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Hyperfine spectroscopy and laser cooling of the fermionic isotopes $^{47}$Ti and $^{49}$Ti

T0 review · 0 major / 6 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read The team reports the first laser cooling and magneto-optical trapping of the stable fermionic titanium isotopes, 47Ti and 49Ti, using hyperfine repumping.

desk verdict A careful, honest extension of Ti laser cooling to the fermionic isotopes, with solid hyperfine spectroscopy and a credible MOT demonstration; the atom-number calibration is the only notable weakness. read the letter →

arxiv 2603.00282 v1 pith:X3SQFO45 submitted 2026-02-27 physics.atom-ph

Jackson Schrott , Scott Eustice , Pouya Sadeghpour , Rowan Duim , Hiromitsu Sawaoka , Dmytro Filin , Marianna S. Safronova , Dan M. Stamper-Kurn This is my paper · ORCID
classification physics.atom-ph
keywords lasercoolingmagneto-opticaltrapfermionicisotopestitaniumhyperfinestructurerepumpingatomicspectroscopyultracoldgases
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper reports the first laser cooling and magneto-optical trapping of the two stable fermionic isotopes of titanium, 47Ti and 49Ti. Because these nuclei carry spin, every optical transition is split into hyperfine multiplets, so a single laser tone cannot cool them. The authors measure the hyperfine structure of the pumping and cooling transitions, then add two repump tones that return atoms to the stretched state, producing traps of roughly 700 and 1100 atoms with lifetimes around 300 ms. If correct, this brings two new fermionic species into the ultracold-atom toolkit for quantum simulation.

What carries the argument

The key mechanism is hyperfine repumping on the 498 nm laser-cooling transition. In addition to the primary cooling tone, two extra tones are resonant with the F=I+J-1 → F'=F+1 and F=I+J-2 → F'=F+1 transitions, returning atoms that are off-resonantly Raman-scattered out of the stretched state back into the cooling cycle. The required frequencies come from measured A and B hyperfine constants, which the authors extract from a two-color 'X marks the spot' spectroscopy method that eliminates Doppler shifts, supplemented by three-color depumping measurements.

What would settle it

Perform absorption imaging (or a calibrated fluorescence measurement) on the trapped 47Ti and 49Ti clouds shortly after switching off the trapping light to directly count atoms; if the numbers do not agree with the fluorescence-derived values of 731(190) and 1142(240), the scattering-rate model is wrong. Alternatively, reproducing the experiment with the stated tone frequencies and observing no trapped atoms would refute the claim.

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Extended reading notes

Core claim

The authors determine the magnetic-dipole and electric-quadrupole hyperfine constants (A and B) for the a3F4 ground term, the metastable a5F5 laser-cooling state, and the excited y5D4o and y5G6o levels of 47Ti and 49Ti, combining atomic-structure calculations with two- and three-color fluorescence spectroscopy of an atomic beam. Using these frequencies, they run the 498 nm cooling transition with three tones: one red-detuned from the stretched-state resonance and two resonant repump tones that drive population from lower hyperfine states back to the stretched state. With this scheme they form magneto-optical traps of each fermionic isotope directly from the atomic flux of a titanium sublimat

Load-bearing premise

The reported fermion atom numbers are derived from fluorescence using a model of the scattering rate rather than from direct absorption imaging, so the absolute numbers could be systematically off even though the existence of the magneto-optical trap is not in question.

