Proton Rms Radii Research Articles

Radiative and chiral corrections to elastic lepton-proton scattering in chiral perturbation theory

A unified treatment of both chiral and radiative corrections to the low-energy elastic lepton-proton scattering processes is presented in Heavy Baryon Chiral Perturbations Theory. The proton hadronic chiral corrections include the next-to-next-to leading order corrections whereas the radiative corrections include the next-to-leading order terms in our novel power counting scheme. We find that the net fractional well-defined chiral corrections with respect to the leading order Born cross section can be as large as $10\%$ ($20\%$) for electron (muon) scattering process for MUon proton Scattering Experiment (MUSE) kinematics. We show {\it via} our model-independent treatment of the low-energy lepton-proton kinematics, that the largest theoretical uncertainty is due to the recent different published values of the proton's rms radius while, e.g., the next higher order hadronic chiral terms are expected to give rather nominal errors. For the radiative corrections we demonstrate a systematic order by order cancellation of all infrared singularities and present our finite ultraviolet regularization results. We find that the radiative corrections for muon-proton scattering is of the order of $2\%$, whereas for electron scattering the radiative corrections could be as large as $25\%$. We attribute such a contrasting result partially to the fact that in muon scattering the leading radiative order correction goes through zero in some intermediate low-momentum transfer region, leaving the sub-leading radiative chiral order effects to play a dominant role in this particular kinematic region. For the low-energy MUSE experiment, the often neglected lepton mass as well as the Pauli form factor contributions of the relativistic leptons are incorporated in all our computations.

Microscopic study of shape evolution and some important ground state properties of 190–210Au isotopes

In this paper, we have examined the nuclear structural properties of 190–210Au isotopes within the framework of the Hartree–Fock–Bogoliubov Model. For the theoretical calculations, we have used the UNEDF2 and SKP interactions. The studies include the shape evolution, quadrupole deformation parameter [Formula: see text], nuclear electric quadrupole moment Q(b), single-particle energy levels, the binding energy per nucleon, nuclear charge radius, neutron rms radius, proton rms radius and neutron skin thickness. To analyze the accuracy of our theoretical results, we have presented the comparative analysis with experimental data and finite-range droplet model calculations. The adequate resemblance with experimental data is supporting our studies. We observe the oblate-prolate shape coexistence for 190Au, 193Au and 195Au using the UNEDF2 interaction.

Microscopic study of shape evolution and ground-state properties of Iodine isotopes

In this paper, we investigated the shape evolution and ground-state properties of 108−144I isotopes using Hartree–Fock-Bogoliubov Model while employing the axially deformed single-particle harmonic oscillator basis for the expansion of quasiparticle wave functions. We have used SKP and UNEDF2 models to perform the theoretical calculations. We have presented the shape evolution and final values of the quadrupole deformation parameter β 2 of iodine isotopes. We have used the final values of the β 2 for studying the ground-state properties of the iodine isotopic chain. The investigated ground-state properties are the nuclear electric quadrupole moment, single-particle energy levels, the binding energy per nucleon, pairing energy, one-neutron separation energy, two-neutron separation energy, nuclear charge radius, neutron rms radius, proton rms radius, and neutron skin thickness. After using the SKP parameterization on 109I, we have observed the shape coexistence of prolate and oblate shape. Similarly, after using the UNEDF2 parameterization on 110I, 112I, 114I, 115I, 116I, 117I, 118I, and 119I, we discover the shape coexistence of prolate and oblate shape.

Electroweak probe of neutron skins of nuclei

We describe a program of elastic electron scattering experiments aimed at direct measurements of the neutral weak form factor of nuclei from which the neutron rms radii of nuclei can be extracted with little theoretical ambiguity. The difference between the neutron and proton rms radii, the neutron skin, is intimately related to the density dependence of the symmetry energy in dense nuclear matter which in turn can be related to neutron star parameters such as mass, radius and mass quadrupole polarizability.

