Nuclear Charge Radii Research Articles

Nuclear charge radii of molybdenum fission fragments

Radioisotopes of molybdenum have been studied using laser spectroscopy techniques at the IGISOL facility, University of Jyväskylä. Differences in nuclear charge radii have been determined for neutron deficient isotopes 90,91Mo and neutron rich isotopes 102–106,108Mo (and all stable isotopes). A smooth transition in the mean square charge radii is observed as the neutron number increases with no sudden shape change observed in the region around N=60. As N increases, the nuclear deformation appears to go beyond a maximum and a fall off at N=66 is observed. The magnetic moments of the odd isotopes 91,103,105Mo are also determined.

Improved Z1/3 Law of Nuclear Charge Radius

An improved Z1/3 law of nuclear charge radius is presented. The comparison between the calculated and experimental nuclear charge radii now available shows that this new formula is better than the other conventional formulae.

High sensitivity skimmers and non-linear mass dependent fractionation in ICP-MS

A number of prototype high sensitivity skimmers have been developed at Nu Instruments. Signal enhancements of up to a factor of 5 were observed, depending on the element and the sampler–skimmer spacing. However, when using these high sensitivity skimmers, the instrumental mass fractionation for neodymium displayed a large non-linear component that could not be corrected for using the accepted mass fractionation laws. It is proposed that the origin of this non-linear mass fractionation is the formation of NdO+ close to the skimmer surface. The degree of oxide formation, and hence fractionation, is isotope dependent but it is not a linear function of mass. A decrease in the measured xNd/144Nd ratio, relative to standard values, is associated with a concomitant increase in the same ratio in NdO+ (and vice versa). The observed inverse relationship between the metal and oxide species is consistent with mass balance calculations. The magnitude of this effect was dependent on conditions at the skimmer surface (geometry, surface coating, etc.) and could be suppressed by the addition of small amounts of N2 to the carrier gas flow. A simplified energy-resonant ion-atom reaction is postulated to explain these observations, and can be extended to a general model of REE oxide formation in the supersonic expansion. The non-linear fractionation observed also appears to correlate with deviations (from a linear function of mass) in the nuclear charge radii. This is the first evidence of nuclear volume effects contributing to the instrumental mass fractionation in ICP-MS.

Zero-point oscillations and nuclear charge radii

We consider the effects of ground state long-range correlations (LRC), which can be interpreted as zero-point oscillations (ZPO) of collective vibrations, on the charge root mean square (rms) radii, rc, of nuclei. We determine the magnitudes of the contributions of ZPO to rc using the collective model transition densities and the transition strengths obtained from fully self-consistent Hartree–Fock (HF)-based random phase approximation (RPA) calculations. We find that the contributions of ZPO to rc are significant and quite sensitive to the effective nucleon–nucleon interaction used in the calculations. We also demonstrate how the contributions of ZPO to rc are affected by self-consistency violations in the HF-based RPA calculations.

Nuclear quantum Monte Carlo: Expanding into the continuum

I discuss calculations of nuclear properties using the variational Monte-Carlo (VMC) and Green’s function Monte-Carlo (GFMC) methods in combination with realistic two- and three-nucleon interactions. Work to date has emphasized energies of bound and narrow states, and the results agree well with measured masses and energies. We are now directing more effort toward other nuclear properties, including weak decay rates and nuclear charge radii. The main new direction is the computation of low-energy scattering and reaction properties. We have incorporated R-matrix-like boundary conditions into GFMC calculations, and our first calculation of this kind has yielded phase shifts for neutron scattering on 4He up to a few MeV. We find strong dependence of the results on the three-nucleon interaction used.

High Precision Atomic Theory for Li andBe+: QED Shifts and Isotope Shifts

High-precision results are presented for calculations of the nonrelativistic energies, relativistic corrections, and quantum electrodynamic corrections for the 2 2S, 2 2P, and 3 2S states of Li and Be+, using nonrelativistic wave functions expressed in Hylleraas coordinates. Bethe logarithms are obtained for the states of Be+. Finite mass corrections are calculated with sufficient accuracy to extract the nuclear charge radius from measurements of the isotope shift for the 2 2S-2 2P and 2 2S-3 2S transitions. The calculated ionization potential for Be+ is 146 882.923+/-0.005 cm{-1}.

