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.     

SHELL (DEFORMATION) EFFECT IN NUCLEAR CHARGE RADIUS

It is shown that without exception the observed rms charge radius constants of strongly deformed nuclei, rp's, are a little larger than those of the neighbouring spherical nuclei. The local variations among the charge radii of the sequence of isotopes, the in complete neutron shells [1p_3/2(N~3—6), 1d_5/2(N~9—14), 1f_7/2(N~20—28), 1g_9/2(N~40—50), 1h_11/2(N~70—82)], display some peculiar behaviors (eg. rms cnarge radii decrease with increasing A) which are sharply conflicting with the traditional A^1/3 law. Taking the deformation effect into account, these strange variations can be accounted for with the Z^1/3-law.     

ON NUCLEAR SINGLE-PARTICLE POTENTIALS（Ⅲ）SINGLEPARTICLE ENERGIES DETERMINED BY THE NONHERMITIAN POTENTIAL Uαβ=Mαβ（εβ）

In this paper the following results are proved:although the single-particle（sp）potential u_αβ=M_αβ（ε_β）defined in terms of the mass operator M_αβ（ω） is nonhermi-tian,the discrete energy eigenvalues determined by the Schrödinger equation h|γ>=（t+u）|γ>=ε_γ|γ> are real;moreover,they satisfy exactly the following relation:（ε_γ⁼±[E_nγ（N±1）—E₀（N）] where E₀（N）denotes the exact ground state energy of a closed-shell nucleus N,and E_nγ（N±1）are excat energy eigenvalues of its neighbouring N±1 nucleus.Further,in order to determine whether the bound state energies obtained by anyother sp potential may or not satisfy the above relation,a simple method is sugges-ted.It is shown that the amplitude renormalization of the sp Green function canalso be calculated easily by means of this method.     

STRATO-GLUON MECHANISM FOR HADRONIC MULTIPLE PRODUCTION AND AVERAGE CHARGED MULTIPLICITY

By assuming that in a high energy hadronic collision process,N pairs of stratonsare produced together with gluons,the number of which is supposed to be propor-tional to the number of“bonds”between any two stratons,we are able to get a rela-tion between the Q-value and the number of pairs N:N=（α²+βQ）^1/2-α.The average charged multiplicity〈n_ch〉_theo is calculated,and is compared withthe experiments.The data of pp、π^±p、K^±p collisions all coincide with the theoreticalcurve in a wide range of energies.The deviation between the energy vs.chargedmultiplicity relations for meson-proton and proton-proton collision processes are ex-plained quantitatively.The average straton mass estimated from the theory is ingood agreement with that.given by other authors.     

SYSTEMIC STUDY ON 1-p SHELL HYPERNUCLEI(Ⅱ) —the Calculation for Binding Energies

Adopting two sets of Λ-N effective interaction given in the paper (I)^[1], we have calculated the binding energies of 1-p shell hypernuclei based on the Hartree-Fock method in the multi-center shell model^[2]. The results show that the effective interaction we have introduced is reasonable. And the further evidence for charge-symmetry-breaking in Λ-N interaction can not be obtained from this kind of 1-p shell binding energy calculation.     

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.     

MEASUREMENT OF NUMBER OF RADIOACTIVE ATOMS AND HALF-LIFE (Ⅳ)—Applications and Accuracy of N0

In present paper, the applications of N₀,the number of atoms of a certain radioactive isotope in a target at a given time t₀ (usually the end of a bombardment by incident particles) in the measurement of the reaction cross section or the beam intensity or in the activation analysis are discussed and the accuracy of N₀ (also the cross section) is analyzed.     

