levels, using collinear laser ion beam spectroscopy S. Werbowya,c,∗, H. H¨uhnermann b,c, J. Kwelaa , L. Windholzc a Institute
of Experimental Physics, University of Gdansk, ul. Wita Stwosza 57, PL-80-952 Gdansk, Poland b Department of Physics, University of Marburg, Renthof 5, 35037 Marburg, Germany c Institut f¨ ur Experimentalphysik, Technische Universit¨at Graz, Petersgasse 16, 8010 Graz, Austria
Abstract By performing laser excitation from the even 4f 4 5d lower levels to the odd 4f 4 6p and 4f 3 5d2 upper levels of the neodymium ion 142 Nd+ , we have observed Zeeman splitting in an external magnetic field up to 330 G. We applied the high resolution spectroscopic method of collinear laser ion beam spectroscopy (CLIBS). With this method (unconventional for studying the Zeeman effect) we recorded very well resolved Zeeman structure patterns with line widths of order of 100 MHz, which is only sometimes the natural line width. The obtained experimental Land´e factors are compared with earlier measurements and with theoretical calculations. Keywords: Zeeman effect, Land´e factors, neodymium PACS: 32.10.Fn, 32.60.+i 1. Introduction Neodymium (Z=59) is a rare earth metal with extremely complex spectra of the neutral atom (Nd I) and its first ion (Nd II). The number of known and classified Nd II energy levels runs into thousands [1]. Additionally, the Nd spectra are complex not only due to the enormous number of electronic levels, but also due to the amount of isotopes in the natural composition of neodymium with comparable abundances: 142- 23%, 143- 13%, 144- 25%, 145- 9%, 146- 18%, 148- 6% and 1506% (see the recorded mass spectrum presented in Fig. 1). Additionally, two odd isotopes (143 and 145) possess both nuclear spin quantum numbers I=7/2 and magnetic dipole and electric quadruple moments, resulting in complex hyperfine structure. Most experimental studies of Nd II lines are connected with hyperfine structure [2, 3] or isotope shifts [4, 5]. One reason for this situation may be that (i) Nd has several isotopes with comparable abundances and (ii) a well developed hyperfine structure of the two odd isotopes allowing the investigation of nuclear properties. However, we found a big gap concerning Zeeman effect analysis of the Nd II spectrum. A rich and dense spectrum, a large number of isotopes and hyperfine structure from some of them - all these factors makes it extremely difficult to interpret properly the observed Zeeman structure and to obtain accurate Land´e-g J factors. An adequate experimental setup, insensitive to the mentioned difficulties, is a Doppler free laser spectroscopic technique like collinear laser ion beam spectroscopy (CLIBS). For our purposes, we chose the Nd isotope 142 (I = 0) to avoid difficulties in analysis due ∗ Corresponding
author Email addresses: [email protected] (S. Werbowy), [email protected] (L. Windholz) Preprint submitted to Journal of Quantitative Spectroscopy & Radiative Transfer
to hyperfine structure splitting. As we have demonstrated successfully for the element Pr [6], a CLIBS apparatus can be used to investigate the Zeeman effect of ions in a fast beam using relatively small magnetic fields (up to few hundreds Gauss), with acceptable broadenings of the line components and no misalignment of the counter-propagating laser and ion beams. For many levels, the calculated g J Land´e factors of Wyart [1] are in agreement with experimental values within uncertainties of ±0.01 . For other levels a larger discrepancy is evident. This could be related either to perturbations caused by other levels, not taken into account in the calculations, or simply by experimental values with large uncertainties. Blaise et. al. [4] have pointed out that even small variations in energy and Land´e factors accepted in calculations for the starting level could lead to large discrepancies in the interpretation of the observed spectra. To avoid a bad analysis of the complex atomic structure, accurate experimental data on hyperfine structure constants, Land´e factors and isotope shifts are indispensable. Besides the theoretical point of view, spectroscopic data for ionized rare earth elements are of interest for astrophysics, since the lines are present in stellar spectra, especially in chemically peculiar stars (CP stars). The purpose of this study is to re-investigate with the use of fast ion beam laser spectroscopy the Zeeman effect of some Nd II lines at weak magnetic fields using selective Doppler free laser excitation of a hyperfine structure-free neodymium isotope. As was noted in [7], attempts were made to investigate Nd II lines starting from metastable levels using fast beam laser spectroscopy with high resolution, but they failed. Fortunately, we have succeeded to perform such experiments. In this way we obtained accurate Land´e factors and we gained information, succeeding the quality of data determined almost 40 years ago. Figure 2 shows some even and odd configurations of Nd II and July 28, 2015
the general scheme of laser induced fluorescence detection related to the investigations in the present paper.
