Equivalence Groups for First-Order Balance Equations and Applications to Electromagnetism

We investigate the groups of equivalence transformations for first-order balance equations involving an arbitrary number of dependent and independent variables. We obtain the determining equations and find their explicit solutions. The approach to this problem is based on a geometric method that depends on Cartan's exterior differential forms. The general solutions of the determining equations for equivalence transformations for first-order systems are applied to a class of the Maxwell equations of electrodynamics.     

巨单极共振和对称能

基于带有混合同位旋标量-矢量非线性耦合的有效拉格朗日量, 在完全自洽的相对论无规位相近似的框架内, 通过单极压缩模式讨论了核物质的不可压缩性. 比较核²⁰⁸Pb,¹⁴⁴Sm,¹¹⁶Sn和⁹⁰Zr实验和计算的巨单极共振能量, 给出了核物质不可压缩系数的取值范围. 新的同位旋标量-矢量非线性耦合软化核物质的对称能, 但无损于基态性质与实验的一致性. 讨论了对称能的软化对巨单极共振的影响.     

On the Mean-Field Spherical Model

Exact solutions are obtained for the mean-field spherical model, with or without an external magnetic field, for any finite or infinite number N of degrees of freedom, both in the microcanonical and in the canonical ensemble. The canonical result allows for an exact discussion of the loci/ of the Fisher zeros of the canonical partition function. The microcanonical entropy is found to be nonanalytic for arbitrary finite N. The mean-field spherical model of finite size N is shown to be equivalent to a mixed isovector/isotensor σ-model on a lattice of two sites. Partial equivalence of statistical ensembles is observed for the mean-field spherical model in the thermodynamic limit. A discussion of the topology of certain state space submanifolds yields insights into the relation of these topological quantities to the thermodynamic behavior of the system in the presence of ensemble nonequivalence.     

General bounds on the isovector coupling constants of the weak neutral current

We show that experimental data on inclusive neutrino reactions can be used to obtain general bounds on the coupling constants of the isovector part of the hadronic weak neutral current provided this isovector current is related to the charged current by isospin rotation. These bounds are free from the assumption of a specific model for the neutral current as well as any dynamical assumption on the hadronic structure functions. We derive upper bounds on the coupling constants which involve only the cross sections for isospin-averaged nucleon target as well as lower bounds which require a knowledge of the cross sections for proton and neutron separately.     

Soft Giant Dipole Modes in Ca Isotopes in the Relativistic RPA

The isovector giant dipole resonance in Ca isotopes is investigated in the framework of the fully consistent relativistic random phase approximation.The calculations are performed in an effective Lagrangian with a parameter set NL3,which was proposed for satisfactorily describing nuclear ground state properties.It is found that a soft isovector dipole mode for Ca isotopes near drip lines exists at energy around 6-7MeV.The soft dipole states are mainly due to the excitation of the weakly bound and pure neutron (proton)states near Fermi surface as well as the correlation of isoscalar and isovector operators.For nuclei with the extreme value of N/Z,the contributions of isoscalar mesons in the isovector mode play a non-negligible role.     

A close look at the competition of isovector and isoscalar pairing in A=18 and 20 even-even N≈Z nuclei

competition of isovector and isoscalar pairing in A=18 and 20 even-even N≈Z nuclei is analyzed in the framework of the mean-field plus the dynamic quadurpole-quadurpole, pairing and particle-hole interactions, whose Hamiltonian is diagonalized in the basis U(24) ?(U(6) ? S U(3) ? S O(3))■(U(4) ? S US(2)■ S UT(2)) in the L = 0 configuration subspace. Besides the pairing interaction, it is observed that the quadurpole-quadurpole and particlehole interactions also play a significant role in determining the relative positions of low-lying excited 0~+ and 1~+ levels and their energy gaps, which can result in the ground state first-order quantum phase transition from J = 0 to J = 1.The strengths of the isovector and isoscalar pairing interactions in these even-even nuclei are estimated with respect to the energy gap and the total contribution to the binding energy. Most importantly, it is shown that although the mechanism of the particle-hole contribution to the binding energy is different, it is indirectly related to the Wigner term in the binding energy.     

Continuum limits and exact finite-size-scaling functions for one-dimensionalO(N)-invariant spin models

We solve exactly the general one-dimensionalO(N)-invariant spin model taking values in the sphereS ^N–1, with nearest-neighbor interactions, in finite volume with periodic boundary conditions, by an expansion in hyperspherical harmonics. The possible continuum limits are discussed for a general one-parameter family of interactions and an infinite number of universality classes is found. For these classes we compute the finite-size-scaling functions and the leading corrections to finite-size scaling. A special two-parameter family of interactions (which includes the mixed isovector/isotensor model) is also treated and no additional universality classes appear. In the appendices we give new formulae for the Clebsch-Gordan coefficients and 6–j symbols of theO(N) group, and some new generalizations of the Poisson summation formula; these may be of independent interest.     

相对论Hartree-Fock研究奇特核的性质

采用相对论Hartree-Fock(RHF)理论来描述奇特核的性质.为了研究Fock项和矢量介子对奇特核性质的贡献和避免有效相互作用的不惟一性,本文推广应用没有自由参数的密度有关的相对论Hartree(RDH)和Hartree-Fock(RDHF)理论来描述奇特核的性质.在RDH和RDHF近似下,计算了钙同位素链的性质,特别研究了Fock交换项和矢量介子的贡献.研究表明交换项和矢量介子对非常丰中子核的性质,如结合能,中子均方根半径,中子密度分布的影响是非常不同于对稳定线附近核性质的影响.同时,对研究滴线奇特核性质的重要性及其理论模型做了简单的讨论.