SPACE-TIME PROPERTY OF FERMION NUMBER

Enlarging the dimensionality of Minkowski space from 4 to 5,and relating the restmass of particle with x₅ as m=—i（∂/（∂x_5）））we discuss the 5-dimensional non-linear con-formal group C（M₅）under which dx₁²+dx₂²+dx₃²-dx₀²+dx₅²=0 is invariant.The C（M₅）group is isomorphic to the linear group SO（5,2）from which we study thespace-time property of Fermion number,and the relations between half-integral（in-tegral）spin and odd（even）Fermion number are obtained.     

AN ANALYSIS OF FOUR-ELEMENT MODELS OF LEPTONS AND NON-DIAGONAL NEUTRAL CURRENTS

Due to the possible production of neutral and charge heavy leptons by v_μ, models consisting of four elements per "line", e.g. v_e, e^-, E⁰, E^- v_μ, μ^-, M^0, M^- v_τ, τ^-, T⁰, T^- ……are analysed. Non-diagonal neutral currents cannot be avoided. Nevertheless, a model is proposed within SU_（2）×U_（1） in which the process μ→eγ can still be suppressed by the Bjorken-Lane-Weinberg mechanism; various production cross-sections for heavy leptons are reasonable when compared with experiments. Models corresponding to SU_（3）×U（1） and still higher symmetries are discussed.     

A DISCUSSION OF THE STRENGTH AND THE RANGE OF THE PHENOMENOLOGICAL NUCLEAR FORCE USING EXPERIMENTAL DATA IN HIGH ENERGY SCATTERING

Under the framework of the Bakamjian-Thomas theory,we discuss the qualitativeproperties of the phenomenological nuclear force V=V_R-iV₁ at high energy arediscussed by a comparision with the small angle scattering data.Because these data inhigh energy are insensitive to the spin,we suppose that the nuclear force at highenergies is spin-independent.The followings are obtained:i)for the Gaussian potential,X₃≌200 MeV and β₃≌0.95 fm,which are thestrength and the range of V₁ respectively;ii)in V_R,there is no hard repulsive core.Under a rough estimation,supposingthe range β₁>0.45 fm,we find the strength of the repulsive force,X₁<480 MeV;iii)all parameters are vary very slowly with energy.     

ON THE IRREDUCIBLE REPRESENTATIONS OF THE COMPACT SIMPLE LIE GROUPS OF RANK 2(I)

In this paper, we analyse the commutation relations of the infintesimal opera-tors of the group SU₃ and find that the eight infinitesimal operators of the groupSU₃ can be written as a scalar operator A, three angular momentum operators (L₁,L_o, L_-1,)and two sets of the irreducible tensor operators of rank 1/2, （T_±1/2,V±1/2）By means of the commutation relations of these operators, all irreducible represen-tations of the group SU₃ can be easily obtained. In this pape, the matrices corresponding to these operators in the irreduciblerepresentation（λμ）, are given; therefore the irreducible representation and its re-presentation space R^λμ are completely defined. Besides, a method for calculatingthe scalar factors of the reduction coefficients and the symmetric relations of thosefactors are also given. As examples, the scalar factors of the reduction coefficientsof （λμ）×（10）, （λμ）×（01）, （λμ）×（20） and （λμ）×（11） are calculated. In the last part of this paper, we define the irreducible tensor operators ofthe group SU₃ and prove the corresponding Wigner-Eckart theory. The method used in the discussion of the group SU₃ be extended to allof the compact simple Lie groups of rank 2 and we shall discuss them in two suc-ceeding papers.     

THE BEHAVIOR OF THE PHASE-SHIFT IN THE BAKAMJIAN-THOMAS THEORY

The behavior of the phase-shift of the Bakamjian-Thomas theory and its relationwith the phenomenological nuclear force V=V_RiV_I at high energy are explored.Two limits are obtained:It is found that the repulsive core with a sharp outer edge may induce a characteris-tic oscillation of Re δ₁,and Im δ₁ is sensitive to V₁.The conclusion is that the analy-sis of the phase-shift extending to higher energy is relevant in determining therepulsive core and the imaginary part of the nuclear force.     

A RECURSIVE FORMULA FOR THE CLEBSCH-GORDAN COEFFICIENTS OF SUn GROUP

It is proved that under the Gelfand-Biedenharn phase convention any SU_n singletfactor （SF） belongs to the type of the derivable or underivable,designated as （SU_nSF）d and （SU_r SF） respectively,and （SU_n SF）d=（SU_r SF）,n=r+1,r+2,….Therefore the calculation of any SU_n Clebsch-Gordan coefficients is reduced to thecalculation of a few underivable singlet factor （SU_r SF）.     