Editorial extensions

If this is right

  • 47Ti and 49Ti become the first fermionic transition-metal isotopes with nonzero nuclear spin to be laser cooled and trapped, joining the list of ultracold Fermi gases.
  • The measured hyperfine constants and isotope shifts provide a benchmark for atomic-structure calculations of titanium and other transition metals.
  • The demonstrated three-tone repumping scheme is a template for cooling other fermionic isotopes of transition-metal atoms with hyperfine structure.
  • With these isotopes, experiments can explore strongly anisotropic optical polarizabilities, state-dependent forces, and tunable s-wave interactions via Feshbach resonances.
  • The observed two-repump lifetimes are consistent with an upper limit on branching to dark states, supporting the use of titanium for optical clocks and quantum computing.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The reported atom numbers rest on an inferred scattering rate rather than direct absorption imaging; a direct measurement would tighten the calibration of the fluorescence-based counting.
  • The low loading rates and small atom numbers suggest that straightforward improvements, such as multi-tone optical pumping and higher repump power, could increase the trapped population by orders of magnitude, bringing these gases closer to quantum degeneracy.
  • The same hyperfine-repumping logic could be applied to other proposed laser-cooled transition metals, potentially expanding the palette of ultracold fermions.
  • A direct measurement of the fermionic MOT temperature, which the authors did not perform, would test whether polarization gradient cooling works as expected in these multi-level systems.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

0 major / 6 minor

Summary. This paper reports the first magneto-optical trapping of the fermionic titanium isotopes 47Ti and 49Ti. The authors measure the hyperfine structure of the 391 nm optical-pumping transition (a3F4 → y5D4o) and the 498 nm laser-cooling transition (a5F5 → y5G6o) using two-color and three-color fluorescence spectroscopy of a collimated thermal beam. The measured A and B coefficients for both isotopes and all four terms agree with CI+all-order calculations and with previous lower-level data. Using these frequencies, they operate a three-tone MOT on the 498 nm transition—a cooling tone red-detuned from the stretched transition plus two hyperfine repump tones—and obtain clouds of 731(190) 47Ti atoms and 1142(240) 49Ti atoms with lifetimes of 330(15) ms and 310(8) ms. They also report loading rates, isotope shifts, a King plot analysis, and a discussion of the dominant loss mechanism.

Significance. The result is significant because it extends laser cooling to the stable fermionic isotopes of titanium, which have non-zero nuclear spin and hyperfine structure. The demonstration is supported by three independent strands: (i) the hyperfine constants are fitted to measured line positions and agree with previous experiments and independent CI+all-order predictions; (ii) the trapped-atom signal and lifetimes respond to the repump tones in the expected way, with one-repump lifetimes of 13–15 ms increasing to 310–330 ms with two repumps; and (iii) the isotope-specific loading-rate ratios and low-gradient optimum rule out residual bosonic contamination. The paper is transparent about the main calibration uncertainty—the absolute fermion atom numbers are derived from fluorescence using scattering rates inferred from photon-budget simulations—but the inferred scattering rates agree with the directly absorption-imaged 48Ti rate, providing a useful cross-check. The tabulated line lists and isotope shifts will be valuable for future ultracold-Ti experiments.

minor comments (6)
  1. [Sec. II, after Eq. (5)] Typo: 'in the the conventional form' should be 'in the conventional form'.
  2. [Sec. I] Typo: 'knowledge of the of this hyperfine structure' should be 'knowledge of this hyperfine structure'.
  3. [Sec. III] The text says 'performing a broad frequency scan of the 319-nm-wavelength light' but the optical-pumping transition is at 391 nm. Please correct to 391 nm.
  4. [Sec. IV, branching-ratio paragraph] The text states that the 'stricter upper bound' α≤4.5(1)×10^-7 'agrees reasonably well' with the predicted α=1.1×10^-6. This is not accurate, since 1.1×10^-6 exceeds the bound by a factor of ~2.4. Moreover, the subsequent photon budget of 2.2×10^6 used in the lifetime prediction corresponds to α≈4.5×10^-7, not to the quoted theory value. Please clarify which value is being compared and which is used for the prediction.
  5. [Sec. IV, photon-budget simulation] The photon-budget simulations that underlie the fermion scattering rates (and hence the absolute atom numbers) are described only as 'simulations of Ti atoms prepared in the stretched hyperfine state... driven by light of isotropic polarization.' No details are given about the model (rate equations vs. optical Bloch equations, number of hyperfine and magnetic sublevels, treatment of re-pumping intensities). Since the 731(190) and 1142(240) numbers depend on this calibration, a brief description of the simulation or a reference would help reproducibility.
  6. [Appendix A, Table III] Several entries in the table are visually ambiguous because multiple numbers appear in a single cell without clear column separation (e.g., the row for F=3/2, F'=5/2). Please reformat the table to clearly associate each value with its isotope and transition.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity identified; central MOT result is independent of fitted hyperfine constants.

