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.
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…
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.
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…
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.
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.
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…
The anomaly in Coulomb energy differences (CED) between the isospin T=1 states in the odd-odd N=Z nucleus 70Br and the analogue states in its even-even partner 70Se has remained a puzzle. This is a direct manifestation of isospin-symmetry breaking in effective nuclear interactions. Here, we perform large-scale shell-model calculations for nuclei with A=66-78 using the new filter diagonalization method based on the Sakurai-Sugiura algorithm. The calculations reproduce well the experimental CED. The observed negative CED for A=70 are accounted for by the cross-shell neutron excitations from the …
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.
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 …
We investigate the role of the Coulomb and the vector-isovector $ρ$ potentials in the asymmetry of the neutron and proton pseudospin splittings in nuclei. To this end, we solve the Dirac equation for the nucleons using central vector and scalar potentials with Woods-Saxon shape and $Z$ and $N-Z$ dependent Coulomb and $ρ$ potentials added to the vector potential. We study the effect of these potentials on the energy splittings of proton and neutron pseudospin partners along a Sn isotopic chain. We use an energy decomposition proposed in a previous work to assess the effect of a pseudospin-orbit…
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.
We study the role the proton-electron gas interaction has on the formation of nuclear structures in neutron star crusts. Using a classical molecular dynamics model we study isospin symmetric and asymmetric matter at subsaturation densities and low temperatures varying the Coulomb interaction strength. The effect of such variation is quantified on the fragment size multiplicity, the inter-particle distance, the isospin content of the clusters, the nucleon mobility and cluster persistence, and on the nuclear structure shapes. We find that the proton-electron Coulomb interaction distributes matte…
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.
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…
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…
The nuclear density functional framework, based on chiral dynamics and the symmetry breaking pattern of low-energy QCD, is extended to the description of collective nuclear excitations. Starting from the relativistic point-coupling Lagrangian previously introduced [Nucl. Phys. A770 (2006) 1], the proton-neutron (quasiparticle) random phase approximation is formulated and applied to investigate the role of chiral pion-nucleon dynamics in excitation modes involving spin and isospin degrees of freedom, e.g. isobaric analog states and Gamow-Teller resonances.
We study Fermi transitions and isospin mixing in an isotopic chain 70-78 Kr considering various approximations that use the same Skyrme-Hartree-Fock single particle basis. We study Coulomb effects as well as the effect of BCS and quasiparticle random phase approximation (QRPA) correlations. A measure of isospin mixing in the approximate ground state is defined by means of the expectation value of the isospin operator squared in N=Z nuclei (which is generalized to N different from Z nuclei). Starting from strict Hartree-Fock approach without Coulomb, it is shown that the isospin breaking is neg…
Unlike their lighter counterparts, most odd-odd N=Z nuclei with mass A > 40 40 have ground states with isospin T=1, suggesting an increased role for the isovector pairing interaction. A simple SO(5) seniority-like model of this interaction reveals a striking and heretofore unnoticed interplay between like-particle and neutron-proton isovector pairing near N=Z that is reflected in the number of each kind of pair as a function of A and T. Large scale shell-model calculations exhibit the same trends, despite the simultaneous presence of isoscalar pairs, deformation, and other correlations.
A selfconsistent approach based on a deformed HF+BCS+QRPA method with density-dependent Skyrme forces is used to describe beta+ decay properties in even-even deformed proton rich nuclei. Residual spin-isospin forces are included in the particle-hole and particle-particle channels. The quasiparticle basis contains neutron-neutron and proton-proton pairing correlations in the BCS approach, while neutron-proton pairing interaction is treated as a residual force in QRPA. We discuss the sensitivity of Gamow-Teller strength distributions and beta+/EC half-lives to deformation, pairing and the streng…
We study the effect of isospin degree of freedom on balance energy throughout the mass range between 50 and 350 for two sets of isobaric systems with N/A = 0.5 and 0.58. Our fndings indicate that different values of balance energy for two isobaric systems may be mainly due to the Coulomb repulsion. We also demonstrate clearly the dominance of Coulomb repulsion over symmetry energy.
