Nuclear charge distribution of41Ca

The mean square nuclear charge radius of⁴¹Ca equals the one of double magic⁴⁰Ca within 0.006 fm.     

Properties of nuclear matter andN=Z closed-shell nuclei

A simple three-parameter density dependent effective interaction is used to study the properties of nuclear matter, neutron matter and some bulk properties such as ground state energies and rms charge radii of three double-closed shell nuclei⁴He,¹⁶O and⁴⁰Ca. The three parameters of the effective interaction are determined by requiring to fit the binding energy and density of infinite nuclear matter at saturation density as well as ground state energy of¹⁶O in the first order perturbation theory. This interaction gives correct saturation in nuclear matter with a value of 283 MeV for compressibility. The symmetry coefficienta _T atk _F=1·36 fm^–1 is 28·58 MeV. The energy per particle in neutron matter is calculated in the range of nuclear matter densities and it compares well with those ofNemeth andSprung. Groundstate energies and rms charge radii of⁴He,¹⁶O and⁴⁰Ca are calculated using oscillator eigen functions as single particle wave functions. Results for ground state energies are in good agreement with empirical values and rms charge radii are slightly better than those obtained byMoszkowski with the MDI.The authors are thankful to the Computer Centre, Utkal University, Bhubaneswar for providing computational facilities for this work.     

On the Yrast levels of106–108Sn

The isotope shift in the Ca-intercombination line withλ=6,573 Å was measured for all isotopes between⁴⁰Ca and⁴⁸Ca with the only exception of 47Ca. The combination of the results with muonic x-ray data yields highly accurate values for the changes of the mean square nuclear charge radii. In addition, the nuclear quadrupole moments of the three isotopes⁴¹Ca,⁴³Ca and⁴⁵Ca have been determined from the hyperfine structure splitting of the 4s 4p ³ P ₁ state.     

Charge Radii of Argon Isotopes in the f7/2 Shell and Radii Systematics in the Ca-Region

Changes in mean square (ms) nuclear charge radii of Ar isotopes across the 1f_7/2 shell are studied by fast-beam collinear laser spectroscopy using an ultra-sensitive detection method based on optical pumping and state-selective collisional ionization. The new data set on Ar, in combination with the known charge radii of K, Ca and Ti in the ν1f_7/2 shell, offers an opportunity to obtain a more complete overview of nuclear radii trends around the proton shell closure Z = 20 and between the neutron shell closures N = 20 and N = 28.     

The beta-decay of95Rb and97Rb

In this paper the spectra ofα particles emitted in (p, α) reactions induced by ～24 MeV protons on adjacent target nuclei, onemagic, with a magic neutron or proton shell and the othernear magic, with one more nucleon outside the shell, are measured and compared. The nuclei investigated are^{90, 91}Zr,¹²²Sn,¹²³Sb,^{142, 143, 144}Nd,²⁰⁸Pb and²⁰⁹Bi. The weak population of low energy levels of the residual nucleus from thenear magic target nucleus and the excitation of homologous states in the residual nuclei from neighbouringmagic andnear magic target nuclei convincingly prove that in most of the cases the unpaired nucleon outside the magic shell acts as a spectator in the process. The implications of these experimental findings are discussed.     

Elastic scattering of 32S on 24Mg, 27Al and 40Ca and the effect of nuclear forces on the grazing collision

Elastic scattering of ³²S ions on ²⁴Mg, ²⁷Al and ⁴⁰Ca has been measured at energies between 67 MeV and 120 MeV. Angular distributions were analyzed with the optical model with Woods-Saxon potentials. Strong absorption radii are extracted with and without consideration of the nuclear interaction at the surface. The nuclear potential decreases the otherwise anomalously large strong absorption radii which can then be described by a radius parameter of r₀ = 1.41 fm.     

