Density Distributions Of Nuclei Research Articles

Υ and ηb nuclear bound states

$\mathrm{\ensuremath{\Upsilon}}$ and ${\ensuremath{\eta}}_{b}$ nuclear bound-state energies are calculated for various nuclei, neglecting any possible effects of the widths. Essential input for the calculations, namely, the medium-modified $B$ and ${B}^{*}$ meson masses, as well as the density distributions in nuclei, are calculated within the quark-meson coupling (QMC) model. The attractive potentials for the $\mathrm{\ensuremath{\Upsilon}}$ and ${\ensuremath{\eta}}_{b}$ mesons in nuclei are calculated from the mass shifts of these mesons in nuclear matter in the local density approximation. These potentials originate from the in-medium enhanced $BB$ and $B{B}^{*}$ loops in their respective self-energy. After an extensive analysis we conclude that our results suggest that the $\mathrm{\ensuremath{\Upsilon}}$ and ${\ensuremath{\eta}}_{b}$ mesons should form bound states with all the nuclei considered.

ηc-nucleus bound states

ηc-nucleus bound state energies are calculated for various nuclei. Essential input for the calculations, namely the medium-modified D and D⁎ meson masses, as well as the density distributions in nuclei, are calculated within the quark-meson coupling (QMC) model. The attractive potentials for the ηc meson in the nuclear medium originate from the in-medium enhanced DD⁎ loops in the ηc self-energy. Our results suggest that the ηc meson should form bound states with all the nuclei considered.

Charge Radii of Tin Isotopes and Their Proton-Density Distributions within the Dispersive Optical Model

Proton single-particle properties of even–even tin isotopes in the mass number range between 100 and 132 were calculated on the basis of the dispersive optical model. The possibility of describing data on the charge radius $$r_{\mathrm{ch}}$$ was studied. A decrease in the rate of growth of $$r_{\mathrm{ch}}$$ with increasing $$N$$ in the region of $$N>76$$ was obtained via increasing the energy interval in the vicinity of $$E_{\mathrm{F}}$$ where the imaginary part of the potential used is close to zero. The predictive power of the dispersive optical model for the density distribution in nuclei far from the beta-stability valley was demonstrated.

Nucleon momentum distributions and elastic electron scattering form factors for 48Ti and 54Fe nuclei

The nucleon momentum distributions (NMD) for the ground state and elastic electron scattering form factors have been calculated in the framework of the coherent fluctuation model and expressed in terms of the weight function (fluctuation function). The weight function has been related to the nucleon density distributions of nuclei and determined from theory and experiment. The nucleon density distributions (NDD) is derived from a simple method based on the use of the single particle wave functions of the harmonic oscillator potential and the occupation numbers of the states. The feature of long-tail behavior at high momentum region of the NMD has been obtained using both the theoretical and experimental weight functions. The observed electron scattering form factors for 48Ti and 54Fe nuclei are in reasonable agreement with the present calculations throughout all values of momentum transfer q.

A study of the nucleus-nucleus total reaction cross section of stable systems at intermediate energies: An application to 12C

A semi-microscopic analytical expression of the nucleus-nucleus total reaction cross section (σR) was proposed based on the strong absorption model. It is suitable for stable nuclei at intermediate energies. The matter density distributions of nuclei and the nucleon-nucleon total cross section were both considered. Particularly, the Fermi motion effect of the nucleons in a nucleus was also taken into account. The parametrization of σR was applied to the colliding systems including 12C. The experimental data at energies from 30 to 1000 MeV/nucleon were well reproduced, according to which an approach of deriving σR without adjustable parameters was developed. The necessity of considering the Fermi motion effect in the parametrization was discussed.

