The isospin-asymmetry dependence of the nuclear matter equation of state obtained from microscopic chiral two- and three-body interactions in second-order many-body perturbation theory is examined in detail. The quadratic, quartic and sextic coefficients in the Maclaurin expansion of the free energy per particle of infinite homogeneous nuclear matter with respect to the isospin asymmetry are extracted numerically using finite differences, and the resulting polynomial isospin-asymmetry parametrizations are compared to the full isospin-asymmetry dependence of the free energy. It is found that in the low-temperature and high-density regime where the radius of convergence of the expansion is generically zero, the inclusion of higher-order terms beyond the leading quadratic approximation leads overall to a significantly poorer description of the isospin-asymmetry dependence. In contrast, at high temperatures and densities well below nuclear saturation density, the interaction contributions to the higher-order coefficients are negligible and the deviations from the quadratic approximation are predominantly from the noninteracting term in the many-body perturbation series. Furthermore, we extract the leading logarithmic term in the isospin-asymmetry expansion of the equation of state at zero temperature from the analysis of linear combinations of finite differences. It is shown that the logarithmic term leads to a considerably improved description of the isospin-asymmetry dependence at zero temperature.
The effects of an isospin asymmetry and in-medium corrections to the nucleon collision cross section on the balance energy are explored. The BUU model for intermediate energy heavy-ion collisions is used with isospin-dependent mean fields to calculate the balance energies of 58Fe + 58Fe and 58Ni + 58Ni for a range of impact parameters. We find that we are able to reproduce the impact parameter dependence of the balance energy, and the sign (but not the magnitude) of the shift in balance balance energy as a function of isospin asymmetry.
Using the isospin dependent quantum molecular dynamics model, we study the effect of charge asymmetry and isospin dependent cross-section on nuclear stopping and multiplicity of free nucleons and LMF's. Simulations were carried out for the reactions $^{124}X_{m}+^{124}X_{m}$, where m varies from 47 to 59 and for $^{40}Y_{n}+^{40}Y_{n}$, where n varies from 14 to 23. Our study shows that nuclear stopping as well as the production of LMF's depend strongly on the isospin of the cross-section.
Using the isospin dependent quantum molecular dynamics model, we study the effect of charge asymmetry and isospin dependent cross-section on different aspects of elliptical flow. Simulations have been carried out for the reactions of $^{124}X_{m}+^{124}X_{m}$, where m = (47, 50, 53, 57 and 59) and $^{40}X_{n}+^{40}X_{n}$, where n= (14, 16, 18, 21 and 23). Our study shows that elliptical flow depend strongly on the isospin of cross-section. The transition energy remains almost constant with increase in N/Z of the system. A good agreement is obtained with experimental measurements.
We examine the properties of the isospin-asymmetry expansion of the nuclear equation of state from chiral two- and three-body forces. We focus on extracting the high-order symmetry energy coefficients that consist of both normal terms (occurring with even powers of the isospin asymmetry) as well as terms involving the logarithm of the isospin asymmetry that are formally nonanalytic around the expansion point of isospin-symmetric nuclear matter. These coefficients are extracted from numerically precise perturbation theory calculations of the equation of state coupled with a new set of finite di…
The Lagrangian density of relativistic mean-field (RMF) theory with non-linear derivative (NLD) interactions is applied to isospin asymmetric nuclear matter. We study the symmetry energy and the density and energy dependences of nucleon selfenergies. At high baryon densities a soft symmetry energy is obtained. The energy dependence of the isovector selfenergy suppresses the Lane-type optical potential with increasing energy and predicts a $ρ$-meson induced mass splitting between protons and neutrons in isospin asymmetric matter.
