Tensorial form and matrix elements of the relativistic nuclear recoil operator

Gaidamauskas, Erikas; Nazé, Cédric; Rynkun, Pavel; Gaigalas, Gediminas; Jönsson, P.; Godefroid, Michel

doi:10.1088/0953-4075/44/17/175003

Cited by 40 publications

(49 citation statements)

References 39 publications

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“…Its analytic expression as well as the ones of the three reduced angular one-electron matrix elements κ C 1 κ , −κ σ 1 κ and κ σ 1 − κ can be found in [9].…”

Section: The Field Shiftmentioning

confidence: 98%

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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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“…Its analytic expression as well as the ones of the three reduced angular one-electron matrix elements κ C 1 κ , −κ σ 1 κ and κ σ 1 − κ can be found in [9].…”

Section: The Field Shiftmentioning

confidence: 98%

“…The present relativistic isotope shift program (ris3), designed as a module of grasp2K version 1 1 multiconfiguration Dirac-Fock package [8], is to a large extent based on the tensorial expressions derived by Gaidamauskas et al [9], and we refer to this paper for a more comprehensive theoretical treatment.…”

Section: Introductionmentioning

confidence: 99%

ris3: A program for relativistic isotope shift calculations

Nazé

Gaidamauskas

Gaigalas

et al. 2013

Computer Physics Communications

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“…The mass shift between two isotopes A and A ′ , caused by the motion of nucleus with the finite mass, is expressed as [18,19] …”

Section: Isotope Shiftsmentioning

confidence: 99%

“…It should be emphasized that the relativistic correction to the mass shift operator [18,20,21,19,17] are rather small (less than 1%) for Ne I and were systematically omitted in the present work.…”

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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“…More complete developments, as well as the derivation of the tensorial form of (4), are detailed in the work of Gaidamaukas et al [31].…”

Section: Mass Shiftmentioning

confidence: 99%

Isotope shifts in beryllium-, boron-, carbon-, and nitrogen-like ions from relativistic configuration interaction calculations

Nazé

Verdebout

Rynkun

et al. 2014

Atomic Data and Nuclear Data Tables

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Energy levels, normal and specific mass shift parameters as well as electronic densities at the nucleus are reported for numerous states along the beryllium, boron, carbon, and nitrogen isoelectronic sequences. Combined with nuclear data, these electronic parameters can be used to determine values of level and transition isotope shifts. The calculation of the electronic parameters is done using first-order perturbation theory with relativistic configuration interaction wave functions that account for valence, core-valence and core-core correlation effects as zero-order functions. Results are compared with experimental and other theoretical values, when available.

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Tensorial form and matrix elements of the relativistic nuclear recoil operator

Cited by 40 publications

References 39 publications

ris3: A program for relativistic isotope shift calculations

ris3: A program for relativistic isotope shift calculations

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

Isotope shifts in beryllium-, boron-, carbon-, and nitrogen-like ions from relativistic configuration interaction calculations

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