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 the Coulomb interaction from the charge of the substituted valence protons. Surprisingly the four energies deviate from each other only by less than a few hundred keV. Any of them could then turn out to be the ground state, due to the uncertainty related to the angular momentum and parity dependence of the three-body potential. Still, our calculations marginally favor the $1/2^+$ state. The structures of these four states in $^{11}$O deviate substantially from the analogue states in the mirror, $^{11}$Li.
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.
We study the mirror symmetry breaking of $^6$He-$^6$Be and $^8$He-$^8$C using the $^4$He + $X$N ($X$=2, 4) cluster model. The many-body resonances are treated for the correct boundary condition using the complex scaling method. We find that the ground state radius of $^8$C is larger than that of $^8$He due to the Coulomb repulsion in $^8$C. On the other hand, the $0^+_2$ resonances of the two nuclei exhibit the inverse relation; the $^8$C radius is smaller than the $^8$He radius. This is due to the Coulomb barrier of the valence protons around the $^4$He cluster core in $^8$C, which breaks the…
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.
Continuum-coupling correction to binding energies in neutron rich oxygen and fluorine isotopes and to excitation energies of 2+ states in 36Ca and 36S mirror nuclei are studied using the real-energy continuum shell model.
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 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…
Asymptotic normalization coefficients (ANCs) are fundamental nuclear constants playing important role in nuclear reactions, nuclear structure and nuclear astrophysics. In this paper the physical reasons of the Coulomb renormalization of the ANC are addressed. Using Pinkston-Satchler equation the ratio for the proton and neutron 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 nuc…
We show how the charge symmetry of strong interactions can be used to relate the proton and neutron asymptotic normalization coefficients (ANCs) of the one nucleon overlap integrals for light mirror nuclei. This relation extends to the case of real proton decay where the mirror analog is a virtual neutron decay of a loosely bound state. In this case, a link is obtained between the proton width and the squared ANC of the mirror neutron state. The relation between mirror overlaps can be used to study astrophysically relevant proton capture reactions based on information obtained from transfer re…
The properties of $T=1/2$ mirror nuclei in the $fp$ shell have been studied with a microscopic residual interaction. The isospin-nonconserving interaction is derived from a high-precision charge-dependent Bonn \textit{NN} potential using the folded-diagram renormalization method. The level structures of the nuclei are calculated, obtaining excellent agreements with experimental observations till the $0f_{7/2}$ band termination. The role played by isospin symmetry breaking on ground-state displacement energies and mirror energy differences is discussed, which may help to explain the long-standi…
We investigate deep inelastic scattering from He-3 and H-3 within a conventional convolution treatment of binding and Fermi motion effects. Using realistic Faddeev wave functions together with a nucleon spectral function, we demonstrate that the free neutron structure function can be extracted in deep-inelastic scattering from A=3 mirror nuclei, with nuclear effects canceling to within 2% for x < 0.85.
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…
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…
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…
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.
Binding energy differences of mirror nuclei for A=15, 17, 27, 29, 31, 33, 39 and 41 are calculated in the framework of relativistic deformed mean-field theory. The spatial components of the vector meson fields and the photon are fully taken into account in a self-consistent manner. The calculated binding energy differences are systematically smaller than the experimental values and lend support to the existency of the Okamoto--Nolen-Schiffer anomaly found decades ago in nonrelativistic calculations. For the majority of the nuclei studied, however, the results are such that the anomaly is signi…
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…
This paper overviews various phenomena related to the concept of isospin symmetry. The focus is on N~Z nuclei, which are excellent laboratories of isospin physics. The theoretical framework applied is nuclear Density Functional Theory and its isospin- and angular-momentum projected extensions, as well as symmetry-projected multi-reference models. The topics covered include: isospin impurities, superallowed beta decays, beta-transitions in mirror nuclei, isospin breaking hadronic interactions, mirror and triplet binding energy differences, and isoscalar pairing.
The elastic and inelastic scattering of protons from mirror nuclei $^{18}$Ne and $^{18}$O are studied in a folding model approach. For comparison, two different effective interactions are folded with Hartree-Fock densities to obtain the nuclear interaction potentials. Both of them provide equivalent descriptions to the data and the deformation parameters extracted from inelastic scattering are reasonable. The density dependence parameters obtained from nuclear matter calculations and used for present analysis also provide a good estimate for the nuclear mean free path. The present formalism un…
By using the quark-exchange formalism, realistic Faddeev wave functions and Fermi motion effect, we investigate deep inelastic electron scattering from A=3 mirror nuclei in the deep-valence region. The initial valence quarks in put are taken from the GRV's next-to-leading order calculations on $F_2^p(x,Q^2)$ which give very good fit to the available data in the $(x,Q^2)$-plane. It is shown that the free neutron to proton structure functions ratio can be extracted from corresponding EMC ratios for $^3He$ and $^3H$ mirror nuclei by using self-consistent iteration procedure and the results are in…
The theoretical evaluation of major nuclear structure effects on the asymmetry of allowed Gamow-Teller beta-decay rates in light mirror nuclei is presented. The calculations are performed within the shell model, using empirical isospin-nonconserving interaction and realistic Woods-Saxon radial wave functions. The revised treatment of p-shell nuclei is supplemented by systematic calculations for sd-shell nuclei and compared to experimental asymmetries when available. The results are important in connection with the possible existence of second-class currents in the weak interaction.
