PROPAGATION EFFECTS OF SOLAR COSMIC RAYS

Computer calculations have been made on the dimensional solution to the anisotropic diffusion convection equation for solar cosmic rays propagating in an uniform and unbounded interplanetary medium. This paper presents the results calculated by means of Jokipii's diffusion coefficients. Discussion is restricted to the influences of solar wind convection on the rise to maximum times and on the peak intensities of solar cosmic ray events with solar corotation effect taken into consideration. The model well explains the asymmetrical variations of the propagation charateristics of the events with solar longitudes of their parents flares relative to the interplanetary magnetic field lines passing through the earth, and the theoretical curves of the rise times fit satisfactorily the observations of solar events ranging from relativistic to about 30 MeV medium energies.     

APPROXIMATE SEQUENCE FOR U（t,t0）-OPERATOR

We give an approximate sequence for U（t,t₀）-operator.We prove the follow-ing theorems:Theorem 1.If the norm ||H（t）|| of H（t）in equation（2.1）is a Lebesgue in-tegrable function with respect to t,then there is an approximate sequence{U_n},such that for any state vector |Φ〉,|Ψ〉,the sequence <Φ|U_1^|Ψ><Φ|U_2^|Ψ>,......,<Φ|U_n^|Ψ>,......is uniform convergent with respect to t.Theorem 2.If in finite time interval,the norm ||H（t）|| of H（t）in equation （2.1）is a Lebesgue integrable function,then equation（2.1）has unique solution.     

The theory of particle diffusion in a strong random magnetic field with an allowance for higher multipole moments of the distribution function

The kinetic equation including a small-scale collisional integral for the particles propagating in a strong random and regular magnetic field [29] is solved by expanding the distribution function into series in spherical harmonics of the particle momentum angles. Using methods of the quantum theory of the angular moment [41], the equations for higher multipole moments of the distribution function in the space of momentum angles are derived and solved in the stationary case for the galactic cosmic rays in interplanetary space. The observed amplitudes and phases of the diurnal variation harmonics can be explained using the results of measurements of the interplanetary magnetic field performed on board the Ulysses spacecraft [12–14] and other satellites [45, 46] with an allowance for redistribution of the interplanetary and interstellar magnetic field lines. The spatial structure of the convection and diffusion fluxes of the galactic cosmic rays is refined. Formulas taking into account a change in the Earth’s axis tilt relative to the direction toward the Sun are derived, which allow the annual changes in contributions to the diurnal variation harmonics to be determined. The equation of diffusion taking into account the 2nd harmonic is obtained, and the contribution of this effect to the relative particle density in the cosmic rays in a spherically symmetric case is analyzed.     

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.     

One Loop PGBs Effects on tt Production in High Energy e+e- Annihilation

The Technicolor(TC)O(αm_t²/m_w²)corrections to top pair production in high energy e⁺e^－ annihilation are calculated in the one generation TC model.The analytic expressions are given for the form factor, the renormalized matrix element and its square.Numerical examples are presented for the corrections to the total cross-section ,the forward-backward asymmetry A_FB and the left-right asymmetry A_LR.We found that the corrections can reach －12.3%, －3.3% and －11.7% to the observables,A_FB and A_LR respectively for the favorable parameter values.The level of these corrections might be achieved at the next-generation linear collider(NLC).It might open a window for testing TC theory.     

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 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.     

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.     

Search for periodicities in galactic cosmic rays,sunspots and coronal index before arrival of relativistic protons from the sun

Using different approaches and techniques of wavelet analysis we analyze variations (oscillations) of galactic cosmic rays, solar spot number, and coronal index of solar activity before ground level enhancements of solar cosmic rays. Obtained results are discussed in frames of recent ideas about periodicity phenomena in the photosphere, and corona of the Sun, interplanetary medium, and cosmic rays.     

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.     

ON THE “DIRECT CHANNEL DIAGRAM” OF THE PRODUCTION OF THE （π+ π-）s S-STATE ATOMS

In this paper we work out the relativistic covariant B-S wave function for the（π⁺ π^-）_s atoms.Some properties of the“direct channel diagram”of the produc-tion the （π⁺ π^-）_s atoms are discussed by calculating the cross-section of the process π⁺ +n→p+（π⁺ π^-）_s with the help of the relativistic covariant wave function and assuming the lowest termin the perturbation expansion series of the quantized composite field theory——the“direct channel diagram”is dominant.Besides this calcuation perhaps presentsa rough estimate for the interesting process μ⁺ +n→（μ⁺ π^-）+p.     

THE BEHAVIOURS OF F2ep(X,Q2)-F2en(X,Q2) AND THE SCALE-BREAKING PARAMETER

The scale-breaking parameter F₂^ep(x, Q²) of non-singlet component F₂^ep-F₂^en and some other quantities in the electro-production process are discussed by usinb the analytic expression for the distribution function of valence quarks in ha.drons up to leading log approximation given by a, previous paper^[1]. Comparisons with data are also given.