locities were simply high enough that inertia forces are high compared to forces caused by the magnetic field. With a set of a Glan prism and a half-wave plate we have produced laser light polarized in direction perpendicular (σcomponent) or parallel (π-component) to the magnetic field direction. In order to analyze the experimental data we have used a software developed in our group, which was used with success earlier in the analysis of the Zeeman-hyperfine structure of other elements, Bi I [13, 14, 15], Pb I and Pb II [16], Sb I [17]. In the calculations we have used a special asymmetric line profile:
2. Experiment and computer analysis The measurements were performed on the CLIBS apparatus which was named MARburg Separator MARS-II, installed originally at the University of Marburg a.d. Lahn (Germany) and moved 2002 to Graz (Austria). Originally it was designed to investigate the hyperfine structures and isotope shifts of lines of different isotopes of single ionized heavy elements, especially of radioactive isotopes with short half-life times [8, 9]. Details of the apparatus were described in [10, 6]. Briefly, a resistance heated oven produces metal atom vapor, which later is passing through a thin hot molybdenum tube and then part of the atoms becomes ionized. The ions are extracted and accelerated up to 20 keV. An ion beam is formed by means of some ion optics lenses and is separated into its isotope composition by a huge sector magnet. Ions of a selected isotope are guided after approximately 6.5 m distance into the interaction chamber, where the ion beam is overlapped with a counterpropagating laser light beam. A narrow band ring-dye laser (laser line width ca. 1 MHz, typical power density 15 mW/mm 2 ), stabilized and fixed to a certain transition (the Doppler shift due to the high ion velocity must be taken into account) continuously excites the ions from a metastable level to a high lying level. The fluorescence decay from the excited level is then observed by a photomultiplier tube. The surface ionization ion source has provided us with Nd ion currents in the order of 0.14 nA/mm2 , sufficient to obtain a good signal to noise ratio of the laser-induced fluorescence signal. Scans over the Zeeman patterns of the investigated transitions are accomplished by applying the Doppler tuning technique. Ions are being post-accelerated in the interaction chamber step-by-step by an acceleration voltage of up to 3.5 kV. In this way it is possible to perform a scan of the wave number of app. 0.75 cm −1 (22 GHz) with a step size as small as 0.00017 cm−1 (5 MHz). In order to produce inside the interaction chamber a homogeneous magnetic field perpendicular to the ion beam, strong permanent neodymium magnets were used. In this way we made the system relatively simple and we avoided vacuum contaminations. The strength and distribution of the magnetic field B was measured with a Hall effect Gauss-meter (Applied Magnetics Laboratory model GM1A - probe model PB71-10) with an accuracy of 0.25% of the reading. Additionally, the magnetic field strength was checked by recording the Ba II 585.368 nm (6p 2 P3/2 →5d 2 D3/2 ) transition, see Fig. 3. For this line we deliberately have rotated the polarization by 5 degrees with respect to the direction perpendicular to the magnetic field, resulting in the presence of the π (ΔM=0) components in the pattern. The Land´e factors for the Ba II levels involved are: 1.328(8) [11] and 0.7993278(3) [12] for lower and upper level, respectively. The magnetic field perpendicular to the moving ions did not cause any deflection of the moving ions that could have an affect on the experiment. The mass of the ions and their ve-
I(ν)= i
I0,i (1 + χ/α1 (ν − ν0,i − ν)) , 2 1+ (α1 (ν − ν0,i − ν)) + (α2 (ν − ν0,i − ν))4
(1)
where I0,i and ν0,i are the intensity and position of a single component calculated from the diagonalization of a Zeeman structure Hamiltonian matrix (for details see [18]), α i =2/δνi is a line shape parameter, (δν 1 is directly the full line width at half maximum), ν shifts the entire pattern. The χ parameter describes the asymmetry of the line due to not symmetric velocity speed distribution of the ion beam, and its typical value was 0.00015. The least-square-fitting procedure has varied the fitted parameters: the Land´e factors, the line shape, background correction and scaling parameters to reproduce the calculated structure to match the experimentally observed Zeeman pattern. 3. Results Zeeman patterns for 12 lines of 142 Nd II in the region 568.8589.2 nm were recorded separately for excitation with σ (ΔM = ±1) and π (ΔM = 0) polarized light. Examples of such records, together with their best fits are presented in Fig. 4 for the Nd II lines 577.050 nm, 580.402 nm, and 581.157 nm. A summary of the obtained Land´e-g J factors is presented in Table 1. The table contains the energy of the level, its classification (if the leading component is more than 50%), angular momentum quantum number J, excitation wavelengths involving the given level, and experimental values of g J factors obtained in this work. For comparison, other known values from the literature are given. It also contains theoretical Hartree-Fock (HFR) and pure LS coupling values. The present experimental results are the mean values from several independent measurements of σ and π components, recorded in some cases at different days and at different transitions. The given experimental errors include the mean standard deviations, and a term g J (ΔB/B) which takes into account the uncertainty of our magnetic field determination, where ΔB=2 G is the uncertainty of the magnetic field strength B. As an example, Fig. 5 presents the Zeeman patterns of line 580.402 nm, recorded at three isotopes (142, 143 and 145) for the same magnetic field of 235 G. Two of them, 143 and 145, exhibits hyperfine structure, resulting in a large number of only partially resolved Zeeman-hyperfine components. In the fitting procedure for 143 and 145 isotopes we have used the set of hyperfine constants from ref. [19]. The spectrum of the 142 isotope (I=0, no hyperfine structure) has a much smaller number 2
of components, leading to a better signal to noise ratio. Additionally, for the even isotope the uncertainty of the hyperfine constants do not propagate to the uncertainty of the Land´e factors. 4. Conclusions The presented Zeeman effect analysis of the experimental spectra of 12 Nd II lines in the ”weak field” regime, having wavelengths between 568.853 and 589.153 nm (in air) allowed us to determine the Land´e-factors for 19 energy levels. 7 of the levels belong to the 4f 4 5d configuration, 3 to 4f 3 5d2 and 9 to 4f4 6p. The experimental data from literature, presented in Table 1, are the results of measurements at fields up to 87 180 G [20], and at fields up to 20 000 G [21]. In our opinion it is of importance to work in the ”weak” magnetic field regime, as the J value of a level remain a good quantum number for weak magnetic fields. For very high magnetic fields (in the direction to the Paschen-Back effect) there could be a disturbance or even a break-down of the coupling between L and S , and quantum number J would be no longer appropriate. Additionally, the splitting at such high fields would probably lead to blend situations with other transitions, as the Nd spectrum is very dense. The very small magnetic field of 330(2) G used by us avoids all these difficulties, and at the same time provides us with acceptable accuracy. Comparing the data collected in Table 1, we can conclude, that most of the Land´e factors determined earlier are in agreement with our recent results. However, there are some cases, where our values differ more than by experimental uncertainties. The question is, if this discrepancy would have affect on a theoretical interpretation of the Nd II fine structure. We hope this work will encourage other researchers to go to the field of Zeeman effect investigations by using this superior and fruitful technique: the collinear ion beam spectroscopy.
