Isospin and mixed symmetry structure in ~(26)Mg

The isospin excitation states and electromagnetic transitions of the ²⁶Mg nucleus are studied with the isospin-dependent interacting boson model (IBM-3). The mixed symmetry states at low spin and the main components of the wave function for some states are also analyzed. The results show good agreement with the available experimental data. From the IBM-3 Hamiltonian expressed in Casimir operator form, the ²⁶Mg is also proved to be a transition nuclei from U(5) to SU(3).     

Isospin and mixed symmetry structure in 24Mg

The interacting boson model with isospin (IBM-3) has been used to study the isospin excitation states and electromagnetic transitions for 24Mg nucleus. The mixed symmetry states at low spin are also analyzed. The theoretical calculations are in agreement with experimental data. The present calculations indicate that the 3+ state is the lowest mixed symmetry state.     

Isospin and Symmetry Structure in 36Ar

The interacting boson model-3(IBM-3) has been used to study the isospin excitation states and electromagnetic transitions for ³⁶Ar nucleus. The mixed symmetry states and superdeformed band at low spin are also analyzed. The theoretical calculations are in agreement with experimental data, and the ³⁶Ar is superdeformed rotational nucleus close to the SU(3) limit. The present calculations indicate that the 2₄⁺ state is the lowest mixed symmetry state and the lowest isospin T=1 excitation state and at about 6.2 MeV, and the bandhead of superdeformed band is 0₂⁺ state.     

Isospin structure in 68Ge

The interacting boson model-3(IBM-3) has been used to study the low-energy level structure and electromagnetic transitions of 68Ge nucleus. The main components of the wave function for some states are also analyzed respectively. The theoretical calculations are in agreement with experimental data, and the 68Ge is in transition from U(5) to SU(3).     

Mixed symmetry states and electromagnetic transition in the N=Z nucleus ^28Si

The interacting boson model with isospin （IBM-3） has been used to study mixed symmetry states and electromagnetic transitions at low-lying states for a ^28Si nucleus. The theoretical calculations show that the 24^＋ state is the lowest mixed symmetry state in ^28Si and the 43＋ state is also a mixed symmetry state.     

Mixed symmetry states and isospin excitation in the N =Z nucleus 28Si

The interacting boson model with isospin (IBM-3) has been used to study the isospin excitation states and mixed symmetry states at low spin for 28Si. The theoretical calculations are in agreement with experimental data. The theoretical results show that the 81+ energy is 14.73 MeV.     

Mixed symmetry states and electromagnetic transition in the N=Z nucleus ~(28)Si

The interacting boson model with isospin (IBM-3) has been used to study mixed symmetry states and electromagnetic transitions at low-lying states for a ²⁸Si nucleus. The theoretical calculations show that the 2₄⁺ state is the lowest mixed symmetry state in ²⁸Si and the 4₃⁺ state is also a mixed symmetry state.     

Mixed symmetry states and isospin excitation in <Emphasis Type="Italic">N</Emphasis> = <Emphasis Type="Italic">Z</Emphasis> nucleus <Superscript>52</Superscript>Fe

The interacting boson model with isospin (IBM-3) was applied to study the band structure and electromagnetic transition properties of the low-lying states in the even-even N = Z nucleus ⁵²Fe. The isospin excitation states with T = 0, 1 and 2 were identified, and compared with the available data. The study shows that the 2₃⁺ state is the lowest mixed symmetry state in ⁵²Fe. The excitation energy of the second 0₂⁺ state with T = 0 in nucleus ⁵²Fe was identified. The model calculations with the data show a reasonably good agreement. Supported by the National Natural Science Foundation of China (Grant Nos. 10765001 and 10547003), the Natural Science Foundation of Inner Mongolian Autonomous Region of China (Grant No. 200607010111), and the Scientific Research Fund of Inner Mongolian Education Bureau (Grant Nos. NJZY07155 and NJZY07153)     

Isospin and F-spin symmetry structure in low-lying levels of 48，50Cr isotopes

The low-energy level structure and electromagnetic transitions of ^48.50Cr nuclei have been studied using the interacting boson model with isospin (IBM-3). A sequence of isospin excitation bands with isospin T = Tz, Tz 1and Tz 2 has been assigned, and compared with available data. According to this study, the 2^3 and 2^2 states are the lowest mixed symmetry states in ^48Cr and ^50Cr, respectively. In particular, the present calculations suggest that a combination of isospin and F-spin excitation can explain the structure in these nuclei. The transition probabilities between the levels are analysed in terms of isoscalar and isovector decompositions which reveal the detailed nature of the energy levels. The results obtained are in good agreement with recent experimental data.     

