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Spin manipulation and nuclear polarization enhancement in particle beams with static magnetic fields

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Pith's one-line read A static, spatially sinusoidal magnetic field can enhance nuclear polarization in hydrogen, deuterium, and HD beams by driving hyperfine transitions, with ground-state H proton polarization reaching 99.12%.

desk verdict A sound numerical demonstration that sinusoidal static magnetic fields can enhance nuclear polarization in H, D, and HD beams; the ground-state results are solid, while the metastable-state peaks rest on an acknowledged but unquantified motional-Stark approximation. read the letter →

arxiv 2505.12365 v1 pith:O6ELLYIV submitted 2025-05-18 physics.chem-ph physics.atom-phquant-ph

Chrysovalantis S. Kannis , Ralf Engels , Tarek El-Kordy , Nicolas Faatz , Simon J. Pütz , Vincent Verhoeven , T. Peter Rakitzis , Markus Büscher This is my paper · ORCID
classification physics.chem-phphysics.atom-phquant-ph
keywords spindynamicshyperfinetransitionsnuclearpolarizationhydrogenbeamdeuteriumdeuteridesinusoidalmagneticfieldmotionalelectric
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

The paper develops a theoretical framework for the spin dynamics of non-relativistic particle beams whose angular momenta interact with each other and with a static, spatially sinusoidal magnetic field. In the beam's rest frame that field looks time-dependent, so a purely static magnet becomes a resonant driver for hyperfine transitions when the time of flight $t_f = \lambda/v$ matches the inverse of a hyperfine splitting frequency. The authors show this can transfer spin polarization from the electron (or, for HD, from molecular rotation) to the nucleus: ground-state hydrogen proton polarization rises from 50% to 99.12% at $B_0 = 25$ mT, deuterium to 63.7% at 6 mT, HD $J=1$ deuteron polarization to about 83%, and HD $J=2$ proton polarization to 73.5%. Because the driving is resonant and the field is static, the scheme offers a way to produce highly polarized hydrogen-isotope beams for fusion fuel and other spin-sensitive experiments without radio-frequency or time-varying magnetic fields.

What carries the argument

The machinery is the effective hyperfine Hamiltonian of each system together with the Zeeman interaction with the external field: for H and D the atomic term $H_0 = (A/\hbar^2)\,\mathbf{I}\cdot\mathbf{S}$, and for HD the full spin-rotation, spin–spin, and tensor-interaction Hamiltonian with experimentally determined constants. The crucial object is the rest-frame transformation of the sinusoidal field, $B_z = B_0\sin(2\pi v t/\lambda)$, which turns a static spatial field into a periodic time-dependent drive. The controlling parameter is the time of flight $t_f=\lambda/v$ set to $1/\nu_{\rm HF}$ (or the corresponding hyperfine splitting for D and HD), and the dynamics are computed by numerically integrating the density-matrix equation of motion, yielding state populations and average spin projections in both coupled and uncoupled bases. The density-matrix formalism also handles the incoherent mixed states that represent realistic partially polarized beams.

What would settle it

Measure the proton polarization of a ground-state hydrogen beam (prepared with 50% electron/proton polarization) after it passes through a sinusoidal field with $B_0 = 25$ mT and $t_f = 1/\nu_{\rm HF}\approx 0.7$ ns; if the peak is not close to 99%, or occurs at a different $B_0$ or $t_f$, the mechanism or the neglect of the motional electric field is wrong. A sharper test uses a metastable $2S$ beam: if the polarization enhancement deviates from the predicted curve as $v B_r$ grows, the motional electric field effect is responsible.

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Extended reading notes

Core claim

The central claim is that a static, spatially periodic magnetic field $B_z = B_0\sin(2\pi z/\lambda)$ can act as a resonant, time-dependent perturbation on a moving particle, because the particle converts spatial variation into temporal variation at frequency $v/\lambda$. Choosing the time of flight $t_f = \lambda/v$ equal to the inverse of a hyperfine splitting makes the field efficiently drive magnetic-dipole transitions between hyperfine states with the same total projection $m_F$ (on-axis), redistributing population and shifting the average spin projection from the electron to the nucleus. For an incoherently prepared ground-state H beam the proton polarization reaches 99.12% at $B_0 = 25$ mT; for ground-state D the deuteron polarization reaches 63.7% at 6 mT; for coherently rotationally selected HD the deuteron polarization reaches about 83% for $J=1$ (at 48.6 mT) and the proton polarization reaches 73.5% for $J=2$ (at 4.3 mT). Off-axis, the radial component $B_r$ breaks the $\Delta m_F = 0$ selection rule, creating transverse polarization and redistributing populations without loss. The effect is robust to the exact field shape: a sine-cubed profile gives slightly higher peaks (99.6% for H, 64.1% for D).