Based on a chiral approach to nuclear matter, we calculate the quartic term in the expansion of the equation of state of isospin-asymmetric nuclear matter. The contributions to the quartic isospin asymmetry energy $A_4(k_f)$ arising from $1π$-exchange and chiral $2π$-exchange in nuclear matter are calculated analytically together with three-body terms involving virtual $Δ(1232)$-isobars. From these interaction terms one obtains at saturation density $ρ_0 = 0.16\,$fm$^{-3}$ the value $A_4(k_{f0})= 1.5\,$MeV, more than three times as large as the kinetic energy part. Moreover, iterated $1π$-exch…
Pseudo-spin symmetry in nuclei is investigated considering the Dirac equation with a Lorentz structured Woods-Saxon potential. The isospin correlation of the energy splittings of pseudo-spin partners with the nuclear potential parameters is studied. We show that in an isotopic chain, the pseudo-spin symmetry is better realized for neutrons than for protons. This behavior comes from balance effects amongst the central nuclear potential parameters. In general, we found an isospin asymmetry of the nuclear pseudo-spin interaction, opposed to the nuclear spin-orbit interaction which is quasi isospi…
We study the one-body momentum distribution at different densities in nuclear matter, with special emphasis on its components at high momentum. Explicit calculations for finite neutron-proton asymmetry, based on the ladder self-consistent Green's function approach, allow us to access the isospin dependence of momentum distributions and elucidate their role in neutron-rich systems. Comparisons with the deuteron momentum distribution indicate that a substantial proportion of high-momentum components are dominated by tensor correlations. We identify the density dependence of these tensor correlat…
The effect of $δ-$ and $ω-ρ-$meson cross couplings on asymmetry nuclear systems are analyzed in the frame-work of an effective Field theory motivated relativistic mean field formalism. The calculations are done on top of the G2 parameter set, where these contributions are absent. We calculate the root mean square radius, binding energy, single particle energy (for the $1^{st}$ and last occupied orbits), density and spin-orbit interaction potential for some selected nuclei and evaluate the $L_{sym}-$ and $E_{sym}-$ coefficients for nuclear matter as function of $δ-$ and $ω-ρ-$meson coupling str…
Nuclear matter within the liquid-gas phase transition region is investigated in a mean-field two-component Fermi-gas model. Following largely analytic considerations, it is shown that: (1) Due to density dependence of asymmetry energy, some of the neutron excess from the high-density phase could be expelled into the low-density region. (2) Formation of clusters in the gas phase tends to counteract this trend, making the gas phase more liquid-like and reducing the asymmetry in the gas phase. Flow of asymmetry between the spectator and midrapidity region in reactions is discussed and a possible …
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 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 computation of the thermodynamic properties of nuclear matter is a central task of theoretical nuclear physics. The nuclear equation of state is an essential quantity in nuclear astrophysics and governs the properties of neutron stars and core-collapse supernovæ. The framework of chiral effective field theory provides the basis for the description of nuclear interactions in terms of a systematic low-energy expansion. In this thesis, we apply chiral two- and three-nucleon interactions in perturbative many-body calculations of the thermodynamic equation of state of infinite homogeneous nucle…
Generalized symmetry energy coefficients of asymmetric nuclear matter are obtained as screening functions. The dependence of the isospin symmetry energy coefficient on the neutron proton (n-p) asymmetry may be determined unless by a constant (exponent) $Z$ which depend on microscopic properties. The dependence of the generalized symmetry energy coefficients with Skyrme forces on the n-p asymmetry and on the density, only from .5 up to 1.5 $ρ_0$, are investigated in the isospin and scalar channels. The use of Skyrme-type effective forces allows us to obtain analytical expressions for these para…
Pseudospin symmetry in nuclei is investigated by solving the Dirac equation with Woods-Saxon scalar and vector radial potentials. We relate the pseudospin interaction with a pseudospin-orbit term in a Schroedinger-like equation for the lower component of the Dirac spinor. We show that this term gives a large contribution to the energy splittings of pseudospin partners, so that the near pseudospin degeneracy arises from a significant cancellation among the different terms in that equation. This is a manifestation of the dynamical character of this symmetry in the nucleus. We analyze the isospin…
