Difference In Charge Radius Research Articles

Precision mass measurements in the zirconium region pin down the mass surface across the neutron midshell at N = 66

Precision mass measurements of 104Y, 106Zr, 104,104m,109Nb, and 111,112Mo have been performed with the JYFLTRAP double Penning trap mass spectrometer at the Ion Guide Isotope Separator On-Line facility. The order of the long-lived states in 104Nb was unambiguously established. The trend in two-neutron separation energies around the N=66 neutron midshell appeared to be steeper with respect to the Atomic Mass Evaluation 2020 extrapolations for the 39Y and 40Zr isotopic chains and less steep for the 41Nb chain, indicating a possible gap opening around Z=40. The experimental results were compared to the BSkG2 model calculations performed with and without vibrational and rotational corrections. All of them predict two low-lying minima for 106Zr. While the unaltered BSkG2 model fails to predict the trend in two-neutron separation energies, selecting the more deformed minima in calculations and removing the vibrational correction, the calculations are more in line with experimental data. The same is also true for the 21+ excitation energies and differences in charge radii in the Zr isotopes. The results stress the importance of improved treatment of collective corrections in large-scale models and further development of beyond-mean-field techniques.

Reconciling mean-squared radius differences in the silver chain through improved measurement and ab initio calculations

Nuclear charge radius differences in the silver isotopic chain have been reported through different combinations of experiment and theory, exhibiting a tension of two combined standard errors. This study investigates this issue by combining high-accuracy calculations for six low-lying states of atomic silver with an improved measurement of the 5s2S1/2−5p2P3/2 transition optical isotope shift. Our calculations predict measured electronic transition energies in Ag at the 0.3% level, the highest accuracy achieved in this system so far. We calculate electronic isotope shift factors by employing analytical response relativistic coupled-cluster theory and find that a consistent charge radius difference between Ag107,109 is returned when combining our calculations with the available optical isotope shift measurements. We therefore recommend an improved value for the mean-squared charge radius difference between Ag107 and Ag109 as 0.207(6) fm2, within one combined error from the value derived from muonic Ag experiments, and an updated set of charge radii differences across the isotopic chain. Published by the American Physical Society 2024

Isospin symmetry breaking in the charge radius difference of mirror nuclei

Isospin symmetry breaking (ISB) effects in the charge radius difference $\mathrm{\ensuremath{\Delta}}{R}_{\mathrm{ch}}$ of mirror nuclei are studied using the test example of $^{48}\mathrm{Ca}$ and $^{48}\mathrm{Ni}$. This choice allows for a transparent study of ISB contributions since pairing and deformation effects, commonly required for the study of mirror nuclei, can be neglected in this specific pair. The connection of $\mathrm{\ensuremath{\Delta}}{R}_{\mathrm{ch}}$ with the nuclear equation of state and the effect of ISB on such a relation are discussed according to an energy density functional approach. We find that nuclear ISB effects may shift the estimated value for the symmetry energy slope parameter $L$ by about 6 to 14 MeV while Coulomb corrections can be neglected. ISB effects on the ground-state energy and charge radii in mirror nuclei have been recently predicted by ab initio calculations to be relatively small, pointing to a negligible effect for the extraction of information on the nuclear EoS. These contrasting results call for a dedicated theoretical effort to solve this overarching problem that impacts not only the neutron-skin thickness or the difference in mass and charge radii of mirror nuclei but also other observables such as the isobaric analog state energy.

Information content of the differences in the charge radii of mirror nuclei

Differences in the charge radii of mirror nuclei have been recently suggested to contain information on the slope of the symmetry energy $L$. To test this hypothesis, we perform statistical correlation analysis using quantified energy density functionals that are consistent with our previous knowledge on global nuclear observables such as binding energies and charge radii. We conclude that the difference in charge radii between a mirror pair, $\mathrm{\ensuremath{\Delta}}{R}_{\mathrm{ch}}^{\mathrm{mir}}$, is an inferior isovector indicator compared to other observables, such at the neutron skin or electric dipole polarizability ${\ensuremath{\alpha}}_{\mathrm{D}}$. In particular, this quantity correlates poorly with both the neutron skin and $L$. We demonstrate that $\mathrm{\ensuremath{\Delta}}{R}_{\mathrm{ch}}^{\mathrm{mir}}$ is influenced by pairing correlations in the presence of low-lying proton continuum in the proton-rich mirror-partner nucleus. Considering the large theoretical uncertainties on $\mathrm{\ensuremath{\Delta}}{R}_{\mathrm{ch}}^{\mathrm{mir}}$, we conclude that the precise data on mirror charge radii cannot provide a stringent constraint on $L$.

