Hydrogen-Deuterium<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>1</mml:mn><mml:mi mathvariant="italic">S</mml:mi><mml:mi>−</mml:mi><mml:mn>2</mml:mn><mml:mi mathvariant="italic">S</mml:mi></mml:math>Isotope Shift and the Structure of the Deuteron

Huber, A.; Udem, Th.; Gross, B.; Reichert, J.; Kourogi, M.; Pachucki, Krzysztof; Weitz, Martin; Hänsch, Theodor W.

doi:10.1103/physrevlett.80.468

Cited by 200 publications

(174 citation statements)

References 23 publications

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“…The calculated phases, which correspond again to model b, include electromagnetic effects, but the latter are negligible beyond 100 MeV. The splitting between the pp and np 3 P J phases is mostly due to the isotensor and isovector terms of v S,CD The static deuteron properties are shown in Table VI and compared to experimental values [60][61][62][63][64]. The binding energy E d is fitted exactly and includes the contributions (about 20 keV) of electromagnetic interactions, among which the largest is that due to the magnetic moment term.…”

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confidence: 99%

Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange includingΔresonances

et al. 2015

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We construct a coordinate-space chiral potential, including ∆-isobar intermediate states in its two-pion-exchange component up to order Q 3 (Q denotes generically the low momentum scale). The contact interactions entering at next-to-leading and next-to-next-to-next-to-leading orders (Q 2 and Q 4 , respectively) are rearranged by Fierz transformations to yield terms at most quadratic in the relative momentum operator of the two nucleons. The low-energy constants multiplying these contact interactions are fitted to the 2013 Granada database, consisting of 2309 pp and 2982 np data (including, respectively, 148 and 218 normalizations) in the laboratory-energy range 0-300 MeV. For the total 5291 pp and np data in this range, we obtain a χ 2 /datum of roughly 1.3 for a set of three models characterized by long-and short-range cutoffs, RL and RS respectively, ranging from (RL, RS) = (1.2, 0.8) fm down to (0.8, 0.6) fm. The long-range (short-range) cutoff regularizes the one-and two-pion exchange (contact) part of the potential.

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Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange includingΔresonances

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“…The accuracy of theoretical predictions achieved for hydrogen [5] leads to the determination of the proton charge radius [5,6], which is far more accurate than from the electron scattering measurements. A similar experimental accuracy achieved for deuterium allowed one to determine very accurately the deuteron radius [1]. Surprisingly, the atomic measurements lead to a slightly different value from the electron scattering determination, which stimulated a reanalysis of electron scattering data.…”

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confidence: 99%

Isotope Shift of the3 S1/22−2 S1/2
Puchalski
¹
,
Moro
²
,
Pachucki
³

2006
Phys. Rev. Lett.
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82
8
122
2
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High precision calculation of the isotope shift of the 3 2 S 1=2 -2 2 S 1=2 transition in lithium is presented. The wave function and matrix elements of relativistic operators are obtained by using recursion relations. Apart from the relativistic contribution, we obtain the nuclear polarizability correction for 11 Li. The resulting difference of the squared charge radii 11 The recent advances in precise spectroscopy of atomic systems make possible the determination of nuclear charge radii from isotope shift measurements [1][2][3][4]. In spite of the fact that the nuclear size is 5 orders of magnitude smaller than the atomic size, the achieved experimental precision for transition frequencies allows one to determine nuclear charge radii much more accurately than from electron scattering measurements. This, however, requires the theoretical calculations to be performed with high relative precision, for example, at least 10 ÿ6 for lithium isotopes. The accuracy of theoretical predictions achieved for hydrogen [5] leads to the determination of the proton charge radius [5,6], which is far more accurate than from the electron scattering measurements. A similar experimental accuracy achieved for deuterium allowed one to determine very accurately the deuteron radius [1]. Surprisingly, the atomic measurements lead to a slightly different value from the electron scattering determination, which stimulated a reanalysis of electron scattering data. What makes the deuteron different from other typical nuclei is its low binding energy of about 2.226 MeV. Such a soft nucleus is distorted by a surrounding electron, which leads to a shift in atomic transition frequencies. Even smaller is the twoneutron separation energy in 11 Li [7], which indicates the possible significance of nuclear structure effects on the isotope shift.In this Letter, we present significantly improved calculations of finite nuclear mass contributions to the isotope shift in the lithium 3 2 S 1=2 -2 2 S 1=2 transition. Such calculations have already been performed by Yan and Drake in Refs. [8][9][10] and were used to determine nuclear charge radii of various lithium isotopes on the basis of recent isotope shift measurements [3,4]. Our result for the relativistic recoil correction is about 10 times smaller than that reported in Refs. [8,9]. Apart from the known nonrelativistic, leading relativistic, and QED corrections, we include higher order recoil corrections and the nuclear polarizability effect E pol , the last being significant for the 11 Li nucleus. Finally, we use our combined results to calculate new nuclear charge radii for the lithium isotopes, taking the experimental isotope shift results from Refs. [3,4].Let us denote ÿ =M. The expansion of an energy level in the fine structure constant iswhere E fs is the nuclear finite size correction, and m, M, are the electron, nucleus, and the reduced mass, respectively. In the following, we obtain these expansion coefficients. The nonrelativistic Hamiltonian of the lithium atom in atomic units is

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“…Ref. [8,9,10,11,12,13,14,15]). In the future, it should become feasible to carry out high-precision experiments on transitions much more effectively than in the past.…”

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confidence: 99%

Calculation of hydrogenic Bethe logarithms for Rydberg states

Mohr

2005

Phys. Rev. A

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We describe the calculation of hydrogenic (one-loop) Bethe logarithms for all states with principal quantum numbers n ≤ 200. While, in principle, the calculation of the Bethe logarithm is a rather easy computational problem involving only the nonrelativistic (Schrödinger) theory of the hydrogen atom, certain calculational difficulties affect highly excited states, and in particular states for which the principal quantum number is much larger than the orbital angular momentum quantum number. Two evaluation methods are contrasted. One of these is based on the calculation of the principal value of a specific integral over a virtual photon energy. The other method relies directly on the spectral representation of the Schrödinger-Coulomb propagator. Selected numerical results are presented. The full set of values is available at arXiv.org/quant-ph/0504002.

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Hydrogen-Deuterium1S−2SIsotope Shift and the Structure of the Deuteron

Cited by 200 publications

References 23 publications

Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange includingΔresonances

Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange includingΔresonances

Isotope Shift of the3 S1/22−2 S1/2
Puchalski
¹
,
Moro
²
,
Pachucki
³

2006
Phys. Rev. Lett.
Self Cite
82
8
122
2
View full text Add to dashboard Cite

Calculation of hydrogenic Bethe logarithms for Rydberg states

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Hydrogen-Deuterium1S−2SIsotope Shift and the Structure of the Deuteron

Cited by 200 publications

References 23 publications

Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange includingΔresonances

Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange includingΔresonances

Isotope Shift of the3 S1/22−2 S1/2Puchalski1, Moro2, Pachucki3 2006Phys. Rev. Lett.Self Cite8281222View full textAdd to dashboardCite

Calculation of hydrogenic Bethe logarithms for Rydberg states

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About

Isotope Shift of the3 S1/22−2 S1/2
Puchalski
¹
,
Moro
²
,
Pachucki
³

2006
Phys. Rev. Lett.
Self Cite
82
8
122
2
View full text Add to dashboard Cite