On the coefficients of the liquid drop model mass formulae and nuclear radii

The coefficients of different mass formulae derived from the liquid drop model and including or not the curvature energy, the diffuseness correction to the Coulomb energy, the charge exchange correction term, different forms of the Wigner term and different powers of the relative neutron excess I = ( N − Z ) / A have been determined by a least square fitting procedure to 2027 experimental atomic masses. The Coulomb diffuseness correction Z 2 / A term or the charge exchange correction Z 4 / 3 / A 1 / 3 term plays the main role to improve the accuracy of the mass formula. The Wigner term and the curvature energy can also be used separately for the same purpose. The introduction of an | I | dependence in the surface and volume energies improves slightly the efficiency of the expansion and is more effective than an I 4 dependence. Different expressions reproducing the experimental nuclear charge radius are provided. The different fits lead to a surface energy coefficient of around 17–18 MeV and a relative equivalent rms charge radius r 0 of 1.22–1.23 fm.

Isotope shifts in the spectrum of Pb I

Isotope shifts in twelve atomic lines of Pb I: 401.9 nm (6p6d 3F3→6p2 1D2), 405.8 nm (6p7s 3P1→6p2 3P2), 416.9 nm (6p6d 3F2→6p2 1D2), 434.0 nm (6p7d 3D1→6p2 1S0), 500.6 nm (6p7s 1P1→6p2 1S0), 520.3 nm (6p8s 3P1→6p2 1S0), 589.6 nm (6p8p 3D1→6p7s 3P0), 600.2 nm (6p8p 3D2→6p7s 3P1), 601.2 nm (6p8p 3D1→6p7s 3P1), 605.9 nm (6p8p 3P0→6p7s 3P1), 611.0 nm (6p8p 3P1→6p7s 3P0) and 723.1 nm (6p7s 3P1→6p2 1D2) have been measured. As a light source the discharge tube was used. The high resolution spectral apparatus consisted of a silver coated Fabry–Perot etalon and a grating spectrograph combined with a CCD camera used as a detector. In the analysis of the spectra a computer simulation technique was used. Our studies enabled us to separate the mass and the field effects and to determine values of changes of the mean square nuclear charge radii.

Nuclear Charge Radius ofHe8

The root-mean-square (rms) nuclear charge radius of ^8He, the most neutron-rich of all particle-stable nuclei, has been determined for the first time to be 1.93(3) fm. In addition, the rms charge radius of ^6He was measured to be 2.068(11) fm, in excellent agreement with a previous result. The significant reduction in charge radius from ^6He to ^8He is an indication of the change in the correlations of the excess neutrons and is consistent with the ^8He neutron halo structure. The experiment was based on laser spectroscopy of individual helium atoms cooled and confined in a magneto-optical trap. Charge radii were extracted from the measured isotope shifts with the help of precision atomic theory calculations.

Nuclear moments and charge radii of argon isotopes between the neutron-shell closures [formula omitted] and [formula omitted

We report the measurement of optical isotope shifts for 40–44Ar relative to 38Ar from which changes in the mean square nuclear charge radii across the 1 f 7 / 2 neutron shell are deduced. In addition, the hyperfine structure of 41Ar and 43Ar yields the spins, magnetic dipole and electric quadrupole moments, in particular the spin I = 5 / 2 for 43Ar. The investigations were carried out by fast-beam collinear laser spectroscopy using highly sensitive detection based on optical pumping and state-selective collisional ionization. Mean square charge radii are now known from 32Ar to 46Ar, covering sd-shell as well as f 7 / 2 -shell nuclei. They are discussed in the framework of spherical SGII Skyrme-type Hartree–Fock calculations, semi-empirically corrected for quadrupole core polarization. The Zamick–Talmi formula excellently describes the charge radii across the f 7 / 2 neutron shell, as it does for the neighbouring elements. The new data on Ar, in addition to those on K, Ca and Ti, provide an extended overview of nuclear radii trends around Z = 20 and between N = 20 and N = 28 . Characteristic features are discussed, the most striking being the absence of any isotopic shell effect in the radii at N = 20 .

Properties of halo nuclei from atomic isotope shifts

This paper reviews progress that has been made in obtaining essentially exact solutions to the nonrelativistic three-body problem for helium by a combination of variational and asymptotic expansion methods. The calculation of relativistic and quantum electrodynamic corrections by perturbation theory is discussed, and in particular, methods for the accurate calculation of the Bethe logarithm part of the electron self energy are presented. As an example, the results are applied to the calculation of isotope shifts for the short-lived 'halo' nucleus 6 He relative to 4 He in order to determine the nuclear charge radius of 6 He from high precision spectroscopic measurements carried out at the Argonne National Laboratory. The results demonstrate that the high precision that is now available from atomic theory is creating new opportunities to create novel measurement tools, and helium, along with hydrogen, can be regarded as a fundamental atomic system whose spectrum is well understood for all practical purposes.