Φ -meson–nucleus bound states

$\phi$-meson--nucleus bound state energies and absorption widths are calculated for seven selected nuclei by solving the Klein-Gordon equation with complex optical potentials. Essential input for the calculations, namely the medium-modified $K$ and $\overline{K}$ meson masses, as well as the density distributions in nuclei, are obtained from the quark-meson coupling model. The attractive potential for the $\phi$-meson in the nuclear medium originates from the in-medium enhanced $K\overline{K}$ loop in the $\phi$-meson self-energy. The results suggest that the $\phi$-meson should form bound states with all the nuclei considered. However, the identification of the signal for these predicted bound states will need careful investigation because of their sizable absorption widths.

Sensitivity of reaction cross sections to halo nucleus density distributions

In order to clear up the sensitivity of the nucleus--nucleus reaction cross sections $\sigma_R$ to the nuclear matter distributions in exotic halo nuclei, we have calculated the values of $\sigma_R$ for scattering of $^6$He, $^{11}$Li, and $^{19}$C nuclei on several nuclear targets at the energy of 0.8 GeV/nucleon. The calculations were performed in the "rigid target" approximation to the Glauber theory, different shapes of the nuclear density distributions in $^6$He, $^{11}$Li, and $^{19}$C being assumed.

Electroweak charge density distributions with parity-violating electron scattering

Parity-violating electron scattering (PVS) is an accurate and model-independent way to investigate the weak-charge density distributions of nuclei. In this paper, we study parity-violating electron scattering with the Helm model where the effects of spin-orbit currents on nuclear weak skins are taken into account. The conditions of two PVS measurements to constrain the surface thickness ${\ensuremath{\sigma}}_{W}$ of Helm weak-charge densities are investigated. According to the plane wave Born approximation, ${A}_{\mathrm{pv}}$ is expressed in terms of parameters of the corresponding Helm charge and weak-charge densities. After fitting the results of ${A}_{\mathrm{pv}}$ calculated from the phase-shift analysis method where the Coulomb distortion effects are incorporated, an empirical formula in terms of Helm model parameters for calculating ${A}_{\mathrm{pv}}$ is obtained. If two PVS measurements with different scattering angles are carried out, the modeled weak-charge density distributions with two parameters could be extracted from this empirical formula.

Sensitivity of cross sections for elastic nucleus-nucleus scattering to halo nucleus density distributions

In order to clear up the sensitivity of the nucleus-nucleus scattering to the nuclear matter distributions of exotic halo nuclei, we have calculated differential cross sections for elastic scattering of the $^6$He and $^{11}$Li nuclei on several nuclear targets at the energy of 0.8 GeV/nucleon with different assumed nuclear density distributions in $^6$He and $^{11}$Li.

Brueckner-Hartree-Fock–based optical potential for proton-4,6,8He and proton-6,7,9,11Li scattering

Proton-nucleus scattering provides a useful tool to determine either the parameters entering in the assumed shape of the neutron distribution or to test the reliability of the theoretically calculated neutron distributions in the target nuclei. We have used the Bethe-Brueckner-Hartree-Fock approach to calculate the optical potentialfor analyzing the experimental observables (e.g., differentialcross section and polarization) for p-4,6,8He and p-6,7,9,11Li scattering. The calculation requires mainly two inputs: (1) the nucleon-nucleon (NN) interaction and (2) the nucleon distributions in target nuclei. Various local realistic internucleon (NN) potentials such as Reid93, Urbana v-14, and Argonne v-18 along with several model nucleon density distributions are employed in generating the nucleon-nucleus optical potential. We study the sensitivity of the calculated physical observables on the NN interaction and the density distributions used. It is observed that all the NN interactions and also the different density distributions eproduce rather well the experimental differential cross sections while the calculated polarization is more sensitive to the NN interaction and also to the density distribution used. Thus the polarization data can be used as an additional constraint on the determination of nucleon (especially neutron) density distributions in nuclei. Some results of the representative cases highlighting these features are presented and discussed in detail for illustration.

