1980 Vol. 4, No. 3
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Abstract:
In this paper, we consider nucleus-nucleus collisions on the basis of nucleon-nucleon elastic scattering and give a formula for the projectile fragment momentumdistribution of high energy heavy ion inclusive reactions using Glauber's approxima-tion. According to the experimental momentum distribution, we obtain a relativemomentum distribution between the various prefragments of the projectile. The theo-retical results show that if the bond of the prefragment is tighter, the relative mo-mentum distribution of the preframents in the nucleus is more narrow, so that the re-lative distance between them is larger.
In this paper, we consider nucleus-nucleus collisions on the basis of nucleon-nucleon elastic scattering and give a formula for the projectile fragment momentumdistribution of high energy heavy ion inclusive reactions using Glauber's approxima-tion. According to the experimental momentum distribution, we obtain a relativemomentum distribution between the various prefragments of the projectile. The theo-retical results show that if the bond of the prefragment is tighter, the relative mo-mentum distribution of the preframents in the nucleus is more narrow, so that the re-lative distance between them is larger.
Abstract:
In this paper, using the method employed in two earlier papers: "On the Irredu-cible Representations of the Compact Simple Lie Groups of Rank 2(I) and (II)",theirreducible representations of the groups B2 and G2 are discussed. A method for cal-culating the irreducible representations of these groups is given. Moreover,some ofthe low dimensional representations of these groups are calculated.
In this paper, using the method employed in two earlier papers: "On the Irredu-cible Representations of the Compact Simple Lie Groups of Rank 2(I) and (II)",theirreducible representations of the groups B2 and G2 are discussed. A method for cal-culating the irreducible representations of these groups is given. Moreover,some ofthe low dimensional representations of these groups are calculated.
Abstract:
A convenient form of the Ward-Takahashi identities for gauge-ghost field propervertices is derived and an example of its application is discussed.
A convenient form of the Ward-Takahashi identities for gauge-ghost field propervertices is derived and an example of its application is discussed.
Abstract:
We discuss the quantization of a massless vector field using the Lagrange mul-tiplier method. The exact solution of the field equations in three dimensional mo-mentum space is given and the existence of dipole ghosts explicitly demonstrated.One of the ghosts is not an eigenstate of the Hamiltonian and can be eliminated byboundary conditions. If the vector field is coupled to conserved currents, the otherghost has no observable effects. So this field theory describes the photon. This pro-blem has been studied by Nakanishi, but his analysis is obscure. The extension ofthis method to spin 3/2 massless field is discussed.
We discuss the quantization of a massless vector field using the Lagrange mul-tiplier method. The exact solution of the field equations in three dimensional mo-mentum space is given and the existence of dipole ghosts explicitly demonstrated.One of the ghosts is not an eigenstate of the Hamiltonian and can be eliminated byboundary conditions. If the vector field is coupled to conserved currents, the otherghost has no observable effects. So this field theory describes the photon. This pro-blem has been studied by Nakanishi, but his analysis is obscure. The extension ofthis method to spin 3/2 massless field is discussed.
Abstract:
The effects of short range correlation in nuclei on elastic scattering of hadronsfrom nuclei at high energy are studied by means of Glauber multiple diffraction the-ory, using Jastrow correlated wave functions. To this end, a determinant form ofJastrow correlated wave functions is used. Calculations have been carried out for π--12C elastic scattering at 260 MeV, and they are compared with the experimentdata. The results show that the influence of the short range correlation on the dif-ferent cross section is quite important.
The effects of short range correlation in nuclei on elastic scattering of hadronsfrom nuclei at high energy are studied by means of Glauber multiple diffraction the-ory, using Jastrow correlated wave functions. To this end, a determinant form ofJastrow correlated wave functions is used. Calculations have been carried out for π--12C elastic scattering at 260 MeV, and they are compared with the experimentdata. The results show that the influence of the short range correlation on the dif-ferent cross section is quite important.