Figure 1: Mass spectrum of the ion beam, recorded with help of a beam scanner in the focus plane of the separator magnet. A Neodymium sample with natural composition is used in the present studies. The spatial separation of isotopes with mass number 142 and 150 is for our apparatus approximately 7 cm.
[7] Koczorowski W, Stachowska E, Furmann B, Stefa´eska D, Jarosz A and Krzykowski A. Laser spectroscopic investigation of isotope shifts in Nd II lines. Spectrochim Acta B 2005;60:44753 [8] H¨uhnermann H, Heddrich W, M¨oller W, Wagner H. Collinear Laser Ion Beam Spectroscopy. Hyp Int 1987;38:741-60 [9] Beiersdorf S, Heddrich W, Kesper K, Huhnermann H, Moller W and Wagner H. J-dependence of optical isotope shifts in Sm II. J Phys G: Nucl Pan Phys 1995;21:215-28 [10] Akhtar N, Anjum N, H¨uhnermann H, Windholz L. A study of hyperfine transitions of singly ionized praseodymium (141 Pr+ ) using collinear laser ion beam spectroscopy. Eur Phys J D 2012;66:264 [11] Poulsen O, Ramanujam PS. Time-differential level-crossing g-value measurements of the 6p 2 P fine-structure levels in Ba138 II using an opticalinduced orientation or alignment of a fast ionic beam. Phys Rev A 1976;14:1463-67 [12] Kn¨oll KH, Marx G, H¨ubner K, Schweikert F, Stahl S, Weber C and Werth G. Experimental gJ factor in the metastable 5 D3/2 level of Ba+ . Phys Rev A 1996;54:1199205 [13] Werbowy S, Kwela J. The E2 admixtures in mixed multipole lines 459.7 nm and 461.5 nm in the spectrum of BiI. Eur Phys J-Special Topics 2007;144:179-84 [14] Sobolewski ŁM, Werbowy S, Kwela J. Hyperfine and Zeeman structure of lines of Bi I. J Opt Soc Am B 2014;31:3038-41 [15] Werbowy S Kwela J. M1-E2 interference in the Zeeman spectra of Bi I. Phys Rev A 2008;77:023410 [16] Werbowy S, Kwela J. M1-E2 interference in the Zeeman spectra of Pb I and Pb II. J Phys B 2009;42:065002 [17] Werbowy S, Kwela J. Observation of the M1-E2 interference in the Zeeman spectra of isotopes 121 Sb and 123 Sb. J Phys B 2010;43:065002 [18] Werbowy S, Kwela J, Drozdowski R and Heldt J. M1-E2 interference in the Zeeman effect of the 461.5 nm line of Bi I. Eur Phys J D 2006;39:5-12 [19] Anjum N, Akhtar N, Hhnermann H, Windholz L. Investigation of the hyperfine structure of 143 Nd+ spectral lines using collinear laser ion beam spectroscopy. J Phys B 2015;48:015003 [20] Albertson WE, Harrison GR, McNally JR, Jr. Phys Rev 1942;61:167-74 [21] Blaise J, Chevillard J, Vergi J, Wyart JF. Etude des spectres demission dans l’infrarouge par lemploi dun SISAM-IV. Spectre demission du n´eodyme*. Spec Chim Acta B 1970;268:333-81 [22] Martin WC, Zalubas R, Hagan L. Atomic Energy Levels - The Rare-Earth Elements. Nat Stand Ref Data Ser. NSRDS-NBS 1978; 60: 422 pp. (Nat. Bur. Stand., U.S., 1978)
Acknowledgments The present work was supported by Wissenschaftlich¨ Technisches Abkommen Osterreich-Polen, projects no. 21/2012 and 12/2014. [1] Wyart JF. Theoretical interpretation of the Nd II spectrum: odd parity energy levels. Phys Scr 2010;82:035302 [2] Maosheng L, Hongliang M, Miaohua C, Fuquan L, Jiayong T, and Fujia Y. Hyperfine-structure measurements in 141 PrII and 143,145 NdII by collinear laser-ion-beam spectroscopy. Phys Rev A 2000;62:052504 [3] Anjum N. Hyperfine Structure of Spectral Lines of 143 Nd+ , 145 Nd+ , 139 La+ , 141 Pr+ and 137 Ba+ Investigated by Collinear Laser Ion Beam Spectroscopy. PhD thesis, Graz University of Technology, Graz; 2012 [4] Blaise J, Wyart JF. Revised Interpretation of the Spectrum of SinglyIonized Neodymium (Nd II). Phys Scr 1984;29:119-31 [5] Yansen W, Fuquan L, Songmao W, Wei S, Linggen S, Jiayong T and Fujia Y. Configuration mixing of the level (23 537)o 9/2 in Nd II deduced from the optical isotope shifts by collinear fast-ion-beam laser spectroscopy. J Phys B 1991;24:45-8 [6] Werbowy S, Anjum N, H¨uhnermann H, Kwela J, Windholz L. Zeeman effect of hyperfine-resolved spectral lines of singly ionized praseodymium using collinear laserion-beam spectroscopy. Phys Rev A 2014;90:032515
3
Figure 4: Recorded Zeeman structure patterns of three 142 Nd II lines at 330 G. The thin line represents the experimental result and the thick line the computer best fit.
