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 for the symmetry energy slope parameter $L$ by more than 10 MeV while Coulomb corrections can be neglected. ISB effects on the ground-state energy and charge radii in mirror nuclei have been recently predicted by {\it ab initio} calculations to be relatively small, pointing to a negligible effect for the extraction of information on the nuclear EoS. These contrasting results call for a dedicated theoretical effort to solve this overarching problem that impacts not only the neutron skin thickness or the difference in mass and charge radii of mirror nuclei but also other observables such as the Isobaric Analog State energy.
The recent experimental observation of isospin symmetry breaking (ISB) in the ground states of the $T=3/2$ mirror pair $^{73}$Sr - $^{73}$Br is theoretically studied using large-scale shell model calculations. The large valence space and the successful PFSDG-U effective interaction used for the nuclear part of the problem capture possible structural changes and provide a robust basis to treat the ISB effects of both electromagnetic and non-electromagnetic origin. The calculated shifts and mirror-energy-differences are consistent with the inversion of the $I^π$= 1/2$^{-}, 5/2^{-}$ states betwee…
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 assumption of an exact isospin symmetry would imply equal strengths for mirror E1 transitions (at least, in the long-wavelength limit). Actually, large violations of this symmetry rule have been indicated by a number of experimental results, the last of which is the 67As - 67Se doublet investigated at GAMMASPHERE. Here, we examine in detail various possible origins of the observed asymmetry. The coherent effect of Coulomb-induced mixing with the high-lying Giant Isovector Monopole Resonance is proposed as the most probable process to produce a large asymmetry in the E1 transitions, with co…
The anomalous rod shape in carbon isotopes has been investigated in the framework of the cranking covariant density functional theory, and two mechanisms to stabilize such a novel shape with respect to the bending motion, extreme spin, and isospin, are simultaneously discussed for the first time in a self-consistent and microscopic way. By adding valence neutrons and rotating the system, we have found the mechanism stabilizing the rod shape; i.e., the $σ$ orbitals (parallel to the symmetry axis) of the valence neutrons, important for the rod shape, are lowered by the rotation due to the Coriol…
The effects of nuclear isospin asymmetry on $α$ decay lifetimes of heavy nuclei are investigated within various phenomenological models of nuclear potential for the $α$ particle. We consider the widely used simple square well potential and Woods-Saxon potential, and modify them by including an isospin asymmetry term. We then suggest a model for the potential of the $α$ particle motivated by a microscopic phenomenological approach of the Skyrme force model, which naturally introduce the isospin dependent form of the nuclear potential for the $α$ particle. The empirical $α$ decay lifetime formul…
The sensitivities of isospin asymmetry and collision geometry dependencies of participant (overlapping region)- spectator (quasiprojectile and quasitarget region) matter towards the symmetry energy using the isospin quantum molecular dynamical model are explored. Particularly, the difference of the number of nucleons in the overlapping zone to the quasi-projectile-target matter is found to be quite sensitive to the symmetry energy at semiperipheral geometries compared to the individual yield. It gives us a clue that this quantity can be used as a measure of isospin migration. Further, the yiel…
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 report the first branching-ratio measurement of the superallowed 0+-to-0+ beta transition from 38Ca. The result, 0.7728(16), leads to an ft value of 3062.3(68)s with a relative precision of +/-0.2%. This makes possible a high-precision comparison of the ft values for the mirror superallowed transitions, 38Ca-to-38mK and 38mK-to-38Ar, which sensitively tests the isospin symmetry-breaking corrections required to extract Vud, the up-down quark-mixing element of the Cabibbo-Kobayashi-Maskawa (CKM) matrix, from superallowed beta decay. The result supports the corrections currently used, and poin…
In this work, the Coulomb mixing and the isospin mixing in the ground states of even-even nuclei are evaluated in perturbation theory. The calculation of the isospin mixing is performed by using the connection to isovector monopole resonance properties. The uncertainty in the results that depends on different choices of the Skyrme interactions is shown. While Coulomb mixing turns out to be large in the ground states of heavy nuclei, isospin mixing is very small.