Two-body and three-body effective interactions in nuclei

Finite-range two-body and zero-range three-body effective forces for use in spin unsaturated systems are determined so as to reproduce the total binding energies, rms radii, and single-particle energies of ¹⁶O, ⁴⁰Ca, ⁴⁸Ca and ⁹⁰Zr; the saturation of nuclear matter; and experimental two-body matrix elements extracted by Schiffer and True. In addition to the Skyrme three-body force which acts only in spatially even states, a spatially odd force is introduced to obtain sufficient generality. The Landau parameters and the effective mass specified by this force are also discussed.     

Isotopic dependence of the nuclear charge radii and binding energies in the relativistic Hartree-Fock formalism

Relativistic nonlinear models based on the Hartree and Hartree-Fock approximations, including the σ, ω, π, and ρ mesons, are worked out to explore the behavior of the nuclear charge radii and the binding energies of several isotopic chains. We find a correlation between the magnitude of the anomalous kink effect (KE) in the Pb isotopic family and the compressibility modulus (K) of nuclear matter. The KE appears to be sensitive, in particular, to the mechanisms which control the K value. The influence of the symmetry energy on the Ca isotopic chain is also studied. The behavior of the charge radii of single-particle states for some special cases and its repercussion on the nuclear charge radius is analyzed. The effect of pairing correlations on the models improves considerably the quality of the results in both binding energy and KE.     

Discrete ambiguity in the experimental 40Ca charge density

Elastic electron scattering and muonic X-ray data are used to determine the ⁴⁰Ca charge density in a model-independent manner. A discrete ambiguity of ρ(r) at small radii is discovered. An analysis of ³⁹K and ⁴⁸Ca data does not allow to remove this ambiguity.     

Odd-even staggering in nuclear charge radii of neutron-rich europium isotopes

Nuclear magnetic dipole and electric quadrupole moments and changes in mean square charge radii for the neutron-rich^155–159Eu isotopes have been measured using resonance ionization spectroscopy at the IRIS facility. It has been found that the isotopes withN>92, unlike the isotopes with 89≦N≦92, have an ordinary character of odd-even staggering in nuclear charge radii. This means that the octupole deformation attributed previously to the europium nuclei around¹⁵⁴Eu does not display itself in the charge radii of heavier europium isotopes.     

Nuclear Rms charge radii from relative electron scattering measurements at low energies

The nuclear rms charge radii measured by low energy electron scattering at Darmstadt are summarized. Improvements in the experimental equipment and method permitted a redetermination of the¹²C radius which yieldedR _m (¹²C)=2.462 ± 0.022fm. This value has been used to recalibrate the radii measured relative to¹²C.     

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.     

Self-consistent hartree description of finite nuclei in a relativistic quantum field theory

Relativistic Hartree equations for spherical nuclei are derived from a relativistic nuclear quantum field theory using a coordinate-space Green function approach. The renormalizable field theory lagrangian includes the interaction of nucleons with σ, ω, ρ and π mesons and the photon. The Hartree equations represent the “mean-field” approximation for a finite nuclear system. Coupling constants and the σ-meson mass are determined from the properties of nuclear matter and the rms charge radius in ⁴⁰Ca, and pionic contributions are absent for static, closed-shell nuclei. Calculated charge densities, neutron densities, rms radii, and single-nucleon energy levels throughout the periodic table are compared with data and with results of non-relativistic calculations. Relativistic Hartree results agree with experiment at a level comparable to that of the most sophisticated non-relativistic calculations to date. It is shown that the Lorentz covariance of the relativistic formalism leads naturally to density-dependent interactions between nucleons. Furthermore, non-relativistic reduction reveals non-central and non-local aspects inherent in the Hartree formalism. The success of this simple relativistic Hartree approach is attributed to these features of the interaction.     

Oscillator parameters in nuclei

The dependence on nucleon numbers of the harmonic oscillator length parameter b or energy spacing ℏω in nuclei is determined, using an extensive tabulation of nuclear charge radii and an empirical expression for the difference between proton and neutron radii. Various possible constraints on the parameters or radii are discussed. Alternative parametrizations are compared and a preferred “universal” parametrization is proposed. It is argued that the established Blomqvist–Molinari formula is perfectly adequate for determining the oscillator parameter for specific applications.     