The binding energy differences of the valence proton and neutron of the mirror nuclei, $^{15}$O -- $^{15}$N, $^{17}$F -- $^{17}$O, $^{39}$Ca -- $^{39}$K and $^{41}$Sc -- $^{41}$Ca, are calculated using the quark-meson coupling (QMC) model. The calculation involves nuclear structure and shell effects explicitly. It is shown that binding energy differences of a few hundred keV arise from the strong interaction, even after subtracting all electromagnetic corrections. The origin of these differences may be ascribed to the charge symmetry breaking effects set in the strong interaction through the u…
Magnetic dipole and electric quadrupole moments of the mirror nuclei 8Li and 8B are analysed in the framework of the multiparticle shell model by using two approaches : i) the one-particle spectroscopic factors and ii) the one-particle fractional parentage coefficients. These two approaches are compared both each to other and with a microscopic multicluster model. The one-particle nucleon states are calculated taking into account the continuum by the method of the expansion of the Sturm - Liouville functions. The experimental magnetic and quadrupole moments of 8Li and 8Bare reproduced well by …
Experimental mirror energy differences (MED) for nuclei lying in the middle and the second part of $1f_{7/2}$ shell are compared with shell model calculations in the $1f_{7/2}$ and in the full $pf$ configuration spaces, as well as with CSM calculations. MED plots are fully consistent with the description which emerges from the interpretation of SM calculations: i.e. the band crossing of the gs band with high-$K$ bands in $A$=51 and 50 mirror pairs, as well as the seniority-3 quasi band-termination at $I^π$=19/2$^-$ in $A$=49. Rotational alignment effects are excluded, contrarily to what even r…
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
Background: An asymptotic normalization coefficient (ANC) characterizes the asymptotic form of a one-nucleon overlap integral required for description of nucleon-removal reactions. Purpose: We investigate the impact of the particle continuum on proton and neutron ANCs for mirror systems from $p$- and $sd$-shell regions. Method: We use the real-energy and complex-energy continuum shell model approaches. Results: We studied the general structure of the single-particle ANCs as a function of the binding energy and orbital angular momentum. We computed ANCs in mirror nuclei for different physical s…
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…
The improved Kelson-Garvey (ImKG) mass relations are proposed from the mass differences of mirror nuclei. The masses of 31 measured proton-rich nuclei with $7\leq A\leq41$ and $-5\leq (N-Z)\leq-3$ can be remarkably well reproduced by using the proposed relations, with a root-mean-square deviation of 0.398 MeV, which is much smaller than the results of Kelson-Garvey (0.502 MeV) and Isobar-Mirror mass relations (0.647 MeV). This is because many more masses of participating nuclei are involved in the ImKG mass relations for predicting the masses of unknown proton-rich nuclei. The masses for 144 u…
It has been suggested recently ({\it Phys. Rev. Lett.} 91, 232501 (2003)) that the widths of narrow proton resonances are related to neutron Asymptotic Normalization Coefficients (ANCs) of their bound mirror analogs because of charge symmetry of nucleon-nucleon interactions. This relation is approximated by a simple analytical formula which involves proton resonance energies, neutron separation energies, charges of residual nuclei and the range of their strong interaction with the last nucleon. In the present paper, we perform microscopic-cluster model calculations for the ratio of proton widt…
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 si…
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 …
We study the isospin asymmetry in the isoscalar (IS) excitations in the mirror nuclei $^{14}$O and $^{14}$C by using the Hartree-Fock(HF)+random phase approximation (RPA) linear response function theory with a Skyrme interaction to take into account the continuum effect properly. The asymmetry in the IS monopole, dipole responses is pointed out in the continuum near the particle threshold with respect to the excitation energy and the sum rule strength. On the other hand, no clear sign of the asymmetry is found in the giant resonance (GR) region. In the quadrupole case, the calculated strengths…
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）
The exotic structures in the 2s_{1/2} states of five pairs of mirror nuclei ^{17}O-^{17}F, ^{26}Na-^{26}P, ^{27}Mg-^{27}P, ^{28}Al-^{28}P and ^{29}Si-^{29}P are investigated with the relativistic mean-field (RMF) theory and the single-particle model (SPM) to explore the role of the Coulomb effects on the proton halo formation. The present RMF calculations show that the exotic structure of the valence proton is more obvious than that of the valence neutron of its mirror nucleus, the difference of exotic size between each mirror nuclei becomes smaller with the increase of mass number A of the mi…
The Transfer to the Continuum method has been applied to describe the $^{11}\text{Li}(p,pn)$ and $^{14}\text{Be}(p,pn)$ reactions in inverse kinematics, using structure overlaps computed within a full three-body model for the projectile. Calculations agree with the available experimental data on the unbound $^{10}$Li and $^{13}$Be nuclei.
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 …
It has been suggested recently (Phys. Rev. Lett. 91, 232501 (2003)) that charge symmetry of nucleon-nucleon interactions relates the Asymptotic Normalization Coefficients (ANCs) of proton and neutron virtual decays of mirror nuclei. This relation is given by a simple analytical formula which involves proton and neutron separation energies, charges of residual nuclei and the range of their strong interaction with the last nucleon. Relation between mirror ANCs, if understood properly, can be used to predict astrophysically relevant direct proton capture cross sections using neutron ANCs measured…