Table 1: Lande-gJ factors of singly ionized Neodymium for even energy levels belonging to the configurations 4f4 5d, 4f3 5d2 and 4f4 6p. Experimental gJ Theoretical gJ Configuration Level Termb Excitation Present Ref. [20]c Ref. [21]c Ref. [1] LS energy Wavelength studies (87 180 G) (20 000 G) HFR coupling [cm−1 ]a [nm] (330 G) 4f4 5d 6005.27 6 K4.5 580.402 0.559 (7) 0.552 0.550 0.546 570.828 0.838 (8) 6931.80 6 K5.5 581.157 0.838 (1) Average: 0.838 (10) 0.842 0.840 0.839 7950.08 6 K6.5 568.853 1.001 (3) 574.477 0.984 (6) Average: 0.998 (9) 1.015 1.015 1.015 8420.32 6 I4.5 572.683 0.834 (7) 589.153 0.843 (2) Average: 0.842 (9) 0.84 0.840 0.828 8716.45 6 G1.5 582.587 0.003 (2) 577.050 0.009 (3) Average: 0.005 (4) 0.008 0.010 0 9357.91 6 I5.5 574.086 1.022 (8) 1.034 1.035 1.035 10337.1 6 I6.5 584.239 1.123 (4) 589.050 1.160 (9) Average: 1.128 (13) 1.144 1.140 1.159 4f3 5d2
24134.1 25352.4 25389.2
5.5 5.5 4.5
581.157 574.477 589.153
1.008 (6) 1.111 (9) 1.034 (7)
1.014 1.152 1.029
1.020 1.150 1.030
4f4 6p
1.018 1.231 1.017
-
23230.0 4.5 580.402 0.785 (9) 0.778 0.780 0.779 24445.4 5.5 570.828 0.918 (8) 0.917 0.915 0.912 25524.5 6 K6.5 568.853 1.022 (7) 1.03 1.030 1.028 1.015 25876.6 2.5 582.587 0.633 (4) 0.642 0.655 0.606 25877.2 4.5 572.683 0.962 (13) 0.957 0.950 0.974 26041.2 2.5 577.050 0.924 (6) 0.940 1.067 26772.1 5.5 574.086 1.036 (7) 1.013 1.020 1.109 27309.0 6.5 589.050 1.088 (12) 1.087 1.090 1.086 27448.7 6.5 584.239 1.148 (8) 1.166 1.135 1.146 a Energy values are taken from [22]. b Because many eigenfunctions have leading components smaller than 10% due to breakdown of LS coupling and CI effects, only leading components when larger than 50% are given. c Experimental uncertainties were not given in [20, 21].
4
Figure 2: Most important even and odd configurations of Nd II. Thin horizontal lines indicate the investigated metastable levels of the 4f4 5d configuration and the excited 4f4 6p and 4f3 5d2 odd levels. A bold upward arrow represents the laser excitation from the metastable levels to the odd levels, from which fluorescence decays back to the lower even levels of the 4f4 6s and 4f4 5d configurations are observed through a Schott glass filter (thin arrows).
Figure 5: Recorded Zeeman structure patterns of line 580.402 nm for three isotopes, 142, 143 and 145, at 235 G. The thin line represents the experimental result and the thick line the computer best fit. The odd isotopes show, beside the Zeeman splitting, also hyperfine structure splitting.
Figure 3: (a) Recorded Zeeman pattern and fit of the 138 Ba II 585.368 nm transition used for the magnetic field check. The best fit was obtained at field strength 330 G. (b) Calculated Zeeman patterns of the line for 325, 330 and 335 G fields (only the first three components from the left are shown).