A systematic study of the ground state properties of W, Os and Pt isotopes using HFB theory

A systematic study of the ground state properties of transitional nuclei W, Os and Pt is conducted with the help of Skyrme–Hartree–Fock–Bogoliubov theory. Different Skyrme interactions are employed in the study. Two different bases, harmonic oscillator and transformed harmonic oscillator, are used in our investigation. 2[Formula: see text]-separation energy, charge radii, neutron and proton rms radii, neutron skin thickness and deformation parameter have been estimated. The results obtained are in good agreement with the available experimental values.

Ab initio no-core solutions for 6Li

We solve for properties of 6Li in the ab initio no-core full configuration (NCFC) approach and we separately solve for its ground state and resonance with the Gamow shell model (GSM) in the Berggren basis. We employ both the JISP16 and chiral realistic nucleon–nucleon interactions and investigate the ground state energy, excitation energies, point proton root mean square (rms) radius and a suite of electroweak observables. We also extend and test methods to extrapolate the ground state energy, point proton rms radius, and electric quadrupole moment. We attain improved estimates of these observables in the NCFC approach by using basis spaces up through that enable more definitive comparisons with experiment. Using the density matrix renormalization group approach with the JISP16 interaction, we find that we can significantly improve the convergence of the GSM treatment of the 6Li ground state and resonance by adopting a natural orbital single-particle basis.

Advanced nucleon electromagnetic structure model and charge proton rms radius

Description of the nucleon electromagnetic structure by advanced Unitary and Analytic approach, respecting SU(3) symmetry and analyzing also the recent Mainz MAMI data with impact on the proton charge radius to be compared with the results from the muon hydrogen atom spectroscopy.

Investigation of the nuclear properties of 181Ta and 182, 183, 184, 186W structural materials

In this paper, the nuclear ground states properties such as binding energies per particle, charge, neutron and proton rms radii, and charge, neutron and proton density distributions of 181Ta and 182, 183, 184, 186W structural materials for acceleration driven subcritical reactor system have been investigated. Calculations have been performed using Skyrme force parameters, which are based on the nuclear saturation properties, in the Hartree–Fock method. The obtained results have been discussed and compared with the results of experimental and relativistic mean field theory.

Neutron densities from parity-violating elastic electron scattering

We analyze parity-violating elastic electron scattering as a complementary tool for precise determination of neutron densities in nuclei. In particular we discuss how to extract the ratio between neutron and proton rms radii and monopole form factors from theoretical and experimental asymmetries. The structure of the nuclear target is obtained from a Skyrme Hartree-Fock mean field with pairing interactions in BCS approximation. We focus on the parity-violation asymmetry for 208Pb and for 12C as examples of N > Z and N = Z nuclei. In the latter case we study the influence of nuclear isospin mixing by means of the asymmetry deviation. Distorted wave calculations are shown and are compared to plane wave impulse approximation.

The RMS charge radius of the proton and Zemach moments

On the basis of recent precise measurements of the electric form factor of the proton, the Zemach moments, needed as input parameters for the determination of the proton rms radius from the measurement of the Lamb shift in muonic hydrogen, are calculated. It turns out that the new moments give an uncertainty as large as the presently stated error of the recent Lamb shift measurement of Pohl et al. De Rújula's idea of a large Zemach moment in order to reconcile the five standard deviation discrepancy between the muonic Lamb shift determination and the result of electronic experiments is shown to be in clear contradiction with experiment. Alternative explanations are touched upon.

Clustering Structure of 10Be Studied with the Deformed RMF + BCS Method

We investigate the nucleus 10Be using the deformed relativistic mean field (RMF) model and BCS theory. The calculated density distribution suggests two α clusters in the nucleus 10Be. According to BCS theory, the two valence neutrons transit to the first excited state 02+ in a pair and form a 2-n cluster. By comparing the two neutron separation energy (S2n) with the single neutron separation energy (Sn), and analyzing the difference between the neutron and proton rms radii (Rn-Rp) calculated by the deformed RMF, we suggest that 10Be is the best candidate for a two-neutron skin. The two-neutron skin clings to the 2α clusters closely and makes the two α clusters have cross and chain distribution.

