Polynomial coefficients. Application to spin–spin splitting by N equivalent nuclei of spin I > 1/2

The NMR intensity pattern of a nucleus split by N identical nuclei of spin 1/2 is given by the binomial coefficients. These are conveniently obtained from Pascal's triangle, equivalent to the chemist's branching diagram. Much less well‐known is the pattern from splitting by N identical nuclei of spin I > 1/2. This was originally presented in terms of multinomial coefficients, but polynomial coefficients are more convenient. These describe the number of ways that N objects can be distributed to 2I + 1 numbered boxes. They arise in the polynomial expansion and are conveniently obtained from generalizations of Pascal's triangle. Examples and predictions are given.     

Relativistic effects on meson spectra

The meson masses are considered to retain total relativistic effects for spinors instead of Fermi-Breit approximation. This necessitates a diagonalization approach instead of solutions of differential equations. Correction over Fermi-Breit form appears to be significant. For heavy quark systems agreement with experiment is found. The method will be quite useful if the quark-antiquark dynamics becomes sufficiently known.     

Mass spectra of light and heavy mesons in the-Dirac equation with power-law potential

The mass spectra of both light and heavy mesons are studied in the Dirac equation with an equally mixed 4-vector and scalar power-law potential model. This potential provides an excellent fit not only to the mass spectra ofp°, ϕ, Ψ and υ families but also to those ofD, F andB mesons. The light quark masses inp° and ϕ as well as in atom-like mesons are very close to the current quark masses.     

A comment on SCF energy partitioning schemes

Starting from the symmetry groupG × SU(2) for the special case of negligible spin-orbit coupling, a general character formula is derived for them-tuplet representation, which is realized in the space of state functions ofn-electron systems in fields with symmetryG. Apart from the characters of the initial representation for the single electron space function, the formula only contains the number of particlesn and the multiplicitym.

Herrn Professor Dr. Hermann Hartmann zu seinem 60. Geburtstag gewidmet.     

Breit势的正规化与ηc-J/ψ的劈裂

研究自旋和轨道量子数不同的介子之间的质量劈裂对检验夸克势模型非常重要。 在以往的夸克势模型计算中,η_c-J/ψ的质量劈裂都很难达到实验的值。 用正规化形状因子μ2/(q2+μ2), 在对完整的动量空间中的Breit夸克势实施一次正规化下研究了η_c-J/ψ和新介子ηb与Υ(1s)之间的质量劈裂。 结果表明, 正规化形状因子中的屏蔽质量μ应与介子折合质量有关, 当将其展开为介子折合质量的三阶多项式时, 上述介子质量劈裂可以精确重现实验的结果。另外, 由于完整的Breit势包含有自旋-轨道耦合相互作用的项,因而还可以研究χc0,χc1和χc2之间的质量劈裂。 The study of the splittings between the masses of mesons with different spin and orbit quantum numbers is important for checking the quark potential model. In the previous calculations with quark potential models, the splitting between ηc and J/ψ is however too small to the experimental result. In this paper the mass splitting of ηc J/ψ and the splitting between the new meson ηb and Υ(1s) are investigated with the complete Breit quark potential regularized by applying the form factor μ2/(q2+μ2) one time in momentum space. In addition, because the complete Breit potential includes the spin orbit interaction, it can be used to investigate the splittings among χc0, χc1 and χc2. The investigated results indicate that the screen mass μ in the form factor of regularization is related to the reduced mass of meson. The splittings of η_c-J/ψ, ηb Υ, and χc0 χc1 χc2 can reproduce the experimental results with high accuracy when the screen mass is expanded to the third order polynomial of meson reduced mass.     

Study of excited nucleon states at EBAC: status and plans

We present an overview of a research program for the excited nucleon states in Excited Baryon Analysis Center (EBAC) at Jefferson Lab. Current status of our analysis of the meson production reactions based on the unitary dynamical coupled-channels model is summarized, and the N~* pole positions extracted from the constructed scattering amplitudes are presented. Our plans for future developments are also discussed.     

Hadro- and photo-production of in quasi-free proton and neutron processes

The η' photoproduction process on quasi-free proton and neutron and the reaction NN→η'NN are investigated within a relativistic effective Lagrangian approach to hadronic interactions. Resonances with spins 1/2 and 3/2 are considered together with the nucleonic and t-channel meson-exchange current contributions. In photoproduction processes, the S_(11) resonance is found to be responsible for the sharp rise of the cross sections near threshold. In pp →η'pp, it is found that the S_(11) resonance dominates the total cross section over the entire energy region considered. The spin observables, in particular the beam and target asymmetries, are shown to be very sensitive to the reaction mechanism and will help impose more stringent constraints on the model parameters.     

Single photo and electroproduction of pions at EBAC@JLAB

Within the Excited Baryon Analysis Center we have performed a dynamical coupled-channels analysis of the available p(e,e'π)N data in the region of W ≤ 1.6 GeV and Q~2≤ 1.45 (GeV/c)~2. The channels included are γN, πN, ηN, and ππN which has π△, ρN, and σN components. With the hadronic parameters of the model determined in our previous investigations of πN→πN reaction, we have found that the available data in the considered W≤1.6 GeV region can be fitted well by only adjusting the bare γ~*N→N~* helicity amplitudes for the lowest N~* states in P_(33), P_(11), S_(11) and D_(13) partial waves. The meson cloud effect, as required by the unitarity conditions, on the γ~*N→ N~* form factors are examined.     

Extraction of resonance parameters from meson production reaction

We have developed an analytic continuation method for extracting parameters of nucleon resonances within a Hamiltonian formulation of meson-nucleon reactions. The method was tested for simple solvable models and then applied for our recent coupled channels model （πN, ηN, π△, ρN, and σN ） of the π＊N and γ＊N reactions. The resonance pole positions and their properties are studied for P11and P11 channels.