THE CLASSIFICATION OF THE WAVE FUNCTIONS OF BOSONS AND FERMIONS

In this paper we have proved that the wave functions for bosons and fermionscan be classified by either of the following two Lie superalgebra chains U(2l+1/2j+1) SU(2l+1/2j+1) SU(2l+1)SU(2j+1) SO(2l+1)Sp(2j+1) SO(3)SO(3), U(2l+1/2j+1) SU(2l+1/2j+1) OSp(2l+1/2j+1) SO(2l+1)Sp(2j+1) SO(3)SO(3) The wave functions for bosons and fermions classified by the Lie superalgebra chain U(2l+1/2j+1) SU(2l+1/2j+1) SU(2l+1)SU(2j+1) SO(2l+1)Sp(2j+1) SO(3)SO(3), are calculated also.     

THREE LIMITS IN THE INTERACTIONS OF THE s,d, g,BOSONS

In the I. B. M., when s, d, g bosons are presented, the boson Hamiltonian has thestructure of group U(15). This paper deals with the various chains of subgroups ofgroap U(15). Especially, the following chains:SU(15)SU(3)SO(3), SU(15)SU(5)SO(5)SO(3), U(15)U(14)SO(5)SO(3).are studied in detail, The formulae of the energy spectra are also given.     

BRANCHING FORMULAS FOR SO(n) SO(n－1) TENSOR AND SPINOR REPRESENTATIONS

Branching formulas for SO(n) SO(n－1) tensor representations are given from the branching rules for SO(n) SO(n－1) which described in F.D.Murnaghan's. Furthermore, these formulas are extended to the spinor representations by using the method of kronecker products. In this way a pair of complete branching formulas for SO(n) SO(n－1) is give in this paper.     

Searches for the technicolor signatures via gg → W±πt± at the Large Hadron Collider

In this paper, we calculate the production of a charged top pion in association with a W boson via gg fusion at CERN's Large Hadron Collider in the context of the topcolor assisted technicolor model. We find that the total cross section of pp → gg → W^±π_t is several dozen femtobarns with reasonable values of the parameters, and the total cross section of pp → W^±π_t can reach a few hundred femtobarns when we consider the sum of the contributions of these two parton subprocesses, gg → W^±π_t and bb → W^±π_t.     

SYMMETRY OF THE ROTATION+VIBRATION SPECTRA FOR NUCLEAR MOLECULE 12C+12C

The rotation-vibration spectra of nuclear molecule ¹²C+¹²C is chassified by the irreducible representations of group U(5). It is shown that the symmetry of rotation-vibration levels of nuclear molecule ¹²C+¹²C are discribed by means of dynamical symmetry U(5)U(4)O(4)O(3).     

SOME ISOSCALAR FACTORS FOR THE GROUP CHAIN SO(6) SO(5)

Some isoscalar factors for the group chain SO(6) SO(5) are calculated by using the method of reduced matrix elements and the building-up principle.     

AN EVENT WITH TWO NON-SYMMETRICAL CORES

A double core event with ΣE_γ1000TeV observed in MEC is reported. The distributions of particles in the two cores are quite dissimilar from each other The possible existence of two different types of clusters is discussed.     

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.     

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.

     

LEVINSON'S THEOREM FOR KLEIN-GORDON EQUATIONS WITH POTENTIAL TAILS

In terms of the modified Sturm-Liouville theorem, the properties of the solutions to the Klein-Gordon equations with the potential tails is discussed and the corresponding Levinson's theorem is proved in this paper.     

THE SU2×SU2 BASIS AND THE PHYSICAL BASES FOR THE STATE VECTORS OF d-BOSON SYSTEMS AND THE TRACELESS BOSON OPERATORS (Ⅰ)

The group chain U₅O₅SU₂×SU₂ used by K. T. Hecht (1965) and by the othersprovides an important representation for expressing the physical basis of d-boson sys-tems. However the methods which have been introduced for this SU₂×SU₂ representa-tion to construct a physical basis is poorer in comparison with those for the otherrepresentations. In view of this we try to find appropriate methods to obtain the SU₂×SU₂ representation wave functions of the existing physical bases constructed byChacon et al. and by Szpikowski et al., In the present paper we analyse the SU₂×SU₂ tensor properties of the,bosonoperators and Vilenkin's traceless boson operators and express succinctly the elementaryvectors of the SU₂×SU₂ basis, the |PP SU₂×SU₂ > vectors, in terms of the tracelessoperators. With the help of this form of the| PP SU₂ SU₂> vectors we derive a simpleformula for obtaining the SU₂×SU₂ -representation wave functions of a physical basisfrom its (n_μ)-representation wave functions. Thus the problem mentioned above is partlysolved. The other parts of the solution of the problem will be found in a coming paper.     