MULTIPLICITY DISTRIBUTIONS,DISPERSION, CORRELATIONS AND KNO SCALING

Secondary charged particles produced in hadron-hadron collisions are divided quantitatively into two kinds in the light of the picture given by the authors [1, 2] and the results deduced therefrom. One of these parts, the genuine newborn particles, is analysed by means of the N(Q) dependence in [1]. Under the assumption that the dependence of the fluctuation of the number of newborn quark pairs on the ratio of kinetic to potential energies takes the form of a compound Poisson distribution, it is shown that the multiplicity distributions, dispersions, correlations and KNO scaling in pp collisions can be fitted with a single parameter on a unified basis. General formula of moments c≡<n>^k/<n>^k are given and their asymptotic properties are studied, resulting in an explanation of the appearance and behavior of the KNO scaling. A brief ldiscussion is given to the possible origin of the multiplicity distribution.     

ON NUCLEAR SINGLE-PARTICLE POTENTIALS (Ⅳ) MANY-BODY FORCES

It is shown that even if the nucleon-nucleon interactions contain many-body forces,the discrete energy eigenvalues ε_γ determined by the non-hermitian sp potential u_αβ=M_αβ（ε_β）still possess the following properties:G_γα（ε_γ）=∞,for at least one α,Since the points at which G_γα（ω） tends to ∞ areeither its poles or the heads of its branch cuts (where G_γα（ω） is log-divergent),itfollows that ε_γ are real and satisfy the relation.ε_γ=±[E_nγ（N±1）-E₀（N）].     

ON THE SU(4) MONOPOLE AND DYON SOLUTIONS

A simple method is proposed to obtain the classical monopole and dyon solutions in the case of SU(4) symmetry, which can be systematically generalized to the general case of SU(N). The solutions obtained in the SU(4) case correspond to magnetic charges of ±1/g,±√3/(2g),±1/(√2g).     

THE EFFECTS INDUCED BY A Λ HYPERON ON THE PAIRING CORRELATION IN NUCLEUS

In this paper, the effects induced by a Λ hyperon on the pairing correlation in nucleus are investigated. For simplicity, the δ-type A-N residual interaction is adopted. We have calculated the energy Spectrum and wave function of the low-lying excited states for _Λ¹⁰O. Then using infinite sum approximation, the correlation effect for two nucleons in the high energy shell induced by a Λ-hyperon is discussed.Finally. by means of Bose approximation, the correlation effects for n pairs of nucleons induced by a Λ is analysed.     

FINE STRUCTURES OF INCLUSIVE SPECTRA(Ⅰ)——SUM RULES AND THE GENERALIZATION OF FEYNMAN-YANG SCALING

Important implications of the fine structure of inclusive spectra(to be calledinclusive and semi-inclusive spectra of nearby particles,which represent the local dis-tributions of nearby particles in three-dimensional phase space with rapidity y and transverse momenta P_⊥x, P_⊥z as independent coordinates are explained,and some basicfeatures of the fine stucture are found,namely,sum rules and the generalized formof the Feynman-Yang scaling.One of the sum rules,for example,is:where f_(1;k) denotes the normalized invariant inclusive cross section of k closely neigh-boring particles.It follows that the inclusive the spectra of nearby particles arequalitatively different from the usual ones.The generalized form of the Feynman-Yang scaling for the case of k closelyneighboring particles,for example,is:f_(1;k)(s,x₁,P_⊥1,…x_k,P_⊥k⁾∞,（s→∞,x₁≤x₂≤…≤x_k）.where‘∞’denotes‘approaches a definite limit’.For k=2,the existing experimentaldata for the rapidity gap-length distributions show that for FNAL energies,f_(1,k） isalready close to its limiting form.The inclusive（semi-inclusive）spectra of nearbyparticles way be able to reflect effectively short-range correlation effects.     

INTERACTING BOSON MODEL FOR ROTATIONAL STATES OF NEGATIVE PARITY

In this paper, rotation of the system consiting of N—1 (sd) bosons and one (pf)boson is discussed on the assumption that the SU(3) limit is just the rotational limit.Using group-theoretical methods, we have given rotational spectra of negative parity,and have derived the analytic expressions of the reduced matrix elements of the E3transition from the v₀-band (K^π=0^-) to the ground band. In terms of the inegualityof the intensities of (sd)-(sd). interaction and (sd)-(pf) interaction, the differencebetween the parmeters of positive-parity bands and those of negative-parity bands areexplained qualitatively.     

