Differences in the charge radii of mirror nuclei have been recently suggested to contain information on the slope of the symmetry energy L. To test this hypothesis, we perform statistical correlation analysis using quantified energy density functionals that are consistent with our previous knowledge on global nuclear observables such as binding energies and charge radii. We conclude that the difference in charge radii between a mirror pair, R_mir, is an inferior isovector indicator compared to other observables, such at the neutron skin or electric dipole polarizability. In particular, this quantity correlates poorly with both the neutron skin and L. We demonstrate that R_mir is influenced by pairing correlations in the presence of low-lying proton continuum in the proton-rich mirror-partner nucleus. Considering the large theoretical uncertainties on R_mir, we conclude that the precise data on mirror charge radii cannot provide a stringent constraint on L.
We present predictions for proton skins based on isospin-asymmetric equations of state derived microscopically from high-precision chiral few-nucleon interactions. Moreover, we investigate the relation between the neutron skin of a nucleus and the difference between the proton radii of the corresponding mirror nuclei.
The neutron skin of atomic nuclei impacts the structure of neutron-rich nuclei, the equation of state of nucleonic matter, and the size of neutron stars. Here we predict the neutron skin of selected light- and medium-mass nuclei using coupled-cluster theory and the auxiliary field diffusion Monte Carlo method with two- and three-nucleon forces from chiral effective field theory. We find a linear correlation between the neutron skin and the isospin asymmetry in agreement with the liquid-drop model and compare with data. We also extract the linear relationship that describes the difference betwe…
We have investigated energy levels mirror nuclei of the 17O and 17F in relativistic and non-relativistic shell model. The nuclei 17O and 17F can be modeled as a doubly-magic 17O=n+(N=Z=8) and 17F=p+(N=Z=8), with one additional nucleon (valence) in the ld5/2 level. Then we have selected the quadratic Hellmann potential for interaction between core and single nucleon. Using Parametric Nikiforov-Uvarov method, we have calculated the energy levels and wave function in Dirac and Schrodinger equations for relativistic and non-relativistic, respectively. Finally, we have computed the binding and exci…
The properties of loosely bound proton-rich nuclei around A = 20 are investigated within the framework of nuclear shell model. In these nuclei, the strength of the effective interactions involving the loosely bound proton s1=2 orbit are significantly reduced in comparison with those in their mirror nuclei. We evaluate the reduction of the effective interaction by calculating the monopole-baseduniversal interaction (VMU) in the Woods-Saxon basis. The shell-model Hamiltonian in the sd shell, such as USD, can thus be modified to reproduce the binding energies and energy levels of the weakly bound…
Electric quadrupole (E2) matrix elements provide a measure of nuclear deformation and related collective structure. Ground-state quadrupole moments in particular are known to high precision in many p-shell nuclei. While the experimental electric quadrupole moment only measures the proton distribution, both proton and neutron quadrupole moments are needed to probe proton-neutron asymmetry in the nuclear deformation. We seek insight into the relation between these moments through the ab initio no-core configuration interaction (NCCI), or no-core shell model (NCSM), approach. Converged ab initio …
Light nuclei fall within a regime of universal physics governed by the fact that the two-nucleon scattering lengths are large compared to the typical nuclear interaction range set by one-pion exchange. This places nuclear physics near the so-called unitarity limit in which the scattering lengths are exactly infinite. Effective field theory provides a powerful theoretical framework to capture this separation of scales in a systematic way. It is shown here that the nuclear force can be constructed as a perturbative expansion around the unitarity limit and that this expansion has good convergence…
Talk given at the "International Workshop on (e,e'p) Processes", July 2-6, 2017, Bled, Slovenia. Various many-body calculations are compared and the results provided by the Normalization Conserving Linked Cluster Expansion with realistic NN interactions are reviewed and analyzed in detail, as far as ground state energies, momentum distributions and spectral functions of few-nucleon system and complex nuclei are concerned.
Pronounced changes of nuclear charge radii provide a stringent benchmark on the theoretical models and play a vital role in recognizing various nuclear phenomena. In this work, the systematic evolutions of nuclear charge radii along even $Z$=84-120 isotopic chains are firstly investigated by the recently developed new ansatz under the covariant density functional. The calculated results show that the shell closure effects of nuclear charge radii are remarkably shown at the neutron numbers $N=126$ and 184. Interestingly, the arch-like shapes of charge radii between these two strong neutron clos…
The neutron skin of nuclei is an important fundamental property, but its accurate measurement faces many challenges. Inspired by charge symmetry of nuclear forces, the neutron skin of a neutron-rich nucleus is related to the difference between the charge radii of the corresponding mirror nuclei. We investigate this relation within the framework of the Hartree-Fock-Bogoliubov method with Skyrme interactions. Predictions for proton skins are also made for several mirror pairs in the middle mass range. For the first time the correlation between the thickness of the neutron skin and the characteri…
We investigate how the Coulomb interaction affects the energy $E$ and width $Γ$ of resonance states in mirror nuclei. We employ a three-cluster microscopic model to determine position of resonance states in two- and three-body continua. Two parameters are introduced to quantify effects of the Coulomb interactions. As the energy and width of the corresponding resonance states of mirror nuclei are displayed on an $E$-$Γ$ plane, these parameters determine a rotation and a dilatation. With the help of these parameters we found resonance states with strong, small and medium effects of the Coulomb i…