full rationale

The paper's derivation chain is non-circular. The hyperfine constants A and B in Table I are obtained by least-squares fitting measured hyperfine transition frequencies to the multiplet formula Eq. 6 (Sec. III); they are not defined in terms of the later MOT outcome. The theoretical HFS predictions in Table I come from independent CI+all-order calculations using known nuclear moments, with uncertainties estimated via Eq. 7, and are compared to—not used to constrain—the experimental fits. The MOT repump tones are set using the measured transition frequencies from the spectroscopy section, and the production of 47Ti and 49Ti MOTs is a separate experimental realization yielding directly observed fluorescence, lifetimes, loading rates, and gradient dependence. The fermion atom numbers are calibrated from fluorescence using a scattering rate inferred from the one-repump lifetime and a simulated photon budget; this is a model-dependent calibration, not a circular reduction, because the photon budget is computed from independent hyperfine and line-strength data and is not fitted to the atom number being reported. The observed lifetimes with two repumps are compared with—but not forced to match—the photon-budget prediction, and the discrepancy is used to infer a different loss mechanism. Self-citations to prior Ti cooling [15], the Ti atomic beam [16], and CI+all-order calculations [22] provide apparatus and methodological context; they do not substitute for the experimental evidence presented here. No step reduces by construction to its own inputs, so no circularity is found.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claim is experimental; the main fitted inputs are hyperfine A/B constants and isotope-shift offsets, all measured in this paper. The theoretical HFS predictions rely on accepted nuclear moments and a previously validated CI+all-order method, neither of which is circular. No new physical entities are introduced.

free parameters (3)
  • Hyperfine A and B constants for upper levels y5D4o and y5G6o (47Ti, 49Ti) = Table I: A47(y5D4o) = -96.6(0.2) MHz, B47(y5D4o) = -0.24(3.4) MHz; A47(y5G6o) = -14.2(0.3) MHz, B47(y5G6o) = -1.1(6.9) M
    Determined by least-squares fit of Eq. 6 to measured hyperfine line positions; they set the repump and cooling frequencies and are the paper's experimental output, not inputs pulled from elsewhere.
  • Hyperfine A and B constants for lower states a3F4 and a5F5 (47Ti, 49Ti) = Table I: A47(a5F5) = -75.3(0.3) MHz, B47(a5F5) = -30.2(6.5) MHz; A49(a5F5) = -74.5(0.3) MHz, B49(a5F5) = -29.2(8.9) MHz
    Measured/fitted in this work and consistent with previous values in Refs [12,13]; used with upper-level constants to place the laser-cooling and repump tones.
  • Isotope-shift center offsets for 391 nm and 498 nm transitions = Table II: delta_nu_391,ctr_47 = -447.8(3.1) MHz, delta_nu_391,ctr_49 = 474.2(3.1) MHz; delta_nu_498,ctr_47 = -345.6(3.2)
    Fitted as overall offsets of each hyperfine multiplet relative to 48Ti; needed to place the cooling/repump frequencies on resonance.
assumptions (5)
  • domain assumption The hyperfine interaction is fully described by magnetic-dipole (k=1) and electric-quadrupole (k=2) terms; higher-order nuclear moments are neglected.
    Eq. 1 is truncated before Eq. 4; standard for I <= 7/2 nuclei at this precision.
  • domain assumption Accepted nuclear moments mu_I and Q for 47Ti and 49Ti from Refs [18,19] are correct.
    Used in Eq. 4 to compute theoretical A/B constants; an error would shift theory but not the experimental HFS or MOT result.
  • domain assumption CI+all-order wavefunctions from the group's prior Ti calculation (Ref [22]) are accurate enough for hyperfine matrix elements.
    Sec. II; validated by comparison to experimental energies and to measured HFS in Table I.
  • domain assumption The 498 nm y5G6o -> a5F5 transition is nearly closed; branching to other terms is <= ~10^-6.
    Sec. IV; inferred from 48Ti low-power lifetime and used to explain fermion trap lifetimes; supported by theory in Ref [22].
  • standard math Wigner-Eckart theorem and standard angular-momentum algebra in Eq. 3.
    Foundation of Eq. 6 hyperfine energy formula.