Load-bearing premise

The load-bearing premise is that the motional electric field $\mathbf{E} = \mathbf{v}\times\mathbf{B}$, present in the beam's rest frame, can be neglected; this is safe for the ground states of H and D (the nearest opposite-parity levels are about 10 eV away), but questionable for metastable $2S$ states whose $2S$–$2P$ energy gap is only a few micro-electronvolts, so the predicted polarization enhancement for those states could be altered by electric-field-induced coupling.

Editorial extensions

If this is right

  • Ground-state hydrogen beams can be raised from 50% to 99.12% proton polarization by a static sinusoidal field with $B_0=25$ mT and $t_f=1/\nu_{\rm HF}$, corresponding to a submillimeter wavelength for keV beams.
  • Ground-state deuterium beams reach 63.7% deuteron polarization at $B_0=6$ mT, slightly exceeding the 59.3% ceiling reported for molecular photodissociation from the same initial incoherent preparation.
  • Coherently rotationally selected HD molecules respond to the same scheme, giving about 83% deuteron polarization for $J=1$ and 73.5% proton polarization for $J=2$ with meter-scale wavelengths for 1 keV beams.
  • The resonance condition is robust to field shape: a sine-cubed profile raises the peaks to 99.6% for H and 64.1% for D, so precise sinusoidal winding is not required.
  • Because the framework accepts arbitrary static field profiles as input, it can predict spin evolution in real beamline magnets, including transitions between homogeneous-field regions, and in stationary systems subject to time-dependent fields if the initial state is a mixture.

Reading between the lines

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

  • The same resonance condition should extend to tritium and tritium deuteride, for which hyperfine parameters are already known; the authors flag this as future work but do not compute it here.
  • The off-axis radial field, which the paper treats as a source of polarization loss at $r/\lambda \sim 1$, could instead be used deliberately as a transverse-polarization rotator, since it drives $\Delta m_F = \pm 1$ transitions.
  • For metastable $2S$ states, the neglected motional electric field effect is not merely a caveat: sweeping beam velocity or $B_0$ through the $2S$–$2P$ gap would test the model and could become an electric-field-assisted spin-control knob.
  • Since the density-matrix solver accepts measured field maps, the design problem for a practical polarizing beamline becomes a numerical search over coil geometries, which the authors do not carry out.
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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

2 major / 5 minor

Summary. The paper develops a numerical framework for spin dynamics in non-relativistic atomic and molecular beams passing through static, spatially sinusoidal magnetic fields. The spatial field is transformed into a time-dependent field in the beam rest frame, and the Liouville-von Neumann equation is solved with hyperfine and Zeeman Hamiltonians using literature values for all parameters. The authors report that such fields can enhance nuclear polarization: ground-state hydrogen rises from 50% to 99.12% proton polarization at B0 = 25 mT, deuterium from 33% to 63.7% at B0 = 6 mT, metastable 2S states of H and D show analogous peaks at lower fields, and HD in J = 1 reaches 83% deuteron polarization while J = 2 reaches 73.5% proton polarization. The paper includes a limitations section that acknowledges the motional Stark effect, decoherence, and non-ideal field shapes, and it compares sinusoidal fields with a sine-cubed shape for the atomic cases.

Significance. If the numerical results are correct, the paper establishes a non-obvious and potentially useful capability: a static, spatially periodic magnetic field can transfer electron or rotational polarization to nuclear spins and enhance nuclear polarization beyond the initial value. The framework is transparent in its inputs: all hyperfine constants and g-factors are taken from independent measurements, the time of flight is set by known hyperfine frequencies, and the enhancement curves are computed rather than fitted, so no free parameters are introduced. The selection-rule argument (Delta mF = 0 for r = 0) is consistent with conservation of the longitudinal angular-momentum projection and provides a simple physical explanation for the on-axis results. The main uncertainty is the neglect of the motional electric field for metastable atomic states; if this is quantified or clearly delimited, the paper would be a useful contribution to polarized-beam and polarized-fusion literature.