Ionization energy ofLi6,7determined by triple-resonance laser spectroscopy

Rydberg level energies for $^{7}\mathrm{Li}$ were measured using triple-resonance laser excitation, followed by drifted field ionization. In addition to the principal $n\phantom{\rule{0.2em}{0ex}}^{2}P$ series, weak Stark mixing from residual electric fields allowed observation of $n\phantom{\rule{0.2em}{0ex}}^{2}S$ and hydrogenic Stark manifold series at higher $n$. Limit analyses for the series yield the spectroscopic ionization energy ${E}_{I}(^{7}\mathrm{Li})=43\phantom{\rule{0.2em}{0ex}}487.159\phantom{\rule{0.2em}{0ex}}40(18)\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$. The $^{6,7}\mathrm{Li}$ isotope shift (IS) was measured in selected $n\phantom{\rule{0.2em}{0ex}}^{2}P$ Rydberg levels and extrapolation to the series limit yields $\mathrm{IS}{({E}_{I})}^{7,6}=18\phantom{\rule{0.2em}{0ex}}067.54(21)\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$. Results are compared with recent theoretical calculations: ${E}_{I}$ values from experiment and theory agree to within $0.0011\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, with the remaining discrepancy comparable to uncertainty in QED corrections of order ${\ensuremath{\alpha}}^{4}Ry$. The difference between experiment and calculated mass-based $\mathrm{IS}({E}_{I})$ yields a change in nuclear charge radii between the two isotopes $\ensuremath{\delta}{⟨{r}^{2}⟩}^{7,6}=\ensuremath{-}0.60(10)\phantom{\rule{0.3em}{0ex}}{\mathrm{fm}}^{2}$.

Nuclear polarizability of helium isotopes in atomic transitions

We estimate the nuclear polarizability correction to atomic transition frequencies in various helium isotopes. This effect is non-negligible for high precision tests of quantum electrodynamics or accurate determination of the nuclear charge radius from spectroscopic measurements in helium atoms and ions. In particular, it amounts to $28(3)$ kHz for 1S-2S transition in 4He+.

Signs of dynamical effects for Cd, Sn, Te, Xe, Ba and Sm nuclear charge radii

The experimental charge radius values along Cd, Sn, Te, Xe, Ba and Sm isotopic series have been extracted from isotope shift measurements using different methods to calibrate the electronic factor and mass shift effects. Static and dynamic charge radii have been calculated in the framework of a microscopic configuration mixing approach on the ground of Hartree–Fock–Bogoliubov solutions obtained with the D1S Gogny effective nucleon–nucleon interaction. Low-energy spectroscopic observables have also been obtained. The theoretical and experimental results are compared and discussed. It is shown that dynamical effects must be taken into account especially for γ-soft and weakly deformed nuclei.

Isotope shifts and fine structures ofLi6,7Dlines and determination of the relative nuclear charge radius

The $^{6,7}\mathrm{Li}\phantom{\rule{0.3em}{0ex}}D$ lines were excited using an electro-optically modulated cw dye laser that intersected an atomic beam. Fluorescence was recorded as the laser was scanned across the resonance. Hence each transition was multiply excited allowing for calibration of the frequency scan. The $^{6,7}\mathrm{Li}\phantom{\rule{0.3em}{0ex}}2P$ fine structures were found to be $10\phantom{\rule{0.2em}{0ex}}052.964\ifmmode\pm\else\textpm\fi{}0.050$ and $10\phantom{\rule{0.2em}{0ex}}053.119\ifmmode\pm\else\textpm\fi{}0.058\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$. The $D1$ and $D2$ isotope shifts were determined to be $10\phantom{\rule{0.2em}{0ex}}534.039\ifmmode\pm\else\textpm\fi{}0.070$ and $10\phantom{\rule{0.2em}{0ex}}534.194\ifmmode\pm\else\textpm\fi{}0.104\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$. The latter imply values for the $^{6,7}\mathrm{Li}$ relative nuclear charge radius that are within $20\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\phantom{\rule{0.3em}{0ex}}\mathrm{fm}$ of each other, which is consistent with the estimated uncertainties.