Isospin splitting of nucleon effective mass and symmetry energy in isotopic nuclear reactions

Within an isospin and momentum dependent transport model, the dynamics of isospin particles(nucleons and light clusters) in Fermi-energy heavy-ion collisions are investigated for constraining the isospin splitting of nucleon effective mass and the symmetry energy at subsaturation densities. The impacts of the isoscalar and isovector parts of the momentum dependent interaction on the emissions of isospin particles are explored, i.e., the mass splittings of m_n~*=m_p~* and m_n~* m_p~*(m_n~* m_p~*). The single and double neutron to proton ratios of free nucleons and light particles are thoroughly investigated in the isotopic nuclear reactions of ~(112)Sn+~(112)Sn and ~(124)Sn+~(124)Sn at incident energies of 50 and 120 MeV/nucleon, respectively. It is found that both the effective mass splitting and symmetry energy impact the kinetic energy spectra of the single ratios, in particular at the high energy tail(larger than 20 Me V). The isospin splitting of nucleon effective mass slightly impacts the double ratio spectra at the energy of 50 MeV/nucleon. A soft symmetry energy with stiffness coefficient of γ_s =0.5 is constrained from the experimental data with the Fermi-energy heavy-ion collisions.     

中能重离子碰撞过程中同位旋分馏的特征和机制

利用同位旋依赖的QMD模型主要对中能重离子碰撞中同位旋分馏机制和主要特征进行了讨论和分析， 得到了一些有趣的结果， 并建议将同位旋分馏强度作为提取同位旋相关平均场和建立同位旋不对称核物质状态方程的探针. The degree of isospin fractionation is measured by (N/Z)gas / (N/Z)liq，where (N/Z)gas and (N/Z)liq are the saturated neutron proton ratio of nucleon emissions ( gas phase) and that of fragment emitted (liquid phase) in heavy ion collision at intermediate energy. The calculated results by using the isospin dependent quantum molecular dynamics model show that the degree of isospin fractionation is sensitive to the neutron proton ratio of colliding system. In particular， the degree of isospin fractionation sensitively depends on the symmetry potential and weakly on the in medium nucleon nucleon cross section for the neutron rich system. In this case， we propose that the degree of isospin fractionation can be directly compared with the experimental data so that the information about symmetry potential can be obtained.     

Mixed Symmetry States in Even—Even ^96—108Mo Nuclei

Excitation energies and electromagnetic transition strengths in even-even ^96-108Mo nuclei have been described systematically be using the proton-neutron interacting boson model (IBM-2).It appears that the properties of low-lying levels in these isotopes,for which the comparison between experiment and theory is possible,can be satisfactorily described by the IBM-2 model,provided proper account is taken of the presence at low energy of states having a mixed-symmetry character.It seems possible to identify,in each isotope,a few states having such a character,the lowest ones being either 22^ or 23^ levels.It is found that these nuclei are in the transition from U(5) to SU(3).     