major comments (2)
  1. [Sec. III C, Eqs. (8)-(9), and Sec. III A] The metastable 2S1/2 results in Sec. III A are computed with a basis truncated to the hyperfine states of a single orbital, as described in Secs. II and III A. Section III C correctly notes that the motional electric field E = v x B couples these states to opposite-parity 2P states, but it does not quantify the effect for the sinusoidal-field parameters used for metastable H (B0 ~ 3.1 mT) and D (B0 ~ 0.75 mT). Because the 2S-2P energy difference is a few micro-electronvolts while the paper's own estimate of evBra0 reaches 5 x 10^-7 eV for Br ~ 100 mT, the 2S-2P mixing is not obviously negligible for off-axis trajectories. I request either a calculation of the metastable dynamics in an expanded basis that includes the 2P states, or a quantitative bound on r/lambda (and hence on Br) below which the motional Stark correction is negligible for these parameters; until then, the reported metastable peak polarizations are not verified within the stated model. The ground-state H/D results are not affected by this concern, since their opposite-parity gaps are orders of magnitude larger.
  2. [Sec. III A, radial-field discussion] The statement that at r/lambda = 10^-3 the polarization loss is 'well below 1% for the magnetic field amplitudes considered here' is presented without a figure, table, or analytical estimate. This claim is used to argue that the r = 0 results are representative for realistic beams, so it should be backed by a numerical scan over B0 for the relevant cases, especially the metastable states where the Zeeman scale is smaller and the motional Stark effect enters at the same order in r/lambda. Please add the calculation or replace the statement with a bounded quantitative estimate.
minor comments (5)
  1. [Abstract] The abstract states that the study spans 'frequency ranges from GHz scales for atoms,' but the metastable H and D examples use hyperfine frequencies of 177.56 MHz and 40.92 MHz; please rephrase to avoid overstatement.
  2. [Author affiliations] The affiliation text contains the typo 'Insitut für Kernphysik'; it should read 'Institut für Kernphysik.'
  3. [References] Reference [50] contains a garbled author name ('P. Wcis/suppress lo') and needs correction.
  4. [Sec. III A] The sentence 'No spin polarization develops along the x- or y-axes' appears immediately before a discussion of off-axis cases where transverse polarization does develop; please qualify this sentence to refer to the r = 0 case.
  5. [Sec. II and App. A] The notation l1,2 for angular-momentum projections is used in Sec. II, while App. A adopts mS and mI; a brief notational connection would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the polarization predictions follow from independently measured hyperfine and Zeeman parameters, and the acknowledged motional-Stark limitation is a correctness risk, not a circular input.

full rationale

The derivation chain is self-contained. The Hamiltonians use independently measured hyperfine constants and free-particle g-factors (Eqs. 3 and 4), and the field profile is prescribed by Eq. (2). Initial density matrices are explicit, and observables are defined by Eq. (5). The Liouville-von Neumann equation is integrated numerically; no parameter is fitted to the polarization output. The times of flight are set by independently measured hyperfine frequencies (e.g., vHF = 1.42 GHz for ground-state H, 327.38 MHz for D, and Ramsey-Lewis parameters for HD), not by optimizing the reported polarization values. Peak polarization values such as 99.12% for H, 63.7% for D, and 73.5% for HD J=2 are computed outcomes of scanning B0. The self-citations used for matrix derivations and for the motional-Stark calculations are supporting, not load-bearing: the paper's own equations determine the dynamics, and the cited matrix derivation is a parameter-free standard result. The Limitations section explicitly acknowledges the motional electric field and the need for an expanded basis for metastable states; this is an open modeling limitation, not a circular step. No equation or fitted parameter is equivalent by construction to the claimed predictions, so there is no significant circularity.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The central claim rests on standard quantum-mechanical evolution, literature hyperfine parameters, the Galilean transformation to the rest frame, and idealized beam and field assumptions. No free parameters are fitted to the target polarization results. The most fragile item is the neglect of the motional Stark effect for metastable states.