5
Investigations of the Zeeman effect of some 142 Nd ionic levels, using collinear laser ion beam spectroscopy S. Werbowy, H. Hühnermann, J. Kwela, L. Windholz
www.elsevier.com/locate/jqsrt
PII: DOI: Reference:
S0022-4073(15)00261-7 http://dx.doi.org/10.1016/j.jqsrt.2015.07.012 JQSRT5037
To appear in:
Journal of Quantitative Spectroscopy & Radiative Transfer
Received date: 7 May 2015 Revised date: 20 July 2015 Accepted date: 21 July 2015 Cite this article as: S. Werbowy, H. Hühnermann, J. Kwela, L. Windholz, Investigations of the Zeeman effect of some 142Nd ionic levels, using collinear laser ion beam spectroscopy, Journal of Quantitative Spectroscopy & Radiative Transfer, http://dx.doi.org/10.1016/j.jqsrt.2015.07.012 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Investigations of the Zeeman effect of some 142Nd ionic levels, using collinear laser ion beam spectroscopy S. Werbowya,c,∗, H. H¨uhnermann b,c, J. Kwelaa , L. Windholzc a Institute
of Experimental Physics, University of Gdansk, ul. Wita Stwosza 57, PL-80-952 Gdansk, Poland b Department of Physics, University of Marburg, Renthof 5, 35037 Marburg, Germany c Institut f¨ ur Experimentalphysik, Technische Universit¨at Graz, Petersgasse 16, 8010 Graz, Austria
Abstract By performing laser excitation from the even 4f 4 5d lower levels to the odd 4f 4 6p and 4f 3 5d2 upper levels of the neodymium ion 142 Nd+ , we have observed Zeeman splitting in an external magnetic field up to 330 G. We applied the high resolution spectroscopic method of collinear laser ion beam spectroscopy (CLIBS). With this method (unconventional for studying the Zeeman effect) we recorded very well resolved Zeeman structure patterns with line widths of order of 100 MHz, which is only sometimes the natural line width. The obtained experimental Land´e factors are compared with earlier measurements and with theoretical calculations. Keywords: Zeeman effect, Land´e factors, neodymium PACS: 32.10.Fn, 32.60.+i 1. Introduction Neodymium (Z=59) is a rare earth metal with extremely complex spectra of the neutral atom (Nd I) and its first ion (Nd II). The number of known and classified Nd II energy levels runs into thousands [1]. Additionally, the Nd spectra are complex not only due to the enormous number of electronic levels, but also due to the amount of isotopes in the natural composition of neodymium with comparable abundances: 142- 23%, 143- 13%, 144- 25%, 145- 9%, 146- 18%, 148- 6% and 1506% (see the recorded mass spectrum presented in Fig. 1). Additionally, two odd isotopes (143 and 145) possess both nuclear spin quantum numbers I=7/2 and magnetic dipole and electric quadruple moments, resulting in complex hyperfine structure. Most experimental studies of Nd II lines are connected with hyperfine structure [2, 3] or isotope shifts [4, 5]. One reason for this situation may be that (i) Nd has several isotopes with comparable abundances and (ii) a well developed hyperfine structure of the two odd isotopes allowing the investigation of nuclear properties. However, we found a big gap concerning Zeeman effect analysis of the Nd II spectrum. A rich and dense spectrum, a large number of isotopes and hyperfine structure from some of them - all these factors makes it extremely difficult to interpret properly the observed Zeeman structure and to obtain accurate Land´e-g J factors. An adequate experimental setup, insensitive to the mentioned difficulties, is a Doppler free laser spectroscopic technique like collinear laser ion beam spectroscopy (CLIBS). For our purposes, we chose the Nd isotope 142 (I = 0) to avoid difficulties in analysis due ∗ Corresponding
author Email addresses: [email protected] (S. Werbowy), [email protected] (L. Windholz) Preprint submitted to Journal of Quantitative Spectroscopy & Radiative Transfer
to hyperfine structure splitting. As we have demonstrated successfully for the element Pr [6], a CLIBS apparatus can be used to investigate the Zeeman effect of ions in a fast beam using relatively small magnetic fields (up to few hundreds Gauss), with acceptable broadenings of the line components and no misalignment of the counter-propagating laser and ion beams. For many levels, the calculated g J Land´e factors of Wyart [1] are in agreement with experimental values within uncertainties of ±0.01 . For other levels a larger discrepancy is evident. This could be related either to perturbations caused by other levels, not taken into account in the calculations, or simply by experimental values with large uncertainties. Blaise et. al. [4] have pointed out that even small variations in energy and Land´e factors accepted in calculations for the starting level could lead to large discrepancies in the interpretation of the observed spectra. To avoid a bad analysis of the complex atomic structure, accurate experimental data on hyperfine structure constants, Land´e factors and isotope shifts are indispensable. Besides the theoretical point of view, spectroscopic data for ionized rare earth elements are of interest for astrophysics, since the lines are present in stellar spectra, especially in chemically peculiar stars (CP stars). The purpose of this study is to re-investigate with the use of fast ion beam laser spectroscopy the Zeeman effect of some Nd II lines at weak magnetic fields using selective Doppler free laser excitation of a hyperfine structure-free neodymium isotope. As was noted in [7], attempts were made to investigate Nd II lines starting from metastable levels using fast beam laser spectroscopy with high resolution, but they failed. Fortunately, we have succeeded to perform such experiments. In this way we obtained accurate Land´e factors and we gained information, succeeding the quality of data determined almost 40 years ago. Figure 2 shows some even and odd configurations of Nd II and July 28, 2015
the general scheme of laser induced fluorescence detection related to the investigations in the present paper.