THE U1 GAUGE FIELD IN A SUN GAUGE FIELD AND THE QUANTIZED VALUES OF DUAL CHARGES

Let F be a SU_N gauge field on the space-time manifold M₄, b_λ（x） （λ=0,1, 2, 3） the gauge potentials, the field strengths and Q（x） a Higgs field. All quantities b, f_λμ and Q（x） are SU_N'-valued, i.e. they are represented by N×N anti-hermitian traceless matrices.Let M₄' be the set of x such that Q（x）≠0 and define on M₄', where The following results are obtained:Theorem 1. The 1st set of Maxwell equations F_λμ,v+F_μv,λ+F_vλ,μ=0 are satisfied for arbitrary b_λ if and only if with Here s is an integer, 1≤s≤N-1.Suppose the conditions in theorem 1 are satisfied.Theorem 2. If s is a space-like two-dimensional surface, the value of dual charges contained in s defined by is equal to lq', where l is an integer and Theorem 3. The value of dual charges contained in S is equal to the integral which is independent of the gauge potentials.Theorem 4. The least positive value q' of dual charge can be attained by some Higgs fields.Remarks（a） When N=2, the results obtained are consistent with those of t Hooft, Arafune and Hou etc.（b） For N=3, we give an answer to the question of quantized values of dual charges which was discussed by Marciano and Pagels.（c） The Higgs field ø（x） is a mapping from M'₄ into the AⅢ type symmetric space SU_N/S(U_s X U_N-s) and the integral is an extension of Kronecker index for N=2.     

THE INFLUENCE OF THE SELF-ENERGY DIAGRAMS ON THE SOLUTIONS OF A SCALAR BETHE SALPETER EQUATION

The influence of the self-energy diagrams on the solutions of the Bethe-Salpe-ter equation is studied by taking a gφ₁*（x）φ₁（x）φ₂（x） interaction and under the ladder approximation. The results show for ground state solution, the self-energy diagrams will diminish the eigenvalues and alter the wave funetions slight-ly. While for the excited states and anti-symmetric solutions, the influence of theself-energy diagrams is considerable. which completely alters the properties of the solutions. The results also show that the solutions from the ladder approximationare meaningful only in the loosly bounded cases, and as the binding becomes tight,the contribution from the self-energy diagrams becomes important.     

THE IRREDUCIBLE REPRESENTATIONS AND THEIR OCCUPATION NUMBER IN DIRECT MULTIPLICATION OF IRREDUCIBLE REPRESENTATIONS OF SU3 GROUP

In this paper, the C-G series of SU₃ group is studied using Racah-Speier theorem. A general formula which can be used to calculate irreducible representations and their occupation number in C-G series of SU₃ group is derived. The general formula is very straight forward and effective for actual calculation One can apply the formula to analyse the distribution rule of occupation number in C-G series of SU₃ group and to define the null space of Winger operator of SU₃ group, the latter is important to the calculation of Wigner coefficients when there is a multiplicity.     

A STRUCTURE MODEL OF STRATONS AND LEPTONS

A subquark model is proposed. According to this model, stratons and leptons are consisted of rishons T and V, which are multiplets of group SU_H(3)×SU_C(3)×SU_G(2)×SU(2)×U(1). Three generations of both stratons and leptons are obtained naturally. In this model, proton decay modes are μ^－e⁺e⁺ or e^－μ⁺μ⁺.     

DECAY PROCESSES IN MASSIVE STRATON MODEL OF MESONS

Using the B-S wave functions of mesons in the massive straton model^[1], we discuss their weak decay, electromagnetic decay, and particularly hadronic decay processes. Not only f_π≈f_K, 1^－→l⁺l^－ rate are successfully explained, the predicted widths for various hadronic decays are also in good agreement with experimental data.     

THE REGGE TRAJECTORY OF MESONS AND THE SU(4) MASS RELATIONS

A relativistic equation of motion of a two particle system under the constraints p_i²-m_i²-U(x²)=0.(i=1,2), where U(x²) is an infinite spherical square well poten-tial, is applied to the SU(4) quark model of mesons. A set of linear mass relations areobtained. Instead of the linear relation between J and M², the Regge trajectory ob-tained is a relation between p_nl² and M², where ζ_nlπ are zeros of the spherical Besselfunctions. The new trajectory seems more satisfactory than the former one.     

ON THE PHASE AND THE REPRESENTATION TRANSFORMATIONS OF SUn BARYON AND MESON WAVE FUNCTIONS

The baryon and meson wave functions of SU_n symmetry under the Baird-Bie-denharn phase convention are given explicitly.The phase confusion is clarified andthe matrices of transformations between I-spin,U-spin and V-spin representationsare given for the IR（8）,（27）,（35） of SU₃.     

