Nucleon Charge and Magnetization Densities from Sachs Form Factors

Relativistic prescriptions relating Sachs form factors to nucleon charge and magnetization densities are used to fit recent data for both the proton and the neutron. The analysis uses expansions in complete radial bases to minimize model dependence and to estimate the uncertainties in radial densities due to limitation of the range of momentum transfer. We find that the charge distribution for the proton is significantly broad than its magnetization density and that the magnetization density is slightly broader for the neutron than the proton. The neutron charge form factor is consistent with the Galster parametrization over the available range of Q^2, but relativistic inversion produces a softer radial density. Discrete ambiguities in the inversion method are analyzed in detail. The method of Mitra and Kumari ensures compatibility with pQCD and is most useful for extrapolating form factors to large Q^2.Comment: To appear in Phys. Rev. C. Two new figures and accompanying text have been added and several discussions have been clarified with no significant changes to the conclusions. Now contains 47 pages including 21 figures and 2 table

Nuclear Charge Radius of 12^{12}Be

The nuclear charge radius of $^{12}$Be was precisely determined using the technique of collinear laser spectroscopy on the $2s_{1/2}\rightarrow 2p_{1/2, 3/2}$ transition in the Be$^{+}$ ion. The mean square charge radius increases from $^{10}$Be to $^{12}$Be by \delta ^{10,12} = 0.69(5) \fm^{2} compared to \delta ^{10,11} = 0.49(5) \fm^{2} for the one-neutron halo isotope $^{11}$Be. Calculations in the fermionic molecular dynamics approach show a strong sensitivity of the charge radius to the structure of $^{12}$Be. The experimental charge radius is consistent with a breakdown of the N=8 shell closure.Comment: 5 pages, 3 figure

Study of the effect of the tensor correlation in oxygen isotopes with the charge- and parity-projected Hartree-Fock method

Recently, we developed a mean-field-type framework which treats the correlation induced by the tensor force. To exploit the tensor correlation we introduce single-particle states with the parity and charge mixing. To make a total wave function have a definite charge number and a good parity, the charge number and parity projections are performed. Taking a variation of the projected wave function with respect to single-particle states a Hartree-Fock-like equation, the charge- and parity-projected Hartree-Fock equation, is obtained. In the charge- and parity-projected Hartree-Fock method, we solve the equation selfconsistently. In this paper we extend the charge- and parity-projected Hartree-Fock method to include a three-body force, which is important to reproduce the saturation property of nuclei in mean-field frameworks. We apply the charge- and parity-projected Hartree-Fock method to sub-closed-shell oxygen isotopes (14O, 16O, 22O, 24O, and 28O) to study the effect of the tenor correlation and its dependence on neutron numbers. We obtain reasonable binding energies and matter radii for these nuclei. It is found that relatively large energy gains come from the tensor force in these isotopes and there is the blocking effect by occupied neutron orbits on the tensor correlation

Atomic Parity Nonconservation: Electroweak Parameters and Nuclear Structure

There have been suggestions to measure atomic parity nonconservation (PNC) along an isotopic chain, by taking ratios of observables in order to cancel complicated atomic structure effects. Precise atomic PNC measurements could make a significant contribution to tests of the Standard Model at the level of one loop radiative corrections. However, the results also depend upon certain features of nuclear structure, such as the spatial distribution of neutrons in the nucleus. To examine the sensitivity to nuclear structure, we consider the case of Pb isotopes using various recent relativistic and non-relativistic nuclear model calculations. Contributions from nucleon internal weak structure are included, but found to be fairly negligible. The spread among present models in predicted sizes of nuclear structure effects may preclude using Pb isotope ratios to test the Standard Model at better than a one percent level, unless there are adequate independent tests of the nuclear models by various alternative strong and electroweak nuclear probes. On the other hand, sufficiently accurate atomic PNC experiments would provide a unique method to measure neutron distributions in heavy nuclei.Comment: 44 pages, INT Preprint DOE/ER/40561-050-INT92-00-1

Charge- and parity-projected Hartree-Fock method for the strong tensor correlation and its application to the alpha particle

We propose a new mean-field-type framework which can treat the strong correlation induced by the tensor force. To treat the tensor correlation we break the charge and parity symmetries of a single-particle state and restore these symmetries of the total system by the projection method. We perform the charge and parity projections before variation and obtain a Hartree-Fock-like equation, which is solved self-consistently. We apply the Hartree-Fock-like equation to the alpha particle and find that by breaking the parity and charge symmetries, the correlation induced by the tensor force is obtained in the projected mean-field framework. We emphasize that the projection before the variation is important to pick up the tensor correlation in the present framework.Comment: 21 pages, 2 figure