Rotational bands in 169Re

Based on the systematic investigation of the data available for nuclei with A≥ 40, a Z ^1/3-dependence for the nuclear charge radii is shown to be superior to the generally accepted A ^1/3 law. A delicate scattering of data around R _c/Z ^1/3 is inferred as owing to the isospin effect and a linear dependence of R _c/Z ^1/3 on N/Z (or (N - Z)/2) is found. This inference is well supported by the microscopic Relativistic Continuum Hartree-Bogoliubov (RCHB) calculation conducted for the proton magic Ca, Ni, Zr, Sn and Pb isotopes including the exotic nuclei close to the neutron drip line. With the linear isospin dependence provided by the data and RCHB theory, a new isospin-dependent Z ^1/3 formula for the nuclear charge radii is proposed. Received: 23 September 2001 / Accepted: 21 January 2002     

Charge radii of high-spin isomers measured using laser spectroscopy methods

The overview of experimental data on charge radii differences between the ground and the high-spin isomeric states is presented. Methods of high-resolution laser spectroscopy were used for measurements. Charge radii differences obtained in two ways are compared: from measurements of isomeric shifts of atomic levels of nuclei under study and from measurements of quadrupole moments in both states under the assumption that the radii differences are determined by the difference of their quadrupole deformations. Isomers formed at a rupture of one or several nucleon pairs and isomers with the configuration of the odd neutron 1h _11/2 for the nuclear region Cd-Ba and 1i _13/2 for the region Hg-Pb are considered. Observed deviations of the above charge radii differences for isomeric states of a different nature are discussed.     

First Measurement of the Nuclear Charge Radii of Short-Lived Lithium Isotopes

A novel method for the determination of nuclear charge radii of lithium isotopes is presented. Precise laser spectroscopic measurements of the isotope shift in the lithium 2s → 3s transition are combined with highly accurate atomic physics calculation of the mass dependent isotope shift to extract the charge-distribution-sensitive information. This approach has been used to determine the charge radii of ^8,9Li for the first time.     

Developments at the SLOWRI facility at RIKEN: precision optical spectroscopy of 7,9,10,11Be+ ions

Precision optical spectroscopy of radioactive Be isotopes produced in projectile fragmentation has been performed for the first time at the prototype SLOWRI facility of RIKEN RI-Beam Factory. The ground state hyperfine constants of ⁷Be⁺ and ¹¹Be⁺ were determined with relative accuracies of 6 × 10^?7 and 3 × 10^?8, respectively, by laser-microwave double resonance spectroscopy of laser-cooled ions in a trap. The optical transition energies from the ground S-state to the excited P-state of Be isotope ions were also measured to determine the nuclear charge radii from the isotope shifts. Development of the universal slow RI-beam facility??SLOWRI??based on the rf-carpet ion guide technique is progressing at RIKEN RI-beam factory. An additional capability of providing parasitic slow RI-beams from the projectile fragment separator BigRIPS is also discussed.     

Nuclear mass form factors from coherent photoproduction of πmesons

Data for coherent photoproduction of π⁰ mesons from nuclei ( ¹²C, ⁴⁰Ca, ⁹³Nb, ^natPb), recently measured with the TAPS detector at the Mainz MAMI accelerator, have been analyzed in view of the mass form factors of the nuclei. The form factors have been extracted in plane-wave approximation of the A(γ,π⁰)A reaction and corrected for final-state interaction effects with the help of distorted-wave impulse approximations. Nuclear mass rms radii have been calculated from the slope of the form factors for q² → 0. Furthermore, the Helm model (hard-sphere form factor folded with Gaussian) was used to extract diffraction radii from the zeroes of the form factor and skin thicknesses from the position and height of its first maximum. The diffraction radii from the Helm model agree with the corresponding charge radii obtained from electron scattering experiments within their uncertainties of a few per cent. The rms radii from the slope of the form factors are systematically lower by up to 5% for PWIA and up to 10% for DWIA. Also the skin thicknesses extracted from the Helm model are systematically smaller than their charge counterparts.