MICROSCOPIC CALCULATION OF THE INERTIA IN HEAVY NUCLEI

A realistic calculation of the inertia for ²³⁶U fisson based on the linear response theory is presented, in which the single particle states are provided by Nilsson model. The dependence of the nuclear inertia M_δiδi on the collective variables δ₂, δ₄ is studied at the range of certain nuclear temperature (0—1 MeV). The pairing effect and the shell effect on the nuclear inertia are discussed. The calculated results show a very prominent structure at level crossing points and when acrossing the critical temperature.     

AN INVESTIGATION OF THE EFFECTS OF CHARGED BOSONIC PARTONS (DIQUARKS) IN e-P DEEP INELASTIC SCATTERING

We point out the possible existence of bosonic charged partons (diquarks) withinnucleons. A certain form of the structure functions of diquarks inside nucleons is as-sumed and the functions are suitably parametrized. Then, by combining their effectswith the usual QCD calculations, we get a better theoretical fit to the experimental R=(σ_L)/(σ_T) value in e-p deep inelastic scattering.     

AN ANALYSIS FOR LOCATION OF BETA STABLE LINE AND CURVATURE OF MASS PARABOLA

The beta decay energies (Wapstra and Bos, 1977) of about 1,000 isobaric nuclei (10≤A≤253) are carefully analyzed. Weighted least squares method is used to determine the parameters of the mass parabola——the location of the moat β-stable nuclei Z₀, the curvature parameter b and even-add mass difference △E. Several mass formulae are compared with the resultes of the present paper.     

SOME CONJECTURES ON THE MASS FORMULA OF CHARGED LEPTONS

In this note we propose that the electromagnetic self energy of lepton may beconnected with quantum number n by（ （δm）/m）=（1/（2π））n^-b ,in which b is a constant.Wefnrther propose that the cut-off value of momentum M is connected with gravitationalconstant κ and fine structure constant α by M=（1/√κ）αe^-1-b.So we obtainthe mass formula of charged leptons M=（1/√κ）α exp{-3/4-b-(1/3α)n^-b}.By using the masses of e^- and μ^- and the value of a as in put,we get the calculatedvalues of κ=（6.67231±0.00026）×10^-8cm³g^-1sec^-2and m_r=（1782.306±0.078）MeVwhich agree very well with experimental values κ=（6.6720±0.0041）×10^-8cm³g^-1sec^-2 and m_τ=(1782_-4⁺³)MeV respectively.The mass of the fourth charged leptonpredicted by the formula should be m=（11725.47±0.51）MeV,which can be checkedby experiments in the near future.We also discuss briefly the proposed formula andthe obtained results.     

TESTING GLUON DISTRIBUTION FUNCTION OF HADRONS IN LARGE PT PROCESS WITH DIRECT PHOTON EMISSION

In this paper we disscuse disscuse the physicsical aspect of cross-section differences Δ_AB^cγ=dσ(AB→cγX)-dσ(AB→cγX) and give the simple rules to select the elementary subprocesses which contribute to cross-section differences.
We bind a way to test the gluon distribution functions of hadrons through the measurement of cross-section difference or combination of cross-section differences in the large P_T process with direct photon emission. Moreover we obtain simple relations between each combination of cross-sections and the corresponding gluon distribution functions of proton, neutron, pion and daon:
G_p⁸(x)/(Δ_pp^hγ－Δ_pp^hγ)=G_n⁸(x)/(Δ_pp^hγ)=G_π⁸(x)/(Δ_π+p^hγ+Δ_π－p^hγ=G_K⁸(x)/(Δ_K+p^hγ+Δ_K－p^hγ)which are expected to be test in experiment.     

A FURTHER EXPLORATION FOR MECHANISM OF ANGULAR MOMENTUM TRANSFER IN HEAVY ION REACTION

The difficulty of the classical dynamics in studing the mechanism of angular momentum transfer is discussed. According to the nuclear rotational concept formed in the study of the nuclear structure for a long time, we point out that it is convenient to divide the total angular momentum I transfered to the target and the projectile into two components-the nuclear collective angular momentum I_R and the rotational alignment angular momentum I_j.     

THE TEST OF SLAC METHOD USING LEE MODEL

Treating Lee Model by Slac method,we find that,to state ||V> of one particle and state ||VN> of two particles,there corresponds a solution of Slac bag type re-spectively.The latter bears resemblance to the former in energy especially for ||V> state with the replacement of the interaction constants g by g/√e only.In addition,the“bag”corresponds precisely to the scalar field in ||V> and ||VN> states.However,for ψ_N^- and ψ_V^- field,we get δ-function type solutions by Slac method.They deviate greatly from the rigorous solutions.The“skin confinement”as statedby Bardeen et al.,and Rafelski is closely related to the δ-confinment in the one par-tiele state found here by coherent state approximation.Thus it may not representthe physical picture in the rigorous solution of a quantum field theory.