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.     

A phenomenological equation of state for isospin asymmetric nuclear matter

A phenomenological momentum-independent(MID) model is constructed to describe the equation of state(EOS) for isospin asymmetric nuclear matter,especially the density dependence of the nuclear symmetry energy Esym(ρ).This model can reasonably describe the general properties of the EOS for symmetric nuclear matter and the symmetry energy predicted by both the sophisticated isospin and momentum dependent MDI model and the Skyrme-Hartree-Fock approach.We find that there exists a nicely linear correlation betwee...     

Progress towards determining the density dependence of the nuclear symmetry energy using heavy-ion reactions

The latest development in determining the density dependence of the nuclear symmetry energy using heavy-ion collisions is reviewed. Within the IBUU04 version of an isospin- and momentum-dependent transport model using a modified Gogny effective interaction, recent experimental data from NSCL/MSU on isospin diffusion are found to be consistent with a nuclear symmetry energy of E _sym(ρ)≈31.6(ρ/ρ₀)^1.05 at subnormal densities. Predictions on several observables sensitive to the density dependence of the symmetry energy at supranormal densities accessible at GSI and the planned Rare Isotope Accelerator (RIA) are also made.     

On the origin of the Wigner energy

Surfaces of experimental masses of even-even and odd-odd nuclei exhibit a sharp slope discontinuity at N = Z. This cusp (Wigner energy), reflecting an additional binding in nuclei with neutrons and protons occupying the same shell model orbitals, is usually attributed to neutron-proton pairing correlations. A method is developed to extract the Wigner term from experimental data. Both empirical arguments and shell-model calculations suggest that the Wigner term can be traced back to the isospin T = 0 part of nuclear interaction. The structure of the Wigner energy is analyzed in terms of neutron-proton pairs of a given angular momentum and isospin. In particular, we find that the Wigner term cannot be solely explained in terms of correlations between the neutron-proton J = 1, T = 0 (deuteron-like) pairs.     

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 statistical 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 difference Δµ_n or Δµ_p as a function of temperature, or in free neutron and proton chemical potential difference Δµ_n−Δµ_p. Density dependence of symmetry energy coefficient C _sym(ρ/ρ ₀) is also studied in the frame of LGM, with the potential parameters which can reproduce the nuclear ground state property, soft density dependence of symmetry energy is deduced from the simulation results. Giant dipole resonance (GDR) induced by isospin asymmetry in entrance channel is also studied via IQMD model, and the dynamic dipole resonance shows isospin sensitivity on the isospin asymmetry of entrance channel and symmetry energy of the nuclear equation of state (EOS). GDR can also be regarded as a possible isospin sensitive signature.

     

A measurement of Kevγ+ decay

The decay K⁺ → e⁺vγ has been observed. In a counter experiment at CERN, 56 events of this type have been identified by detection of a γ with an energy > 100 MeV and of an e⁺ with an energy between 236 MeV and the maximum e⁺ energy, 247 MeV. The angle between γ and e⁺ was > 120°. Thus, the experiment was sensitive only to the structure decay (SD) term proportional to the squared sum of vector- and axialvector amplitudes, |ν_K + a_K|², corresponding to the emission of right handed γ. We find Δ₊(SD)/Δ(K_e2) = 1.05_?0.30^+0.25 and Δ_(SD) < 85 (90% CL). Δ₊ is in agreement with theoretical predictions.     

Global systematics of the Wigner energy

Following Zeldes, double-beta decay Q   values are used as a filter for extracting symmetry energy and Wigner energy coefficients across the full range of nuclei, from A=10$A=10$ to A=246$A=246$. The symmetry coefficient extracted is found to vary smoothly with A and mass formula coefficients can be determined for the corresponding symmetry and surface symmetry terms. However, the extracted Wigner coefficient has large standard errors and fluctuates dramatically with A, even as regards its sign. Shell corrections remove most of the fluctuations and allow the determination of a reliable Wigner coefficient for the mass formula.     