locities were simply high enough that inertia forces are high compared to forces caused by the magnetic field. With a set of a Glan prism and a half-wave plate we have produced laser light polarized in direction perpendicular (σcomponent) or parallel (π-component) to the magnetic field direction. In order to analyze the experimental data we have used a software developed in our group, which was used with success earlier in the analysis of the Zeeman-hyperfine structure of other elements, Bi I [13, 14, 15], Pb I and Pb II [16], Sb I [17]. In the calculations we have used a special asymmetric line profile:
2. Experiment and computer analysis The measurements were performed on the CLIBS apparatus which was named MARburg Separator MARS-II, installed originally at the University of Marburg a.d. Lahn (Germany) and moved 2002 to Graz (Austria). Originally it was designed to investigate the hyperfine structures and isotope shifts of lines of different isotopes of single ionized heavy elements, especially of radioactive isotopes with short half-life times [8, 9]. Details of the apparatus were described in [10, 6]. Briefly, a resistance heated oven produces metal atom vapor, which later is passing through a thin hot molybdenum tube and then part of the atoms becomes ionized. The ions are extracted and accelerated up to 20 keV. An ion beam is formed by means of some ion optics lenses and is separated into its isotope composition by a huge sector magnet. Ions of a selected isotope are guided after approximately 6.5 m distance into the interaction chamber, where the ion beam is overlapped with a counterpropagating laser light beam. A narrow band ring-dye laser (laser line width ca. 1 MHz, typical power density 15 mW/mm 2 ), stabilized and fixed to a certain transition (the Doppler shift due to the high ion velocity must be taken into account) continuously excites the ions from a metastable level to a high lying level. The fluorescence decay from the excited level is then observed by a photomultiplier tube. The surface ionization ion source has provided us with Nd ion currents in the order of 0.14 nA/mm2 , sufficient to obtain a good signal to noise ratio of the laser-induced fluorescence signal. Scans over the Zeeman patterns of the investigated transitions are accomplished by applying the Doppler tuning technique. Ions are being post-accelerated in the interaction chamber step-by-step by an acceleration voltage of up to 3.5 kV. In this way it is possible to perform a scan of the wave number of app. 0.75 cm −1 (22 GHz) with a step size as small as 0.00017 cm−1 (5 MHz). In order to produce inside the interaction chamber a homogeneous magnetic field perpendicular to the ion beam, strong permanent neodymium magnets were used. In this way we made the system relatively simple and we avoided vacuum contaminations. The strength and distribution of the magnetic field B was measured with a Hall effect Gauss-meter (Applied Magnetics Laboratory model GM1A - probe model PB71-10) with an accuracy of 0.25% of the reading. Additionally, the magnetic field strength was checked by recording the Ba II 585.368 nm (6p 2 P3/2 →5d 2 D3/2 ) transition, see Fig. 3. For this line we deliberately have rotated the polarization by 5 degrees with respect to the direction perpendicular to the magnetic field, resulting in the presence of the π (ΔM=0) components in the pattern. The Land´e factors for the Ba II levels involved are: 1.328(8) [11] and 0.7993278(3) [12] for lower and upper level, respectively. The magnetic field perpendicular to the moving ions did not cause any deflection of the moving ions that could have an affect on the experiment. The mass of the ions and their ve-
I(ν)= i
I0,i (1 + χ/α1 (ν − ν0,i − ν)) , 2 1+ (α1 (ν − ν0,i − ν)) + (α2 (ν − ν0,i − ν))4
(1)
where I0,i and ν0,i are the intensity and position of a single component calculated from the diagonalization of a Zeeman structure Hamiltonian matrix (for details see [18]), α i =2/δνi is a line shape parameter, (δν 1 is directly the full line width at half maximum), ν shifts the entire pattern. The χ parameter describes the asymmetry of the line due to not symmetric velocity speed distribution of the ion beam, and its typical value was 0.00015. The least-square-fitting procedure has varied the fitted parameters: the Land´e factors, the line shape, background correction and scaling parameters to reproduce the calculated structure to match the experimentally observed Zeeman pattern. 