Structural trends in atomic nuclei from laser spectroscopy of tin

Tin is the chemical element with the largest number of stable isotopes. Its complete proton shell, comparable with the closed electron shells in the chemically inert noble gases, is not a mere precursor to extended stability; since the protons carry the nuclear charge, their spatial arrangement also drives the nuclear electromagnetism. We report high-precision measurements of the electromagnetic moments and isomeric differences in charge radii between the lowest 1/2+, 3/2+, and 11/2− states in 117–131Sn, obtained by collinear laser spectroscopy. Supported by state-of-the-art atomic-structure calculations, the data accurately show a considerable attenuation of the quadrupole moments in the closed-shell tin isotopes relative to those of cadmium, with two protons less. Linear and quadratic mass-dependent trends are observed. While microscopic density functional theory explains the global behaviour of the measured quantities, interpretation of the local patterns demands higher-fidelity modelling.

Measuring the difference in nuclear charge radius of Xe isotopes by EUV spectroscopy of highly charged Na-like ions.

The difference in the mean-square nuclear charge radius of xenon isotopes was measured utilizing a method based on extreme ultraviolet spectroscopy of highly charged Na-like ions. The isotope shift of the Na-like D1 (3s 2 S 1/2 - 3p 2 P 1/2) transition between the 124Xe and 136Xe isotopes was experimentally determined using the electron-beam ion-trap facility at the National Institute of Standards and Technology. The mass-shift and the field-shift coefficients were calculated with enhanced precision by the relativistic many-body perturbation theory and multiconfiguration Dirac-Hartree-Fock method. The mean-square nuclear charge radius difference was found to be δ〈r 2〉136,124 = 0.269(42) fm2. Our result has smaller uncertainty than previous experimental results and agrees with the literature values.

Difference in proton radii of mirror nuclei as a possible surrogate for the neutron skin

It has been recently suggested that differences in the charge radii of mirror nuclei are proportional to the neutron-skin thickness of neutron-rich nuclei and to the slope of the symmetry energy $L$ [B.A. Brown Phys. Rev. Lett. 119, 122502 (2017)]. The determination of the neutron skin has important implications for nuclear physics and astrophysics. Although the use of electroweak probes provides a largely model-independent determination of the neutron skin, the experimental challenges are enormous. Thus, the possibility that differences in the charge radii of mirror nuclei may be used as a surrogate for the neutron skin is a welcome alternative. To test the validity of this assumption we perform calculations based on a set of relativistic energy density functionals that span a wide region of values of $L$. Our results confirm that the difference in charge radii of various neutron-deficient nickel isotopes and their corresponding mirror nuclei is indeed strongly correlated to both the neutron-skin thickness and $L$. Moreover, given that various neutron-star properties are also sensitive to $L$, a data-to-data relation emerges between the difference in charge radii of mirror nuclei and the radius of low-mass neutron stars.

Changes in mean-squared charge radii and magnetic moments of Tl179–184 measured by in-source laser spectroscopy

Hyperfine structure and isotope shifts have been measured for the ground and isomeric states in the neutron-deficient isotopes $^{179--184}\mathrm{Tl}$ using the 276.9-nm transition. The experiment has been performed at the CERN-Isotope Separator On-Line facility using the in-source resonance-ionization laser spectroscopy technique. Spins for the ground states in $^{179,181,183}\mathrm{Tl}$ have been determined as $I=1/2$. Magnetic moments and changes in the nuclear mean-square charge radii have been deduced. By applying the additivity relation for magnetic moments of the odd-odd Tl nuclei the leading configuration assignments were confirmed. A deviation of magnetic moments for isomeric states in $^{182,184}\mathrm{Tl}$ from the trend of the heavier Tl nuclei is observed. The charge radii of the ground states of the isotopes $^{179--184}\mathrm{Tl}$ follow the trend for isotonic (spherical) lead nuclei. The noticeable difference in charge radii for ground and isomeric states of $^{183,184}\mathrm{Tl}$ has been observed, suggesting a larger deformation for the intruder-based $9/{2}^{\ensuremath{-}}$ and ${10}^{\ensuremath{-}}$ states compared to the ground states. An unexpected growth of the isomer shift for $^{183}\mathrm{Tl}$ has been found.