A concept of \emph{isospin blocking} in the process of isospin diffusion in heavy-ion collisions is raised. Generally, in the process of isospin diffusion, isospin asymmetry would diffuse from the place with large asymmetry to the place with small asymmetry. However, our study shows that the isospin diffusion could be blocked in case the local value of the symmetry energy is larger. We dub this phenomenon ``isospin blocking''. To check this behavior, in the framework of an Isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model, isospin diffusions in the isotope Sn+Sn reactions at…
We investigate the $^1S_0$ neutron and proton superfluidity in isospin asymmetric nuclear matter. We have concentrated on the isospin dependence of the pairing gaps and the effect of a microscopic three-body force. It is found that as the isospin asymmetry goes higher, the neutron $^1S_0$ superfluid phase shrinks gradually to a smaller density domain, while the proton one extends rapidly to a much wider density domain. The three-body force turns out to weaken the neutron $^1S_0$ superfluidity slightly, but it suppresses strongly the proton $^1S_0$ superfluidity at high densities in nuclear mat…
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 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…
It has been argued by Buckley et. al.(Phys. Rev. Lett. 92, 151102, 2004) that nuclear matter is a type-I rather than a type-II superconductor. The suggested mechanism is a strong interaction between neutron and proton Cooper pairs, which arises from an assumed U(2) symmetry of the effective potential, which is supposed to originate in isospin symmetry of the underlying nuclear interactions. To test this claim, we perform an explicit mean-field calculation of the effective potential of the Cooper pairs in a model with a simple four-point pairing interaction. In the neutron star context, matter …
We studied the effect of cross section on mass asymmetric systems. The mass asymmetry of a reaction can be defined by the asymmetry parameter η = |(AT - AP)/(AT + AP)|; [1] where AT and AP are the masses of the target and projectile, respectively. The η = 0 corresponds to the symmetric reactions, whereas non-zero values of η define different asymmetries of a reaction. Reactions include 208Pb82 + 208Pb82 having η = 0, 40Ca20 + 208Pb82 having η = 0.6 and 12C6 + 197Au79 having η = 0.8 This work has been carried out within the frame work of isospin dependent quantum molecular dynamics (IQMD) model…
We use the Isospin Quantum Molecular Dynamics model (IQMD) to analyze the centrality dependence of the isospin ratio of pions, $π^-/π^+$. We find that the density dependence of the asymmetry potential, the Pauli blocking of the $Δ$-decay and the thickness of the neutron skin influence in different ways this observable. Using the centrality dependence of this ratio at different beam energies we can disentangle the different contributions and open the way for their experimental determination.
Correlation between nuclear isospin asymmetry and $α$-particle preformation probability for superheavy nuclei from a Bayesian inference
University of South China（南华大学）；School of Mathematics and Physics, University of South China（南华大学数学与物理学院）；Hunan Provincial Key Laboratory of Mathematical Modeling and Scientific Computing, University of South China（南华大学湖南省数学建模与科学计算重点实验室）；School of Nuclear Science and Technology, University of South China（南华大学核科学与技术学院）；School of Physical Science and Technology, Southwest Jiaotong University（西南交通大学物理科学与技术学院）
We study the thermodynamic properties of QCD at nonzero isospin chemical potential using improved staggered quarks at physical quark masses. In particular, we discuss the determination of the equation of state at zero and nonzero temperatures and show results. Using the results for the isospin density $n_I$, we also determine the phase diagram in the $(n_I,T)$-plane.
We study the influence of the isospin asymmetry on the phase structure of strongly interacting quark matter near the critical point (CP) using a Ginzburg-Landau approach. The effect is found to be drastic, not only bringing about the shift of the location of the CP, but resulting in a rich phase structure in the vicinity of the CP. In particular, new tricritical and triple points emerge as soon as the isospin density becomes finite. Moreover, we find the CP being washed out from the phase diagram due to the stabilization of a homogeneous charged pion condensate when the isospin chemical potent…
We study the phase diagram and the thermodynamic properties of QCD at nonzero isospin asymmetry at physical quark masses with staggered quarks. In particular, continuum results for the phase boundary between the normal and the pion condensation phases and the chiral/deconfinement transition are presented. Our findings indicate that the pion condensation phase is restricted to $T\lesssim170$~MeV for isospin chemical potentials up to 325~MeV. We also use the data to test the range of validity of the Taylor expansion method and show first results for the equation of state.