3. Results Zeeman patterns for 12 lines of 142 Nd II in the region 568.8589.2 nm were recorded separately for excitation with σ (ΔM = ±1) and π (ΔM = 0) polarized light. Examples of such records, together with their best fits are presented in Fig. 4 for the Nd II lines 577.050 nm, 580.402 nm, and 581.157 nm. A summary of the obtained Land´e-g J factors is presented in Table 1. The table contains the energy of the level, its classification (if the leading component is more than 50%), angular momentum quantum number J, excitation wavelengths involving the given level, and experimental values of g J factors obtained in this work. For comparison, other known values from the literature are given. It also contains theoretical Hartree-Fock (HFR) and pure LS coupling values. The present experimental results are the mean values from several independent measurements of σ and π components, recorded in some cases at different days and at different transitions. The given experimental errors include the mean standard deviations, and a term g J (ΔB/B) which takes into account the uncertainty of our magnetic field determination, where ΔB=2 G is the uncertainty of the magnetic field strength B. As an example, Fig. 5 presents the Zeeman patterns of line 580.402 nm, recorded at three isotopes (142, 143 and 145) for the same magnetic field of 235 G. Two of them, 143 and 145, exhibits hyperfine structure, resulting in a large number of only partially resolved Zeeman-hyperfine components. In the fitting procedure for 143 and 145 isotopes we have used the set of hyperfine constants from ref. [19]. The spectrum of the 142 isotope (I=0, no hyperfine structure) has a much smaller number 2
of components, leading to a better signal to noise ratio. Additionally, for the even isotope the uncertainty of the hyperfine constants do not propagate to the uncertainty of the Land´e factors. 4. Conclusions The presented Zeeman effect analysis of the experimental spectra of 12 Nd II lines in the ”weak field” regime, having wavelengths between 568.853 and 589.153 nm (in air) allowed us to determine the Land´e-factors for 19 energy levels. 7 of the levels belong to the 4f 4 5d configuration, 3 to 4f 3 5d2 and 9 to 4f4 6p. The experimental data from literature, presented in Table 1, are the results of measurements at fields up to 87 180 G [20], and at fields up to 20 000 G [21]. In our opinion it is of importance to work in the ”weak” magnetic field regime, as the J value of a level remain a good quantum number for weak magnetic fields. For very high magnetic fields (in the direction to the Paschen-Back effect) there could be a disturbance or even a break-down of the coupling between L and S , and quantum number J would be no longer appropriate. Additionally, the splitting at such high fields would probably lead to blend situations with other transitions, as the Nd spectrum is very dense. The very small magnetic field of 330(2) G used by us avoids all these difficulties, and at the same time provides us with acceptable accuracy. Comparing the data collected in Table 1, we can conclude, that most of the Land´e factors determined earlier are in agreement with our recent results. However, there are some cases, where our values differ more than by experimental uncertainties. The question is, if this discrepancy would have affect on a theoretical interpretation of the Nd II fine structure. We hope this work will encourage other researchers to go to the field of Zeeman effect investigations by using this superior and fruitful technique: the collinear ion beam spectroscopy.
Figure 1: Mass spectrum of the ion beam, recorded with help of a beam scanner in the focus plane of the separator magnet. A Neodymium sample with natural composition is used in the present studies. The spatial separation of isotopes with mass number 142 and 150 is for our apparatus approximately 7 cm.
[7] Koczorowski W, Stachowska E, Furmann B, Stefa´eska D, Jarosz A and Krzykowski A. Laser spectroscopic investigation of isotope shifts in Nd II lines. Spectrochim Acta B 2005;60:44753 [8] H¨uhnermann H, Heddrich W, M¨oller W, Wagner H. Collinear Laser Ion Beam Spectroscopy. Hyp Int 1987;38:741-60 [9] Beiersdorf S, Heddrich W, Kesper K, Huhnermann H, Moller W and Wagner H. J-dependence of optical isotope shifts in Sm II. J Phys G: Nucl Pan Phys 1995;21:215-28 [10] Akhtar N, Anjum N, H¨uhnermann H, Windholz L. A study of hyperfine transitions of singly ionized praseodymium (141 Pr+ ) using collinear laser ion beam spectroscopy. Eur Phys J D 2012;66:264 [11] Poulsen O, Ramanujam PS. Time-differential level-crossing g-value measurements of the 6p 2 P fine-structure levels in Ba138 II using an opticalinduced orientation or alignment of a fast ionic beam. Phys Rev A 1976;14:1463-67 [12] Kn¨oll KH, Marx G, H¨ubner K, Schweikert F, Stahl S, Weber C and Werth G. Experimental gJ factor in the metastable 5 D3/2 level of Ba+ . Phys Rev A 1996;54:1199205 [13] Werbowy S, Kwela J. The E2 admixtures in mixed multipole lines 459.7 nm and 461.5 nm in the spectrum of BiI. Eur Phys J-Special Topics 2007;144:179-84 [14] Sobolewski ŁM, Werbowy S, Kwela J. Hyperfine and Zeeman structure of lines of Bi I. J Opt Soc Am B 2014;31:3038-41 [15] Werbowy S Kwela J. M1-E2 interference in the Zeeman spectra of Bi I. Phys Rev A 2008;77:023410 [16] Werbowy S, Kwela J. M1-E2 interference in the Zeeman spectra of Pb I and Pb II. J Phys B 2009;42:065002 [17] Werbowy S, Kwela J. Observation of the M1-E2 interference in the Zeeman spectra of isotopes 121 Sb and 123 Sb. J Phys B 2010;43:065002 [18] Werbowy S, Kwela J, Drozdowski R and Heldt J. M1-E2 interference in the Zeeman effect of the 461.5 nm line of Bi I. Eur Phys J D 2006;39:5-12 [19] Anjum N, Akhtar N, Hhnermann H, Windholz L. Investigation of the hyperfine structure of 143 Nd+ spectral lines using collinear laser ion beam spectroscopy. J Phys B 2015;48:015003 [20] Albertson WE, Harrison GR, McNally JR, Jr. Phys Rev 1942;61:167-74 [21] Blaise J, Chevillard J, Vergi J, Wyart JF. Etude des spectres demission dans l’infrarouge par lemploi dun SISAM-IV. Spectre demission du n´eodyme*. Spec Chim Acta B 1970;268:333-81 [22] Martin WC, Zalubas R, Hagan L. Atomic Energy Levels - The Rare-Earth Elements. Nat Stand Ref Data Ser. NSRDS-NBS 1978; 60: 422 pp. (Nat. Bur. Stand., U.S., 1978)