Recent experimental data have revealed large mirror energy differences (MED) between high-spin states in the mirror nuclei 67Se and 67As, the heaviest pair where MED have been determined so far. The MED are generally attributed to the isospin symmetry breaking caused by the Coulomb force and by the isospin nonconserving part of the nucleon-nucleon residual interaction. The different contributions of the various terms have been extensively studied in the fp shell. By employing large-scale shell model calculations, we show that the inclusion of the g9/2 orbit causes interference between the elec…
To understand the role of isospin effects on fragmentation due to the collisions of charge asymmetric nuclei, we have performed a complete systematical study using isospin dependent quantum molecular dynamics model. Here simulations have been carried out for $^{124}X_{n}+ ^{124}X_{n}$, where n varies from 47 to 59 and for $^{40}Y_{m}+ ^{40}Y_{m}$, where m varies from 14 to 23. Our study shows that isospin dependent cross-section shows its influence on fragmentation in the collision of neutron rich nuclei.
Mass and isospin dependence of symmetry energy coefficients $a_{sym}$ of finite nuclei is investigated with the measured nuclear masses incorporating the liquid drop mass formula. The enhanced $a_{sym}$ for nearly symmetric nuclei are observed. To describe the mass and isospin dependence of $a_{sym}$, a modified formula based on the conventional surface-symmetry term is proposed and the corresponding rms deviation of nuclear masses is checked.
Precision Tests of Isospin Symmetry through Coulomb excitation of A = 62 Nuclei
GSI Helmholtzzentrum für Schwerionenforschung（GSI亥姆霍兹重离子研究中心）；Department of Physics, The University of Tokyo（东京大学物理系）；RIKEN Nishina Center（理化学研究所仁科中心）；Instituto de Fisica Corpuscular, CSIC-Universidad de Valencia（瓦伦西亚大学-CSIC粒子物理研究所）；Dipartimento di Fisica e Astronomia, Università di Padova（帕多瓦大学物理与天文学系）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；Departamento de Física Teórica, Universidad Autónoma de Madrid（马德里自治大学理论物理系）；School of Physics, Engineering and Technology, University of York（约克大学物理、工程与技术学院）；College of Education, Yokohama National University（横滨国立大学教育学部）；Center for Nuclear Study, University of Tokyo（东京大学核研究分中心）；Instituto de Estructura de la Materia, CSIC（CSIC物质结构研究所）
We present the self-consistent, non-perturbative analysis of isospin mixing using the nuclear density functional approach and the rediagonalization of the Coulomb interaction in the good-isospin basis. The largest isospin-breaking effects are predicted for N = Z nuclei and they quickly fall with the neutron excess. The unphysical isospin violation on the mean-field level, caused by the neutron excess, is eliminated by the proposed method. We find a significant dependence of the magnitude of isospin breaking on the parametrization of the nuclear interaction term. A rough correlation has been fo…
For $N=Z$ odd-odd nuclei, a three-body model assuming two valence particles and an inert core can provide an understanding of pairing correlations in the ground state and spin-isospin excitations. However, since residual core-nucleon interactions can have a significant impact on these quantities, the inclusion of core excitations in the model is essential for useful calculation to be performed. The effect of core excitations must be included in order to gain a detailed understanding of both the ground state and spin-isospin properties of these systems. To this end, we include the vibrational e…
We show that a consequence of isospin symmetry, recently discovered in mirror conjugated one-nucleon decays, can be extended to mirror-conjugated $α$-particles decays, both virtual and real. For virtual $α$-decays of bound mirror pairs this symmetry manifests itself as a relation between the Asymptotic Normalization Coefficients (ANCs) of $α$-particle overlap integrals. This relation is given by a simple analytical formula which involves $α$-particle separation energies and charges of residual nuclei. For bound-unbound mirror pairs, the ANC of a bound nucleus is related to the $α$-width of the…
The relations between the strengths of spin-isospin transition operators extracted from direct nuclear reactions, magnetic scattering of electrons and processes of semi-leptonic weak interactions are discussed.
Isospin singlet (pn) pairing as well as quartetting in nuclei is expected to arise near the symmetry line $N=Z$. Empirical values can be deduced from the nuclear binding energies applying special filters. Within the local density approximation, theoretical estimates for finite nuclei are obtained from results for the condensation energy of asymmetric nuclear matter. It is shown that the isospin singlet condensation energy drops down abruptly for |N-Z|~4 for medium nuclei in the region A=40. Furthermore, alpha-like quartetting and the influence of excitations are discussed.
