Gamow-Teller Transitions of Nuclei With A=147-153

In this paper the Gamow-Teller transitions are systematically investigated for nuclei with A=147-1.53 in terms of the shell-model. These nuclei have only GT decay channel π1h_11/2→v1h_9/2. The overall comparisons of the experimental reduced probabilities B_exp(GT) with the calculated B_cal(GT) show that there is a quenching factor γ² with optimum value 0.17±0.05 in this mass region.     

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.     

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 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.     

DISCOVERY OF MULTIPLE,COLLECTIVE BAND STRUCTURES IN NUCLEI WITH A=60—80

Recent studies of levels in even-even ^68,70,72Ge,^70,72,74Se,^74,76,78,80Kr and ⁶⁵Ga and ⁷⁴Br have led to the discovery of a wide variety of different collective band structures.These include bands built on near spherical ground states and excited more well de-formed shapes that may include triaxial shapes,rotation-aligned bands built on thesame orbital （g_（9/2））² for both protons and neutrons,RAL negative parity bands witheven and odd spins,and ΔI=1 γ-type vibrational bands in even-even nuclei.As recent as 1974,a survey of the energy level in the even-even Ge and Se iso-topes^[1] revealed little was known above a spin of 4⁺ （see for examples Figs.1 and 2 of Ref.1）.With the exception of the unusally low-lying excited 0⁺ states in ^70,72Ge,first discovered in ⁷²Ge in 1948 at Vanderbilt^[2],the theoretical treatment of thesenuclei was limited primarily to some variation of the vibrational model.However,very recently there has been a surge of information on nuclei in this region that hasrevealed fascinating new features and also provided new insight into the excited 0^+’states.Particularly striking are the multiple,independent and highly collective bandstructures which we have discovered in our in-beam γ-ray spectroscopy studies fol-lowing heavy-ion induced reaction.Evidence for and the theoretical understandingof the richness of the collective band structures that are found in our studies of^68,70,72Ge （Refs.3—6）,^70,72,74Se （Refs.7—13） and ^74,76,78,80Kr （Refs.14—18）,as illustratedby the at least seven different bands found in our studies of the levels of ⁶⁸Ge ⁷⁴Se,and ⁷⁶Kr （Figs.1—3）,are described in this paper.These multiple structures includethe following:a) coexistence of ground bands built on near-spherical shapes andexcited bands with larger deformation built on O^+′ band heads;b) bands with 8⁺ band heads interpreted as rotation-aligned,RAL,bands built on both neutron and/orproton （g_（9/2））² quasiparticle configurations coexisting with the ground-state band;c)RAL neutron and proton odd-parity bands formed from coupling of a g_{（9/2 ）}quasipar-ticle and a p_（1/2）,p_（3/2） or f_（5/2）,quasiparticle with the core;d) ΔI=1 even-parity bands,which are best characterized as gamma-vibrational bands;and e) additional bandswhose nature are presently not known.     

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 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⁺.     

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.     

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.     

U(6/20) SUPERSYMMETRY IN NUCLEI AND ITS Spin (6) LIMIT

The U(6/20) supersymmetry is discussed in this paper. Particularly we discuss its Spin (6) limit. First we discuss the reduction of the group chain of the Spin(6) limit. Secondly we derive the wave functions and excited energy formulas for the nuclei in which the Spin(6) limit of U(6/20) supersymmetry exists. Thirdly we make comparison of the nuclear energy spectra between the theoretical calculation and experimental measurement in the case of nucleus ₇₇¹⁹³Ir₁₁₆. The comparison shows that the Spin(6) limit of U(6/20) supersymmetry possibly exists in nucleus ₇₇¹⁹³Ir₁₁₆.     

SOME PROBABLE APPROACHES TO THE PRODUCTION OF HYPERSYMMETRY STATES

The angular distributions of the strangeness exchange reations ⁹Be （K^-,π^-） ^_A9Be*and ¹³C（K^-,π^-）^_A13C with K^- in flight have been calculated on the basis of our pre-vious work^[2].In the framework of the plane-wave impulse approximation we havecalculated the relative rations of the differential cress-sections of the associated produc-tion reactions leading to the strangeness analoque states and the supersym-metric states of _A⁹Be and _A¹³C,and have estimated the absolute values of these dif-ferential cross-sections.The possibility of producing supersymmetric states bystrangeness exchange reactions and associated production reactions have been discus-sed on the basis of these calculations.     

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.     

Diffractive production of charm in DIS and gluon nuclear shadowing

We evaluate nuclear shadowing of the total cross section of charm particles production in DIS within the framework of Gribov theory of nuclear shadowing generalized to account for the QCD evolution. We use as an input the recent QCD Pomeron parton density analysis of the HERA diffractive data. Assuming that the QCD factorization theorem is applicable to the charm production off nuclei we also calculate shadowing of the gluon densities in nuclei and find it sufficiently large for heavy nuclei: G_A~200(x,Q²)/AG_N(x,Q²) ~ 0.45 m 0.5 · (A/200)^т.15 for x ~ 10^х1ц, Q² ~ 20 1 40 GeV² to influence significantly the physics of heavy ion collisions at LHC. We evaluate also suppression of minijet and hidden charm production in the central AA collisions. We also discuss some properties of the final states for %^*A processes dominated by the scattering off small x gluons like the high p_t jet and charm production.     

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.     

INVESTIGATION OF THE NUCLEAR SHADOWING EFFECT IN THE SMALL x REGION

In this paper,we analyse the spatial overlapping behavior of sea quarks of neighboring nucleons in nuclei in the small x region and give a relation between the nuclear shadowing factor R(x,Q²,A) and the spatial overlapping factor ΔV_A(x)/V_A(x).By using this nuclear shadowing factor R(x,Q²,A),we calculate the ratios of the average nuclear structure functions of nuclei ¹²C、⁶³Cu and ¹¹⁶Sn,to the deuteron structure function and obtais a better agreement between the calculated result and the experimental data.     

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.     

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.     

TESTING GLUON DISTRIBUTION FUNCTION OF HADRONS IN LARGE PT PROCESS WITH DIRECT PHOTON EMISSION

In this paper we disscuse disscuse the physicsical aspect of cross-section differences Δ_AB^cγ=dσ(AB→cγX)-dσ(AB→cγX) and give the simple rules to select the elementary subprocesses which contribute to cross-section differences.
We bind a way to test the gluon distribution functions of hadrons through the measurement of cross-section difference or combination of cross-section differences in the large P_T process with direct photon emission. Moreover we obtain simple relations between each combination of cross-sections and the corresponding gluon distribution functions of proton, neutron, pion and daon:
G_p⁸(x)/(Δ_pp^hγ－Δ_pp^hγ)=G_n⁸(x)/(Δ_pp^hγ)=G_π⁸(x)/(Δ_π+p^hγ+Δ_π－p^hγ=G_K⁸(x)/(Δ_K+p^hγ+Δ_K－p^hγ)which are expected to be test in experiment.     

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.     

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.