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Cite this review

Pith. "Pith review of Hyperfine spectroscopy and laser cooling of the fermionic isotopes $^{47}$Ti and $^{49}$Ti." pith.science (2026). https://pith.science/paper/X3SQFO45

@misc{pith2026260300282,
  author       = {Pith},
  title        = {Pith review of: Hyperfine spectroscopy and laser cooling of the fermionic isotopes $^47$Ti and $^49$Ti},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/X3SQFO45}},
  note         = {Machine review of arXiv:2603.00282}
}
abstract

We report on magneto-optical trapping of the two fermionic isotopes of atomic titanium, $^{47}$Ti and $^{49}$Ti. Unlike the even mass-number isotopes, which were recently laser cooled, $^{47}$Ti and $^{49}$Ti have nonzero nuclear spins and, consequently, their atomic levels are split by hyperfine structure. Combining and comparing theoretical calculations and atomic beam-spectroscopy measurements, we determine the hyperfine structures and isotope shifts of the $\mathrm{3d^24s^2}$ $\mathrm{a^3F_4\rightarrow 3d^2(^3P)4s4p(^3P^o)}$ $\mathrm{y^5D_4^o}$ optical-pumping transition at optical wavelength 391nm and the $\mathrm{3d^3(^4F)4s}$ $\mathrm{a^5F_5\rightarrow 3d^3(^4F)4p}$ $\mathrm{y^5G_6^o}$ laser-cooling transition at wavelength 498nm. With this information, we produce magneto-optical traps of both $^{47}$Ti and $^{49}$Ti by applying two additional tones of light to repump atoms to the maximum-spin states on the laser-cooling transition. Directly loading from the atomic flux of a titanium sublimation pump, we produce $^{47}$Ti and $^{49}$Ti traps with 731(190) and 1142(240) atoms, and with lifetimes of 330(15)ms and 310(8)ms, respectively.

Figures

Figures reproduced from arXiv: 2603.00282 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Atomic structure of Ti, including all levels below 31 000 cm [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Optical pumping on the [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Diagram of the atomic beam spectroscopy setup. [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a,b) Simultaneous determination of optical pumping and laser cooling resonances using the “X marks the spot” [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Apparatus used to produce magneto-optical traps [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. (a,b,c) Optimization of the number of [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Modified King plots for the optical pumping and [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]

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Works this paper leans on

32 extracted references

  1. [1]

    C. A. Regal, M. Greiner, and D. S. Jin, Observation of Resonance Condensation of Fermionic Atom Pairs, Phys- ical Review Letters92, 040403 (2004)

    2004

  2. [2]

    Nascimb` ene, N

    S. Nascimb` ene, N. Navon, K. J. Jiang, F. Chevy, and C. Salomon, Exploring the thermodynamics of a univer- sal Fermi gas, Nature463, 1057 (2010)

    2010

  3. [3]

    Greiner, O

    M. Greiner, O. Mandel, T. Esslinger, T. W. H¨ ansch, and I. Bloch, Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms, Nature415, 39 (2002)

    2002

  4. [4]