THE MULTISYNCHRO-SPHERICAL SOLUTIONS OF THE SU(N)GAUGE THEORY

We study the monopole solutions of the SU(N) gauge group systematically,generalize the current synchro-spherical symmetrical monopole to the multi synchro-spherical symmetrical case,and give the complete classification of the monopole so-lutions.As examples,we have calculated the SU(3) and SU(4) monopoles in detail,and discuss some problems such as angular momenta and topological quantum num-bers.     

THE COLLECTIVE MOTION OF THE BAG AND THE NUCLEON STRUCTURE FUNCTIONS

Using the hypothesis of the bag-quarks' wave-function with the property of transla-tion invariance, and introducing a Lorentz-invariant effective Lagrangian, we have cal-culated the nucleon deep -inelastic structure functions In our calculation the4-momentum conservation is satisfied automatically, while the resultant structurefunctions are positive-definite and vanish when x>1. Furthermore, using the assumptionof the asymptotic freedom, we obtain explicitly the Bjorken scaling, the approximateexpession F₁ (x～1)∝(1--x)⁴, and by the way, a new counting rule Computercalculation gives the F₂(x) curve which seems to be consistent with the data in therange of 0.4<x<1.     

THE MASS GAP IN 2+1 DIMENSIONAL SU(2) LATTICE GAUGE THEORY

A variational calculation of the mass gap in 2+1 dimensional SU(2) lattice gauge theory by using a Hamiltonian with the ground state being exactly known is made.In the range 0≤1/g²≤7,a good scaling behaviour am=2.28g² is obtained,which is in agreement with weak-coupling perturbation theory.     

EFFECT OF N PRODUCTION ON HIGH ENERGY PROTON SCATTERING BY NUCLEUS

The variable separation method of Glauber multiple scattering theory is developedto include the N^* production in the intermediate states and is used to calculate theinelastic scattering of proton by nucleus.Numerical results are compared with dataon p-¹²C^*（4⁺,14.08）at 1 GeV and it implies that the effects of N^* production tothe high-energy proton-nucleus scattering are noticeable.     

A METHOD FOR FINDING POTENTIALS CORRESPONDING TO POLYNOMIAL-FACTOR EIGENFUNCTIONS IN QUANTUM MECHANICS

A method for finding potentials corresponding to polynomial-factor eigenfunc-tions is given for the Schr（?）dinger equation as an example.It is shown that theeigen-solutions for harmonic and Columb's potentials in quantum mechanics are the twoexamples which can be given by this method and some other examples are discovered.This method and some results of this paper may be useful for hadron structure mo-del theory.One of the examples is the equation in Ref.（4）which is derived fromBethe-Salpeter equation for the case that the straton is tightly bounded in certain po-tential well.When this method is applied to that equation for three dimensionalcentral symmetric potential V（r）=V₀—2（N+（1/2））β^-1（√V₆r²）+（V₆r⁶）, some resultsare obtained as shown in Fig. 2 in which λ′ must be considered as a linear function of m².The so called“quasic Regge trajectory”behavior is manifested.     

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.     

STUDY OF ANOMALOUS LARGE ANGLE α-SCATTERING ON 24Mg

Angular distribution for the elastic and some inelstic scattering of α particle on²⁴Mg isotope between 12°and 178°in steps of 2°(Lab) have been measured at 18.1MeV α bombarding energy. α+²⁴Mg elastic scattering angular distribution at back-ward angles displays more pronounced oscillation and a strong overall rise of crosssection. The calculation by the standard optical model together with compound nuclearscattering (via H-F) cannot predict this anomalous enhancement. The calculation byuse of an L-dependent imaginary potential optical model is in good agreement withthe experimental data. The fits of L-dependent optical model to the experimentalangular distributions of other energies are also discussed.