Nuclear deformation effect on the binding energies in heavy ions

Kozhedub, Y. S.; Андреев, О. В.; Shabaev, V. M.; Tupitsyn, I. I.; Brandau, C.; Kozhuharov, C.; Plunien, G.; Stöhlker, Thomas

doi:10.1103/physreva.77.032501

Cited by 101 publications

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“…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].…”

Section: Summary Of Revisionsmentioning

confidence: 99%

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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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“…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].…”

Section: Summary Of Revisionsmentioning

confidence: 99%

“…Shabaev and Artemyev [6] and, in an independent way, Palmer [7], derived these relativistic corrections to the mass shift. Since then several papers have shown the importance of such relativistic effects to the isotope shift [1,2,3,4,5].…”

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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“…This deformed nuclear charge distribution has been taken into account to calculate field shifts and derive approximate analytical formulas for nuclear-size corrections to binding energies of uranium and neodymium isotopes [18]. The authors of Ref.…”

Section: B Volume or Field Shiftmentioning

confidence: 99%

Nuclear effects in atomic transitions

Pálffy

2010

Contemporary Physics

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Atomic electrons are sensitive to the properties of the nucleus they are bound to, such as nuclear mass, charge distribution, spin, magnetization distribution, or even excited level scheme. These nuclear parameters are reflected in the atomic transition energies. A very precise determination of atomic spectra may thus reveal information about the nucleus, otherwise hardly accessible via nuclear physics experiments. This work reviews theoretical and experimental aspects of the nuclear effects that can be identified in atomic structure data. An introduction to the theory of isotope shifts and hyperfine splitting of atomic spectra is given, together with an overview of the typical experimental techniques used in high-precision atomic spectroscopy. More exotic effects at the borderline between atomic and nuclear physics, such as parity violation in atomic transitions due to the weak interaction, or nuclear polarization and nuclear excitation by electron capture, are also addressed.

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“…The values of the rms charge radii used were taken from the compilation [13] for all ions except for uranium; the uranium rms radius was taken from Ref. [14]. …”

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Nuclear-size correction to the Lamb shift of one-electron atoms

Yerokhin

2011

Phys. Rev. A

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The nuclear size effect on the one-loop self energy and vacuum polarization is evaluated for the 1s, 2s, 3s, 2p 1/2 , and 2p 3/2 states of hydrogen-like ions. The calculation is performed to all orders in the binding nuclear strength parameter Zα. Detailed comparison is made with previous all-order calculations and calculations based on the expansion in the parameter Zα. Extrapolation of the all-order numerical results obtained towards Z = 1 provides results for the radiative nuclear size effect on the hydrogen Lamb shift.PACS numbers: 31.30.jf, 12.20.Ds, 31.15.A- IntroductionThe distribution of charge of the nucleus influences the Dirac energies of atomic systems as well as the quantum electrodynamical corrections to the energy levels. This effect, termed as the nuclear size (NS) correction, is important for comparison of theoretical predictions with experimental data for the whole range of the nuclear charges Z, from hydrogen (Z = 1) up to uranium (Z = 92). The NS corrections to the one-loop self energy and vacuum polarization have been previously investigated both within the approach based on the expansion in the nuclear binding strength parameter Zα [1][2][3][4][5][6] (where α is the fine structure constant) and within the numerical approach that accounts the parameter Zα to all orders [7,8]. In the high-Z region, the numerical allorder approach provides accurate predictions for the NS effect on the radiative corrections. For lower Z, however, the NS effect diminishes and becomes increasingly more difficult to identify in a numerical calculation. On the contrary, the Zα-expansion approach provides accurate predictions for the low-Z ions and only the qualitative estimates in the high-Z region. A quantitative cross-check of the two complementary approaches is not simple and has not been accomplished up to now.The NS corrections became of particular interest recently, after the results of the muonic hydrogen Lambshift experiment were announced [9]. It turned out that the value for the proton charge radius r p deduced from the muonic hydrogen differs by five standard deviations from the spectroscopic value of r p derived from the hydrogen atom. This unexplained disagreement stimulates the scientific community to double-check all contributions originating from the nuclear charge distribution, both for the muonic and normal atoms.The aim of the present investigation is to perform an accurate numerical all-order calculation of the NS correction to the one-loop self energy and vacuum polarization and to make a detailed comparison with the Zα-expansion results available.The relativistic units (m = = c = 1) and the charge units α = e 2 /(4π) are used in this paper. I. NS CORRECTION TO DIRAC ENERGYThe leading-order NS correction to the energy levels of a hydrogen-like atom is defined as the difference of the corresponding eigenvalues of the Dirac equation with the point-Coulomb and the extended-nucleus potentials. The two most commonly used models of the nuclear charge distribution are the uniformly charged sphere ("sp...

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Nuclear deformation effect on the binding energies in heavy ions

Cited by 101 publications

References 54 publications

ris3: A program for relativistic isotope shift calculations

ris3: A program for relativistic isotope shift calculations

Nuclear effects in atomic transitions

Nuclear-size correction to the Lamb shift of one-electron atoms

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