J/Ψ-nuclear bound states

$J/\Psi$-nuclear bound state energies are calculated for a range of nuclei by solving the Proca (Klein-Gordon) equation. Critical input for the calculations, namely the medium-modified $D$ and $D^*$ meson masses, as well as the nucleon density distributions in nuclei, are obtained from the quark-meson coupling model. The attractive potential originates from the $D$ and $D^*$ meson loops in the $J/\Psi$ self-energy in nuclear medium. It appears that $J/\Psi$-nuclear bound states should produce a clear experimental signature provided that the $J/\Psi$ meson is produced in recoilless kinematics.

Deformation Effect on the Center-of-Mass Correction Energy in Nuclei Ranging from Oxygen to Calcium

The microscopic c.m. correction energies for nuclei ranging from oxygen to calcium are systematically calculated by both spherical and axially deformed relativistic mean-field (RMF) models with the effective interaction PK1. The microscopic c.m. correction energies strongly depend on the isospin as well as deformation and deviate from the phenomenological ones. The deformation effect is discussed in detail by comparing the deformed with the spherical RMF calculation. It is found that the direct and exchange terms of the c.m. correction energies are strongly correlated with the density distribution of nuclei and are suppressed in the deformed case.

Systematic study of charge form factors of elastic electron-nucleus scattering with the relativistic eikonal approximation

We systematically investigate the elastic electron scattering on both stable and unstable nuclei with the relativistic eikonal approximation, where the charge density distributions of nuclei are from the self-consistent relativistic mean field model. Calculations show that the relativistic eikonal approximation can reproduce the experimental data of electron scattering on nuclei ranging from the light region, such as $^{12}\mathrm{C}$, to the heavy region, such as $^{208}\mathrm{Pb}$. This is the systematic test of the relativistic eikonal approximation for elastic electron scattering for both light and heavy nuclei. With this method, further studies are made of the variation of charge form factors along isotopic chains and the sensitivity of charge form factors to the changes of charge distribution. For isotopic chains with Z = 20 and 28, we find that the charge form factors vary significantly with neutron number. The charge form factors shift outward and downward when the target nucleus moves from the neutron-rich region to the proton-rich region along the isotopic chain. The significant shift shows that the charge form factor is very sensitive to a change of neutron number. If the isotopic shifts of the charge form factor are measured on the next-generation electron-nucleus collider (at RIKEN and GSI), the charge size and charge distribution can be determined for unstable nuclei. The calculations will provide a reference for future experiments.

π+-π- ASYMMETRY AND THE NEUTRON SKIN IN HEAVY NUCLEI

In heavy nuclei the spatial distribution of protons and neutrons is different. At CERN SPS energies production of π+ and π- differs for pp, pn, np and nn scattering. These two facts lead to an impact parameter dependence of the π+ to π- ratio in 208Pb+208Pb collisions. A recent experiment at CERN seems to confirm qualitatively these predictions. It may open a possibility for determination of neutron density distribution in nuclei.

Neutron spatial distribution in nuclei and the impact-parameter dependence of theπ+−π−asymmetry in heavy-ion collisions

The theoretical nuclear physics predictions and experimental results on antiprotonic atoms lead to different proton and neutron spatial distributions. At CERN SPS energies production of positive and negative pions differs for $pp,pn,np$, and $nn$ scattering. These two facts lead to an impact-parameter dependence of the ${\ensuremath{\pi}}^{+}$ to ${\ensuremath{\pi}}^{\ensuremath{-}}$ ratio in $^{208}\mathrm{Pb}+^{208}\mathrm{Pb}$ collisions. A recent experiment at CERN seems to qualitatively confirm these predictions. The results for two models considered are almost identical. This may open a new possibility for determination of the neutron density distribution in nuclei.