BH2和AlH2分子的结构及其解析势能函数

运用二次组态相关(QCISD)方法，分别选用6-311++G(3df,3pd)和D95(3df,3pd)基组，对BH₂和AlH₂分子的结构进行了优化计算，得到BH₂分子的稳态结构为C_2v构型，电子态为²A₁、平衡核间距R_BH=0.1187nm、键角∠HBH=128.791°、离解能D_e=3.65eV、基态振动频率ν₁(a₁)=1020.103cm^-1,ν₂(a₁)=2598.144cm^-1,ν₃(b₂)=2759.304cm^-1.AlH₂分子的稳态结构也为C_2v构型，电子态为²A₁、平衡核间距R_AlH=0.1592nm、键角∠HAlH=118.095°、离解能D_e=2.27eV、基态振动频率ν₁(a₁)=780.81cm^-1,ν₂(a₁)=1880.81cm^-1，ν₃(b₂)=1910.46cm^-1.采用多体项展式理论推导了基态BH₂和AlH₂分子的解析势能函数，其等值势能图准确再现了BH₂和AlH₂分子的结构特征及其势阱深度与位置.分析讨论势能面的静态特征时得到BH+H→BH₂反应中存在鞍点，活化能为150.204kJ/mol；AlH+H→AlH₂反应中也存在鞍点，活化能为54.8064kJ/mol. 关键词： 2')" href="#">BH₂ 2')" href="#">AlH₂ Murrell-Sorbie函数 多体项展式理论 解析势能函数     

Lorentz covariant nucleon self-energy decomposition of the nuclear symmetry energy

Using the Hugenholtz–Van Hove theorem, we derive analytical expressions for the nuclear symmetry energy _Esym(ρ)$E_{\mathrm{sym}}(\rho )$ and its density slope L(ρ)$L(\rho )$ in terms of the Lorentz covariant nucleon self-energies in isospin asymmetric nuclear matter. These general expressions are useful for determining the density dependence of the symmetry energy and understanding the Lorentz structure and the microscopic origin of the symmetry energy in relativistic covariant formulism. As an example, we analyze the Lorentz covariant nucleon self-energy decomposition of _Esym(ρ)$E_{\mathrm{sym}}(\rho )$ and L(ρ)$L(\rho )$ and derive the corresponding analytical expressions within the nonlinear σ–ω–ρ–δ relativistic mean field model.     

Main channels of the decay of the giant dipole resonance in the 20,22Ne nuclei and isospin splitting of the giant dipole resonance in the 22Ne nucleus

Data published in the literature on various photonuclear reactions for the ^20,22Ne isotopes and for their natural mixture are analyzed with the aim of exploring special features of the decay of giant-dipole-resonance states in these two isotopes. With the aid of data on the abundances of the isotopes and on the energy reaction thresholds, the cross sections for the reactions ^20,22Ne[(γ, n)+(γ, np)] and ^20,22Ne[(γ, p)+(γ, np)] are broken down into the contributions from the one-nucleon reactions (γ, n) and (γ, p) and the contributions from the reactions (γ, np). The cross sections for the reactions ^20,22Ne(γ, n)^19,21Ne and ^20,22Ne(γ, p)^19,21F in the energy range E _γ=16.0–28.0 MeV and the cross sections for the reactions ^20,22Ne(γ, np)^18,20F in the energy range E _γ=23.3–28.0 MeV are estimated. The behavior of the cross-section ratio r=σ(γ, p)/σ(γ, n) for the ²²Ne nucleus as a function of energy is analyzed, and the isospin components of the giant dipole resonance in the ²²Ne nucleus are identified. The contributions of the isospin components of the giant dipole resonance in the ²²Ne nucleus to the cross sections for various photonuclear reactions are determined on the basis of an analysis of the diagram of the excitation and decay of pure isospin states in the ²²Ne nucleus and in nuclei neighboring it, which are members of the corresponding isospin multiplets. The isospin splitting of the giant dipole resonance and the ratio of the intensities of the isospin components are determined to be ΔE=4.57±0.69 MeV and R=0.24±0.04, respectively.     

Lifetime measurements on the compound nucleus 236U by means of the shadow effect

The lifetime of the ²³⁶U nucleus is measured in the range of excitation energies E_x = 6.7–11.5 MeV by a method based on the shadow (blocking) effect. The results obtained, as well as those of an earlier measurement of the lifetime for the ²³⁹U nucleus in the range E_x = 6.4–9.1 MeV, are compared with the results of calculations based on the level density ρ(E_x) in the Fermi-gas model and on the empirical level density ρ(E)_x) calculated as a result of an analysis of(n, γ) and (n, n') cross sections. An increase of excitation energy produces a substantial reduction in the rate of decrease of the lifetime at E_x ? 7.5 MeV for both compound nuclei as compared to the theoretical dependence τ(e_x).     