Proton-neutron pairing correlations in the self-conjugate nucleus (38)K probed via a direct measurement of the isomer shift.

A marked difference in the nuclear charge radius was observed between the I^{π}=3^{+} ground state and the I^{π}=0^{+} isomer of ^{38}K and is qualitatively explained using an intuitive picture of proton-neutron pairing. In a high-precision measurement of the isomer shift using bunched-beam collinear laser spectroscopy at CERN-ISOLDE, a change in the mean-square charge radius of ⟨r_{c}^{2}⟩(^{38}K^{m})-⟨r_{c}^{2}⟩(^{38}K^{g})=0.100(6) fm^{2} was obtained. This is an order of magnitude more accurate than the result of a previous indirect measurement from which it was concluded that both long-lived states in ^{38}K have similar charge radii. Our observation leads to a substantially different understanding since the difference in charge radius is, moreover, opposite in sign to previously reported theoretical predictions. It is demonstrated that the observed isomer shift can be reproduced by large-scale shell-model calculations including proton and neutron excitations across the N,Z=20 shell gaps, confirming the significance of cross-shell correlations in the region of ^{40}Ca.

Shell and isospin effects in nuclear charge radii

The shell effect and isospin effect in nuclear charge radii are systematically investigated, and a four-parameter formula is proposed for the description of the root-mean-square (rms) charge radii by combining the shell corrections and deformations of nuclei obtained from the Weizs\"acker-Skyrme mass model. The rms deviation with respect to the 885 measured charge radii falls to 0.022 fm. The proposed formula is also applied for the study of the charge radii of superheavy nuclei and nuclear symmetry energy. The linear relationship between the slope parameter $L$ of the nuclear symmetry energy and the rms charge radius difference of the ${}^{30}\mathrm{S}\ensuremath{-}{}^{30}\mathrm{Si}$ mirror pair is clearly observed. The estimated slope parameter is about $L=54\ifmmode\pm\else\textpm\fi{}19\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ from the coefficient of the isospin term in the proposed charge radius formula.

D1andD2lines in6Li and7Li including QED effects

Accurate theoretical predictions including leading QED corrections for $2^2P_{1/2} - 2^2S_{1/2}$ (D1) and $2^2P_{3/2} - 2^2S_{1/2}$ (D2) transition energies have been obtained for $^{6,7}$Li isotopes. Our results for the Bethe logarithms $\ln k_0(2^2S) = 5.178\,169(4)$, and for mass polarization corrections $\Delta \ln k_0(2^2S) = 0.113\,81(3)$ are in disagreement with ones obtained recently in the literature. In contrast, results $\ln k_0(2^2P) = 5.179\,81(7)$ and $\Delta \ln k_0(2^2P) = 0.111\,3(5)$ are in good agreement with them. From our theoretical predictions and recent measurements of $^{6,7}$Li D-lines at NIST, we determine the mean square charge radius difference between $^7$Li and $^6$Li nuclei, in agreement with determinations based on the $3^2S_{1/2}-2^2S_{1/2}$ transition, what demonstrates consistency of atomic spectroscopy determination of fundamental properties of nuclei.