We present a new procedure of isospin symmetry breaking of cooper-quartets in nuclear matter using Ginzburg-Landau theory, namely we couple the cooper-quartets to the pion-meson field and $SU(2)$ gluons. The paper also describes phenomena resulting from this approach.
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…
We propose a semi-empirical nuclear mass formula based on the macroscopic-microscopic method in which the isospin and mass dependence of model parameters are investigated with the Skyrme energy density functional. The number of model parameters is considerably reduced compared with the finite range droplet model. The rms deviation with respect to 2149 measured nuclear masses is reduced by 21%, falls to 0.516 MeV. The new magic number N=16 in light neutron-rich nuclei and the shape coexistence phenomena for some nuclei have been examined with the model. The shell corrections of super-heavy nucl…
Theoretical approaches that use one-body densities as dynamical variables, such as Hartree-Fock or the density functional theory (DFT), break isospin symmetry both explicitly, by virtue of charge-dependent interactions, and spontaneously. To restore the spontaneously broken isospin symmetry, we implemented the isospin-projection scheme on top of the Skyrme-DFT approach. This development allows for consistent treatment of isospin mixing in both ground and exited nuclear states. In this study, we apply this method to evaluate the isospin impurities in ground states of even-even and odd-odd N~Z n…
The magic numbers in exotic nuclei are discussed, and their novel origin is shown to be the spin-isospin dependent part of the nucleon-nucleon interaction in nuclei. The importance and robustness of this mechanism is shown in terms of meson exchange, G-matrix and QCD theories. In neutron-rich exotic nuclei, magic numbers such as N = 8, 20, etc. can disappear, while N = 6, 16, etc. arise, affecting the structure of lightest exotic nuclei to nucleosynthesis of heavy elements.
We study the implications of isospin symmetry in nuclear systems on two-body distributions and derive relations between different densities or momentum distributions of a given nucleus or of different nuclei in the same isospin multiplet. A connection between neutrinoless double beta decay transition of mirror nuclei and two-body densities is also obtained. The relations are numerically verified by means of quantum Monte Carlo calculations. We discuss the relevance of these results to the analysis of nuclear short-range correlations and also show that isospin symmetry allows us to extract info…
It is generally believed that isospin would diminish in its importance as we go towards heavy mass region due to isospin mixing caused by the growing Coulomb forces. However, it was realized quite early that isospin could become an important and useful quantum number for all nuclei including heavy nuclei due to neutron richness of the systems~\cite{robson}. Lane and Soper~\cite{lane} also showed in a theoretical calculation that isospin indeed remains quite good in heavy mass neutron rich systems. In this paper, we present isospin based calculations~\cite{jain,swati} for the fission fragment d…
Using a pair of the lightest mirror nuclei, $^3$He and $^3$H, we study the effect of the medium modification of pion fields on the flavor non-singlet structure function. The change of the pion fields leads to an enhancement of the flavor asymmetry of the antiquark distributions in a nucleus.
For nuclei with N = Z, the isospin degree of freedom is important and, for deformed systems, rotational bands of different isospin may be expected at low excitation energies. We have investigated, in a simple model space, the influence of the isospin-breaking Coulomb interaction on the degree of chaoticity of these rotational bands. The statistical measures used rely on an analysis of level-spacing distributions, which are extremely difficult to measure experimentally. We show, however, that the overlap intergrals between states of similar frequency reflect well the degree of chaoticity. This …
This work presents an approach to nuclear spin-isospin response, which is capable of describing the overall strength distribution up to high excitation energies, including the fine structure of the low-lying strength, and resolving the long-standing quenching problem. The model is a covariant realization of the nuclear field theory and based on the self-consistent extensions of the covariant energy density functional (CEDF) theory. Results of the recent calculations for spin-isospin response of ordinary and exotic medium-mass nuclei are presented and discussed.
By the use of the latest experimental data on the spectra of $^{133}$Sb and $^{131}$Sn and on the analysis of properties of other odd nuclei adjacent to doubly magic closed shells the isospin dependence of a mean spin-orbit potential is defined. Such a dependence received the explanation in the framework of different theoretical approaches.
