Theory of Hyperfine Structure

Schwartz, Charles

doi:10.1103/physrev.97.380

Cited by 409 publications

(163 citation statements)

References 18 publications

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“…When considering only up to the quadrupole interaction and neglecting the off-diagonal interactions (Schwartz 1955), the energy shift for the total angular momentum F = I + J due to the hyperfine interaction is given by…”

Section: Theory and Calculation Methodsmentioning

confidence: 99%

Spectral properties of a few F-like ions

Nandy

Sahoo

2014

A&A

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Aims. We intend to provide accurate data for the oscillator strengths, transition probabilities, lifetimes, and hyperfine shifts of the atomic energy levels in the fluorine (F)-like Ti, V, Cr, Mn, Co, Ni, Cu, Zn, and Mo ions for the diagnostic of the astrophysical plasma. Furthermore, we propose these ions for probing possible variation in the fine structure constant (α e ) by observing their transition lines from the distant astronomical objects. Methods. We have employed an all-order perturbative method in the relativistic coupled-cluster framework using the Dirac-Coulomb Hamiltonian for calculating the atomic wave functions in the considered F-like ions. We adopted the Fock-space formalism to account for the correlation effects among the occupied electrons by allowing all possible singly and doubly excited configurations in two steps: first considering the correlations between the electrons in a closed-shell configuration, and second constructing the openshell configurations of the first three low-lying states in the considered atomic systems by removing the respective electron from the core orbitals. This procedure enormously simplifies the computational complexity and overcomes the need to select important configuration state functions in determining the atomic state functions in contrast to a truncated configuration interaction method. Moreover, corrections from the frequency-independent Breit interaction and the lowest order quantum electrodynamic effects are incorporated self-consistently. Results. We present the calculated ionization potential energies of the electrons that are detached to form the above considered F-like ions. The correctness of our estimated results are ensured by comparing them with the available experimental values and other calculations. From these calculations, we evaluate the relativistic sensitivity coefficients that we propose here to be used for probing possible temporal variation of the fine structure constant (α e ) through the precise astrophysical observation of the spectral lines of the transitions involving the above low-lying states. The accuracies of these sensitivity coefficients are appraised from the comparison of our calculated energies with the experimental values. We also present the line strengths by calculating the reduced matrix elements of the allowed transitions and of the M1 and E2 forbidden transitions. By combining our calculated line strengths with the observed wavelengths, we determine the oscillator strengths, transition probabilities, and lifetimes of the first two excited states of the above ions and compare them with the other theoretical calculations. The hyperfine splittings of the states are also presented by calculating their magnetic dipole and electric quadrupole hyperfine structure constants.

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Section: Theory and Calculation Methodsmentioning

confidence: 99%

Spectral properties of a few F-like ions

Nandy

Sahoo

2014

A&A

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“…All coils are powered by homemade current drivers having a relative drift of less than 2 · 10 −5 in 24 h. Light for the spectroscopy on the S 1/2 ↔ D 5/2 quadrupole transition is generated by a Ti:Sapphire laser stabilized to an ultra-stable high finesse reference cavity (finesse F = 410000) [13]. The free spectral range of the cavity was measured to be ∆ F SR = 1933.07309 (20) MHz by using a second independently stabilized laser and observing the beat note for the Ti:Sa laser locked to several different modes. From this measurement, also an upper limit of less than 50 Hz could be determined for the laser line width.…”

Section: Methodsmentioning

confidence: 99%

“…Here h is Planck's constant and A D 5/2 (A S 1/2 ) and B D 5/2 are the hyperfine constants describing the magnetic dipole and electric quadrupole interactions in the D 5/2 (S 1/2 ) state; higher-order multipoles [20] are not taken into account. Terms arising from second-order perturbation theory [20] are expected to shift the levels by only negligible amounts as (A D 5/2 · A D 3/2 )/∆ F S ≈ 100 Hz where ∆ F S denotes the fine-structure splitting of the D states.…”