The BCS-BEC crossover and phase diagram for asymmetric nuclear superfluid with pairings in isospin I = 0 and I = 1 channels are investigated at mean field level, by using a density dependent nucleon-nucleon potential. Induced by the in-medium nucleon mass and density dependent coupling constants, neutron-proton Cooper pairs could be in BEC state at sufficiently low density, but there is no chance for the BEC formation of neutron-neutron and proton-proton pairs at any density and asymmetry. We calculate the phase diagram in asymmetry-temperature plane for weakly interacting nuclear superfluid, …
The influence of nuclear isospin mixing on parity-violating elastic electron scattering is studied for the even-even, N=Z nuclei 12C, 24Mg, 28Si, and 32S. Their ground-state wave functions have been obtained using a self-consistent axially-symmetric mean-field approximation with density-dependent effective two-body Skyrme interactions. Some differences from previous shell-model calculations appear for the isovector Coulomb form factors which play a role in determining the parity-violating asymmetry. To gain an understanding of how these differences arise, the results have been expanded in a sp…
We investigate the equation of state of asymmetric nuclear matter and its isospin dependence in various spin-isospin $ST$ channels within the framework of the Brueckner-Hartree-Fock approach extended to include a microscopic three-body force (TBF). It is shown that the potential energy per nucleon in the isospin-singlet T=0 channel is mainly determined by the contribution from the tensor SD coupled channel. At high densities, the TBF effect on the isospin-triplet T=1 channel contribution turns out to be much larger than that on the T=0 channel contribution. At low densities around and below th…
This study uses classical molecular dynamics to simulate infinite nuclear matter and study the effect of isospin asymmetry on bulk properties such as energy per nucleon, pressure, saturation density, compressibility and symmetry energy. The simulations are performed on systems embedded in periodic boundary conditions with densities and temperatures in the ranges $ρ$=0.02 to 0.2 fm$^{-3}$ and T = 1, 2, 3, 4 and 5 MeV, and with isospin content of $x=Z/A$=0.3, 0.4 and 0.5. The results indicate that symmetric and asymmetric matter are self-bound at some temperatures and exhibit phase transitions f…
This thesis explores nuclear systems under extreme conditions of isospin asymmetry and strong magnetic fields. Its first chapter is devoted to the phase diagram of isospin-asymmetrical nuclear matter in the density-temperature plane. Four competing phases of matter are included into the consideration: the unpaired phase, the ordinary Bardeen-Cooper-Schrieffer (BCS) phase, a phase where normal fluid and superfluid separate into distinct domains and the superfluid phase with a non-zero total momentum of Cooper pairs. The evolution of these phases from the weakly BCS limit to the strongly coupled…
Using the isospin dependent quantum molecular dynamics model, we study the effect of charge asymmetry and isospin dependent cross-section on $\frac{dN}{d(<Cos2ϕ>)}$ and $\frac{dN}{p_tdp_t}$. Simulations have been carried out for the reactions of $^{124}X_{m}+^{124}X_{m}$, where m = (47, 50 and 59) and $^{40}S_{16}+^{40}S_{16}$. Our study shows that these parameters depend strongly on the isospin of cross-section and charge asymmetry. The distribution of nucleons and fragments is not symmetric around the beam axis.
We study baryonic matter with isospin asymmetry, including fully dynamically its interplay with pion condensation. To this end, we employ the holographic Witten-Sakai-Sugimoto model and the so-called homogeneous ansatz for the gauge fields in the bulk to describe baryonic matter. Within the confined geometry and restricting ourselves to the chiral limit, we map out the phase structure in the presence of baryon and isospin chemical potentials, showing that for sufficiently large chemical potentials condensed pions and isospin-asymmetric baryonic matter coexist. We also present first results of …
An isospin lattice-gas model, which is a spin-1 Ising model, is employed to investigate the liquid-gas phase transition in asymmetric nuclear matter. We consider nuclear matter as a lattice where each lattice site can be either empty or occupied by a proton or a neutron, with a nearest-neighbor interaction among the nucleons. With the Bragg-Williams mean field approximation, we calculate various thermodynamic properties of nuclear matter for different densities and different proton-neutron asymmetry parameter $s$. Our model exhibits liquid-gas phase transition below a critical temperature $T_c…
The $π^-/π^+$ ratio is examined as a function of isospin asymmetry and beam energy for central collisions induced by neutron-rich nuclei within an isospin-dependent hadronic transport model. The $π^-/π^+$ ratio is found to increase with the isospin asymmetry, but decrease with the beam energy of the reaction. For neutron-rich systems, such as, $^{124}Sn+^{124}Sn$ and $^{132}Sn+^{124}Sn$, the sensitivity of $π^-/π^+$ ratio to nuclear symmetry energy is almost beam energy independent.