Relation between widths of proton resonances and neutron asymptotic normalization coefficients in mirror states of light nuclei in a microscopic cluster model
Effects of the relativistic correction of the Coulomb interaction on doubly-magic nuclei are discussed with Skyrme Hartree--Fock calculations. The relativistic correction is treated by using the local density approximation. It is found that the correction to the total energy is about $ 2.4 \, \mathrm{MeV} $ for $ {}^{208} \mathrm{Pb} $, while proton and neutron radii do not change significantly. This difference is larger than the difference of the Coulomb exchange (Fock) energy calculated with the local density (Hartree--Fock--Slater) approximation and that with the exact treatment and the neu…
Isospin-symmetry breaking is responsible for the energy difference of excited states in mirror nuclei. It also influences the coefficient of the isobaric multiplet mass equation. In the present work, we extensively investigate isospin-symmetry breaking in medium mass nuclei within ab initio frameworks. For this, we employ the ab initio valence-space in-medium similarity renormalization group approach, in which charge-symmetry and charge-independence breakings are included in the adopted nuclear force. The mirror energies of sd- and pf- shell nuclei are computed for that matter. The effects of …
It has been recently suggested that differences in the charge radii of mirror nuclei are proportional to the neutron-skin thickness of neutron-rich nuclei and to the slope of the symmetry energy $L$ [B.A. Brown Phys. Rev. Lett. 119, 122502 (2017)]. The determination of the neutron skin has important implications for nuclear physics and astrophysics. Although the use of electroweak probes provides a largely model-independent determination of the neutron skin, the experimental challenges are enormous. Thus, the possibility that differences in the charge radii of mirror nuclei may be used as a su…
The spectra of mass-11 nuclei are unusual, and so pose a challenge for theoretical models of their structure. The set of isobars range from being well bound to nucleon emission (11B,11C) through weakly bound (11Li, 11Be), with the former taking the form of a two neutron halo, to being proton unstable (11N,11O). A self-consistent approach to understand this set of nuclei is especially important as the mirror pair 11Be-11N exhibit a parity-inverted ground state compared to their neighbouring nuclei. Herein the Multi-Channel Algebraic Scattering (MCAS) method has been used to describe the low exc…
Ab initio charge form factors and radii of light isoscalar nuclei: Role of the two-body charge density
Forschungszentrum Jülich（于利希研究中心）；Ruhr-Universität Bochum（波鸿鲁尔大学）；Universität Bonn（波恩大学）；Helmholtz-Institut für Strahlen- und Kernphysik（亥姆霍兹射线与核物理研究所）；Bethe Center for Theoretical Physics（贝特理论物理中心）；Peng Huanwu Collaborative Center for Research and Education, International Institute for Interdisciplinary and Frontiers, Beihang University（北京航空航天大学国际交叉前沿研究院彭桓武教研协同中心）
Charge-symmetry-breaking effects on displacement energies and charge radius differences in mirror nuclei
Kyungpook National University（庆北国立大学）；Soongsil University（崇实大学）；RIKEN, Nishina Center for Accelerator-Based Science（理化学研究所，基于加速器的科学西村中心）；University of Aizu（会津大学）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）
Radii of nuclear charge distributions carry information about the strong and electromagnetic forces acting inside the atomic nucleus. While the global behavior of nuclear charge radii is governed by the bulk properties of nuclear matter, their local trends are affected by quantum motion of proton and neutron nuclear constituents. The measured differential charge radii $δ\langle r^2_c\rangle$ between neutron numbers $N=28$ and $N=40$ exhibit a universal pattern as a function of $n=N-28$ that is independent of the atomic number. Here we analyze this remarkable behavior in even-even nuclei from c…
We discuss the determination of electromagnetic form factors from the {\em world} data on electron-nucleus scattering for nuclei $Z \leq 3$, with particular emphasis on the derivation of the moments required for comparison with measurements from electronic/muonic atoms and isotope shifts.
Proton and neutron density profiles of 760 nuclei in the mass region of A=16-304are analyzed using the Skyrme energy density for the parameter set SLy4. Simple formulae are obtained to fit the resulting radii and diffuseness data. These formulae may be useful to estimate the values of the unmeasured radii, and especially in extrapolating charge radius values for nuclei which are far from the valley of stability or to perform analytic calculations for bound and/or scattering problems. The obtained neutron and proton root-mean-square radii and the neutron skin thicknesses are in agreement with t…
Studying antiproton scattering by nuclei (atoms) in the range of low energies, we found out that the increase in the antiproton-nucleus scattering amplitude through Coulomb interaction provides the possibility to investigate spin-dependent processes accompanying the interaction of antiprotons with nuclei (polarized or unpolarized) by means of mirror reflection of antiprotons from the vacuum-matter boundary, diffraction and channeling (surface diffraction and channeling) of antiprotons in crystals.
We studied the charge radius ($r_{c}$), neutron radius ($r_n$), and neutron skin-thickness ($Δr=r_n-r_p$) over a chain of isotopes from C to Zr with the stable region to the neutron drip line. Theoretical calculations are done with axially deformed self-consistent relativistic mean-field theory (RMF) with effective nonlinear NL3 and NL3* interactions. The theoretically estimated values are compared with available experimental data and a reasonable agreement are noted. We additionally assessed the two-neutron separation energy ($S_{2n}$) to mark the drip line nuclei of the considered isotopic s…
Asymptotic normalization coefficients (ANCs) are fundamental nuclear constants playing important role in nuclear reactions, nuclear structure and nuclear astrophysics. In this paper a connection between ANCs and resonance widths of the mirror states is established. Using Pinkston-Satchler equation the ratio for resonance widths and ANCs of mirror nuclei is obtained in terms of the Wronskians from the radial overlap functions and regular solutions of the two-body Schrödinger equation with the short-range interaction excluded. This ratio allows one to use microscopic overlap functions for mirror…