Abstract:
In this paper four kinds of singular state problems in relativistic quantum me-chanics and its solutions are summarized. In the references [2,3,5,6,11], it hasbeen pointed out that in some quantum mechanial problems involving singular statesthere exists phase angle uncertainty. The principle eliminating this kind of nncer-tainty——the orthogonality-variation principle has been obtained in [11] The re-sults of scattering and bound state problems of a neutral monopole and a chargedDirac particle are consistent with those obtained by C. N. Yang, Kazama, and Gold-haber. In [5], [11] and this paper the Case-type equations determining the boundstates of monopole pair and exotic atoms consisting of a charged monopole and anelectron are obtained. In this paper these energy levels are calculated numericallyBecause in these equations the number of singular points is infinite and the rune-tions oscillate rapidly, usual calculation methods are not suitable in these cases. Afteranalysing these equations and determining the positions of singular points and theranges of energy levels, these energy levels are calculated by computer. It is pointed out that the number of these energy levels is infinite and the posi-tions of positive and negative energy levels are asymmetric. The negative energylevels do not appear untilεis very near -1. The values of the positive energy levelsare spread in the range 0.9998
ε<1 They are near those of the hydrogen-like atomand similar to those of impurity in solid. This is a perturbation problem of singularstates to which the usual perturbation theory can not be applied. The energy levels of monopole pair are not similar to those of the hydrogen-likeatom. In the range 0<|ε|≤0.99 there are many energy levels with positive andnegative energy. It is also pointed out that for the hydrogen-like atoms, 119<z<137, somenegative energy bound state solutions satisfying square integrability condition arepossible. The ordinary standard condition does not exclude these states, but the or-thogonality criterion does exclude them. The conclusion is in agreement with thatreached by Professor C. N. Yang. The results shown suggest that the orthogonality-variation principle is reasona-ble.
In this paper four kinds of singular state problems in relativistic quantum me-chanics and its solutions are summarized. In the references [2,3,5,6,11], it hasbeen pointed out that in some quantum mechanial problems involving singular statesthere exists phase angle uncertainty. The principle eliminating this kind of nncer-tainty——the orthogonality-variation principle has been obtained in [11] The re-sults of scattering and bound state problems of a neutral monopole and a chargedDirac particle are consistent with those obtained by C. N. Yang, Kazama, and Gold-haber. In [5], [11] and this paper the Case-type equations determining the boundstates of monopole pair and exotic atoms consisting of a charged monopole and anelectron are obtained. In this paper these energy levels are calculated numericallyBecause in these equations the number of singular points is infinite and the rune-tions oscillate rapidly, usual calculation methods are not suitable in these cases. Afteranalysing these equations and determining the positions of singular points and theranges of energy levels, these energy levels are calculated by computer. It is pointed out that the number of these energy levels is infinite and the posi-tions of positive and negative energy levels are asymmetric. The negative energylevels do not appear untilεis very near -1. The values of the positive energy levelsare spread in the range 0.9998
ε<1 They are near those of the hydrogen-like atomand similar to those of impurity in solid. This is a perturbation problem of singularstates to which the usual perturbation theory can not be applied. The energy levels of monopole pair are not similar to those of the hydrogen-likeatom. In the range 0<|ε|≤0.99 there are many energy levels with positive andnegative energy. It is also pointed out that for the hydrogen-like atoms, 119<z<137, somenegative energy bound state solutions satisfying square integrability condition arepossible. The ordinary standard condition does not exclude these states, but the or-thogonality criterion does exclude them. The conclusion is in agreement with thatreached by Professor C. N. Yang. The results shown suggest that the orthogonality-variation principle is reasona-ble.
Abstract:
In this paper, we discuss how to assign a metric on a principal bundle and howto rewrite the variational principles for a particle and for matter fields in an inva-riant from on the bundle in the principal-bundle formulation of gauge theories. Weshow that the right-translation invariant metric on the bundle must contain quantitieswhich transform exactly as gauge potentials, thus providing a new formalism for gaugefields. And we formulate the variational principle for a particle moving in the gaugefield as follows: The particle moves along a horizontal geodesic on the principalbundle. Starting from this we derive the Wong's equations of motion. Moreover, we elucidate the physical view-point which treats the bundle space asthe union of space-time and the internal space. Advantages of this viewpoint for un-derstanding the essentialities of gauge transformations and gauge invariance and forestablishing unified theories of gravitation and gauge fields are also discussed.