Isospin effects of projectile fragmentation in a Boltzmann-Langevin approach

The iso spin effects of projectile fragmentation at intermediate energies are investigated using an iso spindependent Boltzmann-Langevin model.The collisions of mass-symmetric reactions including ~(58)Fe,~(58)Ni+~(58)Fe,and~(58)Ni at intermediate energies,in the 30 to 100 MeV/A range,are studied for different symmetry energies.Yield ratios of the isotopic,isobaric,and isotonic pairs of fragments from the intermediate-mass region using three symmetry energies are extracted as functions of the N/Z ratio of the composite systems in the entrance channel and the incident energies.It is found that the yield ratios are sensitive to symmetry energies,especially for neutron-rich systems,and the calculations using soft symmetry energy are closer to the experimental data.The iso spin effect is stronger for the soft symmetry energy,owing to the competition of the repulsive Coulomb force and the symmetry energy attractive force on the proton.For the first time,the splits are presented,revealing a transition from the iso spin equilibrium at lower energies to translucency at intermediate energies.The results show a degree of transparency in that intermediate mass fragments undergo a transition from dependence on the composite systems in the entrance channel to reliance on the projectile and target nuclei.     

重离子反应中核子前平衡发射的同位旋效应

考虑了同位旋相关的对称能、库仑能及核子—核子碰撞截面，对反应４０Ａｒ＋４０Ａｒ（Ｅ＝２５ＭｅＶ／ｕ，ｂ＝０）进行了量子分子动力学模拟，讨论了同位旋效应对核子发射的影响．观察到前平衡发射的中子和质子的比率大于反应系统的中质比，发现对称能有利于中子的发射而阻碍质子的发射，而同位旋相关的核子—核子碰撞截面对中子和质子的发射都有利，但似乎更有利于质子的发射。     

Electromagnetic transition properties and isospin excitation in the cross-conjugate nuclei 44Ti and 52Fe

The interacting boson model with isospin (IBM-3) is applied to study the band structure and electromagnetic transition properties of the low-lying states in the cross-conjugate nuclei 44Ti and S2Fe. The isospin excitation states with T=0, 1 and 2 are identified and compared with available data. The E2 and M1 matrix elements for the low-lying states have been investigated. According to this study, the 2+3 state is the lowest mixed symmetry state in the cross-conjugate nuclei 44Ti and 52Fe. The excitation energy of the second 0+2 and 2+2 states with T=0 in the nucleus 52Fe are identified. The agreement between the model calculations and data is reasonably good.     

Description of nucleus ^44Ti in new symmetry limit in IBM-3

Analysis of the spectra and E2 transition rates shows that the empirical scheme of {}^{44}Ti is in good agreement with the predictions of the [U_d (5) \otimes U_{T_d} (3)]⊕U_{T_s} (3) symmetry limit.     

Isospin and symmetry energy study in nuclear EOS

This paper summarizes the isoscaling and isospin related studies in asymmetry nuclear reactions by different dynamic and sta tistical models. Isospin dependent quantum molecular dynamics model (IQMD) and lattice gas model (LGM) are used to study the isoscaling properties and isoscaling parameters dependence on incident energies, impact parameters, temperature and other parameters. In the LGM model, the signal of phase transition has been found in free neutron (proton) chemical potential dif ference Δμn or Δ...     

Isospin dependent properties of the isotopic chains of Scandium and Titanium nuclei within the relativistic mean-field formalism

