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.     

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.     

FURTHER DISCUSSION ON THE EQUATION AND ITS SOLUTIONS FOR THE BOUND STATES OF MESONS

We continue the investigation of the equation and its solutions for the bound states of mesons discussed previously, emphasizing on large values of v, a parameter characterizing the shape of the potential. The results show that the dependence of the eigenvalues λ and some related physical quantities upon the potential parameters v and E is approximately the same as in our previous work. But the average radii of the bound mesons cease increasing as v increases. For each value of v, there exists a maximum average radius√<R²>_max, and all these √<R²>_max are approximately equal to 12.6 M^-1 （M being the mass of the straton）, which is much smaller than the experimental value of the radius of the π meson. However, if we assume, in addition to the attractive potential, there exists, for the straton-anti-straton superstrong interactions, also a repulsive potential, and, in particular, if we introduce a differencetype potential V_D（r） corresponding to the potential V_v（r） in our previous work, the calculated radii of the bound mesons do approach the experimental value.     

A MODIFICATION FOR COMPLEX-PARTICLE EMISSION PROBABILITY IN THE PRE-EQUILIBRIUM EXCITON MODEL

Starting from the state density formula which accounts for proton-neutron distinguish ability, a modification for complexparticle emission probability in the preequilibrium exciton model is given, which modified the complex-particle emission probability W_αβ and the pure combination probability R_αβ given by C.K.Cline and I.Ribansky et al. The calculated results by using modification formula are in better agreement with the experimental data compared to that of Cline and Ribansky.     

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.     

THE EFFECTS OF THE CHARM STATE IN e-p DEEP INELASTIC SCATTERING

Using the fact that the proton contains the Charm State │uudcc〉 and combining its effects with the result of the usual calculations of A.J. Buras et.al., a better agreement of the theoretical value of the ratio R=σ_L/σ_T in e-p deep inelastic scattering with the experimental data is obtained.     

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.     

QUANTUM EXPANSION AROUND THE VERTEX TYPE SOLUTION OF N-O MODEL

By means of the generalized method of quantum expansion and the general treatement for quantization of gauge fields recently proposed by S. N. Gupta, we calculate the quantum expansion around the vertex type solution of N-O model. Under special conditions, the eigen-value of the energy of quantum excitation can be obtained.It is shown that both P^o（-1） and II^o （-1） are equal to zero in the case we considered. As a result, our calculations are greatly simplified.     

A φ4-TYPE BAG MODEL OF HADRONS——THE “RUBBER BAG” MODEL（Ⅰ）——THEORY

In this paper a new bag model of hadrons,the“Rubber Bag”model,is proposed.This model treats each hadron as a bag system in the centre-of-mass frame.The bag,with its outer radius R_e and inner radius（R_c-D）,is characterized by its“averagesurface tension”T and the quarks are confined in it“temporarily”.This model isa field theoretical model which can also be used for quantitative calculations.Thus,ithas the merits of the SLAC bag model as well as those of the MIT bag model.     

THE CP VIOLATION OF SU(7) MODEL

We discuss the CP violation problem of SU(7) models of Grand Unified Theoryincluding four genarations^[1,2]. It is shown that if we properly choose the complex phaseangles in quark mass matrix elements, we are able to obtain the CP violation phaseangle which agrees well with the experimental value. If the Higgs potential is pro-perly choosen we find that the strong CP violation parameter θ is equal to zero atthe tree level.     

CANONICAL QUANTIZATION OF GAUGE FIELDS(Ⅱ)——SPONTANEOUSLY BROKEN GAUGE FIELDS

In R_ξ gauges a SU（2）spontaneonly broken gauge theory is qnantized within the canonical formalism,and the gauge compensating term is derived.     