In this paper, we discuss how to assign a metric on a principal bundle and howto rewrite the variational principles for a particle and for matter fields in an inva-riant from on the bundle in the principal-bundle formulation of gauge theories. Weshow that the right-translation invariant metric on the bundle must contain quantitieswhich transform exactly as gauge potentials, thus providing a new formalism for gaugefields. And we formulate the variational principle for a particle moving in the gaugefield as follows: The particle moves along a horizontal geodesic on the principalbundle. Starting from this we derive the Wong's equations of motion. Moreover, we elucidate the physical view-point which treats the bundle space asthe union of space-time and the internal space. Advantages of this viewpoint for un-derstanding the essentialities of gauge transformations and gauge invariance and forestablishing unified theories of gravitation and gauge fields are also discussed.
Abstract:
The cross sections and energy spectra of the Coulomb disintegration of （e+e-） and（μ+μ-）at high energies are calculated by using the perturbation expansion of com-posite field theory [1] and the approximate covariant solution to Bethe-salpeter equa-tion with Coulomb potential and spin 1/2, -1/2[2] . The cross sections of disintegrationof （e+t-） are about 20% less than the cross sections calculated by others [3]. Be-sides; the results obtained in this paper indicate that the cross sections of coulomb di-sintegration of （e+e-） or （μ+μ-） at high energies in singlet state and triplet stateare equal exactly, while in [3] this oicurs only when n=2, and when n=1 the dif-ferenles betwees the rross sections in the two states are about 25%. It is very likelythat there were some mistakes in these calculutions.
The cross sections and energy spectra of the Coulomb disintegration of （e+e-） and（μ+μ-）at high energies are calculated by using the perturbation expansion of com-posite field theory [1] and the approximate covariant solution to Bethe-salpeter equa-tion with Coulomb potential and spin 1/2, -1/2[2] . The cross sections of disintegrationof （e+t-） are about 20% less than the cross sections calculated by others [3]. Be-sides; the results obtained in this paper indicate that the cross sections of coulomb di-sintegration of （e+e-） or （μ+μ-） at high energies in singlet state and triplet stateare equal exactly, while in [3] this oicurs only when n=2, and when n=1 the dif-ferenles betwees the rross sections in the two states are about 25%. It is very likelythat there were some mistakes in these calculutions.
Abstract:
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=CSk. Using the Glauber theory we get R(A)≡nPA/nPP
1.26A 1/3(A 1/3+1) -2/3 This formula explains the current experimental result quite well.
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=CSk. Using the Glauber theory we get R(A)≡nPA/nPP
1.26A 1/3(A 1/3+1) -2/3 This formula explains the current experimental result quite well.
Abstract:
An emulsion chamber of 13 tons Pb was exposed on Mt. Kanbala (5500 m abovesea level) of Tibet. A very interesting ultra-high energy event with total observedenergy ΣEΥ=445 TeV was obtained. The profile of the event is characterised by twogroups of high energy showers, separated clearly from each other. Preliminary analysisshows that the particles giving rise to these two shower groups have extraordina-rily large transverse momenta. This predicts the possible existence of a new mechanismin ultra-high energy nuclear interactions, which has certain characteristics differentfrom those predicted by the H-quantum and SH-quantum models.
An emulsion chamber of 13 tons Pb was exposed on Mt. Kanbala (5500 m abovesea level) of Tibet. A very interesting ultra-high energy event with total observedenergy ΣEΥ=445 TeV was obtained. The profile of the event is characterised by twogroups of high energy showers, separated clearly from each other. Preliminary analysisshows that the particles giving rise to these two shower groups have extraordina-rily large transverse momenta. This predicts the possible existence of a new mechanismin ultra-high energy nuclear interactions, which has certain characteristics differentfrom those predicted by the H-quantum and SH-quantum models.
Abstract:
It is well known that cellulose acetate SSNTD can be sensitized by adding oxi-dizing agents in etching solutions, but the effect is not very strong. In search of moreeffective methods, we have put forward the hypothesis of the possibility of catalyticoxidation sensitization, in the light of which we found that copper salt can catalizehypochlorite oxidation sensitization. Then we have established the optimum etchingconditions that can significantly enhance the sensitivity of the specially selected cel-lulose acetate detector material, thus enabling it to record a particles more than 9.5MeV and protons up to 750-800 ar a little higher KeV in energy that is to say, itssensitivity is higher than any cellulose acetate plastic SSNTD yet known.
