A reformulation of the theory of field isotope shift in atoms

Blundell, S. A.; Baird, P E G; Palmer, Charlotte; Stacey, D. N.; Woodgate, G. K.

doi:10.1088/0022-3700/20/15/015

Cited by 90 publications

(79 citation statements)

References 8 publications

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“…The field shift, arising from the difference in the charge distribution between two isotopes with mass number A and A ′ (A > A ′ ), is given in the approximation of the first-order perturbation theory by [13,14] …”

Section: Isotope Shiftsmentioning

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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Section: Isotope Shiftsmentioning

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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“…Adopting the electronic density ρ e i,A for the zeroth-order picture, perturbation theory can be used instead to get the first-order energy correction [22,23] …”

Section: Field Shift Theorymentioning

confidence: 99%

“…Using (20) for levels i = ( , u) involved in transition k, the frequency field shift of the spectral line k can be written as [12,22,23] …”

Section: Field Shift Theorymentioning

confidence: 99%

ris3: A program for relativistic isotope shift calculations

Nazé

Gaidamauskas

Gaigalas

et al. 2013

Computer Physics Communications

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An atomic spectral line is characteristic of the element producing the spectrum. The line also depends on the isotope. The program ris3 (Relativistic Isotope Shift) calculates the electron density at the origin and the normal and specific mass shift parameters. Combining these electronic quantities with available nuclear data, isotope-dependent energy level shifts are determined.Keywords: Isotope shift, field shift, mass shift, normal mass shift, specific mass shift, relativistic nuclear recoil, nuclear radius The nuclear motion and volume effects are treated in first order perturbation theory. Taking the zero-order wave function in terms of a configuration state expansion |Ψ P JM J = µ c µ |Φ(γ µ P JM J ) , where P , J and M J are, respectively, the parity and angular quantum numbers, the electron density at the nucleus and the normal and specific mass shift parameters may generally be expressed as µ,ν c µ c ν γ µ P JM J |ϑ|γ ν P JM J where ϑ is the relevant operator. The matrix elements, in turn, can be expressed as sums over radial integrals multiplied by angular coefficients. All the angular coefficients are calculated using routines from grasp2K version 1 1 package [1]. NEW VERSION PROGRAM SUMMARY Reasons for the new version:This new version takes the nuclear recoil corrections into account within the (αZ) 4 m 2 /M approximation [2] and also allows a storage of the angular coefficients for a series of calculations within a given isoelectronic sequence. Furthermore, the program jj2lsj, a module of grasp2K version 1 1 toolkit that allows a transformation of ASFs from a jj-coupled CSF basis into an LSJ-coupled CSF basis, has been especially adapted to present ris3 results using LSJ labels of the states. This additional tool is called ris3 lsj. Summary of revisions:This version is compatible with the new angular approach of grasp2K version 1 1 package [1] and can store necessary angular coefficients. According to the formalism of the relativistic nuclear recoil, the "uncorrected" expression of the normal mass shift has been fundamentally modified compared with its expression in [3]. Restrictions:The complexity of the cases that can be handled is entirely determined by grasp2K package [1] used for the generation of the electronic wave functions. Unusual features: Angular data stored on disc and can be reused. LSJ labels are used for the states. Additional comments: ?? 2Running time:As an example, we evaluated the isotope shifts parameters and the electron density at the origin using the wave functions of Be-like system. We used MCDHF wave function built on a complete active space (CAS) with n = 8 (296 626 CSFs -62 orbitals) that contains 3 non-interacting blocks of given parity and J values involving 6 different eigenvalues in total. Calculations take around 10 hours on one AMD Opteron 6100 @ 2.3GHz CPU with 8 cores (64GB DDR3 RAM 1.333GHz). If angular files are available the time is reduced to 20 minutes. The storage of the angular data takes 139Mb and 7.2Gb for the one-body and the two-body elements, r...

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“…By contrast, to the best of our knowledge, no recent paper reporting on theoretical IS electronic factors in Zn I has been published since the pioneering works led by Bauche and Crubellier [28,29] reporting only on SMS factors, and by Blundell et al [30,31] only on FS factors. Hence, we reinvestigate the two above-cited transitions in Zn I by performing ab initio calculations of IS electronic factors using the multiconfiguration Dirac-Hartree-Fock (MCDHF) method implemented in the RIS3/GRASP2K program package [1,32].…”

Section: Introductionmentioning

confidence: 93%

“…Neglecting terms of higher order than δ r 2 in the Seltzer moment (or nuclear factor) [43], (6) the line frequency shift in the transition k arising from the difference in nuclear charge distributions between two isotopes, A and A , can be written as [31,44,45] …”

Section: Isotope-shift Theorymentioning

confidence: 99%

Multiconfiguration calculations of electronic isotope-shift factors in Zn i

et al. 2017

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The present work reports results from systematic multiconfiguration Dirac-Hartree-Fock calculations of electronic isotope-shift factors for a set of transitions between low-lying states in neutral zinc. These electronic quantities, together with observed isotope shifts between different pairs of isotopes, provide the changes in mean-square charge radii of the atomic nuclei. Within this computational approach, different models for electron correlation are explored in a systematic way to determine a reliable computational strategy and to estimate theoretical error bars of the isotope-shift factors.

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A reformulation of the theory of field isotope shift in atoms

Cited by 90 publications

References 8 publications

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

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

ris3: A program for relativistic isotope shift calculations

Multiconfiguration calculations of electronic isotope-shift factors in Zn i

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