Neutron skin deduced from antiprotonic atom data

The relationship between the nucleon density at large radii and the value of the rms radius is investigated in the framework of Skyrme Hartree-Fock and relativistic mean-field models. From a comparison to the charge density we constrain the models in terms of the nuclear matter incompressibility and effective mass properties required to reproduce the density shape. The results are used to extract the rms neutron radius for $^{208}\mathrm{Pb}$ from antiprotonic atom data. The result for the difference between the neutron and proton rms radii, the so-called neutron-skin thickness, is $S=0.20(\ifmmode\pm\else\textpm\fi{}0.04)(\ifmmode\pm\else\textpm\fi{}0.05)$ fm, where $\ifmmode\pm\else\textpm\fi{}0.04$ fm is experimental error from the antiprotonic line width, and $\ifmmode\pm\else\textpm\fi{}0.05$ fm is the theoretical error suggested from the comparison of the models with the experimental charge density.

Proton radii ofHe4,6,8isotopes from high-precision nucleon-nucleon interactions

Recently, precision laser spectroscopy on 6He atoms determined accurately the isotope shift between 4He and 6He and, consequently, the charge radius of 6He. A similar experiment for 8He is under way. We have performed large-scale ab initio calculations for 4,6,8He isotopes using high-precision nucleon-nucleon (NN) interactions within the no-core shell model (NCSM) approach. With the CD-Bonn 2000 NN potential we found point-proton root-mean-square (rms) radii of 4He and 6He 1.45(1) fm and 1.89(4), respectively, in agreement with experiment and predict the 8He point proton rms radius to be 1.88(6) fm. At the same time, our calculations show that the recently developed nonlocal INOY NN potential gives binding energies closer to experiment, but underestimates the charge radii.

Investigation of Exotic Structure of the Largely DeformedNucleus 23Al in the Relativistic-Mean-Field Model

A candidate for proton halo nucleus 23Al is investigatedbased on the constrained calculations in the framework of the deformedrelativistic mean field (RMF) model with the NL075 parameter set.It is shown by the constrained calculations that the ground stateof 23Al has a large deformation that corresponds to the prolateshape. With that large deformation, the non-constrained RMFcalculation predicts that there appears an inversion between the2s1/2 [211] and 1d5/2 [202] shells. The valence protonof 23Al is weakly bound and occupies 2s1/2 [211] and1d5/2 [202] with the weights of 56% and 29%,respectively. The calculated RMS radius for matter is in agreementwith the experimental one. It is also predicted that thedifference between the proton RMS radius and the neutron one isvery large. This suggests that there exists a proton halo in23Al.

Neutron and proton densities and the symmetry energy

The neutron/proton distributions in nuclei, in particular, the n-p difference, are considered in a ``macroscopic'' Thomas-Fermi approach. The density dependence $F(\ensuremath{\rho})$ of the symmetry-energy density, where \ensuremath{\rho} is the total density, drives this difference in the absence of Coulomb and density-gradient contributions when we obtain an explicit solution for the difference in terms of F. If F is constant then the n-p difference and, in particular, the difference $\ensuremath{\delta}R$ between the neutron and proton rms radii are zero. The Coulomb energy and gradient terms are treated variationally. The latter make only a small contribution to the n-p difference, and this is then effectively determined by F. The Coulomb energy reduces $\ensuremath{\delta}R.$ Switching off the Coulomb contribution to the n-p difference then gives the maximum $\ensuremath{\delta}R$ for a given F. Our numerical results are for ${}^{208}\mathrm{Pb}.$ We consider a wide range of F; for these, both $\ensuremath{\delta}R$ and the ratio \ensuremath{\chi} of the surface to volume symmetry-energy coefficient depend, approximately, only on an integral involving ${F}^{\ensuremath{-}1}.$ For $\ensuremath{\delta}R\ensuremath{\lesssim}0.45\mathrm{fm}$ this dependence is one valued and approximately linear for small $\ensuremath{\delta}R,$ and this integral is then effectively determined by $\ensuremath{\delta}R.$ There is a strong correlation between $\ensuremath{\delta}R$ and \ensuremath{\chi}, allowing an approximate determination of \ensuremath{\chi} from $\ensuremath{\delta}R.$ $\ensuremath{\delta}R$ has a maximum of \ensuremath{\cong}0.65 fm.