It is well known that cellulose acetate SSNTD can be sensitized by adding oxi-dizing agents in etching solutions, but the effect is not very strong. In search of moreeffective methods, we have put forward the hypothesis of the possibility of catalyticoxidation sensitization, in the light of which we found that copper salt can catalizehypochlorite oxidation sensitization. Then we have established the optimum etchingconditions that can significantly enhance the sensitivity of the specially selected cel-lulose acetate detector material, thus enabling it to record a particles more than 9.5MeV and protons up to 750-800 ar a little higher KeV in energy that is to say, itssensitivity is higher than any cellulose acetate plastic SSNTD yet known.
Abstract:
Fission process is considered as a multidimensional Brownian motion. The Planck-Fokker equation is solved and the fission probability in the steady state approximationis calculated. The results is compared with the Bohr-Wheeler theory. Numerical cal-culations are performed for the fission of 236U and the results are discussed.
Fission process is considered as a multidimensional Brownian motion. The Planck-Fokker equation is solved and the fission probability in the steady state approximationis calculated. The results is compared with the Bohr-Wheeler theory. Numerical cal-culations are performed for the fission of 236U and the results are discussed.
Abstract:
By using the iteration of the linear relationship between two sets of radial wavefunctions at two neighboring points, the coupled channel optical model calculation isimproved. The merits of this method are: (i) No assumption needs to be made on the valuesof the radial wave functions near the origin. (ii) Multi-point formula can be con-veniently adopted at the starting stage, (iii) Iteration process can always be proceed-ed to the external region from the origin.
By using the iteration of the linear relationship between two sets of radial wavefunctions at two neighboring points, the coupled channel optical model calculation isimproved. The merits of this method are: (i) No assumption needs to be made on the valuesof the radial wave functions near the origin. (ii) Multi-point formula can be con-veniently adopted at the starting stage, (iii) Iteration process can always be proceed-ed to the external region from the origin.
Abstract:
Some discussion is made for the angular momentum difference i(ω) introduced byA. Bohr and B. Mottelson.
Some discussion is made for the angular momentum difference i(ω) introduced byA. Bohr and B. Mottelson.
Abstract:
A possible explanation of the mechanism for the double backbending in the yrastband of nuclei 122,124,126Te is given.
A possible explanation of the mechanism for the double backbending in the yrastband of nuclei 122,124,126Te is given.
Abstract:
In this paper we investigate some properties of the "linear" superfields, and givethe variation of this "linear" multiplet under an infinitesimal supersymmetry trans-formation.
In this paper we investigate some properties of the "linear" superfields, and givethe variation of this "linear" multiplet under an infinitesimal supersymmetry trans-formation.
Abstract:
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-)18Neg.s. in a recent experiment,exhibits an evident dip around 23°.
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-)18Neg.s. in a recent experiment,exhibits an evident dip around 23°.
Abstract:
By taking proper self-energy subdiagrams of phonon as Fig. 1(1), the Dyson'sequation and the corresponding eigenequations of the renormalized phonon are obtained.The sum rule and the energy weighted sum rule of phonons are given.
By taking proper self-energy subdiagrams of phonon as Fig. 1(1), the Dyson'sequation and the corresponding eigenequations of the renormalized phonon are obtained.The sum rule and the energy weighted sum rule of phonons are given.
Abstract:
A formula describing the ion beam envelope in RF choppers with frinviny field isderived. An analytical expression for "Magic φ" and related examples are given.Methods for eliminating the inclination of the chopped beam are discussed.
A formula describing the ion beam envelope in RF choppers with frinviny field isderived. An analytical expression for "Magic φ" and related examples are given.Methods for eliminating the inclination of the chopped beam are discussed.
Abstract:
In the present paper, the parametrization for the nuclear surface is chosen properly.The formulae for the nuclear deformation energy, including surface energy, coulombenergy and curvature energy are derived. The potential energy surface of the heavynuclei like 235U, 252 Fm et a1. and the barrier heights of many heavy nuclei are cal-culated.
In the present paper, the parametrization for the nuclear surface is chosen properly.The formulae for the nuclear deformation energy, including surface energy, coulombenergy and curvature energy are derived. The potential energy surface of the heavynuclei like 235U, 252 Fm et a1. and the barrier heights of many heavy nuclei are cal-culated.
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