    J¨ ordens, N

    R. J¨ ordens, N. Strohmaier, K. G¨ unter, H. Moritz, and T. Esslinger, A Mott insulator of fermionic atoms in an optical lattice, Nature455, 204 (2008)

    2008

  5. [5]

    Zhai, Degenerate quantum gases with spin–orbit cou- pling: a review, Reports on Progress in Physics78, 026001 (2015)

    H. Zhai, Degenerate quantum gases with spin–orbit cou- pling: a review, Reports on Progress in Physics78, 026001 (2015)

    2015

  6. [6]

    Naylor, A

    B. Naylor, A. Reigue, E. Mar´ echal, O. Gorceix, B. Laburthe-Tolra, and L. Vernac, Chromium dipolar Fermi sea, Physical Review A91, 011603 (2015)

    2015

  7. [7]

    S. Taie, R. Yamazaki, S. Sugawa, and Y. Takahashi, An SU(6) Mott insulator of an atomic Fermi gas realized by large-spin Pomeranchuk cooling, Nature Physics8, 825 (2012)

    2012

  8. [8]

    M. Lu, N. Q. Burdick, and B. L. Lev, Quantum Degen- erate Dipolar Fermi Gas, Physical Review Letters108, 215301 (2012)

    2012

Show all 32 references
  1. [9]

    Aikawa, S

    K. Aikawa, S. Baier, A. Frisch, M. Mark, C. Ravensber- gen, and F. Ferlaino, Observation of Fermi surface de- 12 formation in a dipolar quantum gas, Science345, 1484 (2014)

    2014

  2. [10]

    Chomaz, D

    L. Chomaz, D. Petter, P. Ilzh¨ ofer, G. Natale, A. Traut- mann, C. Politi, G. Durastante, R. Van Bijnen, A. Patscheider, M. Sohmen, M. Mark, and F. Ferlaino, Long-Lived and Transient Supersolid Behaviors in Dipo- lar Quantum Gases, Physical Review X9, 021012 (2019)

    2019

  3. [11]

    H¨ ofer, L

    M. H¨ ofer, L. Riegger, F. Scazza, C. Hofrichter, D. Fer- nandes, M. Parish, J. Levinsen, I. Bloch, and S. F¨ olling, Observation of an Orbital Interaction-Induced Feshbach Resonance in Yb 173, Physical Review Letters115, 265302 (2015)

    2015

  4. [12]

    K. H. Channappa and J. M. Pendlebury, Hyperfine struc- ture measurements in some low-lying multiplets of 47Ti, 49Ti, 59Co and 105Pd, Proceedings of the Physical Soci- ety86, 1145 (1965)

    1965

  5. [13]

    Aydin, E

    R. Aydin, E. Stachowska, U. Johann, J. Dembczy´ nski, P. Unkel, and W. Ertmer, Sternheimer free determination of the47Ti nuclear quadrupole moment from hyperfine structure measurements, Zeitschrift f¨ ur Physik D Atoms, Molecules and Clusters15, 281 (1990)

    1990

  6. [14]

    Eustice, K

    S. Eustice, K. Cassella, and D. Stamper-Kurn, Laser cooling of transition-metal atoms, Physical Review A 102, 053327 (2020)

    2020

  7. [15]

    Eustice, J

    S. Eustice, J. Schrott, A. St¨ oltzel, J. Wolf, D. Novoa, K. Cassella, and D. M. Stamper-Kurn, Magneto-optical trap of titanium atoms, Physical Review Research7, 023025 (2025)

    2025

  8. [16]

    Schrott, D

    J. Schrott, D. Novoa, S. Eustice, and D. M. Stamper- Kurn, An atomic beam of titanium for ultracold atom experiments, Review of Scientific Instruments95, 113201 (2024)

    2024

  9. [17]

    N. E. Holden, Table of the isotopes, inCRC Handbook of Chemistry and Physics, edited by J. R. Rumble (CRC Press/Taylor & Francis, Boca Raton, FL.) 105th ed

