Effects of the momentum dependence of nuclear symmetry potential on pion observables in Sn+Sn collisions at 270 MeV/nucleon

Within a transport model,we investigated the effects of the momentum dependence of the nuclear symmetry potential on the pion observables in central Sn+Sn collisions at 270 MeV/nucleon.To this end,the quantity U^(∞)_(sym)(ρ_(0))(i.e.,the value of the nuclear symmetry potential at the saturation densityρ_(0) and infinitely large nucleon momentum)was used to characterize the momentum dependence of the nuclear symmetry potential.With a certain L(i.e.,the slope of the nuclear symmetry energy at(ρ_(0))),the characteristic parameter U^(∞)_(sym)(ρ_(0))of the symmetry potential significantly affects the production of−and+and their pion ratios.Moreover,by comparing the charged pion yields,pion ratios,and spectral pion ratios of the theoretical simulations for the reactions ^(108) Sn+^(112) Sn and ^(132)Sn+^(124)Sn with the corresponding data in the SRIT experiments,we found that our results favor a constraint on U^(∞)_(sym)(ρ_(0))(i.e.,−160_(−9)^(+18) MeV),and L is also suggested within a range of 62.7 MeV<L<93.1 MeV.In addition,the pion observable for^(197)Au+^(197)Au collisions at 400 MeV/nucleon also supports the extracted value for U^(∞)_(sym)(ρ_(0)).

Momentum-Dependent Symmetry Potential from Nuclear Collective Flows in Heavy Ion Collisions at Intermediate Energies

Within the isospin-dependent quantum molecular dynamics model, we investigate the nuclear collective flows produced in semi-central 197 Au＋197 Au collisions at intermediate energies. The neutron proton differential flows and difference of neutron proton collective flows are sensitive to the momentum-dependent symmetry potential. This sensitivity is less affected by both the isoscalar part of nuclear equation of state and in-medium nucleon- nucleon cross sections. Moreover, this sensitivity becomes pronounced with increasing the rapidity cut.

Potential symmetries and conservation laws for generalized quasilinear hyperbolic equations

Based on the Lie group method, the potential symmetries and invariant solutions for generalized quasilinear hyperbolic equations are studied. To obtain the invariant solutions in an explicit form, the physically interesting situations with potential symmetries are focused on, and the conservation laws for these equations in three physi- cally interesting cases are found by using the partial Lagrangian approach.

NONCLASSICAL POTENTIAL SYMMETRIES AND INVARIANT SOLUTIONS OF HEAT EQUATION

Some nonclassical potential symmetry generators and group-invariant solutions of heat equation and wave equation were determined. It is shown that some new explicit solutions of partial differential equations in conserved form can he constructed by using the nonclassical potential symmetry generators which are derived from their adjoint system. These explicit solutions cannot he obtained by using the Lie or Lie-Baeicklund symmetry group generators of differential equations.

Spin and pseudospin symmetries of the Dirac equation with shifted Hulthe′n potential using supersymmetric quantum mechanics

In this paper, we obtain approximate analytical solutions of the Dirac equation for the shifted Hulthén potential within the framework of spin and pseudospin symmetry limits for arbitrary spin–orbit quantum number κ using the supersymmetry quantum mechanics. The energy eigenvalues and the corresponding Dirac wave functions are obtained in closed forms.

Using “Particle Density” of “Graviton Gas”, to Obtain Value of Cosmological Constant

We use the work of de Vega, Sanchez, and Comes (1997), to approximate the “particle density” of a “graviton gas”. This “particle density” derivation is compared with Dolgov’s (1997) expression of the Vacuum energy in terms of a phase transition. The idea is to have a quartic potential, and then to utilize the Bogomol’nyi inequality to refine what the phase transition states. We utilize Ng, Infinite quantum information procedures to link our work with initial entropy and other issues and close with a variation in the HUP: at the start of the expansion of the universe.