Higher order bulk characteristic parameters of asymmetric nuclear matter

The bulk parameters characterizing the energy of symmetric nuclear matter and the symmetry energy defined at normal nuclear density ρ ₀ provide important information on the equation of state (EOS) of isospin asymmetric nuclear matter. While significant progress has been made in determining some lower order bulk characteristic parameters, such as the energy E ₀(ρ ₀) and incompressibility K ₀ of symmetric nuclear matter as well as the symmetry energy E _sym(ρ ₀) and its slope parameter L, yet the higher order bulk characteristic parameters are still poorly known. Here, we analyze the correlations between the lower and higher order bulk characteristic parameters within the framework of Skyrme Hartree-Fock energy density functional and then estimate the values of some higher order bulk characteristic parameters. In particular, we obtain J ₀ = (−355±95) MeV and I ₀ = (1473±680) MeV for the thirdorder and fourth-order derivative parameters of symmetric nuclear matter at ρ ₀ and K _sym = (−100 ± 165) MeV, J _sym = (224 ± 385) MeV, I _sym = (−1309 ± 2025) MeV for the curvature parameter, third-order and fourth-order derivative parameters of the symmetry energy at ρ ₀, using the empirical constraints on E ₀(ρ ₀), K ₀, E _sym(ρ ₀), L, and the isoscalar and isovector nucleon effective masses. Furthermore, our results indicate that the three parameters E ₀(ρ ₀), K ₀, and J ₀ can reasonably characterize the EOS of symmetric nuclear matter up to 2ρ ₀ while the symmetry energy up to 2ρ ₀ can be well described by E _sym(ρ ₀), L, and K _sym.

     

Charge-exchange resonances and restoration of Wigner’s supersymmetry in heavy and superheavy nuclei

Various facets of the question of whether Wigner’s supersymmetry [SU(4) symmetry] may be restored in heavy and superheavy nuclei are analyzed on the basis of a comparison of the results of calculations with experimental data. The energy difference between the giant Gamow–Teller resonance and the analog resonance (the difference of E _G and E _A) according to calculations based on the theory of finite Fermi systems is presented for the case of 33 nuclei for which experimental data are available. The calculated difference ΔE _G–A of E _G and E _A tends to zero in heavier nuclei, showing evidence of the restoration of Wigner’s SU(4) symmetry. Also, the isotopic dependence of the Coulomb energy difference between neighboring isobaric nuclei is analyzed within the SU(4) approach for more than 400 nuclei in the mass-number range of A = 5–244. The restoration of Wigner’s SU(4) symmetry in heavy nuclei is confirmed. It is shown that the restoration of SU(4) symmetry is compatible with the possible existence of the stability island in the region of superheavy nuclei.     

Photoproton cross section for 26Mg in the giant dipole resonance region

Using bremsstrahlung from the 35 MeV betatron the ²⁶Mg(γ, xp) reaction cross section has been obtained in the excitation energy region up to 29 MeV. The role of isospin splitting in the formation of a giant dipole resonance is discussed in the case of light nuclei.     

Search for ψ(4S) → ηJ/ψ in B~±→ ηJ/ψK~± and e~+e~-→ ηJ/ψ processes

We search for the ψ(4S) state in the B~±→ηJ/ψK~± and e~+e~-→ηJ/ψ processes based on the Belle measurements with the assumed mass M =(4230±8) MeV/c~2 and width Γ =(38±12) MeV. No significant signal is observed in the ηJ/ψ mass spectra. The 90% confidence level upper limit on the product branching fraction B(B~±→ψ(4S)K~±)B(ψ(4S)→ηJ/ψ) 6.8×10~(-6) is obtained in the B~±→ηJ/ψK~± decays. By assuming the partial width of ψ(4S)→e~+e~-to be 0.63 ke V, a branching fraction limitB(ψ(4S)→ηJ/ψ) 1.3% is obtained at the 90%confidence level in e~+e~-→ηJ/ψ, which is consistent with the theoretical prediction.     