assumptions (6)
  • standard math The time evolution of the spin density matrix follows the Liouville-von Neumann equation iℏ∂ρ/∂t = [H, ρ].
    Fundamental equation of quantum mechanics, used in Sec. II Eq. (1).
  • domain assumption The effective hyperfine Hamiltonian H0 = A I·S/ℏ² correctly describes the hyperfine structure of H and D ground and metastable S states, with literature values of A.
    Sec. III A Eq. (3) and Refs. [14,19,20,30] supply the hyperfine constants.
  • domain assumption A Galilean transformation maps the static spatial field to a time-dependent field in the particle rest frame without changing the time coordinate; valid for non-relativistic beams (β < 1%).
    Sec. II and Sec. III C; limits beam kinetic energy to below 46.9 keV (H), 93.8 keV (D), 140.7 keV (HD).
  • domain assumption The motional Stark effect E = v × B is negligible for the considered hyperfine dynamics.
    Sec. III C Eq. (8); acknowledged as an approximation, safe for ground states but potentially unsafe for metastable 2S states.
  • domain assumption Initial states are ideal: incoherent equal-population mixtures for H/D (ρc=diag(1/2,1/2,0,0) for H, diag(1/3,1/3,1/3,0,0,0) for D) and coherent rotational state selection for HD (mJ=1 or 2 with equal distribution over nuclear spin projections).
    Sec. III A and III B; these preparations are discussed as achievable but idealized.
  • domain assumption Particles travel at constant velocity v and constant radial coordinate r through an ideal sinusoidal field Bz = B0 sin(2πz/λ) with Br from Gauss's law.
    Sec. II Eq. (2); off-axis effects are considered, but no velocity spread or beam divergence.

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Pith. "Pith review of Spin manipulation and nuclear polarization enhancement in particle beams with static magnetic fields." pith.science (2026). https://pith.science/paper/O6ELLYIV

@misc{pith2026250512365,
  author       = {Pith},
  title        = {Pith review of: Spin manipulation and nuclear polarization enhancement in particle beams with static magnetic fields},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/O6ELLYIV}},
  note         = {Machine review of arXiv:2505.12365}
}
read the original abstract

A theoretical study of spin dynamics in non-relativistic particle beams with interacting angular momenta traversing static, spatially varying magnetic fields is presented. The computational framework evaluates sinusoidal magnetic field configurations, calculating key observables such as average spin projections and state populations during the interaction. It is demonstrated that such fields can effectively enhance nuclear polarization in partially, incoherently polarized hydrogen and deuterium atomic beams, as well as coherently rotationally state-selected hydrogen deuteride molecular beams. This enhancement is attributed to transitions induced within the hyperfine regime of these systems. The study spans frequency ranges from GHz scales for atoms to hundreds of kHz for molecules, corresponding to magnetic field variations on spatial scales from submillimeters to meters.

Figures

Figures reproduced from arXiv: 2505.12365 by the authors.

Figure 1
Figure 1. FIG. 1. Schematic of two particles (cyan spheres), one at [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Longitudinal and radial magnetic field components [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Average spin projections [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (13 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Populations of uncoupled (subscript [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Average spin projections [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Populations of uncoupled ( [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Average spin projections [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Populations of coupled states during the motion [PITH_FULL_IMAGE:figures/full_fig_p006_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Average spin projections [PITH_FULL_IMAGE:figures/full_fig_p007_10.png]
Figure 11
Figure 11. Figure 11: illustrates the variation of the average spin projections for the rotational level J = 1 at the exit of the applied magnetic field Bz with a frequency 1/tf = 153935 Hz, plotted as a function of the magnetic field amplitude B0. The initial preparation assumes coherent …
Figure 12
Figure 12. Figure 12: FIG. 12. Average spin projections [PITH_FULL_IMAGE:figures/full_fig_p008_12.png]
Figure 14
Figure 14. Figure 14: FIG. 14. Average spin projections [PITH_FULL_IMAGE:figures/full_fig_p009_14.png]
Figure 15
Figure 15. Figure 15: FIG. 15. Comparison of average spin projections [PITH_FULL_IMAGE:figures/full_fig_p010_15.png]
Figure 16
Figure 16. Figure 16: FIG. 16. Comparison of average spin projections [PITH_FULL_IMAGE:figures/full_fig_p010_16.png]
Figure 19
Figure 19. Figure 19: FIG. 19. Average spin projections [PITH_FULL_IMAGE:figures/full_fig_p013_19.png]
Figure 20
Figure 20. Figure 20: FIG. 20. Average spin projections [PITH_FULL_IMAGE:figures/full_fig_p013_20.png]

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Works this paper leans on

58 extracted references · 56 canonical work pages

  1. [1]

