1979 Vol. 3, No. 4
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Abstract:
By acting the operator D of the renormalization group equation on the amputa-ted Green's function of N particles,we can deduce the generalized Wroblewski rela-tionship and the corresponding differential equations.Naturally,the Kendall scalingdistribution of the multiplicity is obtained.The scaling variable is proved to be N/〈N〉.Under certain conditions,the inelasticity scaling distribution is also of theKendall type.The parameter of distribution represents relative statistical fluctuationof energy in the central region.
By acting the operator D of the renormalization group equation on the amputa-ted Green's function of N particles,we can deduce the generalized Wroblewski rela-tionship and the corresponding differential equations.Naturally,the Kendall scalingdistribution of the multiplicity is obtained.The scaling variable is proved to be N/〈N〉.Under certain conditions,the inelasticity scaling distribution is also of theKendall type.The parameter of distribution represents relative statistical fluctuationof energy in the central region.
Abstract:
Electron deep inelastic scattering processes are discussed using the method de-veloped in previous paper [1].General expressions of the irreducible diagrams ofthe structure functions are obtained.The relations between these irreducible diagramsand the kernels of the nucleon's B-S equations and the nucleon's transition matrixelements of the electric current are given by through Ward Identities.Neglectingthe contribution from the straton loop diagrams and using the potential assumptionfor the kernel of the equation,expressions of the structure functions and their calcu-lating method are given.The structure functions can be computed by using thekernel of the equations and solved wave functions.
Electron deep inelastic scattering processes are discussed using the method de-veloped in previous paper [1].General expressions of the irreducible diagrams ofthe structure functions are obtained.The relations between these irreducible diagramsand the kernels of the nucleon's B-S equations and the nucleon's transition matrixelements of the electric current are given by through Ward Identities.Neglectingthe contribution from the straton loop diagrams and using the potential assumptionfor the kernel of the equation,expressions of the structure functions and their calcu-lating method are given.The structure functions can be computed by using thekernel of the equations and solved wave functions.
Abstract:
Based on the analysis of output current pulse shapes of a counter,it appearsthat the discrimination between low-energy X-rays and high-energy charged parti-cles,even both of which exist in the counter simultaneously (e.g.in the detection oftransition radiation XA-rays),could be performed,if we select adequate counter fillinggases or use a counter with a drift space.
Based on the analysis of output current pulse shapes of a counter,it appearsthat the discrimination between low-energy X-rays and high-energy charged parti-cles,even both of which exist in the counter simultaneously (e.g.in the detection oftransition radiation XA-rays),could be performed,if we select adequate counter fillinggases or use a counter with a drift space.
Abstract:
The baryon and meson wave functions of SUn symmetry under the Baird-Bie-denharn phase convention are given explicitly.The phase confusion is clarified andthe matrices of transformations between I-spin,U-spin and V-spin representationsare given for the IR（8）,（27）,（35） of SU3.
The baryon and meson wave functions of SUn symmetry under the Baird-Bie-denharn phase convention are given explicitly.The phase confusion is clarified andthe matrices of transformations between I-spin,U-spin and V-spin representationsare given for the IR（8）,（27）,（35） of SU3.
Abstract:
Packet-like soliton solution of the non-linear Schrödinger's equation has been in-vestigated.We found that a state of a free particle can possibly be described by thissoliton solution,with the quantum property and the classical property of a particleas its limiting cases.A set of biorthogonal eigen-functions of non-hermitian opera-tor,which can be used in the pertubation expansion,has been found.We discoveredthat the discrete eigenvalue mode corresponds to the“classical”motion of a particle,and the continuous eigenvalue modes correspond to the“quantum”motion.Wesuggested that the parameter u describing the state of a system can be used to identifywhether the system is“quantum”or“classical”.