APPROXIMATE B.S. WAVE FUNCTIONS FOR AN ELECTROMAGNETIC BOUND SYSTEM OF SPINS (1/2, 1/2) OR (1/2, 1/2) WITH UNEQUAL MASSES

The Bethe-Salpeter equation for an electromagnetic bound system of spins (1/2—1/2) or (1/2—1/2) with unequal masses are solved in this paper. The approximate B.S. wave functions for these systems are given. Utilising these wave functions, the decay rate and branching ratio for Ξ⁰→(Σ⁺μ^－)+v_μ are calculated with accuracy up to order O(α). The results are wΞ⁰→(Σ⁺μ^－)+v_μ1.12(1/sec) and R=[wΞ⁰→(Σ⁺μ^－)+v_μ]/[wΞ⁰→(Σ⁺μ^－)+v_μ]4.7×10^-7. Similarly, the process Λ→(pμ^－)+v_μ is also discussed.     

NUCLEAR PAIRING PHASE TRANSITION

The intrinsic structure of the eigenfunctions of Cranking Shell Model hamiltonian and the pairing phase transition at high rotational frequency are investigated with the particle-number-conserving approach.Pair-transfer matrix elements and the K-structure of the wave functions display similar behaviour under the Coriolis interaction and hence both of them may be used to indicate the pairing phase transition.The blocking effects on pairing parameter,,are much more important than the Coriolis anti-pairing effects.     

New Approach for Normalizing Photon-Added and Photon-Subtracted Squeezed States

We present a new concise approach for normalizing m-photon-added squeezed state a^tmS（s）｜0〉≡｜r〉m and mphoton-subtracted squeezed state a^m S （ r ） ｜0〉） ≡ ｜r〉m, i.e., we construct the generating function ∑m=0^∞ t^m/m!m〈r｜r〉m and ∑m=0^∞ t^m/m!_m〈r｜r〉_m respectively, after calculating them and comparing the result with the standard form of generating function of Legendre polynomials Pm, we find m〈r｜r〉m=m!cosh^m rPm（cosh r）,amd _m〈r｜r〉_m=m! （-i sinh r）^ m pm （ i sinh r）, where r is the squeezing parameter.     

QCD PREDICTION FOR THE REACTION γ+p→2γ+X

In the framework of the perturbative QCD, the two-fold differential cross section d²σ/dx_Tdx_L of the reaction γ+p→2γ+X and its two backgrounds (γ+p→γ++X, γ+p→γ++X) are calculated in c.m.s.. The results show that, in a large range of (x_T, x_L), the calculated reaction cross section can be measured in current laboratory condition. And due to the properties of this reaction, i.e., large p_T photoproduction and direct photon pair emission, all of the backgrounds can be greatly suppressed.

     

INCREASE OF BEAM PROJECTIVE EMITTANCE IN SYSTEM WITH DISPERSION

In this paper, the increase of beam projective emittance caused by the momentum dispersion in the transport systems is discussed, and the incrementary ratio is derived. If the bending plane is (XOZ), the incrementary ratio of the transversal emittance is

and the longitudinal one is

Here ε_x0 and ε_z0 are original emittances in the x-direction and z-direction respectively, (Δp/p)_maxis beam momentum spread β_xf, α_xf, γ_xf being acceptance parameters of the system in x-direction for betatron oscillations, η and η' are dispersion function and its derivative.     

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.     

MAGNETIC FIELD ANALYSIS OF PERMANENT MAGNET UNDULATOR

2 Dimensional magnetic field expression of permanent magnet undulator with gradually varied magnetization is derived. Conditions for minimizing high order harmonics are given. Three different types of permanent magnet undulator —— the "gradually varied" type, mixed type and simple type ——are compared. Upon these comparisions we conclude that "gradually varied" type is superior to mixed type except for Δh/λ0.1.     

INTRODUCTION OF THE CONCEPT OF THE DEPAIRING PROBABILITY TO EXPLORE NUCLEAR HIGH SPIN STATES

In order to explore nuclear high spin states,a physical concept of depairingprobability has been suggested,which is based on the CAP and the RAL effects inthe nuclear rotating system.We think that the depairing process,might be gradualat begin—then dramatic and finally gradual again.According to the concept ofthe depairing probability and the particle-rotor model,a formula for the spectrum ofrotational energy has been obtained,and the spectra for more than fifty nuclei have been calculated by using this for-mula.The calculated results are found to be in reasonable agreement with experi-mental data,and are able to reproduce the experimentally observed various backbending phenomena on the plots of g_eff—ω_eff².