Medium energy antiproton absorption, a tool to study neutron halo nuclei

A novel method is proposed to measure the difference of neutron and proton density distributions of nuclei far off stability by medium energy antiproton absorption. The radioactive nuclei are produced by projectile fragmentation at medium energies (400–800) A MeV, separated and stored in a medium energy storage ring. The antiprotons are produced with 30 GeV protons, accumulated, cooled, decelerated and stored at energies of about 5 MeV in a small storage ring. The medium energy radioactive beams are brought to head on collisions with the low energy antiproton beam in an interaction section of both rings. The coasting radioactive beam and the reaction products from the collisions with the antiprotons are observed with the Schottky noise frequency analysis method, which allows one to separate all reaction products and measure their production rates as well as the loss rate of the primary beam. From these observations, the total and partial reaction cross sections may be determined, even with a small number of rare ion species in the ring. An analysis of the total and partial reaction cross sections will allow to determine both 〈 r p 2〉 as well as 〈 r n 2〉 for nuclei far off the stability.

Renormalization of the isovector πN amplitude in pionic atoms

The extraction of the isovector s-wave πN amplitude from pionic atoms is studied with special emphasis on uncertainties and their dependence on the assumptions made regarding the neutron density distributions in nuclei and on the size of the data base used. Only ‘global’ analyses of pionic-atom data reveal a discrepancy between the extracted isovector s-wave πN amplitude b 1=(−0.108±0.007) m π −1 and its free πN counterpart b 1 free =−0.0885 +0.0010 −0.0021 m π −1 , where the uncertainty in the neutron densities is included in the error analysis. The role of ‘deeply bound’ pionic atom states is discussed and the reason for failure of these states to provide new information is explained.

Direct Evidence of Nucleation During the Induction Period of Polyethylene Crystallization by SAXS

Direct evidence that nuclei are formed during the induction period of crystallization is obtained for the first time by means of small-angle X-ray scattering (SAXS). Polyethylene (PE) was used as a model crystalline polymer. The nucleating agent was mixed with PE in order to increase the scattering intensity I x from nuclei as large as 104 times bigger than usual. I x increased soon after quenching to the crystallization temperature from the melt and saturated after some time. A new theory is proposed to estimate the size of the nuclei N, the number density distribution of nuclei with N at time t, f(t,N), and the induction time τ i, by analyzing the SAXS scattering intensity. The volume-averaged size of the nuclei was nearly the same as that of critical nuclei and does not change so much with time during the induction period. Lamellae start stacking much later than nuclei start forming.

Karyometry of secretory cell nuclei in high-grade PIN lesions.

The goal of this study was a karyometric characterization of secretory cell nuclei in high-grade prostatic intraepithelial neoplasia (PIN) lesions. Specifically, the hypothesis is tested that distinctly different subgroups of nuclei exist in these lesions. High-resolution images of 1,713 nuclei from high-grade PIN lesions were recorded. Karyometric features were computed. Discriminant function scores against normal reference nuclei, and nuclear abnormality values were derived. Data sets were processed by a nonsupervised learning algorithm to establish the presence of subgroups of nuclei with statistically different nuclear chromatin distributions. Three sets of nuclei were formed, facing an intact basal cell layer, a near vanishing basal cell layer, and a gap in the basal cell layer. For each set, a nonsupervised learning algorithm formed three statistically different subgroups of approximately equal sizes. Each subgroup is found in every one of the three sampling locations. The total optical density distribution of nuclei in two subgroups suggests an aneuploid distribution, the third subgroup has a near diploid distribution. Secretory cell nuclei in high-grade PIN lesions are a heterogeneous population, forming statistically different subgroups. Studies aimed at characterizing the progression of such lesions should consider the inhomogeneous nature of these nuclei.

Uniform precipitation of oxygen in large diameter wafers

In the present stage of development, 300 mm crystals often contain a transition from vacancy-rich to interstitial-rich. Due to this radially varying concentration of intrinsic point defects, the radial size distribution of grown-in oxide precipitate nuclei is also inhomogeneous in these wafers. In order to achieve a radially uniform bulk defect density for internal gettering, a slow temperature ramp induced growth of all grown-in oxide precipitate nuclei is the appropriate procedure to overcome problems resulting from the inhomogeneous size distribution of grown-in nuclei. This approach is based on the observation that in contrast to the nuclei size distribution, the nuclei density distribution is homogeneous over the wafer, independent of the dominant intrinsic point defect.