THE IBM EXPRESSIONS OF B(E2) FOR INTER REPRESENTATION TRASITIONS IN DEFORMED NUCLEI

The general one body E2 operator is used to derive the analytic expressions of B(E2) from the first β and γ bands to the ground band under the SU(3) basis.     

THE PARTIALLY VIOLATED U(3) LIMITS OF THE DYNAMICAL SUPERSYMMETRY U(6/12) IN EUROPIUM-GADOLINIUM REGIONS

The partially violated U(3) limits of the U(6/12) model is presented. The theoretical predictions are compared with existing experimental data of energy spectra and B(E2). The theory tallies with experiment fairly good.     

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 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.     

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 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.     

EXCITATION CURVES FOR SOME REACTIONS OF Al、Ti、V AND I

Excitation curves for the reaction ²⁷Al（n,α）²⁴Na,⁴6Ti（n,p）⁴⁶Sc,⁴⁸Ti（n,p）⁴⁸Sc,⁵¹V（n,α）⁴⁸Sc and ¹²⁷I（n,2n）¹²⁶I have been measured by the activation method in the4.5—18.3 MeV energy region.The cross section for the reactio ²⁷Al（n,α）²4Na was determined at 14.61±0.20 MeV.The measurement of neutron flux was performed using the associated particle method.The cross sections for other reactions were de-termined relative to the measured ²⁷Al（n,α）²⁴Na cross section.The resulting activities were measured employing a calibrated NaI（TI）scintillation counter.The values obtained were 117.5±3.0 mb,291.4±14.0mb,63.7±3.2 mb,16.8±0.9mb and 1656±68 mb respectively.A brief comparison with existing data was made.     

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.     

RELATIVISTIC SEMICLASSICAL THEORY OF CONDENSATION (Ⅰ)

Exact relations between the energy of a symmetric nuclear matter loaded in a classical π field and the value φ and wave number k of this π field were obtained for pseudoscalar coupling and pseudovector coupling. Results show that there is no π condensation under pseudoscalar coupling. If pseudovector coupling (which is not renormalizable) were permitted, π condensation emerges as a result of π nucleon P wave interaction, and the chiral symmetry is not necessary. π nucleon interaction itself leads to saturation of the condensed π field. Nonlinear selfinteractions of π field, such as φ⁴ term and so on, are not necessary. The influence of nucleonic repulsive core were considered under Yan der Waals approximation. It leads to upper and lower limits on wave numbers of the condensed π fields. If the radius of the repulsive core were larger than a critical value, π condesation becomes impossible again.     

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 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.     

SU（4）×S3α SCHEME OF STRATON MODEL AND THE NEWLY DISCOVERED HEAVY PARTICLE γ（9.5）

In this paper, the possibility that the newly discovered heavy particle γ （9.5） is a colour excited state of mesons in the SU（4）×S₃^α scheme of straton model is discussed. We point out that in the γ region, there are three colour excited states appearing as two peaks with mass difference about 0.5 GeV. The leptonic decays, hadronie decays, radiative decays, hadronic decays with electromagnetic interaction of the second order and the production behavior of γ are discussed. This model also predicts that many colour excited states of mesons accompanied with γ should exist with masses around 9.5 GeV and at least four weakly decaying particles should exist.     

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.     

TRANSFORMATION COEFFICIENTS BETWEEN SO(6) AND SU(4) GELFAND-ZETLIN STATES

In this note, we have given a method of calculating the transformation coefficients between SO(6) and SU(4) Gelfand Zetlin states.     

STUDY OF THE DEEP INELASTIC SCATTERING OF 12C ON 27AI

The deep inelastic scattering of 71.5 ¹²C ions on a ²⁷Al target was measured.ΔE-E telescope was used to identify the reaction products.The contour plots in the E-θ plane for the measured cross sections in the C.M.S.for B and Be show the generalfeatures of quasi-elastic scattering at grazing angles and the deep inelastic scatteringridge extending from smaller angles and flattening at larger ones.Two special featuresmay be worthwhile to mention.First,there are some fine structures near the Q.E.peak.Secondly,the average C.M.kinetic energy of the completely damped part is notequal to the Coulomb energy of the final state.     

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.     

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 ANALYTIC RESULTS FOR U1 AND SU2 AVERAGE PLAQUETTE TO THE THIRD ORDER APPROXIMATION IN THE CUMULANT EXPANSION

In the lattice gauge theory, by using cumulant expansion, we calculate the average plaquette for U₁ and SU₂ group up to the third order approximation in 4 and 5 dimensions analytically. Our results are consistent with MC data. We also discuss the application of cumulant expansion techneque in lattice theory.     

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 SU(4)×SU(2)×U(1) UNIFIED MODEL

In this paper we propose an SU(4)×SU(2)×U(1) unified model, in which the stratons and leptons of every generation belong to the same Multiplet, and the leptons will couple to the stratons. But this kind of coupling cannot cause the proton decay, and has only some effects in high energy scatterings. This model predicts the existense of two neutral intermediate bosons, instead of one, and the value of Weinberg angle to be sin²θ_w=0.25. The neutrinos have reasonable masses in the model.