The one- plus two-body isospin nonconserving nuclear interactions are included in the prediction of ground state energies of fp shell nuclei using spectral distribution theory. This in turn is used to calculate the linear term in the isobaric mass-multiplet equation and the predictions are then compared to experimental values after the addition of the Coulomb contribution. The agreement is found to be reasonable as observed for sd shell nuclei earlier. One also sees that in this method the contribution to the linear term comes almost completely from the one body isovector Hamiltonian and that …
A detailed study fusion of neutron-rich colliding nuclei is performed using various isospin dependent potentials. For present study, Three different series namely, Ne-Ne, Ca-Ca, and Zr-Zr are taken into account and N/Z ratio.A monotonous increase (decrease) in the fusion barrier positions (heights) using a unified second order nonlinear parametrization in the normalized fusion barrier positions and heights with (N/Z-1) is presented. These predications are in good agreement with the available theoretical as well as experimental results.
Stability of nuclei beyond the drip lines in the presence of an enveloping gas of nucleons and electrons, as prevailing in the inner crust of a neutron star, is studied in the temperature-dependent Thomas-Fermi framework. A limiting asymmetry in the isospin space beyond which nuclei cannot exist emerges from the calculations. The ambient conditions like temperature, baryon density and neutrino concentration under which these exotic nuclear systems can be formed are studied in some detail.
Recent studies have shown that the per-nucleon number of Short-Range Correlated (SRC) pairs in nuclei and the strength of the EMC effect are linearly correlated, increasing from light nuclei up to iron and then saturating. This paper shows that the per-proton number of SRC pairs and the strength of the EMC effect are linearly correlated and increase from light to heavy asymmetric neutron-rich nuclei without saturation. These quantities, calculated per neutron, are also linearly related, but saturate (have constant value) remarkably early, starting with 12C. We propose that the observed phenome…
Nuclear many-body theory is used to study nuclear matter and finite nuclei at extreme isospin. In-medium interactions in asymmetric nuclear matter are obtained from (Dirac-) Brueckner theory. Neutron skin formation in Ni and Sn isotopes is investigated by relativistic mean-field calculations in DDRH theory with density dependent meson-nucleon vertices. Applications to light nuclei are discussed with special emphasis on pairing and core polarization in weakly bound nuclei. Approaches accounting for continuum coupling in dripline pairing and core polarization are presented. Calculations for the …
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 …
We present systematic study of isospin impurities ($α_{\rm ISB}$) to the wave functions of $T=1/2$, $11\leq A \leq 47$ mirror nuclei and the isospin-symmetry-breaking (ISB) corrections ($δ_{\rm ISB}^{\rm V}$) to their ground state vector $β$-decays using, for the first time, multi-reference charge-dependent density functional theory (MR-DFT) that includes strong-force-rooted class-III interaction adjusted to correct for the Nolen-Schiffer anomaly in nuclear masses. We demonstrate that, unexpectedly, the strong-force-rooted isovector force gives rise to a large systematic increase of $α_{\rm IS…
The magnetic dipole (M1) and the Gamow-Teller (GT) excitations of finite nuclei have been studied in a fully self-consistent Hartree-Fock (HF) plus random phase approximation (RPA) approach by using a Skyrme energy density functional with spin and spin-isospin densities. To this end, we adopt the extended SLy5st interaction which includes spin-density dependent terms and stabilize nuclear matter with respect to spin instabilities. The effect of the spin-density dependent terms is examined in both the mean field and the spin-flip excited state calculations. The numerical results show that those…
The roles of isospin asymmetry in nuclei and neutron stars are investigated using a range of potential and field-theoretical models of nucleonic matter. The parameters of these models are fixed by fitting the properties of homogeneous bulk matter and closed-shell nuclei. We discuss and unravel the causes of correlations among the neutron skin thickness in heavy nuclei, the pressure of beta-equilibrated matter at a density of 0.1 fm$^{-3}$, and the radii of moderate mass neutron stars. The influence of symmetry energy on observables in heavy-ion collisions is summarized.
It has been proposed that multifragmentation can be related to the liquid-gas phase transition of nuclear matter. We study the statistical properties of finite nuclear matter near the phase transition with the help of a Lattice Gas Model (LGM). The original version of LGM with only one type of charge-neutral particles is well known to feature the properties of the liquid-gas phase transition. In this contribution, we address the effect of Coulomb and isospin dependence interaction for the finite nuclei transition, and study the symmetry energy properties of finite temperature systems.