Acknowledgments The present work was supported by Wissenschaftlich¨ Technisches Abkommen Osterreich-Polen, projects no. 21/2012 and 12/2014. [1] Wyart JF. Theoretical interpretation of the Nd II spectrum: odd parity energy levels. Phys Scr 2010;82:035302 [2] Maosheng L, Hongliang M, Miaohua C, Fuquan L, Jiayong T, and Fujia Y. Hyperfine-structure measurements in 141 PrII and 143,145 NdII by collinear laser-ion-beam spectroscopy. Phys Rev A 2000;62:052504 [3] Anjum N. Hyperfine Structure of Spectral Lines of 143 Nd+ , 145 Nd+ , 139 La+ , 141 Pr+ and 137 Ba+ Investigated by Collinear Laser Ion Beam Spectroscopy. PhD thesis, Graz University of Technology, Graz; 2012 [4] Blaise J, Wyart JF. Revised Interpretation of the Spectrum of SinglyIonized Neodymium (Nd II). Phys Scr 1984;29:119-31 [5] Yansen W, Fuquan L, Songmao W, Wei S, Linggen S, Jiayong T and Fujia Y. Configuration mixing of the level (23 537)o 9/2 in Nd II deduced from the optical isotope shifts by collinear fast-ion-beam laser spectroscopy. J Phys B 1991;24:45-8 [6] Werbowy S, Anjum N, H¨uhnermann H, Kwela J, Windholz L. Zeeman effect of hyperfine-resolved spectral lines of singly ionized praseodymium using collinear laserion-beam spectroscopy. Phys Rev A 2014;90:032515
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Figure 4: Recorded Zeeman structure patterns of three 142 Nd II lines at 330 G. The thin line represents the experimental result and the thick line the computer best fit.
Table 1: Lande-gJ factors of singly ionized Neodymium for even energy levels belonging to the configurations 4f4 5d, 4f3 5d2 and 4f4 6p. Experimental gJ Theoretical gJ Configuration Level Termb Excitation Present Ref. [20]c Ref. [21]c Ref. [1] LS energy Wavelength studies (87 180 G) (20 000 G) HFR coupling [cm−1 ]a [nm] (330 G) 4f4 5d 6005.27 6 K4.5 580.402 0.559 (7) 0.552 0.550 0.546 570.828 0.838 (8) 6931.80 6 K5.5 581.157 0.838 (1) Average: 0.838 (10) 0.842 0.840 0.839 7950.08 6 K6.5 568.853 1.001 (3) 574.477 0.984 (6) Average: 0.998 (9) 1.015 1.015 1.015 8420.32 6 I4.5 572.683 0.834 (7) 589.153 0.843 (2) Average: 0.842 (9) 0.84 0.840 0.828 8716.45 6 G1.5 582.587 0.003 (2) 577.050 0.009 (3) Average: 0.005 (4) 0.008 0.010 0 9357.91 6 I5.5 574.086 1.022 (8) 1.034 1.035 1.035 10337.1 6 I6.5 584.239 1.123 (4) 589.050 1.160 (9) Average: 1.128 (13) 1.144 1.140 1.159 4f3 5d2
24134.1 25352.4 25389.2
5.5 5.5 4.5
581.157 574.477 589.153
1.008 (6) 1.111 (9) 1.034 (7)
1.014 1.152 1.029
1.020 1.150 1.030
4f4 6p
1.018 1.231 1.017
-
23230.0 4.5 580.402 0.785 (9) 0.778 0.780 0.779 24445.4 5.5 570.828 0.918 (8) 0.917 0.915 0.912 25524.5 6 K6.5 568.853 1.022 (7) 1.03 1.030 1.028 1.015 25876.6 2.5 582.587 0.633 (4) 0.642 0.655 0.606 25877.2 4.5 572.683 0.962 (13) 0.957 0.950 0.974 26041.2 2.5 577.050 0.924 (6) 0.940 1.067 26772.1 5.5 574.086 1.036 (7) 1.013 1.020 1.109 27309.0 6.5 589.050 1.088 (12) 1.087 1.090 1.086 27448.7 6.5 584.239 1.148 (8) 1.166 1.135 1.146 a Energy values are taken from [22]. b Because many eigenfunctions have leading components smaller than 10% due to breakdown of LS coupling and CI effects, only leading components when larger than 50% are given. c Experimental uncertainties were not given in [20, 21].
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Figure 2: Most important even and odd configurations of Nd II. Thin horizontal lines indicate the investigated metastable levels of the 4f4 5d configuration and the excited 4f4 6p and 4f3 5d2 odd levels. A bold upward arrow represents the laser excitation from the metastable levels to the odd levels, from which fluorescence decays back to the lower even levels of the 4f4 6s and 4f4 5d configurations are observed through a Schott glass filter (thin arrows).
Figure 5: Recorded Zeeman structure patterns of line 580.402 nm for three isotopes, 142, 143 and 145, at 235 G. The thin line represents the experimental result and the thick line the computer best fit. The odd isotopes show, beside the Zeeman splitting, also hyperfine structure splitting.
Figure 3: (a) Recorded Zeeman pattern and fit of the 138 Ba II 585.368 nm transition used for the magnetic field check. The best fit was obtained at field strength 330 G. (b) Calculated Zeeman patterns of the line for 325, 330 and 335 G fields (only the first three components from the left are shown).
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