    System of two spin-1/2 particles As described in Sec. II, a system of two angular mo- menta with L1,2 = 1 2 can be described by the basis vec- tors |l1, l2⟩, where l1,2 are the projections along the quan- tization axis, taking values l1,2 = ± 1 2 . The four elements |l1, l2⟩ compose the uncoupled representation (note that the notation will change from the...

    work page

  2. [2]

    The same 12 procedure as in App

    System of a spin-1/2 and a spin-1 particle The electron and deuteron spin quantum numbers, considered here, are 1 /2 and 1, respectively. The same 12 procedure as in App. A 1 is followed. The uncoupled ba- sis comprises of the following vector states, {|mS, mI ⟩} : { ⏐ ⏐ ⏐ ⏐ 1 2 , 1 ⟩ , ⏐ ⏐ ⏐ ⏐ 1 2 , 0 ⟩ , ⏐ ⏐ ⏐ ⏐ 1 2 , −1 ⟩ , ⏐ ⏐ ⏐ ⏐− 1 2 , −1 ⟩ , ⏐ ⏐ ⏐ ...

    work page

  3. [3]

    Deuterium plots 0 10 20 30 40 50 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 B0 (mT) Population ρ ' ' ( u ρ ) ) ( u ρ * * ( u ρ + + ( u ρ 5 5 ( u ρ 6 6 ( u sum/3 FIG. 17. Populations of uncoupled states at time tf ∼ 3 ns as a function of B0, at r ∼ 0.9 mm. The states are ordered according to App. A 2. 0 10 20 30 40 50 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 B...

    work page

  4. [4]

    Hydrogen deuteride plots 0 10 20 30 40 50 60 700.0 0.2 0.4 : ; < : ; = B0 (mT) 〈mz〉 0 0.2 0.4 : ; < : ; = 1.0 p > ? @ A B C D A E C ? F FIG. 19. Average spin projections ⟨mp⟩, ⟨md⟩, and ⟨mJ ⟩ along the z-axis for J = 1 at tf ∼ 6.5 µs as a function of B0. The right vertical axis represents the proton spin polar- ization, while the deuteron polarization is ...

    work page

  5. [5]

    M. P. M. Letertre, P. Giraudeau, and P. de Tullio, Front. Mol. Biosci. 8, 698337 (2021)

    work page 2021

  6. [6]

    Jørgensen, N

    S. Jørgensen, N. Bøgh, E. Hansen, M. Vægge- mose, H. Wiggers, and C. Laustsen, Semin. Nucl. Med. 52, 374 (2022)

    work page 2022

  7. [7]

    Eills, D

    J. Eills, D. Budker, S. Cavagnero, E. Y. Chekmenev, S. J. Elliott, S. Jannin, A. Lesage, J. Matysik, T. Meersmann, T. Prisner, J. A. Reimer, H. Yang, and I. V. Koptyug, Chem. Rev. 123, 1417 (2023)

    work page 2023

  8. [8]

    N. A. Gershenfeld and I. L. Chuang, Science 275, 350 (1997)

    1997

Show all 58 references
  1. [9]

    P. G. Harris, C. A. Baker, K. Green, P. Iaydjiev, S. Ivanov, D. J. R. May, J. M. Pendlebury, D. Shiers, K. F. Smith, M. van der Grinten, and P. Geltenbort, Phys. Rev. Lett. 82, 904 (1999)

    1999

  2. [10]

    M. P. Mendenhall, R. W. Pattie, Y. Bagdasarova, D. B. Berguno, L. J. Broussard, R. Carr, S. Currie, X. Ding, B. W. Filippone, A. Garc´ ıa, P. Geltenbort, K. P. Hick- erson, J. Hoagland, A. T. Holley, R. Hong, T. M. Ito, A. Knecht, C.-Y. Liu, J. L. Liu, M. Makela, R. R. Mammei,...

    2013

  3. [11]

    A. K. Spiliotis, M. Xygkis, K. Tazes, G. E. Katsopri- nakis, D. Sofikitis, G. Vasilakis, and T. P. Rakitzis, Phys. Chem. Chem. Phys. 23, 21521 (2021)

    2021

  4. [12]

    C. P. Koch, M. Lemeshko, and D. Sugny, Rev. Mod. Phys. 91, 035005 (2019)

    2019

  5. [13]

    R. M. Kulsrud, H. P. Furth, E. J. Valeo, and M. Gold- haber, Phys. Rev. Lett. 49, 1248 (1982)

    1982

  6. [14]