Packet-like soliton solution of the non-linear Schrödinger's equation has been in-vestigated.We found that a state of a free particle can possibly be described by thissoliton solution,with the quantum property and the classical property of a particleas its limiting cases.A set of biorthogonal eigen-functions of non-hermitian opera-tor,which can be used in the pertubation expansion,has been found.We discoveredthat the discrete eigenvalue mode corresponds to the“classical”motion of a particle,and the continuous eigenvalue modes correspond to the“quantum”motion.Wesuggested that the parameter u describing the state of a system can be used to identifywhether the system is“quantum”or“classical”.
Abstract:
The Levinson Theorem in non-relativistic quantum mechanics is derived by Green function method which leads to the following expression:nl=1/π[δl（0）—δl（∞）]—（（—1）l）/2 sin2δl（0）Then its generalization in Dirae equation is fuond as:nk（+）—nk-=1/π[δk（m）—δk（∞）+δk（—∞）—δk（—m）]—（k/（|k|））（（—1）x/2）[sin2δk（m）+sin2δk（—m）].对于 Klein-Gordon There are two expressions for Klein-Gordon equation:nl(+)±nl-=1/π{δl（m）—δl（∞）±[δl（—m）—δl（—∞）]}—（（—1）l/2）[sin2δl（m）±sin2δl（—m）].The implication of these theorems and the range of their validity with relevantproblems are discussed.An example of S state ease in square well potential is trea-ted for testing these formulas.
The Levinson Theorem in non-relativistic quantum mechanics is derived by Green function method which leads to the following expression:nl=1/π[δl（0）—δl（∞）]—（（—1）l）/2 sin2δl（0）Then its generalization in Dirae equation is fuond as:nk（+）—nk-=1/π[δk（m）—δk（∞）+δk（—∞）—δk（—m）]—（k/（|k|））（（—1）x/2）[sin2δk（m）+sin2δk（—m）].对于 Klein-Gordon There are two expressions for Klein-Gordon equation:nl(+)±nl-=1/π{δl（m）—δl（∞）±[δl（—m）—δl（—∞）]}—（（—1）l/2）[sin2δl（m）±sin2δl（—m）].The implication of these theorems and the range of their validity with relevantproblems are discussed.An example of S state ease in square well potential is trea-ted for testing these formulas.
Abstract:
In this report,the stable corona discharge region of multi-wire proportional cham-ber（MWPC）has been measured.In this region we observed double peak pheno- menon in Fe55 pulse amplitude distribution,and establish the fact that,once cornadischarge region is present in MWPC,the spatial resolution power for light partic-les will be lost.
In this report,the stable corona discharge region of multi-wire proportional cham-ber（MWPC）has been measured.In this region we observed double peak pheno- menon in Fe55 pulse amplitude distribution,and establish the fact that,once cornadischarge region is present in MWPC,the spatial resolution power for light partic-les will be lost.
Abstract:
In this paper we use the central and two-body spin-orbit coupling forces as theresidual interaction to calculate the energy spectra of f7/2 shell nuclei,with the valuesof the exchanged parameters suitably regulated.The harmonic oscillator wave functionis employed as the radial wave function.The consistency between the calculated energylevels of the nuclei and the experimental data is rather satisfactory.The results showthat the effects of two-body spin-orbit coupling term in the residual interaction cannot be neglected.
In this paper we use the central and two-body spin-orbit coupling forces as theresidual interaction to calculate the energy spectra of f7/2 shell nuclei,with the valuesof the exchanged parameters suitably regulated.The harmonic oscillator wave functionis employed as the radial wave function.The consistency between the calculated energylevels of the nuclei and the experimental data is rather satisfactory.The results showthat the effects of two-body spin-orbit coupling term in the residual interaction cannot be neglected.
Abstract:
Starting from the Neuman equation,the statistical description of nuclear reactionprocesses is achieved with coarse graining and the assumption of random distribu-tion of matrix etements Of residual interactions.The reaction cross section obtainedincludes a part from precompound single and multistep processes and a part fromcompound reactions.The exciton model is discussed in Comparison with the above results.
Starting from the Neuman equation,the statistical description of nuclear reactionprocesses is achieved with coarse graining and the assumption of random distribu-tion of matrix etements Of residual interactions.The reaction cross section obtainedincludes a part from precompound single and multistep processes and a part fromcompound reactions.The exciton model is discussed in Comparison with the above results.
