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 Bose-Einstein-Condensate limit is studied by varying the density from high to low values at various temperatures and asymmetries. The emergence of tri-critical points (including a Lifshitz point) and various intrinsic properties of the condensate (pair wave-function, occupation numbers, quasiparticle spectra) are discussed. The second chapter studies the nuclei $^{12}$C, $^{16}$O, and $^{20}$Ne in a magnetic field $B\approx 10^{17}\,$G by utilizing the SKY3D code, suitably extended to include the magnetic field. Our solutions of time-independent Hartree-Fock equations on a Cartesian three-dimensional grid with a Skyrme interaction demonstrate a number of interesting phenomena, such as level splitting in the magnetic field, spontaneous rearrangement of energy levels, changes in the nuclear shape, etc. The third chapter studies the pairing in low-density neutron matter in the presence of a strong magnetic field. In particular, we find the limiting field for the destruction of the superfluidity of neutrons in the crust and outer core of magnetars. This field is density-dependent but is generally of the order of $B\geq 10^{17}\,$G. The phase diagram of spin-polarized neutron matter is constructed in the case where only the BCS phase is allowed along with the (spin-polarized) normal phase.
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…
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…
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…
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…
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…
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…
Isospin asymmetry and type-I superconductivity in neutron star matter
它一直认为巴克利等。al.（Phys. Rev. Lett. 92，151102，2004），核物质是I型而不是II型超导体。所提出的机制是中子和质子库珀对之间的强相互作用，这是由假设的有效势的U（2）对称性引起的，它被认为起源于基础核相互作用的同位旋对称性。为了验证这一说法，我们执行一个明确的平均场计算的有效潜力的库珀对在一个简单的四点配对相互作用的模型。在中子星的背景下，物质是非常丰富的中子与不到10%的质子，所以没有中子质子配对。我们发现，在这些条件下，我们的模型表明质子库珀对和中子库珀对之间没有相互作用的平均场水平。我们估计了平均场以外的主导贡献，发现在弱耦合下，它是很小的，并且是吸引的。
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…
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 …
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 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…
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…
本文用核子物质的一系列势场理论模型研究了原子核和中子星中同位旋不对称性的作用。这些模型的参数是通过拟合均匀块体物质和闭壳层核的性质来确定的。讨论并揭示了重核中子皮厚度、密度为0.1 fm $^{-3}$的β平衡物质压力、密度相同的核对称能导数和中等质量中子星半径之间相关性的原因。考察了原子核结合能对核物质对称性的限制。在何种程度上即将到来的中子皮测量将进一步界定的对称性进行了研究。探讨了对称性能量约束对中子星壳内质量和转动惯量的影响以及核子直接Urca过程的阈值密度，所有这些都是潜在的可测量的。我们还评论了最小中子星半径，假设只有核子物质存在的恒星。
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.