Density-dependent nuclear symmetry energy is directly related to isospin asymmetry for finite and infinite nuclear systems. It is critical to determine the coefficients of symmetry energy and their related observables because they hold great importance in different areas of nuclear physics, such as the analysis of the structure of ground state exotic nuclei and neutron star studies. The ground state bulk properties of Scandium (Z = 21) and Titanium (Z = 22) nuclei are calculated, such as their nuclear binding energy (begin{document}$ B.E. $end{document}), quadrupole deformation (begin{document}$ beta_2 $end{document}), two-neutron separation energy (begin{document}$ S_{ {2n}} $end{document}), differential variation in the two-neutron separation energy (begin{document}$ {rm d}S_{ {2n}} $end{document}), and root-mean-square charge radius (begin{document}$ r_{rm ch} $end{document}). The isospin properties, namely the coefficient of nuclear symmetry energy and its components, such as the surface and volume symmetry energy of a finite isotopic chain, from the corresponding quantities of infinite nuclear matter, are also estimated. Finally, we correlate the neutron-skin thickness with the coefficient of symmetry energy and the related observables corresponding to the isotopic chains of these nuclei. The coherent density fluctuation model (CDFM) is used to estimate the isospin-dependent properties of finite nuclei, such as symmetry energy, surface symmetry energy, and volume symmetry energy, from their corresponding component in infinite nuclear matter. The relativistic mean-field (RMF) formalism with non-linear NL3 and relativistic-Hartree-Bogoliubov theory with density-dependent DD-ME2 interaction parameters are employed in the analysis. The weight function begin{document}$ vert {cal{F}}(x) vert^{2} $end{document} is estimated using the total density of each nucleus, which in turn is used with the nuclear matter quantities to obtain the effective symmetry energy and its components in finite nuclei. We calculate the ground state bulk properties, such as nuclear binding energy, quadrupole deformation, two-neutron separation energy, differential variation in the two-neutron separation energy, and root-mean-square charge radius, for the Sc- and Ti- isotopic chains using the non-linear NL3 and density-dependent DD-ME2 parameter sets. Furthermore, the ground state density distributions are used within the CDFM to obtain the effective surface properties, such as symmetry energy and its components, namely volume and surface symmetry energy, for both the parameter sets. The calculated quantities are used to understand the isospin dependent structural properties of finite nuclei near and beyond the drip line, which broadens the scope of discovering new magicity along the isotopic chains. A shape transition is observed from spherical to prolate near begin{document}$ N geq $end{document} 44 and begin{document}$ N geq $end{document} 40 for the Sc- and Ti- isotopic chains, respectively. Notable signatures of shell and/or sub-shell closures are found for the magic neutron numbers N = 20 and 28 for both isotopic chains using the nuclear bulk and isospin quantities. In addition to these, a few shell/sub-shell closure signatures are observed near the drip-line region at N = 34 and 50 by following the surface/isospin dependent observables, namely symmetry energy and its component, for both the isotopic chain of odd-A Sc- and even-even Ti- nuclei.     

核物质热力学性质的同位旋和动量相关性

利用3个具有不同的同位旋和动量相关性的热力学模型研究了非对称核物质的热力学性质, 它们是重离子碰撞中同位旋弥散数据约束下的、 同位旋和动量相关的MDI模型, 完全动量无关的MID模型, 以及同位旋标量动量相关的extended MDYI(eMDYI)模型。 主要研究了同位旋非对称热核物质的对称能和系统力、 化学不稳定性以及液气相变的温度效应。 MDI模型对称能的温度效应来源于动能和势能两部分贡献, 而MID和eMDYI模型只有势能部分对对称能的温度效应有贡献。 研究结果还表明, 力学不稳定性区域、 化学不稳定性区域和液气共存区都依赖于模型的同位旋和动量相关性, 以及对称能的密度依赖关系。In this article, three models with different isospin and momentum dependence are used to study the thermodynamical properties of asymmetric nuclear matter. They are isospin and momentum dependent MDI interaction constrained by the isospin diffusion data of heavy ion collision, the momentum independent MID interaction and the isoscalar momentum dependent eMDYI interaction. Temperature effects of symmetry energy, mechanical and chemical instability and liquid gas phase transition are analyzed. It is found that for MDI model the temperature effects of the symmetry energy attribute from both the kinetic and potential energy, while only potential part contributes to the decreasing of the symmetry energy for MID and eMDYI models. We also find that the mechanical instability, chemical instability and liquid gas phase transition are all sensitive to the isospin and momentum dependence and the density dependence of the symmetry energy.     

Exploring nuclear symmetry energy with isospin dependence in neutron skin thickness of nuclei

We propose an alternative way to constrain the density dependence of the symmetry energy from 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. The relation of the neutron skin thickness to the nuclear charge and isospin asymmetry is systematically studied with the data from antiprotonic atom measurement, and with the extended Thomas-Fermi approach incorporating the Skyrme energy density functional. An obviously linear relationship between the slope parameter L of the nuclear symmetry energy and the isospin asymmetry dependent parameter of the neutron skin thickness can be found, by adopting 70 Skyrme interactions in the calculations. Combining the available experimental data, the constraint of -20 MeV L 82 MeV on the slope parameter of the symmetry energy is obtained. The Skyrme interactions satisfying the constraint are selected.