Abstract:
In this paper the following results are proved:although the single-particle（sp）potential uαβ=Mαβ（εβ）defined in terms of the mass operator Mαβ（ω） is nonhermi-tian,the discrete energy eigenvalues determined by the Schrödinger equation h|γ>=（t+u）|γ>=εγ|γ> are real;moreover,they satisfy exactly the following relation:（εγ=±[Enγ（N±1）—E0（N）] where E0（N）denotes the exact ground state energy of a closed-shell nucleus N,and Enγ（N±1）are excat energy eigenvalues of its neighbouring N±1 nucleus.Further,in order to determine whether the bound state energies obtained by anyother sp potential may or not satisfy the above relation,a simple method is sugges-ted.It is shown that the amplitude renormalization of the sp Green function canalso be calculated easily by means of this method.
In this paper the following results are proved:although the single-particle（sp）potential uαβ=Mαβ（εβ）defined in terms of the mass operator Mαβ（ω） is nonhermi-tian,the discrete energy eigenvalues determined by the Schrödinger equation h|γ>=（t+u）|γ>=εγ|γ> are real;moreover,they satisfy exactly the following relation:（εγ=±[Enγ（N±1）—E0（N）] where E0（N）denotes the exact ground state energy of a closed-shell nucleus N,and Enγ（N±1）are excat energy eigenvalues of its neighbouring N±1 nucleus.Further,in order to determine whether the bound state energies obtained by anyother sp potential may or not satisfy the above relation,a simple method is sugges-ted.It is shown that the amplitude renormalization of the sp Green function canalso be calculated easily by means of this method.
Abstract:
The variable separation method of Glauber multiple scattering theory is developedto include the N* production in the intermediate states and is used to calculate theinelastic scattering of proton by nucleus.Numerical results are compared with dataon p-12C*（4+,14.08）at 1 GeV and it implies that the effects of N* production tothe high-energy proton-nucleus scattering are noticeable.
The variable separation method of Glauber multiple scattering theory is developedto include the N* production in the intermediate states and is used to calculate theinelastic scattering of proton by nucleus.Numerical results are compared with dataon p-12C*（4+,14.08）at 1 GeV and it implies that the effects of N* production tothe high-energy proton-nucleus scattering are noticeable.
Abstract:
From the microscopical many body theory,the formula of the projected varia-tion method for three Well-Cluster shell model is given.The calculation has beenmade for the positive parity excited energy levels of 9Be,and then discuss the 8Becorrelation and the 5He corrlation in the possible chain-like molecular structure.
From the microscopical many body theory,the formula of the projected varia-tion method for three Well-Cluster shell model is given.The calculation has beenmade for the positive parity excited energy levels of 9Be,and then discuss the 8Becorrelation and the 5He corrlation in the possible chain-like molecular structure.
Abstract:
In this paper the generized coupling master equations are derived by means ofthe time-dependent projection operator.In first order Born approximation,the cou-pling master equations for any N-subsystems,which only include diagonal elementsare derived.
In this paper the generized coupling master equations are derived by means ofthe time-dependent projection operator.In first order Born approximation,the cou-pling master equations for any N-subsystems,which only include diagonal elementsare derived.
Abstract:
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{Un},such that for any state vector |Φ〉,|Ψ〉,the sequence <Φ|U1|Ψ><Φ|U2|Ψ>，......，<Φ|Un|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.
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{Un},such that for any state vector |Φ〉,|Ψ〉,the sequence <Φ|U1|Ψ><Φ|U2|Ψ>，......，<Φ|Un|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.
Abstract:
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 mr=（1782.306±0.078）MeVwhich agree very well with experimental values κ=（6.6720±0.0041）×10-8cm3g-1sec-2 and mτ=(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.
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 mr=（1782.306±0.078）MeVwhich agree very well with experimental values κ=（6.6720±0.0041）×10-8cm3g-1sec-2 and mτ=(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.
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