  10. [18]

    N. J. Stone,Table of recommended nuclear magnetic dipole moments: Part I - Long-lived States., Tech. Rep. (International Atomic Energy Agency, International Nu- clear Data Committee, Vienna (Austria), 2019)

    2019

  11. [19]

    N. J. Stone,Table of Nuclear Electric Quadrupole Mo- ments., Tech. Rep. (International Atomic Energy Agency, International Nuclear Data Committee,Vienna (Austria), 2021)

    2021

  12. [20]

    W. R. Johnson,Atomic Structure Theory: Lectures on Atomic Physics(Springer Berlin Heidelberg, Berlin, Hei- delberg, 2007)

    2007

  13. [21]

    Cheung, M

    C. Cheung, M. G. Kozlov, S. G. Porsev, M. S. Safronova, I. I. Tupitsyn, and A. I. Bondarev, pCI: A parallel con- figuration interaction software package for high-precision atomic structure calculations, Computer Physics Com- munications308, 109463 (2025)

    2025

  14. [22]

    Eustice, D

    S. Eustice, D. Filin, J. Schrott, S. Porsev, C. Cheung, D. Novoa, D. M. Stamper-Kurn, and M. S. Safronova, Optical telecommunications-band clock based on neutral titanium atoms, Physical Review A107, L051102 (2023)

    2023

  15. [23]

    V. A. Dzuba, V. V. Flambaum, M. G. Kozlov, and S. G. Porsev, Using effective operators in calculating the hy- perfine structure of atoms, Journal of Experimental and Theoretical Physics87, 885 (1998)

    1998

  16. [24]

    S. G. Porsev, Y. G. Rakhlina, and M. G. Kozlov, Calcula- tion of hyperfine structure constants for ytterbium, Jour- nal of Physics B: Atomic, Molecular and Optical Physics 32, 1113 (1999)

    1999

  17. [25]

    S. G. Porsev, Y. G. Rakhlina, and M. G. Kozlov, Electric- dipole amplitudes, lifetimes, and polarizabilities of the low-lying levels of atomic ytterbium, Physical Review A 60, 2781 (1999)

    1999

  18. [26]

    Ketterle, K

    W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, High densities of cold atoms in adark spontaneous-force optical trap, Physical Review Letters 70, 2253 (1993)

    1993

  19. [27]

    C. G. Townsend, N. H. Edwards, K. P. Zetie, C. J. Cooper, J. Rink, and C. J. Foot, High-density trapping of cesium atoms in a dark magneto-optical trap, Physical Review A53, 1702 (1996)

    1996

  20. [28]

    Lopes, Radio-frequency evaporation in an optical dipole trap, Physical Review A104, 033313 (2021)

    R. Lopes, Radio-frequency evaporation in an optical dipole trap, Physical Review A104, 033313 (2021)

    2021

  21. [29]

    A. C. Lee, J. Smith, P. Richerme, B. Neyenhuis, P. W. Hess, J. Zhang, and C. Monroe, Engineering large Stark shifts for control of individual clock state qubits, Physical Review A94, 042308 (2016)

    2016

  22. [30]

    A. O. Neely, K. Cassella, S. Eustice, and D. M. Stamper- Kurn, Isotope shifts in the metastable a 5 F and excited y 5 G o terms of atomic titanium, Physical Review A 103, 032818 (2021)

    2021

  23. [31]

    Furmann, D

    B. Furmann, D. Stefa´ nska, A. Krzykowski, A. Jarosz, and A. Kajoch, Isotope shift in titanium atom, Zeitschrift f¨ ur Physik D Atoms, Molecules and Clusters37, 289 (1996)

    1996

  24. [48]

    X marks the spot

    The fermion isotope shifts are relative to the center-of-mass frequency of the hyperfine multiplet. Pre- vious measurements are also given, with references noted in the right column. The measurements obtained in this work have nothing in the reference column. For each line mea...

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