New Parameters for Nuclear Charge Radius Formulas

Parameters of widely used nuclear rms charge radius formulas have been refitted based on the latest experimental data for about 900 nuclei. It has been seen that the new parameters in the formulas give better results than the previous ones. Besides, an N 1 = 3 -dependent formula has been proposed and discussed. This formula gives effective results for rms charge radius. The standard deviation in all formulas with new parameters are concentrated between 0.1 and 0.1. In other words, for about 90% of nuclei, the differences of charge radii from experimental values are lower than 0.1 fm

Frequency metrology in quantum degenerate helium

We have measured the absolute frequency of the 1557-nm doubly forbidden transition between the two metastable states of helium, 2 3 S 1 (lifetime 8000 s) and 2 1 S 0 (lifetime 20 ms), with 1 kHz precision. With an Einstein coefficient of 10 −7 s −1 this is one of weakest optical transitions ever measured. The measurement was performed in a Bose-Einstein condensate of 4 He* as well as in a Degenerate Fermi Gas of 3 He*, trapped in a crossed dipole trap. From the isotope shift we deduced the nuclear charge radius difference between the α-particle and the helion. Our value differs by 4σ with a very recent result obtained on the 2 3 S → 2 3 P transition.

Charge radii and quadrupole-deformation parameters of high-spin isomers

Experimental data on the differences of charge radii of nuclei in the ground and high-spin isomeric states are surveyed. High-resolution laser-spectroscopy methods were used for measurements. The results obtained for the differences of these radii by two methods—from measurements of isomeric shifts of the levels of atoms containing the nuclei being studied and from measurements of their quadrupole moments in both states under the assumption that the differences of the radii are determined by the difference in their quadrupole deformations—were compared. Two-particle isomers in odd—odd nuclei, isomers formed upon the break of one or several nucleon pairs, and isomers featuring the 1i13/2 configuration of the odd neutron in mercury nuclei were considered. The observed distinctions between the aforementioned differences of charged radii are discussed for isomeric states of different nature.

Relativistic mean-field study for Zn isotopes

The ground-state properties of Zn isotopes have been investigated using the deformed relativistic mean-field (RMF) theory with the NL-SH and TM1 forces. The π-meson and the spatial component of the ω-meson are taken into account. Shell effects in nuclear sizes and neutron skins are well described. Strong deformations are found for most of Zn isotopes. The shape coexistence of prolate-oblate types exists for a high portion of Zn isotopes. The occurrence of the superdeformed minimum in even isotopes is discussed. The π-meson contribution in ground-state properties of odd Zn isotopes is very limited, whereas the spatial component of the ω-meson that couples to the nonzero vector current in deformed odd nuclei gives rise to the degeneracy breaking of the level with opposite spin projections, playing the role of anti-pairing. The anti-pairing role in odd nuclei and pairing correlations with the Bardeen-Cooper-Schrieffer description in even nuclei are important to give the odd-even difference in charge radii, the prediction of the proton drip line, and possible abundance of the halo structure for neutron-rich isotopes.

Electromagnetic form factors of hadrons

Electromagnetic form factors of a variety of hadrons are calculated, using Wilson fermions with SU(3) color on a quenched 24 × 12 × 12 × 24 lattice at β = 5.9, from three-point correlation functions constructed using the lattice conserved vector current. With small errors, the computed pion form factor is consistent with the monopole form suggested by the vector dominance model. Differences in charge radii between hadrons, and the electric and magnetic form factors of nucleons depend on the quark mass in a physically reasonable way.

The K α1 X-ray isotopic shift for 140Ce– 142Ce and the differences in nuclear charge radii of Ce isotopes

The volume isotopic shift of the K α 1 X-rays was measured for 140Ce– 142Ce. From the result ΔE V = 51.4±1.9 meV the difference in the mean square nuclear charge radii was derived: Δ〈 r 2〉 = 0.274 ± 0.010 fm 2. By using this value to normalize optical isotopic shift data, the differences in the charge radii of all stable Ce isotopes are obtained.

Isotopieverschiebung bei (4f–5d) — elektronenünbergängen im Eu-III- u. Eu-II-spektrum und kernradienänderung

Isotopic shifts of + (160 ± 15) and + (168 ± 5) mK were determined for (4 f 7) − (4 f 65 d) and (4 f 7)6 s − (4 f 65 d)6 s transitions in free Eu 2+ and Eu 3+ ions resp. With Mössbauer isometric shift data they now yield more accurate differences in charge radii for excited 151,153Eu nuclei.