THE LOOP PHASE-FACTOR APPROACH TO GAUGE FIELDS

The gauge field theory is formulated via loop phase factors with a fixed point O as their initial and final point. Let G be the gauge group. When the base space is the Minkowski space E₄, we introduce a set of standard paths Ox （for example, the set of line segments Ox）, where x is arbitrary. The phase factor for the infinitesimal loop Oxx+dxO corresponds to an element in the Lie algebra g and can be expressed as a g-valued differential form k（x, dx） which satisfies the following conditions of consistency （a） k（O, dx）=0, （b） k（x, v）=0, where v is the tangential vector of Ox at x. It is shown that an equivalent class of gauge fields is determined by k（x, dx） or （ad a） k（x, dx） where a is a fixed element of G. Hence if we adopt k（x, dx） for the fundamental physical quantity of a gauge field then a great part of gauge indefiniteness is eliminated. Moreover if the phase factors Φ_xo for standard paths Ox are given then the phase factors for differential arcs x x+dx are easily calculated, and hence a gauge field in the equivalent class is extracted. We call the set of phase factors for standard paths a gauge and k（x, dx） may be interpretated as the gauge potential under a special gauge under which Φ_xo=the unit element of G.The method is useful in considering the equivalence problem and the spacetime symmetry of gauge fields. For example, it is quite easy to determine all spherically symmetric gauge fields if they are free of singularities. By using the method it can also be proved that if two gauge fields have the same gauge and the same field strength then their gauge potentials are equal to each other. Consequently, under a given gauge in the above sense the field strength determines the gauge potential completely.For a general base manifold M_n, every equivalent class of gauge fields over M_n can be defined by loop phase factors also. In this case, M_n is expressed as the sum of a set of neighborhoods each of which is homeomorphic to the Euclidean space. The standard paths are constructed according a certain rule, the phase factors for standard differential loops are also introduced. The transition functions and gauge potentials of a gauge field in the given equivalent class are derived as the phase factors for some finite loops and standard differential loops respectively. Further it is remarkable that a global gauge field is determined completely by the field strength and some discrete loop factors, if the phase factors for the standard paths are gwen.In mathematical terminology principal G-bundle structure as well as a connection in it is determined by the holonomic mapping which maps the set of loops through a fixed point into the group G, provided the mapping is differentible in a certain.The author is very grateful to Prof. Yang Chen Ning for many helpful discussions.     

Quark-Chiral Field interaction in SU(3) Model

A quark-quark potential is derived from the linear expression of the Lagrangian Which is invariant under the SU(3)_L×SU(3)_R infinitesimal transformation,and further used to make a qualitative analysis on the Λ-N interaction.The result shows that the SU(3)chiral scalar fields are important in explaining the spin-dependence feature of the Λ-N interaction.     

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.     

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 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 FOLDING POTENTIAL OF THE DOUBLE WELL-CLUSTER SHELL MODEL

In this paper, the folding potential of the double well-cluster shell model fol-ding potential is derived. We use this potential to calculate the α-α elastic scatter-ing up to 27 MeV energy. the theoretical results agree with experiments rather well.It shows that for heavy-ion elastic scattering, the intrinsic state excitation should betaken into account properly.     

THE VERTICAL INTEGRATED MOMENTUM SPECTRUM OF THE MUON WITH MOMENTUM LARGER THAN 4 GeV/c AT 3220m ABOVE SEA-LEVEL

At an altitude of 3220 meters above sea level in Yunnan Province, we measured, by using a G-M counter-magnetic spectrometer, the vertical integratted momentum spectrum of the cosmic muon with momentum larger than 4 GeV/c. The spectrum obtained from this experiment is expressed by a power function in the form of I（>p）=Q （p+4）^-1.86±0.06(cm^-2·sr^-1·s^-1), where p is in GeV/c and Q is a constant. We also measured the charge ratio of muon in the 4—23 GeV/c momentum range. The result is N_μ/N_μ-=1.26±0.11. The error in the momentum measurement with spectrometer has been discussed and calculated.     

THE INTERACTION OF A HIGH ENERGETIC PROTON WITH A NUCLEUS—THE RELATION OF THE PRODUCED PARTICLES WITH THE NUCLEAR MASS NUMBER A

Suppose that a high energetic proton interacts with a cluster of m particles in anucleus the mean multiplicity of this interaction and that of PP interaction followthe same law: n=CS^k. Using the Glauber theory we get R(A)≡n_PA/n_PP1.26A ^1/3(A ^1/3+1) ^-2/3 This formula explains the current experimental result quite well.