Properties of spin polarized isospin asymmetric nuclear matter are studied within the framework of the Brueckner--Hartree--Fock formalism. The single-particle potentials of neutrons and protons with spin up and down are determined for several values of the neutron and proton spin polarizations and the asymmetry parameter. It is found an almost linear and symmetric variation of the single-particle potentials as increasing these parameters. An analytic parametrization of the total energy per particle as a function of the asymmetry and spin polarizations is constructed. This parametrization is em…
The QCD phase diagram is studied in the presence of an isospin asymmetry using continuum extrapolated staggered quarks with physical masses. In particular, we investigate the phase boundary between the normal and the pion condensation phases and the chiral/deconfinement transition. The simulations are performed with a small explicit breaking parameter in order to avoid the accumulation of zero modes and thereby stabilize the algorithm. The limit of vanishing explicit breaking is obtained by means of an extrapolation, which is facilitated by a novel improvement program employing the singular va…
Spin-polarized isospin asymmetric nuclear matter is studied within the Dirac-Brueckner-Hartree-Fock approach. After a brief review of the formalism, we present and discuss the self-consistent single-particle potentials at various levels of spin and isospin asymmetry. We then move to predictions of the energy per particle, also under different conditions of isospin and spin polarization. Comparison with the energy per particle in isospin symmetric or asymmetric unpolarized nuclear matter shows no evidence for a phase transition to a spin ordered state, neither ferromagnetic nor antiferromagneti…
We calculate the density-dependent spin-isospin asymmetry energy $J(k_f)$ of nuclear matter in the three-loop approximation of chiral perturbation theory. The interaction contributions to $J(k_f)$ originate from one-pion exchange, iterated one-pion exchange, and irreducible two-pion exchange with no, single, and double virtual $Δ$-isobar excitation. We find that the approximation to $1π$-exchange and iterated $1π$-exchange terms (which leads already to a good nuclear matter equation of state by adjusting an emerging contact-term) is spin-isospin stable, since $J(k_{f0})\simeq 24 {\rm MeV}>0$. …
Symmetry energy coefficients of explicitly isospin asymmetric nuclear matter at variable densities (from .5$ρ_0$ up to 2 $ρ_0$) are studied as generalized screening functions. An extended stability condition for asymmetric nuclear matter is proposed. We find the possibility of obtaining stable asymmetric nuclear matter even in some cases for which the symmetric nuclear matter limit is unstable. Skyrme-type forces are extensively used in analytical expressions of the symmetry energy coefficients derived as generalized screening functions in the four channels of the particle hole interaction pro…
We suggest an extension to isospin asymmetric matter of the quarkyonic model from McLerran and Reddy. This extension allows us to construct the $β$-equilibrium between quarks, nucleons and leptons. The concept of the quarkyonic matter originates from the large number of color limit for which nucleons are the correct degrees of freedom near the Fermi surface -- reflecting the confining forces -- while deep inside the Fermi sea quarks naturally appear. In isospin asymmetric matter, we suggest that this new concept can be implemented within a global isoscalar relation between the shell gaps diffe…
We study the isospin singlet pairing in asymmetric nuclear matter with nonzero total momentum of the condensate Cooper pairs. The quasiparticle excitation spectrum is fourfold split compared to the usual BCS spectrum of the symmetric, homogeneous matter. A twofold splitting of the spectrum into separate branches is due to the finite momentum of the condensate, the isospin asymmetry, or the finite quasiparticle lifetime. The coupling of the isospin singlet and triplet paired states leads to further twofold splitting of each of these branches. We solve the gap equation numerically in the isospin…
Experimental correlation between the rms nucleus charge radius and the neutron-proton asymmetry is discussed. Simple attempt of explanation of this correlation using a semi-empirical liquid drop model which takes into account nuclear compressibility, nuclear deformation and neutron skin effects is presented. It seems that such procedure could be used as a tool for determination of the nuclear equation of state.
We calculate the mean free path of protons and neutrons in symmetric and asymmetric nuclear matter, based on microscopic in-medium nucleon-nucleon cross sections. Those are obtained from calculations of the G-matrix including relativistic "Dirac" effects. The dependence of the mean free path on energy and isospin asymmetry is discussed. We conclude by suggesting possible ways our microscopic predictions may be helpful in conjunction with studies of rare isotopes.
Isoscaling is found to hold for fragment yields in the antisymmetrized molecular dynamics (AMD) simulations for collisions of calcium isotopes at 35 MeV/nucleon. This suggests the applicability of statistical considerations to the dynamical fragment emission. The observed linear relationship between the isoscaling parameters and the isospin asymmetry of fragments supports the above suggestion. The slope of this linear function yields information about the symmetry energy in low density region where multifragmentation occurs.
The free energy and the equation of state of isospin-asymmetric nuclear matter are calculated at finite temperature up to three loop order in the framework of in-medium chiral perturbation theory, systematically incorporating one- and two-pion exchange dynamics to this order. Effects from the two-pion exchange with explicit Δ-isobar excitation are included, as well as three-body forces. We construct the phase diagram of nuclear matter for different proton fractions x_p and investigate the dependence of nuclear matter properties on the isospin-asymmetry. A detailed study of the liquid-gas phase…
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$^{-3}$, the derivative of the nuclear symmetry energy at the same density and the radii of moderate mass neutron stars. Constraints on the symmetry properties of nu…
A two-components isospin lattice gas model has been employed to study the liquid-gas phase transition for asymmetric nuclear matter. An additional degree of freedom, namely, the asymmetry parameter alpha has been considered carefully for studying the phase transition. We have shown that under the mean field approximation, the liquid-gas phase transition given by this model is of second order. The entropy continues at the phase transition point. The binodal surface is addressed.