Hamiltonian analysis of 4-dimensional spacetime in Bondi-like coordinates

We discuss the Hamiltonian formulation of gravity in four-dimensional spacetime under Bondi-like coordinates {v,r,x~a,a=2,3}. In Bondi-like coordinates, the three-dimensional hypersurface is a null hypersurface, and the evolution direction is the advanced time v. The internal symmetry group SO(1,3) of the four-dimensional spacetime is decomposed into SO(1,1), SO(2), and T~±(2), whose Lie algebra so(1,3) is decomposed into so(1,1), so(2), and t~±(2) correspondingly. The SO(1,1) symmetry is very obvious in this type of decomposition, which is very useful in so(1,1) BF theory. General relativity can be reformulated as the four-dimensional coframe(e_μ~I) and connection(ω_μ~(IJ))dynamics of gravity based on this type of decomposition in the Bondi-like coordinate system. The coframe consists of two null 1-forms e~-, e~+and two spacelike 1-forms e~2, e~3. The Palatini action is used. The Hamiltonian analysis is conducted by Dirac's methods. The consistency analysis of constraints has been done completely. Among the constraints, there are two scalar constraints and one two-dimensional vector constraint. The torsion-free conditions are acquired from the consistency conditions of the primary constraints about π_(IJ)~μ. The consistency conditions of the primary constraints π_(IJ)~0=0 can be reformulated as Gauss constraints. The conditions of the Lagrange multipliers have been acquired. The Poisson brackets among the constraints have been calculated. There are 46 constraints including 6 first-class constraints π_(IJ)~0=0 and 40 second-class constraints. The local physical degrees of freedom is 2.The integrability conditions of Lagrange multipliers n_0, l_0, and e_0~A are Ricci identities. The equations of motion of the canonical variables have also been shown.     

Coupled-channels analysis of energy-dependent isospin violation in the 12C(d, α)10B(1.74 MeV,T = 1) reaction

We have studied the isospin non-conserving ¹²C(d, α)¹⁰B(1.74 MeV, 0⁺, T= 1) reaction at several incident energies of 9 ≦ E_d ≦ 16 MeV in terms of a coupled-channels method. The reaction processes involved in the present analysis are the successive single-nucleon pick-up processes as well as the inelastic scattering of deuterons from ¹²C. It is assumed that the isospin violation should occur in the intermediate mirror cluster states of ³He + ¹¹B and t + ¹¹C, due to the Coulomb interaction. The calculation reproduces fairly well the observed features of the reaction, i.e. the decreasing cross section with increasing incident energy, and the variation of the angular distribution. We also note that the calculation shows the energy-dependent localization of isospin violation in the angular momentum space, i.e. a specifically narrow localization at the lower incident energies studied and its broadening at the higher energies. This fact is associated with the variation of the angular distribution from a forward-backward symmetry at the lower incident energies to a forward peak at the higher energies.     

Giant M2 and transversal E1 resonances in light nuclei

The cross section for inelastic backward electron scattering on 1p shell nuclei at incident energy E_e = 70 MeV is calculated in the shell model. Comparison is made with radiative pion capture and muon capture. It is shown that the T_> branch of the M2 resonance in (e, e') and the main maxima in the (π^?, γ) response function are formed by identical partial transitions. We consider the basic features of the M2 resonance excitation in 1p shell nuclei and predict configurational and isospin splitting of this mode.     

On the properties of asymmetric nuclear matter

The properties of asymmetric nuclear matter withα=(ρ _n-ρ _p)/ρ≦ 0.4 are studied within the framework of the lowest order Brueckner theory, atk _F =1.35fm^?1 (ρ=0.166 fm^?3). TheK-matrix is calculated self-consistently from the Reid soft core nucleon-nucleon interaction. In the case ofρ _n ≠ρ _p theK-matrix contains a term which does not conserve the total isospin of the interacting unlike-nucleon pair. At α=0.4 the relative magnitude of this term is of the order of 1 %. The symmetry energy is found equal to 23.1 MeV.     

Measurement of the spectral functions of vector current hadronic tau decays

A measurement of the spectral functions of non-strange τ vector current final states is presented, using 124 358 τ pairs recorded by the ALEPH detector at LEP during the years 1991 to 1994. The spectral functions of the dominant two- and four-pion τ decay channels are compared to published results of e ⁺ e ^- annihilation experiments via isospin rotation. A combined fit of the pion form factor from τ decays and e ⁺ e ^- data is performed using different parametrizations. The mass and the width of the ρ ^±(770) and the ρ ⁰(770) are separately determined in order to extract possible isospin violating effects. The mass and width differences are measured to be M _ρ ^± ₍₇₇₀₎ - M _ρ ⁰ ₍₇₇₀₎ = (0.0 ± 1.0) MeV/c ² and Γ _ρ ^± ₍₇₇₀₎ - Γ _ρ ⁰ ₍₇₇₀₎ = (0.1 ± 1.9) MeV/c ².