The macroscopic-microscopic mass formula is further improved by considering mirror nuclei constraint. The rms deviation with respect to 2149 measured nuclear masses is reduced to 0.441 MeV. The shell corrections, the deformations of nuclei, the neutron and proton drip lines, and the shell gaps are also investigated to test the model. The rms deviation of alpha-decay energies of 46 super-heavy nuclei is reduced to 0.263 MeV. The central position of the super-heavy island could lie around N=176~178 and Z=116~120 according to the shell corrections of nuclei.
Isospin symmetry breaking (ISB) effects in the charge radius difference $ΔR_{\rm ch}$ of mirror nuclei are studied using the test example of ${}^{48}$Ca and ${}^{48}$Ni. This choice allows for a transparent study of ISB contributions since paring and deformation effects, commonly required for the study of mirror nuclei, can be neglected in this specific pair. The connection of $ΔR_{\rm ch}$ with the nuclear Equation of State and the effect of ISB on such a relation are discussed according to an Energy Density Functional approach. We find that nuclear ISB effects may shift the estimated value f…
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.
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…
We investigate the dripline mirror nuclei, $^{11}$Li and $^{11}$O, located on the neutron and proton dripline, respectively. We calculate the lowest four states, $3/2^-$, $1/2^+$, $3/2^+$ and $5/2^+$, built on double occupancy in the nuclear $s_{1/2}$ and $p_{1/2}$ valence single-particle states. We use the hyperspherical adiabatic expansion method to solve the three-body problem for a frozen nuclear core surrounded by two identical nucleons. The four analogue states in $^{11}$O are obtained with precisely the same interactions as used for the four states in $^{11}$Li, except for addition of t…
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 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 studied the proton-rich $T_z=-1$ nucleus $^{70}$Kr through inelastic scattering at intermediate energies in order to extract the reduced transition probability, $B(E2;\;0^+ \rightarrow 2^+)$. Comparison with the other members of the $A=70$ isospin triplet, $^{70}$Br and $^{70}$Se, studied in the same experiment, shows a $3σ$ deviation from the expected linearity of the electromagnetic matrix elements as a function of $T_z$. At present, no established nuclear structure theory can describe this observed deviation quantitatively. This is the first violation of isospin symmetry at this level ob…
Scattering of Antiprotons by Nuclei (Atoms) in the Range of Low Energies $E\lesssim 10^5$ eV. Mirror Reflection, Diffraction, and Channeling of Antiprotons in Crystals
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 qu…
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 …
Isospin is an approximate symmetry in atomic nuclei, arising from the rather similar properties of protons and neutrons. Perhaps the clearest manifestation of isospin within nuclei is in the near-identical structure of excited states in mirror nuclei: nuclei with inverted numbers of protons and neutrons. Isospin symmetry, and therefore mirror-symmetry, is broken by electromagnetic interactions and the difference in the masses of the up and down quarks. A recent study by Hoff and collaborators presented evidence that the ground-state spin of $^{73}$Sr is different from that of its mirror, $^{73…
Mechanisms of mirror energy difference for states exhibiting Thomas-Ehrman shift: Gamow shell model case studies of $^{18}$Ne/$^{18}$O and $^{19}$Na/$^{19}$O
Asymptotic normalization coefficients and continuum coupling in mirror nuclei
背景资料：渐近归一化系数（ANC）表征描述核子去除反应所需的一核子重叠积分的渐近形式。目的：我们研究了粒子连续性对$p$ -和$sd$ -壳层区域的镜系统质子和中子ANC的影响。方法：采用实能和复能连续壳模型方法。结果：我们研究了单粒子ANCs的一般结构与结合能和轨道角动量的关系。我们计算了不同物理情况下镜像核中的ANC，包括对弱束缚态和非束缚态的俘获反应。结论：我们证明了单粒子ANC表现出带电粒子和中性粒子不同的一般行为。我们验证了先前提出的关系[N. K.费尤克河Johnson和A.M. Mukhamedzhanov，Phys. Rev. Lett. 91，232501（2003）; Phys.Rev.Lett. 97，069904（E）（2006）; N. K. Descouvemont，Phys.Rev.C72，064324（2005）]。我们发现轻微的修改，如果光谱强度是本地化在一个单一的状态或广泛分布。对于几个状态强烈耦合到衰变通道的情况，这些修改可能达到30%。
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
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 …
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…
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）
B(E2) strength in $^{36,38}$Ca and in mirror nuclei 36S, 38Ar
Institute of Nuclear Physics, Polish Academy of Sciences（波兰科学院核物理研究所）；Grand Accélérateur National d’Ions Lourds (GANIL), CEA/DSM - CNRS/IN2P3（大型重离子加速器（GANIL），CEA/DSM-CNRS/IN2P3）
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…
Mirror and triplet energy differences in $sd$-shell nuclei using microscopic interactions with isospin-symmetry breaking effects
Indian Institute of Technology Roorkee（印度理工学院卢尔基分校）；University of Surrey（萨里大学）；Nihon University（日本大学）；NAT Corporation（NAT公司）；Beihang University（北京航空航天大学）；University of Tsukuba（筑波大学）
The nuclear symmetry energy plays a key role in determining the equation of state (EoS) of dense, neutron-rich matter, which connects the atomic nuclei with the hot and dense matter in universe, thus has been the subject of intense investigations in laboratory experiments, astronomy observations and theories. Various probes have been proposed to constrain the symmetry energy and its density dependence. Currently, the extensive data yield already a good and consistent constraint to the symmetry energy ($E_\text{sym}(ρ)$) at saturation density, but do not yet give a consistent result of one crit…
Background: Small asymmetry between neutrons and protons, caused by the differences in masses and charges of the up and down constituent quarks leads to the isospin symmetry breaking. The isospin non-conservation affects broad range of observables from superallowed Fermi weak interaction to isospin-forbidden electromagnetic rates. Its most profound and cleanest manifestation are systematic shifts in masses and excitation energies of mirror atomic nuclei. Purpose: Recently, we constructed the charge-dependent DFT that includes class II and III local interactions and demonstrated that the model …
The values of the antineutron-nucleus scattering lengths, and in particular their imaginary parts, are needed to evaluate the feasibility of using neutron mirrors in laboratory experiments to search for neutron-antineutron oscillations. We analyze existing experimental and theoretical constraints on these values with emphasis on low $A$ nuclei and use the results to suggest materials for the neutron/antineutron guide and to evaluate the systematic uncertainties in estimating the neutron-antineutron oscillation time. As an example we discuss a scenario for a future neutron-antineutron oscillati…