Background: The isospin mixing is an interesting feature of atomic nuclei. It plays a crucial role in astrophysical nuclear reactions. However, it is not straightforward for variational nuclear structure models to describe it. Purpose: We propose a tractable method to describe the isospin mixing within a framework of the generator coordinate method and demonstrate its usability. Method: We generate the basis wave functions by applying the Fermi transition operator to the wave functions of isobars. The superposition of these basis wave functions and variationally obtained wave functions quantit…
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.
The $Λ$ separation energies in the mirror hypernuclei ${_Λ^4}{\rm H}-{_Λ^4}{\rm He}$ exhibit large charge symmetry breaking (CSB). Analyzing this CSB within pionless effective field theory while using partially conserved baryon-baryon SU(3) flavor symmetry, we deduce a $Λ-Σ^0$ induced in-medium admixture amplitude ${\cal A}_{I=1}\approx 1.5\%$ in the dominantly isospin $I=0$ $Λ$ hyperon. Our results confirm the free-space value ${\cal A}^{(0)}_{I=1}$ inferred directly within the SU(3) baryon octet by Dalitz and von-Hippel in 1964 and reaffirmed in a recent QCD+QED lattice calculation. Furtherm…
The isospin breaking effects due to the Coulomb interaction in weakly-bound nuclei are studied using the Gamow Shell Model, a complex-energy configuration interaction approach which simultaneously takes into account many-body correlations between valence nucleons and continuum effects. We investigate the near-threshold behavior of one-nucleon spectroscopic factors and the structure of wave functions along an isomultiplet. Illustrative calculations are carried out for the T=1 isobaric triplet. By using a shell-model Hamiltonian consisting of an isoscalar nuclear interaction and the Coulomb term…
By analyzing the energy-weighted moments of the strength function calculated in RPA and beyond it is shown that the explanation of the effect of missing strength of Gamow-Teller transitions requires that residual interaction produce high-excited $1^{+}$ particle-hole collective states. The example of this interaction is presented. The manifestations of spin-isospin nuclear response in nuclear muon capture are discussed.
The question of isospin-symmetry breaking in nuclei of the $sd$ shell is addressed. We propose a new global parameterization of the isospin-nonconserving (INC) shell-model Hamiltonian which accurately describes experimentally known isobaric mass splittings. The isospin-symmetry violating part of the Hamiltonian consists of the Coulomb interaction and effective charge-dependent forces of nuclear origin. Particular attention has been paid to the effect of the short-range correlations. The behavior of $b$ and $c$ coefficients of the isobaric-mass-multiplet equation (IMME) is explored in detail. I…
Isospin violation effects in nuclei are investigated within a microscopic approach which takes into account the influence of the residual strong interaction on the Coulomb interaction. The renormalization of the off-diagonal Coulomb field acting within a nucleus, by the residual strong interaction is calculated analytically in a simplified RPA. From the expression for the suppression coefficient of the isospin violating part of the Coulomb field, the isospin violating spreading widths of isobaric analog states are derived. The resulting reduction of the width is in agreement with the data on t…
Physics of nuclei at extreme values of the isospin is at the focus of present-day nuclear science. Experimentally, thanks to existing and emerging radioactive-ion-beam facilities, we are on the verge of invading the territory of extreme N/Z ratios in an unprecedented way. Theoretically, nuclear exotica represent a formidable challenge for the nuclear many-body theories and their power to predict nuclear properties far from stability. Going to the limits of the nuclear binding is also important for an improvement of our description of normal nuclei from the neighborhood of the beta stability va…
We study the extension of our translationally invariant treatment of few-body nuclear systems to heavier nuclei. At the same time we also introduce state-dependent correlation operators. Our techniques are tailored to those nuclei that can be dealt with in $LS$ coupling, which includes all nuclei up to the shell closure at $A=40$. We study mainly $p$-shell nuclei in this paper. A detailed comparison with other microscopic many-body approaches is made, using a variety of schematic nuclear interactions. It is shown that our methodology produces very good energies, and presumably also wave functi…
Recently, we have applied for the first time the angular momentum and isospin projected nuclear density functional theory to calculate the isospin-symmetry breaking (ISB) corrections to the superallowed beta-decay. With the calculated set of the ISB corrections we found |V_{ud}|=0.97447(23) for the leading element of the Cabibbo-Kobayashi-Maskawa matrix. This is in nice agreement with both the recent result of Towner and Hardy [Phys. Rev. {\bf C77}, 025501 (2008)] and the central value deduced from the neutron decay. In this work we extend our calculations of the ISB corrections covering all s…