Approximate Generalized Conditional Symmetries for the Perturbed Nonlinear Diffusion-Convection Equations

The concept of approximate generalized conditional symmetry （A GCS） as a generalization to both approximate Lie point symmetry and generalized conditional symmetry is introduced, and it is applied to study the perturbed nonlinear diffusion-convection equations. Complete classification of those perturbed equations which admit cerrain types of AGCSs is derived. Some approximate solutions to the resulting equations can be obtained via the AGCS and the corresponding unperturbed equations.

Linearization of Systems of Nonlinear Diffusion Equations

We investigate the linearization of systems of n-component nonlinear diffusion equations; such systems have physical applications in soil science, mathematical biology and invariant curve flows. Equivalence transformations of their auxiliary systems are used to identify the systems that can be linearized. We also provide several examples of systems with two-component equations, and show how to linearize them by nonlocal mappings.

Probing the symmetry potential with neutron-proton bremsstrahlung in heavy-ion collisions

In the framework of the isospin-dependent quantum molecular dynamics transport model （QMD）, the effects of symmetry potential on the collision number and the neutron-proton bremsstrahlung photon in the reactions of 40Ca＋40Ca, 124Sn＋124Sn, 40Ca＋64Zn, 40Ca＋124Sn at different incident beam energies are studied. It is found that the collision number shows moderate sensitivity to the stiffness of the symmetry potential and the number of hard photons calculated with stiff symmetry potential is obviously smaller than that with soft symmetry potential. Thus, the neutron-proton bremsstrahlung photons produced in heavy-ion collisions may be a useful probe for the high-density behavior of the nuclear symmetry potential.

THE MEAN VALUE THEOREM AND CONVERSE THEOREM OF ONE CLASS THE FOURTH-ORDER PARTIAL DIFFERENTIAL EQUATIONS

For the formal presentation about the definite problems of ultra-hyperbolic equations, the famous Asgeirsson mean value theorem has answered that Cauchy problems are ill-posed to ultra-hyperbolic partial differential equations of the second-order. So it is important to develop Asgeirsson mean value theorem. The mean value of solution for the higher order equation hay been discussed primarily and has no exact result at present. The mean value theorem for the higher order equation can be deduced and satisfied generalized biaxial symmetry potential equation by using the result of Asgeirsson mean value theorem and the properties of derivation and integration. Moreover, the mean value formula can be obtained by using the regular solutions of potential equation and the special properties of Jacobi polynomials. Its converse theorem is also proved. The obtained results make it possible to discuss on continuation of the solutions and well posed problem.

Single particle potentials of asymmetric nuclear matter in different spin-isospin channels

We investigate the neutron and proton single particle （s.p.） potentials of asymmetric nuclear matter and their isospin dependence in various spin-isospin ST channels within the framework of the BruecknerHartree-Fock approach. It is shown that in symmetric nuclear matter, the s.p. potentials in both the isospinsinglet T = 0 channel and isospin-triplet T = 1 channel are essentially attractive, and the magnitudes in the two different channels are roughly the same. In neutron-rich nuclear matter, the isospin-splitting of the proton and neutron s.p. potentials turns out to be mainly determined by the isospin-singlet T = 0 channel contribution which becomes more attractive for the proton and more repulsive for the neutron at higher asymmetries.

Tunneling of Electrons in Multibarrier Heterostructures under Crossed Electric and Magnetic Fields

Taking Hermitian functions as envelope functions, this paper presents a calculation of the transmission coefficient for electrons tunneling through multibarrier heterostructures with parabolic quantum wells under crossed electric and magnetic fields by using the transfer matrix method. Electric field effect, magnetic field effect, well width and barrier height effects on resonant tunneling are studied in detail. It is found that all of these four factors affect the peak value and peak position of the transmission coefficient. For symmetric double barrier systems, the wider the well is and the lower the barrier is, the more drastically are peaks reduced by the magnetic field. But for triple barrier systems, with increasing magnetic field strength, the variation of peak value exhibits complicated behavior due to the coupling of the quasibound states in two quantum wells of the system.