Proton drip-line nuclei in relativistic Hartree-Bogoliubov theory

Ground-state properties of spherical even-even nuclei $14<~Z<~28$ and $N=18,20,22$ are described in the framework of relativistic Hartree-Bogoliubov (RHB) theory. The model uses the NL3 effective interaction in the mean-field Lagrangian, and describes pairing correlations by the pairing part of the finite range Gogny interaction D1S. Binding energies, two-proton separation energies, and proton rms radii that result from fully self-consistent RHB solutions are compared with experimental data. The model predicts the location of the proton drip line. The isospin dependence of the effective spin-orbit potential is discussed, as well as pairing properties that result from the finite range interaction in the $\mathrm{pp}$ channel.

Comparison of π+ and π− elastic scattering on the isotopic pair 16O 18O in the resonance region

The experimental comparative study of π + and π − elastic scattering from the isotopes 16O and 18O at 163 MeV performed at SIN is analyzed. Complementary information is provided by the measurements of elastic angular distributions on 16O and 18O at several incident pion energies performed at SIN and by the total cross-section difference measurements at LAMPF. Using a momentum-space first-order nonstatic optical potential, we present a study of these data with several phenomenological or theoretical proton and neutron distributions for each isotope. In the framework of the model, the position of the first minima, the relative differences and isotopic shifts for the differential cross sections, as well as the isotopic shifts for the total cross sections are well reproduced by using harmonic oscillator densities with identical neutron and proton distributions for 16O, the same distributions for the proton density in 18O, while the neutron distribution in 18O is more extended by about 0.15 fm, in agreement with theoretical estimates of the difference between the neutron and proton rms radii in 18O. However, almost similar agreement with the data can be obtained with phenomenological densities, where the proton and neutron distributions are identical in each isotope. More precise experiments at several incident pion energies, and probably improved theoretical analyses, are needed before unambiguous conclusions may be extracted.

The difference between neutron and proton radii in the Ca isotopes

We take a close look at the recent analysis of 1 GeV proton scattering on Ca isotopes. Considering the more accurate values of relevant differences of matter and proton rms radii, a value of r n − r p = 0.10 ± 0.03 fm is obtained for 48Ca. This value is much smaller than those quoted recently and is consistent with Coulomb displacement energies.

Random-phase-approximation ground-state correlations and the isotope effect in theCa40andCa48

Ellis's method of constructing the random-phase-approximation ground-state wave function which avoids the earlier dubious and incorrect quasiboson approximation is extended to the N not-equal to Z nuclei. The most important effects arise from the appropriate treatment of the isospin quantum number. In application to the calcium isotopes we find that the calculated relative shift of the proton rms radius from /sup 40/Ca to /sup 48/Ca, R = - 0.35%, for the first time agrees with the high-energy electron scattering result, R = - 0.31%. Excellent agreement is also obtained for the difference of the neutron and proton rms radii in /sup 48/Ca. It should be emphasized, however, that our conclusions concerning the magnitude of the effects on the rms radii due to ground-state correlations are more significant than the detailed comparison with experiment. (AIP)

On the determination of the proton RMS-radius from electron scattering data

It is shown that the proton rms radius should be determined from fitting a polynomial of second order to the low-q 2 form factors. The commonly used polynomial of first order yields radius values which are too small. The proton rms radius has been redetermined from an analysis of the electron scattering data measured at three laboratories. The best fit value is 〈r E 2 〉1/2=0.87±0.02 fm.