     

THE DIFFICULTY OF THE DECAY τ→πντ AND SPIN 3/2 HEAVY LEPTON

We discuss the suppression of the decay of heavy lepton τ into πv_τ,by assuming that τ and/or v_τ carry spin 3/2. For the case of spin 3/2 T and spin 1/2 v_τ, using the weak current ψ_μ^(τ)(a+b_^γ5)Ψ^(v_τ)we find that the πv_τ decay channel relative to the v_τv_ll^-channel is suppressed 12/5 times, while other decay channels are not changed appreciably. △R=σ（e⁺e^-→τ⁺τ^-）/σ（e⁺e^-→μ⁺μ^-） is also discussed.     

A Statistic Model for Galactic Cosmic Rays

Supposed that all of cosmic ray particles of energy below 3×10¹⁸eV are mainly originated and accelerated in an individual explosion of the galactic supernovae(SNs).By using an isotropic diffusion propagation model,non-steady state density of the iron nucleus is investigated.Considering the effect of extra-galactic cosmic rays and the variety of the galactic cosmic ray nuclei,the statistic model of galactic cosmic rays with a reasonable distribution of the SNs in space and time can account for the spectrum of cosmic ray in the energy range of 10¹²—10²⁰eV quitewell.     

ON NUCLEAR SINGLE-PARTICLE POTENTIALS (Ⅱ) THE NONHERMITIAN CHOICE

The cancellation properties of the nonhermitian single-particle （SP） potential u_αβ=M_αβ （ε_β） [or M_αβ（ε_α）] according to the principle of maximal cancellation of perturbation diagrams are investigated in detail. The mass operator M_αβ（ω） is separated into two parts M_αβ^on （ω） and M_αβ^off （ω） as usual, however, a new criterion for their definition will be proposed. It is shown that the exact mass operator insertion is equal to the sum of the following three types of terms:（1） terms contributed by the poles of M_αβ^off（ω）. They are truly non-factorizable and must be considered separately,（2） terms which can be cancelled to all orders by the nonhermitian choice u_αβ=M_αβ （ε_β） [or M_αβ（ε_α）]. Hence, they serve to define u_αβ,（3） the remaining terms, which can be summed to all orders in a simple way and may be interpreted as amplitude renormalization of the SP Green function.In order to illustrate the usefulness of the above results, we have considered the renormalized random phase approximation （RRPA） for the particle-hole Green function as an example. Related formulae are derived. In RRPA, not only the SP propagator renormalization which includes all the effects except those contributed by the poles of M_αβ^off （ω）, but also the off energy shell property of the G matrix elements have been taken into account.     

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（&#8706;/（&#8706;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.     

Determination of J/ψ Leptonic Branching Fraction Via ψ(2S)→π+π－J/ψ

Two processes ψ(2S)→π⁺π^－J/ψ,J/ψ→1⁺1^－ and J/ψ→anything are carefully studied to get the J/ψ leptonic branching fractions with the ψ(2S)data at BES/BEPC.The results are B(J/ψ→e⁺e^－)=(5.90±0.07±0.16)% and B(J/ψ→μ⁺μ^－)=(5.96 ±0.08±0.16)%,and B_e/B_μ is estimated to be 0.990±0.018±0.024.Assuming B_e=B_μ,the leptonic branching fraction of the J/ψ is B(J/ψ→1⁺1^－)=(5.93±0.05 ± 0. 16 )%.This result is used to estimate the QCD scale factor ∧(nf/MS) and the strong coupling constant α_s.     

The Spin Effect of Antiproton-Nucleus Inelastic Collison

If the antiproton optical potential is inclusive of the spin orbit interaction term,the A(p,p)A* inelastic scattering not only can excited the normal parity states,but also can excited the abnormal parity states.There are also induced the polarization P_f(θ) at the inelastic scattering.In the framework of DWIA,we derived the inelastic scattering cross section (dσ/dΩ)_f,i,and polarization P_f(θ),and calculated the (dσ/dΩ)_f,i, and P_f(θ) for ¹²C(p,p)¹²C* with 2⁺,3^－ and 1⁺ states at antiproton energies of 46.8 and 179.7MeV.They fited experiment data quite well.Due to the abnormal partity states in the inelastic process have been measured,the spin orbit term can not be neglect.     

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⁺.     

A TWO-NUCLEON MODEL OF THE（p,π-） REACTION

In this paper,we suggest a two-nucleon model of the A（p,π^-） B reaction.Areduced formulation of the reactoin amplitude and a relation between the reactionamplitude and the nuclear structure are given.The differential cross section of ¹³C（p,π^-）¹⁴O_g.s,at E_P=185 MeV is calculated in the plane wave approximation.The results+s can explain the experimental data qualilatively.