Nuclear charge radius of 11Li

We have determined the nuclear charge radius of 11Li by high-precision laser spectroscopy. The experiment was performed at the TRIUMF-ISAC facility where the 7Li-11Li isotope shift (IS) was measured in the 2s→3s electronic transition using Doppler-free two-photon spectroscopy with a relative accuracy better than 10−5. The accuracy for the IS of the other lithium isotopes was also improved. IS’s are mainly caused by differences in nuclear mass, but changes in proton distribution also give small contributions. Comparing experimentally measured IS with advanced atomic calculation of purely mass-based shifts, including QED and relativistic effects, allows derivation of the nuclear charge radii. The radii are found to decrease monotonically from 6Li to 9Li, and then increase with 11Li about 11% larger than 9Li. These results are a benchmark for the open question as to whether nuclear core excitation by halo neutrons is necessary to explain the large nuclear matter radius of 11Li; thus, the results are compared with a number of nuclear structure models.

New Mass Value forLi7

A high-accuracy mass measurement of $^{7}\mathrm{Li}$ was performed with the SMILETRAP Penning-trap mass spectrometer via a cyclotron frequency comparison of $^{7}\mathrm{Li}^{3+}$ and $\mathrm{H}_{2}{}^{+}$. A new atomic-mass value of $^{7}\mathrm{Li}$ has been determined to be $7.016\text{ }003\text{ }425\text{ }6(45)\text{ }\text{ }\mathrm{u}$ with a relative uncertainty of 0.63 ppb. It has uncovered a discrepancy as large as $14\ensuremath{\sigma}$ ($1.1\text{ }\text{ }\ensuremath{\mu}\mathrm{u}$) deviation relative to the literature value given in the Atomic-Mass Evaluation AME 2003. The importance of the improved and revised $^{7}\mathrm{Li}$ mass value, for calibration purposes in nuclear-charge radii and atomic-mass measurements of the neutron halos $^{9}\mathrm{Li}$ and $^{11}\mathrm{Li}$, is discussed.

Nuclear Charge Radii ofLi9,11: The Influence of Halo Neutrons

The nuclear charge radius of 11Li has been determined for the first time by high-precision laser spectroscopy. On-line measurements at TRIUMF-ISAC yielded a 7Li-11Li isotope shift (IS) of 25 101.23(13) MHz for the Doppler-free [FORMULA: SEE TEXT]transition. IS accuracy for all other bound Li isotopes was also improved. Differences from calculated mass-based IS yield values for change in charge radius along the isotope chain. The charge radius decreases monotonically from 6Li to 9Li, and then increases from 2.217(35) to 2.467(37) fm for 11Li. This is compared to various models, and it is found that a combination of halo neutron correlation and intrinsic core excitation best reproduces the experimental results.

Hyperfine structure and isotope shift study in singly ionized lead

Hyperfine structure and isotope shifts in five optical transitions: 424.5 nm (\(6s^25f\ ^2\textrm{F}_{7/2}\)–\(6s^26d^2\ \textrm{D}_{5/2}\)), 537.2 nm (\(6s^25f\ ^2\textrm{F}_{7/2}\)–\(6s6p^2\ ^4\textrm{P}_{5/2}\)), 554.5 nm (\(6s^27d\ ^2\textrm{D}_{5/2}\)–\(6s^27p\ ^2\textrm{P}_{3/2}\)), 560.9 nm (\(6s^27p^2\ \textrm{P}_{3/2}\)–\(6s^27s\ ^2\textrm{S}_{1/2}\)) and 666.0 nm (\(6s^27p\ ^2\textrm{P}_{1/2}\)–\(6s^27s\ ^2\textrm{S}_{1/2}\)) of Pb II have been measured. As a light source the discharge tube was used. The hyperfine structure measurements were performed using metallic isotope 207Pb. For isotope shifts measurements natural lead was used. The high resolution spectral apparatus consisted of a silver coated Fabry-Perot etalon and a grating spectrograph combined with a CCD camera used as a detector. In the analysis of the spectra a computer simulation technique was used. The hyperfine structure observations yielded the splitting constants A for seven levels of Pb II. The isotope shift studies enabled to separate the mass and the field shifts and to determine values of changes of the mean square nuclear charge radii.

Calculation of isotope shifts for cesium and francium

We perform ab initio calculations of isotope shifts for isotopes of cesium (from $A=123$ to $A=137$) and francium (from $A=207$ to $A=228$). These calculations start from the relativistic Hartree-Fock method and make use of several techniques to include correlations. The field (volume) isotope shift is calculated by means of an all-order correlation potential method and within the singles-doubles--partial-triples linearized coupled-cluster approach. Many-body perturbation theory in two different formulations is used to calculate the specific mass shift. We discuss the strong points and shortcomings of the different approaches and implications for parity nonconservation in atoms. Changes in nuclear charge radii are found by comparing the present calculations with experiment.