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.     

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.     

THEORY OF （π+,d） REACTION

In this paper the DWBA cross section formula for the（π⁺,d）reaction is deri-ved in the model of one-nucleon absorption of pion,and the differential cross sectionsfor ¹²C（π⁺,d）¹⁰C_g.5.2+reactions are estimated in PWBA.This kind of reaction isregarded as a worthnoting one for the studies of π absorption processes and the nu-clear pair structure.     

π-NUCLEAR DOUBLE CHARGE EXCHANGE REACTION AND NUCLEAR STRUCTURE

Using Glauber's multiple scattering theory, and using coherent fluctuation nuclearmodel, the double charge exchange (DEC) reaction cross sections for πon ¹⁶O and ¹⁸Ohave been calculated. The calculated values of the ratio of σ(¹⁸O(π⁺,π^-)¹⁸Ne)_g.s. toσ(¹⁶O(π⁺,π^-)¹⁶Ne)_g.s. fit the experimental data quite well. Just as predicted by ourcalculation, the angular distribution of ¹⁸O(π⁺,π^-)¹⁸Ne_g.s. in a recent experiment,exhibits an evident dip around 23°.     

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.     

STUDY OF THE MECHANISM OF 12C（d,d）12C AND 12C（d,p）13C* REACTIONS

A formalism for studying the interference between the direct reaction and the compound resonance processes is presented by the S-matrix theory; The mechanism of ¹²C（d, d） ¹²C, ¹²C（d, p₁） ¹³C* and ¹²C（d, p₂） ¹³C* reactions in the energy range E_d=1.63 MeV to 2.05 MeV is analysed.Te results show that: the interference between these two processes exists; and the quantitative relation between them is given. While the parameters of direct reactions and compound resonance processes, particularly for four resonance states with E_d=1.726, 1.767, 1.792 and 1.86 MeV are determined.     

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.     

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.     

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.     

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.     

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.     

DECAY PROCESSES IN MASSIVE STRATON MODEL OF MESONS

Using the B-S wave functions of mesons in the massive straton model^[1], we discuss their weak decay, electromagnetic decay, and particularly hadronic decay processes. Not only f_π≈f_K, 1^－→l⁺l^－ rate are successfully explained, the predicted widths for various hadronic decays are also in good agreement with experimental data.     

COULOMB EFFECT IN π-NUCLEUS SCATTERING AT LOW ENERGY

The importance of Coulomb effect for π-¹²C, ¹⁶O scatterings is studied at incidentenergy T_π=80, 70, 50, MeV. Results show that the discrepancy between the data andthe calculation that appears in differential cross section for T_π=50 MeV in referenceis not attributed to ignoring Coulomb effect. The Coulomb effect in such energy regionis negligible, except small angle region in the differential cross sections at. T_π=50 MeV.     

PION-18O INELASTIC SCATTERING

In the framework of the eikonal form of DWIA and using the transition densitymethod, the differential cross sections for ¹³O (π,π') .¹⁸O^* (2⁺, 1.98 MeV) inelasticscattering at T_π=230 MeV are calculated. The ratios of the integrated cross sectionsfor π^- vs. π⁺ bombardments, are analyzed and the effects of changing the neutron radiusto the differential cross sections are studied as well. Our results fit the data quite well.     

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.     

Strangeness exchange reaction on nuclei

Population of hypernuclear states has been observed in recoiless Λ production of the strangeness exchange reaction (K^?, π^?) on ⁹Be, ¹²C, ¹⁶O, ³²S and ⁴⁰Ca.     

UNIFIED ELECTRO-WEAK MODEL IN SU (3)

In this paper a unified electro-weak model for leptons based on the SU(3) gaugegroup is suggested by means of four kinds of realization for the generators of thegroup. For all low energy electro-weak processes, this model predicts the same resultsas the conventional Weinberg-Salam model does. The Weinberg angle is shown to be sin²θ_w=1/4 in a natural way. When the Higgs self potential respects a discrete symme-try Φ→-Φ, a new conserved quantum number called weak strangeness emerges fromthe model after spontaneous symmetry breaking. In the present model there existanother four heavy vector gauge bosons V^± and U^±± together with some heavyfermions and Higgs scalars, which have non vanishing weak strangeness quantumnumbers. These weak strange particles have no direct couplings with leptons. Theirexistence will not influence the low energy electro-weak processes. Nevertheless, theycan be produced in pairs in high energy collisions and the lightest of them should bestable if the conservation of weak strangeness is exact. The experimental implicationsand the possibility of violation of the conservation of weak strangeness are also dis-cussed.     

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.     

THE STUDY OF SOME NON-SOLATED RESONANCES FOR THE 23Na （p,α）20Ne REACTION

The excitation functions of the ²³Na（p,α₀）²⁰Ne_g·s.and the ²³Na（p,α₁）²⁰Ne_lst reae-tion have been measured from E_p=1 to 2.5 MeV at θ_L=30°,150° and 30°,respectively.Around the resonance at 2.171 MeV,the excitation functions of the（p,α₀）reactionhave been measured at 12 angles,then,some angular distributions have been obtained from these excitation functions.In addition,the angular distribution of the（p,α₀）reaction for the resonance at 2.171 MeV has also been measured directly at energy ofthe resonance peak of the excitation function at 150°.For the resonance at 2.117MeV,the angular distribution have been measured at two energies,one at the energyof the resonance peak of the excitation function at 150°,another at the energy of thehalf maximum point of the resonance peak on the higher energy side.Around the re-sonance at 2.075 MeV,the excitation functions have been measured at 16 angles,andthe angular distribution has been obtained from three excitation functions.The an-gular distributions of the three resonances are not symmetric about 90°,and the posi-tions of the resonance peaks of these resonances varies with the angle of measurement.By means of the compound nucleus theory,discussions have been made for these non-solated resonances.     

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.