Consistent description of nuclear charge radii and electric monopole transitions

A systematic study of energy spectra throughout the rare-earth region (even-even nuclei from $_{58}$Ce to $_{74}$W) is carried out in the framework of the interacting boson model (IBM), leading to an accurate description of the spherical-to-deformed shape transition in the different isotopic chains. The resulting IBM Hamiltonians are then used for the calculation of nuclear charge radii (including isotope and isomer shifts) and electric monopole transitions with consistent operators for the two observables. The main conclusion of this study is that an IBM description of charge radii and electric monopole transitions is possible for most of the nuclei considered but that it breaks down in the tungsten isotopes. It is suggested that this failure is related to hexadecapole deformation.Comment: 13 pages, 5 tables, 3 figures, accepted for publication in Physical Review

Quasiparticle Random Phase Approximation with Interactions from the Similarity Renormalization Group

We have developed a fully consistent framework for calculations in the Quasiparticle Random Phase Approximation (QRPA) with $NN$ interactions from the Similarity Renormalization Group (SRG) and other unitary transformations of realistic interactions. The consistency of our calculations, which use the same Hamiltonian to determine the Hartree-Fock-Bogoliubov (HFB) ground states and the residual interaction for QRPA, guarantees an excellent decoupling of spurious strength, without the need for empirical corrections. While work is under way to include SRG-evolved 3N interactions, we presently account for some 3N effects by means of a linearly density-dependent interaction, whose strength is adjusted to reproduce the charge radii of closed-shell nuclei across the whole nuclear chart. As a first application, we perform a survey of the monopole, dipole, and quadrupole response of the calcium isotopic chain and of the underlying single-particle spectra, focusing on how their properties depend on the SRG parameter $\lambda$. Unrealistic spin-orbit splittings suggest that spin-orbit terms from the 3N interaction are called for. Nevertheless, our general findings are comparable to results from phenomenological QRPA calculations using Skyrme or Gogny energy density functionals. Potentially interesting phenomena related to low-lying strength warrant more systematic investigations in the future.Comment: 18 pages, 17 figures, 3 tables (RevTeX 4.1), v2: fixed typos & figures, as publishe

Mean Field Theoretical Structure of He and Be Isotopes

The structures of He and Be even-even isotopes are investigated using an axially symmetric Hartree-Fock approach with a Skyrme-IIIls mean field potential. In these simple HF calculations, He and Be isotopes appear to be prolate in their ground states and Be isotopes have oblate shape isomeric states. It is also shown that there exists a level crossing when the nuclear shape changes from the prolate state to the oblate state. The single neutron levels of Be isotopes exhibit a neutron magic number 6 instead of 8 and show that the level inversion between 1/2- and 1/2+ levels occurs only for a largely deformed isotope. Protons are bound stronger in the isotope with more neutrons while neutron levels are somewhat insensitive to the number of neutrons and thus the nuclear size and also the neutron skin become larger as the neutron number increases. In these simple calculations with Skyrme-IIIls interaction no system with a clear indication of neutron halo was found among He and Be isotopes. Instead of it we have found 8He+2n, 2n+8He+2n, and 16Be+2n like chain structures with clusters of two correlated neutrons. It is also shown that 8He and 14Be in their ground states are below the neutron drip line in which all nucleons are bound with negative energy and that 16Be in its ground state is beyond the neutron drip line with two neutrons in positive energy levels.Comment: CM energy correction, 1 figure and more discussions adde

Impact of spin-orbit currents on the electroweak skin of neutron-rich nuclei

Background: Measurements of neutron radii provide important constraints on the isovector sector of nuclear density functionals and offer vital guidance in areas as diverse as atomic parity violation, heavy-ion collisions, and neutron-star structure. Purpose: To assess the impact of spin-orbit currents on the electromagnetic- and weak-charge radii of a variety of nuclei. Special emphasis is placed on the experimentally accessible electroweak skin, defined as the difference between weak-charge and electromagnetic-charge radii. Methods: Two accurately calibrated relativistic mean field models are used to compute proton, neutron, charge, and weak-charge radii of a variety of nuclei. Results: We find that spin-orbit contributions to the electroweak skin of light neutron-rich nuclei, such as 22O and 48Ca, are significant and result in a substantial increase in the size of the electroweak skin relative to the neutron skin. Conclusions: Given that spin-orbit contributions to both the charge and weak-charge radii of nuclei are often as large as present or anticipated experimental error bars, future calculations must incorporate spin-orbit currents in the calculation of electroweak form factors.Comment: 17 pages, 2 figures, and 2 table

Quark Coulomb Interactions and the Mass Difference of Mirror Nuclei

We study the Okamoto-Nolen-Schiffer (ONS) anomaly in the binding energy of mirror nuclei at high density by adding a single neutron or proton to a quark gluon plasma. In this high-density limit we find an anomaly equal to two-thirds of the Coulomb exchange energy of a proton. This effect is dominated by quark electromagnetic interactions---rather than by the up-down quark mass difference. At normal density we calculate the Coulomb energy of neutron matter using a string-flip quark model. We find a nonzero Coulomb energy because of the neutron's charged constituents. This effect could make a significant contribution to the ONS anomaly.Comment: 4 pages, 2 figs. sub. to Phys. Rev. Let