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 spin magnetic dipole transitions and the neutron-proton spin-spin correlations in $sd-$shell even-even nuclei with $N=Z$ are investigated using shell model wave functions. The isoscalar spin-triplet pairing correlation provides a substantial quenching effect on the spin magnetic dipole transitions, especially the isovector (IV) ones. Consequently, an enhanced isoscalar spin-triplet pairing interaction influences the proton-neutron spin-spin correlation deduced from the difference between the isoscalar (IS) and the IV sum rule strengths. The effect of the $Δ$ ($Δ_{33}$ resonance)-hole coupl…
We calculate the isospin-mixing parameter for several Tz=-1, Tz=0 and Tz=1 nuclei from Mg to Sn in the particle-number conserving Higher Tamm-Dancoff approach taking into account the pairing correlations. In particular we investigate the role of the Coulomb interaction and the |Tz|=1 pairing correlations. To do so the HTDA approach is implemented with the SIII Skyrme effective nucleon-nucleon interaction in the mean-field channel and a delta interaction in the pairing channel. We conclude from this investigation that the pairing correlations bring a large contribution to isospin-symmetry break…
We adapt the local density approximation to add the high-momentum tails (HMTs) to finite nuclei's Slater-determinant momentum distributions. The HMTs are extracted by the extended Brueckner-Hartree-Fock (EBHF) method or by the lowest order cluster approximation. With a correction factor being added to EBHF, it is sufficiently in agreement with the experimental benchmark, i.e., the high-momentum $N/Z$ ratios approximately equal to $1$, and the low-momentum $N/Z$ ratios approximately equal to $N/Z$ of the systems. It is also found that the tensor force makes the nucleon-nucleon correlations appe…
The structures of odd-odd $N=Z$ nuclei in the lower \emph{fp} shell have been investigated with a new isospin-nonconserving microscopical interaction. The interaction is derived from a high-precision charge-dependent Bonn nucleon-nucleon potential using the folded-diagram renormalization method. Excellent agreements with experimental data have been obtained up to band terminations. Particularly, the relative positions of T=0 and T=1 bands were well reproduced. Calculations with another interaction obtained from the Idaho-A chiral potential showed similar results. Our calculations also give a g…
Explicit relations between the isospin mixing probability, the spreading width $Γ_{IAS}^{\downarrow}$ of the Isobaric Analog State (IAS) and the statistical decay width $Γ_c$ of the compound nucleus at finite excitation energy, are derived by using the Feshbach projection formalism. The temperature dependence of the isospin mixing probability is discussed quantitatively for the first time by using the values of $Γ_{IAS}^{\downarrow}$ and of $Γ_c$ calculated by means of microscopic models. It is shown that the mixing probability remains essentially constant up to a temperature of the order of 1…
Effects of the isospin-symmetry breaking (ISB) beyond mean-field Coulomb terms are systematically studied in nuclear masses near the $N=Z$ line. The Coulomb exchange contributions are calculated exactly. We use extended Skyrme energy density functionals (EDFs) with proton-neutron-mixed densities, to which we add new terms breaking the isospin symmetry. Two parameters associated with the new terms are determined by fitting mirror and triplet displacement energies (MDEs and TDEs) of isospin multiplets. The new EDFs reproduce MDEs for the $T=\frac12$ doublets and $T=1$ triplets, and TDEs for the …
We study the effect of isospin degree of freedom on the balance energy (E$_{bal}$) as well as its mass dependence throughout the mass range 48-270 for two sets of isobaric systems with N/Z = 1 and 1.4 at different colliding geometries ranging from central to peripheral ones. Our findings reveal the dominance of Coulomb repulsion in isospin effects on E$_{bal}$ as well as its mass dependence throughout the range of the colliding geometry. Our results also indicate that the effect of symmetry energy and nucleon-nucleon cross section on E$_{bal}$ is uniform throughout the mass range and throughou…
The density-dependent nuclear symmetry energy is directly related to the isospin asymmetry for finite and infinite nuclear systems. It is critical to determine the coefficients of symmetry energy and its related observables as it holds great importance in different areas of nuclear physics, such as analyzing the structure of ground state exotic nuclei and neutron star study. The ground state bulk properties such as nuclear binding energy, quadrupole deformation, two-neutron separation energy, the differential variation of two-neutron separation energy, and root-mean-square charge radius for Sc…
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 discuss the sensitivity of fission barrier for heavy neutron-rich nuclei to fission paths in the two dimensional neutron-proton quadrupole plane. To this end, we use the constrained Skyrme-Hartree-Fock + BCS method, and examine the difference of fission barriers obtained with three constraining operators, that is, the neutron, proton, and mass quadrupole operators. We investigate $^{220}$U, $^{236}$U, and $^{266}$U, %from proton-rich to neutron-rich uranium isotopes, that is relevant to r-process nucleosynthesis. We find that the fission barrier heights are almost the same among the three c…
We study the effect of isospin degree of freedom on balance energy throughout the mass range between 50 and 350 for two sets of isotopic systems with N/Z = 1.16 and 1.33 as well as isobaric systems with N/A = 1.0 and 1.4. Our findings indicate that different values of balance energy for two isobaric systems may be mainly due to the Coulomb repulsion. We also demonstrate clearly the dominance of Coulomb repulsion over symmetry energy.
The Gamow-Teller resonances (GTR) and isobaric analog states (IAS) of a sequence of even-even Sn target nuclei are calculated by using the framework of the relativistic Hartree-Bogoliubov model plus proton-neutron quasiparticle random-phase approximation. The calculation reproduces the experimental data on ground-state properties, as well as the excitation energies of the isovector excitations. It is shown that the isotopic dependence of the energy spacings between the GTR and IAS provides direct information on the evolution of neutron skin-thickness along the Sn isotopic chain. A new method i…
Heavy Ion Collisions (HIC) represent a unique tool to probe the in-medium nuclear interaction in regions away from saturation. In this report we present a selection of new reaction observables in dissipative collisions particularly sensitive to the symmetry term of the nuclear Equation of State (Iso-EoS). We will first discuss the Isospin Equilibration Dynamics. At low energies this manifests via the recently observed Dynamical Dipole Radiation, due to a collective neutron-proton oscillation with the symmetry term acting as a restoring force. At higher beam energies Iso-EoS effects will be see…
We study the effect of isospin degree of freedom on balance energy throughout the mass range between 50 and 350 for two sets of isotopic systems with N/Z = 1.16 and 1.33 as well as isobaric systems with N/Z = 1.0 and 1.4. Our findings indicate that different values of balance energy for two isobaric systems may be mainly due to the Coulomb repulsion. We also demonstrate clearly the dominance of Coulomb repulsion over symmetry energy.