An alternative way to constrain the density dependence of the symmetry energy with the slope of the neutron skin thickness of nuclei which shows a linear relation to both the isospin asymmetry and the nuclear charge with a form of Z^{2/3} is proposed. The linear dependence of the neutron skin thickness on the nuclear charge and isospin asymmetry is systematically studied with the data from antiprotonic atom measurement experimentally and the extended Thomas-Fermi approach incorporated the Skyrme energy density functional theoretically. An obviously linear relationship between the slope paramet…
According to perturbation theory predictions, QCD matter in the zero-temperature, high-density limits of QCD at nonzero isospin chemical potential is expected to be in a superfluid Bardeen-Cooper-Schrieffer (BCS) phase of $u$ and $\bar{d}$ Cooper pairs. It is also expected, on symmetry grounds, that such phase connects via an analytical crossover to the phase with Bose-Einstein condensation (BEC) of charged pions at $μ_\text{I}\geq m_π/2$. With lattice results, showing some indications that the deconfinement crossover also smoothly penetrates the BEC phase, the conjecture was made that the for…
The formalism of linear response theory for a Skyrme functional including spin-orbit and tensor terms is generalized to the case of infinite nuclear matter with arbitrary isospin asymmetry. Response functions are obtained by solving an algebraic system of equations, which is explicitly given. Spin-isospin strength functions are analyzed varying the conditions of density, momentum transfer, asymmetry and temperature. The presence of instabilities, including the spinodal one, is studied by means of the static susceptibility.
We have studied the influences of isospin symmetry breaking of nucleon-nucleon interaction on the various properties of asymmetrical nuclear matter and $β$-stable matter. For asymmetrical nuclear matter, it is found that by including this isospin symmetry breaking, the changes of bulk properties increase by increasing both density and asymmetry parameter. However, these effects on the total energy and equation of state of $β$-stable matter are ignorable. For asymmetrical nuclear matter, the validity of the empirical parabolic law in the isospin symmetry breaking case is shown. It is observed t…
Isospin symmetry of atomic nuclei is explicitly broken by the charge-dependent interactions, primarily the Coulomb force. Within the nuclear density functional theory, isospin is also broken spontaneously. We propose a projection scheme rooted in a mean field theory, that allows the consistent treatment of isospin breaking in both ground and exited nuclear states. We demonstrate that this scheme is essentially free from spurious divergences plaguing particle-number and angular-momentum restoration approaches. Applications of the new technique include excited high-spin states in medium-mass N=Z…
Symmetry energy terms from macroscopic mass formulae are investigated as generalized polarizabilities of nuclear matter. Besides the neutron-proton (n-p) symmetry energy the spin dependent symmetry energies and a scalar one are also defined. They depend on the nuclear densities ($ρ$), neutron-proton asymmetry ($b$), temperature ($T$) and exchanged energy and momentum ($q$). Based on a standard expression for the generalized polarizabilities, a differential equation is proposed to constrain the dependence of the symmetry energy on the n-p asymmetry and on the density. Some solutions are discuss…
Medium modification of the magnetic moments of octet baryons in the isospin asymmetric nuclear medium at finite temperature has been calculated using medium modified quark and baryon masses derived in chiral SU(3) quark mean field model. The magnetic moments of baryons are found to vary significantly as a function of density of nuclear medium as well as with the increase in isospin asymmetry of the medium. The rise of temperature is found to decrease the effect of isospin asymmetry on masses and magnetic moments of baryons. The results of present investigation may be helpful to understand the …
The dispersive optical model (DOM) as presently implemented can investigate the isospin (nucleon asymmetry) dependence of the Hartree-Fock-like potential relevant for nucleons near the Fermi energy. Data constraints indicate that a Lane-type potential adequately describes its asymmetry dependence. Correlations beyond the mean-field can also be described in this framework, but this requires an extension that treats the non-locality of the Hartree-Fock-like potential properly. The DOM has therefore been extended to properly describe ground-state properties of nuclei as a function of nucleon asym…