    Ciullo, R

    G. Ciullo, R. Engels, M. B¨ uscher, and A. Vasilyev, eds., Nuclear Fusion with Polarized Fuel , Springer Pro- ceedings in Physics, Vol. 187 (Springer International Publishing, Switzerland, 2016)

    2016

  7. [15]

    W. W. Heidbrink, L. R. Baylor, M. B¨ uscher, R. W. Engels, A. V. Garcia, A. G. Ghiozzi, G. W. Miller, A. M. Sandorfi, X. Wei, and X. Zheng, Front. Phys. 12, 1355212 (2024)

    2024

  8. [16]

    Parisi, A

    J. Parisi, A. Diallo, and J. Schwartz, Nucl. Fusion 64, 126019 (2024)

    2024

  9. [17]

    M. W. Ahmed and H. R. Weller, J. Fusion Energy 33, 103 (2014)

    2014

  10. [18]

    H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One- and Two-Electron Atoms (Springer Berlin, Heidelberg, 1957)

    1957

  11. [19]

    Cesati, F

    A. Cesati, F. Cristofori, L. M. Colli, and P. G. Sona, Energ. Nucl. 13, 649 (1966)

    1966

  12. [20]

    Kponou, A

    A. Kponou, A. Zelenski, S. Kokhanovski, and V. Zubets, AIP Conf. Proc. 980, 241 (2008)

    2008

  13. [21]

    Steffens and W

    E. Steffens and W. Haeberli, Rep. Prog. Phys. 66, R02 (2003)

    2003

  14. [22]

    Practically, a small, well-controlled magnetic field aligned with the polarization axis (quantization axis) is often ap- plied to minimize unwanted spin precession

  15. [23]

    Diermaier, C

    M. Diermaier, C. B. Jepsen, B. Kolbinger, C. Malbrunot, O. Massiczek, C. Sauerzopf, M. C. Simon, J. Zmeskal, and E. Widmann, Nat. Commun. 8, 15749 (2017)

    2017

  16. [24]

    Kolachevsky, A

    N. Kolachevsky, A. Matveev, J. Alnis, C. G. Parthey, S. G. Karshenboim, and T. W. H¨ ansch, Phys. Rev. Lett. 102, 213002 (2009)

    2009

  17. [25]

    Engels, R

    R. Engels, R. Emmerich, J. Ley, G. Tenck- hoff, H. Paetz gen. Schieck, M. Mikirtytchiants, F. Rathmann, H. Seyfarth, and A. Vassiliev, Rev. Sci. Instrum. 74, 4607 (2003)

    2003

  18. [26]

    Kannis, Theoretical and experimental investigation of Sona transitions , Ph.D

    C. Kannis, Theoretical and experimental investigation of Sona transitions , Ph.D. Thesis, RWTH Aachen Univer- sity, Aachen (2023)

    2023

  19. [27]

    Engels, M

    R. Engels, M. B¨ uscher, P. Buske, Y. Gan, K. Grigoryev, C. Hanhart, L. Huxold, C. S. Kan- nis, A. Lehrach, H. Soltner, and V. Verhoeven, Eur. Phys. J. D 75, 257 (2021)

    2021

  20. [28]

    P. G. Sona, Energ. Nucl. 14, 295 (1967)

    1967

  21. [29]

    T. P. Rakitzis, P. C. Samartzis, R. L. Toomes, T. N. Kit- sopoulos, A. Brown, G. G. Balint-Kurti, O. S. Vasyutin- skii, and J. A. Beswick, Science 300, 1936 (2003)

    2003

  22. [30]

    A. K. Spiliotis, M. Xygkis, M. E. Koutrakis, K. Tazes, G. K. Boulogiannis, C. S. Kannis, G. E. Katsoprinakis, D. Sofikitis, and T. P. Rakitzis, Light Sci. Appl. 10, 35 (2021)

    2021

  23. [31]

    T. P. Rakitzis, Chem. Phys. Chem. 5, 1489 (2004)

    2004

  24. [32]

    Sofikitis, C

    D. Sofikitis, C. S. Kannis, G. K. Boulogiannis, and T. P. Rakitzis, Phys. Rev. Lett. 121, 083001 (2018)

    2018

  25. [33]

    Cesati, F

    A. Cesati, F. Cristofori, and L. M. Colli, Phys. Lett. 21, 331 (1966)

    1966

  26. [34]

    D. J. Wineland and N. F. Ramsey, Phys. Rev. A 5, 821 (1972)

    1972

  27. [35]

