Applying them to the study of the electron dynamics in the intense laser pul se field, we found that as long as ω 0t 0>20, the zeroth-order approxima tion (long pulse approximation) is adequate for describing the interaction.

In Lax's study, he found that the paraxial result is the zeroth-order solution of Maxwell's equations when the fields are expanded in the powers of an expansion parameter f, which is the ration of the beam waist and the so-called diffraction length.

The zeroth-order nuclear potential is taken tobe Woods-Saxon potential. The non-spherical symmetric part V_1 of the nuclear potential induced by the vibration of the target nucleus is considered as a perturbation.

In this article some Feynman rules in the method of collectivc bag-quark current are given, and, by use of these rules, the zeroth-order transition matrix elements of various photon-hadron processes are obtained.

It has been found that the characteristic equations can be expressed as rapidly converging infinite series of functions of the mode refractive index. Rather accurate results can be obtained by only taking the zeroth-order approximation.

In the theory of superfluidity and superconductivity, a jump of the free energy was discovered theoretically and was naturally called a zeroth-order phase transition.

The only term with unambiguous coefficient is the zeroth-order Nambu-Goto term.

The configurations of extra holographically reconstructed images of the diffuse screen (conjugate image, halo, and zeroth-order spot) are analyzed.

Analysis of the images projected shows that the luminance of the zeroth-order spot, while relatively low, should be diminished in one way or another.

The Breit equation as a zeroth-order approximation for calculation of the bound-state energy

Two additional postulates of the eightfold way are suggested on the basis of the analysis of experiments: (1) The nonlinear contribution of the isospin T and the hyper-charge Y to the mass-splitting is independent of the spin-parity of multiplets; (2) In all cases where the octet-singlet mixing takes place, nine particles are grouped into a reducible nine-dimensional representation and are represented by a 3X3 matrix. The trace of this matrix appears neither in the zeroth order term of the mass relation nor...

Two additional postulates of the eightfold way are suggested on the basis of the analysis of experiments: (1) The nonlinear contribution of the isospin T and the hyper-charge Y to the mass-splitting is independent of the spin-parity of multiplets; (2) In all cases where the octet-singlet mixing takes place, nine particles are grouped into a reducible nine-dimensional representation and are represented by a 3X3 matrix. The trace of this matrix appears neither in the zeroth order term of the mass relation nor in the production and decay interactions of particles. On the basis of these postulates, the classification of the strongly interacting particles, especially the classification of the scalar mesons and the baryon resonances with higher spins, is further discussed. Some predictions are obtained and compared with experiments. The predictions of scalar mesons are discussed in detail and are compatible with experiments. Finally, the results and the implications of the classification are discussed.

The quadrupole-octupole two-phonon excitations in inelastic scattering (α, α') at energies of 31 and 43 MeV are studied with DWBA method. Both- nuclear potential and Coulomb potential are considerd. The zeroth-order nuclear potential is taken tobe Woods-Saxon potential. The non-spherical symmetric part V_1 of the nuclear potential induced by the vibration of the target nucleus is considered as a perturbation. In this calculation we onlykeep second-order term of the collective variable α_(λv) of nuclear...

The quadrupole-octupole two-phonon excitations in inelastic scattering (α, α') at energies of 31 and 43 MeV are studied with DWBA method. Both- nuclear potential and Coulomb potential are considerd. The zeroth-order nuclear potential is taken tobe Woods-Saxon potential. The non-spherical symmetric part V_1 of the nuclear potential induced by the vibration of the target nucleus is considered as a perturbation. In this calculation we onlykeep second-order term of the collective variable α_(λv) of nuclear surface for V_1 and first-order of V_1 for the total initial wave function ψ_i~((+)) In distorted wave Green function, the absorptive channels as intermediate states are neglected. Furthermore, in the two-phonon excitation mechanism, it is assumed that the contribution of direct two-phonon excitation is important and the contribution of multiple two-phonon excitation is of less importance. The agreement between the theoretical and experimental angular distributions is reasonably well. It follows front this agreement that the 3.72 and 4.19 MeV levels in ~(64)Zn may be quadrupole-octupole two-phonon exciation levels abd the J~π of these levels may be 3~- and 5~- respectively.

The (56,0~+), (70,1~-) and (56,2~+) baryon mass Spectra are calculated in a diquark-quark model. The zeroth order potential between a diquark and a quarks is Coulombic at short distances and linearly confininq at large distances. Spliting between various states are calculated by using the Breit-Fermi potential due to One gluon exehange (OGE) and the Thomas term generated by the scalar confining interaction. The results show that when appropriate values for parameteres in the model are chsen, the observed spin-orbit...

The (56,0~+), (70,1~-) and (56,2~+) baryon mass Spectra are calculated in a diquark-quark model. The zeroth order potential between a diquark and a quarks is Coulombic at short distances and linearly confininq at large distances. Spliting between various states are calculated by using the Breit-Fermi potential due to One gluon exehange (OGE) and the Thomas term generated by the scalar confining interaction. The results show that when appropriate values for parameteres in the model are chsen, the observed spin-orbit forces can be properly supressed for the P and D wave states and good agreement between the model and the data can be obtained.