Section: Methodsmentioning

confidence: 99%

Measurement of the hyperfine structure of theS1∕2−D5∕2transition in
Benhelm
¹
,
Kirchmair
²
,
Rapol
³

et al. 2007
Phys. Rev. A
34
1
13
0
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The hyperfine structure of the 4s 2 S 1/2 − 3d 2 D 5/2 quadrupole transition at 729 nm in 43 Ca + has been investigated by laser spectroscopy using a single trapped 43 Ca + ion. We determine the hyperfine structure constants of the metastable level as AD 5/2 = −3.8931(2) MHz and BD 5/2 = −4.241(4) MHz. The isotope shift of the transition with respect to 40 Ca + was measured to be ∆ 43,40 iso = 4134.713(5) MHz. We demonstrate the existence of transitions that become independent of the first-order Zeeman shift at non-zero low magnetic fields. These transitions might be better suited for building a frequency standard than the well-known 'clock transitions' between m=0 levels at zero magnetic field.

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“…where T (k) and M (k) are spherical tensor operators of rank k in the electronic and the nuclear spaces, respectively [12]. The k = 1 term of the expansion represents the magnetic dipole interaction and the k = 2 term the electric quadrupole interaction.…”

Section: Hyperfine Interaction Constantsmentioning

confidence: 99%

Atomic parameters for the $2{p}^{5}3p\;{}^{2}{[3/2]}_{2}-2{p}^{5}3s\;{}^{2}{[3/2]}_{2}^{o}$ transition of Ne I relevant in nuclear physics

Godefroid

Wang

2016

J. Phys. B: At. Mol. Opt. Phys.

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We calculated the magnetic dipole hyperfine interaction constants and the electric field gradients of 2p 5 3p 2 [3/2] 2 and 2p 5 3s 2 [3/2] o 2 levels of Ne I by using the multiconfiguration Dirac-Hartree-Fock method. The electronic factors contributing to the isotope shifts were also estimated for the λ = 614.5 nm transition connecting these two states. Electron correlation and relativistic effects including the Breit interaction were investigated in details. Combining with recent measurements, we extracted the nuclear quadrupole moment values for 20 Ne and 23 Ne with a smaller uncertainty than the current available data. Isotope shifts in the 2p 5 3p 2 [3/2] 2 − 2p 5 3s 2 [3/2] o 2 transition based on the present calculated field-and mass-shift parameters are in good agreement with the experimental values. However, the field shifts in this transition are two or three orders of magnitude smaller than the mass shifts, making rather difficult to deduce changes in nuclear charge mean square radii. According to our theoretical predictions, we suggest to use instead transitions connecting levels arising from the 2p 5 3s configuration to the ground state, for which the normal mass shift and specific mass shift contributions counteract each other, producing relatively small mass shifts that are only one order of magnitude larger than relatively large field shifts, especially for the 2p 5 3s 2 [1/2] o 1 − 2p 6 1 S 0 transition.

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Theory of Hyperfine Structure

Cited by 409 publications

References 18 publications

Spectral properties of a few F-like ions

Spectral properties of a few F-like ions

Measurement of the hyperfine structure of theS1∕2−D5∕2transition in
Benhelm
¹
,
Kirchmair
²
,
Rapol
³

et al. 2007
Phys. Rev. A
34
1
13
0
View full text Add to dashboard Cite

Atomic parameters for the $2{p}^{5}3p\;{}^{2}{[3/2]}_{2}-2{p}^{5}3s\;{}^{2}{[3/2]}_{2}^{o}$ transition of Ne I relevant in nuclear physics

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Theory of Hyperfine Structure

Cited by 409 publications

References 18 publications

Spectral properties of a few F-like ions

Spectral properties of a few F-like ions

Measurement of the hyperfine structure of theS1∕2−D5∕2transition inBenhelm1, Kirchmair2, Rapol3 et al. 2007Phys. Rev. A341130View full textAdd to dashboardCite

Atomic parameters for the $2{p}^{5}3p\;{}^{2}{[3/2]}_{2}-2{p}^{5}3s\;{}^{2}{[3/2]}_{2}^{o}$ transition of Ne I relevant in nuclear physics

Contact Info

Product

Resources

About

Measurement of the hyperfine structure of theS1∕2−D5∕2transition in
Benhelm
¹
,
Kirchmair
²
,
Rapol
³

et al. 2007
Phys. Rev. A
34
1
13
0
View full text Add to dashboard Cite