    Sofikitis, P

    D. Sofikitis, P. Glodic, G. Koumarianou, H. Jiang, L. Bougas, P. C. Samartzis, A. Andreev, and T. P. Rak- itzis, Phys. Rev. Lett. 118, 233401 (2017)

    2017

  28. [36]

    Kolachevsky, P

    N. Kolachevsky, P. Fendel, S. G. Karshenboim, and T. W. H¨ ansch, Phys. Rev. A70, 062503 (2004)

    2004

  29. [37]

    N. F. Ramsey and H. R. Lewis, Phys. Rev. 108, 1246 (1957)

    1957

  30. [38]

    N. F. Ramsey, Phys. Rev. 91, 303 (1953)

    1953

  31. [39]

    N. F. Ramsey, Molecular Beams (Oxford University Press, New York, 1955)

    1955

  32. [40]

    Mukherjee and R

    N. Mukherjee and R. N. Zare, J. Chem. Phys. 132, 154302 (2010)

    2010

  33. [41]

    N. V. Vitanov, A. A. Rangelov, B. W. Shore, and K. Bergmann, Rev. Mod. Phys. 89, 015006 (2017)

    2017

  34. [42]

    Altkorn, R

    R. Altkorn, R. N. Zare, and C. H. Greene, Mol. Phys. 55, 1 (1985)

    1985

  35. [43]

    Orr-Ewing, W

    A. Orr-Ewing, W. Simpson, T. Rakitzis, and R. Zare, Isr. J. Chem. 34, 95 (1994)

    1994

  36. [44]

    T. P. Rakitzis, Phys. Rev. Lett. 94, 083005 (2005)

    2005

  37. [45]

    N. C.-M. Bartlett, J. Jankunas, R. N. Zare, and J. A. Harrison, Phys. Chem. Chem. Phys. 12, 15689 (2010)

    2010

  38. [46]

    N. C.-M. Bartlett, D. J. Miller, R. N. Zare, A. J. Alexander, D. Sofikitis, and T. P. Rakitzis, Phys. Chem. Chem. Phys. 11, 142 (2009)

    2009

  39. [47]

    C. S. Kannis, G. E. Katsoprinakis, D. Sofikitis, and T. P. Rakitzis, Phys. Rev. A 98, 043426 (2018)

    2018

  40. [48]

    Galili and D

    I. Galili and D. Kaplan, Am. J. Phys. 65, 657 (1997)

    1997

  41. [49]

    K¨ onig, Eur

    J. K¨ onig, Eur. J. Phys.42, 045204 (2021)

    2021

  42. [50]

    F. M. Levinton, Rev. Sci. Instrum. 70, 810 (1999)

    1999

  43. [51]

    Faatz, Simulation of the occupation numbers of hy- perfine substates passing external fields , Master’s Thesis, RWTH Aachen University, Aachen (2023)

    N. Faatz, Simulation of the occupation numbers of hy- perfine substates passing external fields , Master’s Thesis, RWTH Aachen University, Aachen (2023). 15

    2023

  44. [52]

    Faatz, R

    N. Faatz, R. Engels, C. Kannis, B. Breitkreutz, and H. Soltner, Phys. Open 22, 100248 (2025)

    2025

  45. [53]

    P. A. Ivanov, N. V. Vitanov, and K. Bergmann, Phys. Rev. A 70, 063409 (2004)

    2004

  46. [54]

    J´ o´ zwiak, H

    H. J´ o´ zwiak, H. Cybulski, and P. Wcis/suppress lo, J. Quant. Spectrosc. Radiat. Transfer 270, 107662 (2021)

    2021

  47. [55]

    C. S. Kannis and T. P. Rakitzis, Chem. Phys. Lett. 784, 139092 (2021)

    2021

  48. [56]

    C. S. Kannis, J. Suarez, and T. P. Rakitzis, Mol. Phys. 120, e1975053 (2022)

    2022

  49. [57]

    Nagata, S

    Y. Nagata, S. Kurokawa, and A. Hatakeyama, J. Phys. B: At. Mol. Opt. Phys. 50, 105002 (2017)

    2017

  50. [58]

    Chadwick, M

    H. Chadwick, M. F. Somers, A. C. Stewart, Y. Alkoby, T. J. D. Carter, D. Butkovicova, and G. Alexandrowicz, Nat. Commun. 13, 2287 (2022)

    2022

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