1980 Vol. 4, No. 2
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Abstract:
In this paper, we analyse the commutation relations of the infinitesimal opera-tors of the group C2 and find that the ten infinitesimal operators of the group canbe written as two mutually commuting sets of angular momentum operators(υ1, υ0,υ=1), (τ1, τ0,τ-1), and one set of dual irreducible tensor operators of rank (1/2 1/2),U±1∕2,±1∕2. By means of their commutation relations, all irreducible representations ofthe group C2 can be easily obtained. In this paper,the matrices corresponding to the irreducible representation (λμ) are given; therefore the irreducible representation (λμ) and its representation space Rλμ）are completely defined. Besides, a method for calculating the scalar factors ofthe reduction coefficients and the symmetric relations of these factors are also given.As examples, the algebriac formulae of the scalar factors of the reduction coefficientsof (λμ)×(10), (λμ)×(01) and (λμ)×(20) are derived. In the last part of this paper, we define the irreducible tensor operators of thegroup C2 and prove the corresponding Wigner-Eckart Theory.
In this paper, we analyse the commutation relations of the infinitesimal opera-tors of the group C2 and find that the ten infinitesimal operators of the group canbe written as two mutually commuting sets of angular momentum operators(υ1, υ0,υ=1), (τ1, τ0,τ-1), and one set of dual irreducible tensor operators of rank (1/2 1/2),U±1∕2,±1∕2. By means of their commutation relations, all irreducible representations ofthe group C2 can be easily obtained. In this paper,the matrices corresponding to the irreducible representation (λμ) are given; therefore the irreducible representation (λμ) and its representation space Rλμ）are completely defined. Besides, a method for calculating the scalar factors ofthe reduction coefficients and the symmetric relations of these factors are also given.As examples, the algebriac formulae of the scalar factors of the reduction coefficientsof (λμ)×(10), (λμ)×(01) and (λμ)×(20) are derived. In the last part of this paper, we define the irreducible tensor operators of thegroup C2 and prove the corresponding Wigner-Eckart Theory.
Abstract:
We show that in dividing the Lagrangian of a pure Yang-Mills field system writ-ten in the winding number space into the "kinetic" and "potential" energy parts,the "potential" energy part corresponds to a periodic potential. Therefore, by an-alogy to the results of the solid state physics, the lowest energy state of the systemare shown to have the energy band structure. Comparison of such structure withthe θ-vacuum is made. The vacuum state established in this way is shown to satisfythe general requirements satisfied by the θ-vacuum.
We show that in dividing the Lagrangian of a pure Yang-Mills field system writ-ten in the winding number space into the "kinetic" and "potential" energy parts,the "potential" energy part corresponds to a periodic potential. Therefore, by an-alogy to the results of the solid state physics, the lowest energy state of the systemare shown to have the energy band structure. Comparison of such structure withthe θ-vacuum is made. The vacuum state established in this way is shown to satisfythe general requirements satisfied by the θ-vacuum.
Abstract:
We study the Rossmanith[3] problem for the acceleration of single electron in the electromagnetic field. By the method of a new field theory of [2], we give somenew and more important results, such as formula (17) in section 3 of this paper.
We study the Rossmanith[3] problem for the acceleration of single electron in the electromagnetic field. By the method of a new field theory of [2], we give somenew and more important results, such as formula (17) in section 3 of this paper.
Abstract:
The connections of SU2-dual charges and the topological properties in 4-dimen-sional space of constant curvature are discussed. The conclusions derived here arenatural generalization of topological charges in 3-dimensions isospace.
The connections of SU2-dual charges and the topological properties in 4-dimen-sional space of constant curvature are discussed. The conclusions derived here arenatural generalization of topological charges in 3-dimensions isospace.
Abstract:
In this paper, using the method of power series expansion, all spherical symme-tric exact solutions of the non-linear equation∂2Φ(x)=cΦ3(x) are given. These solu-tions fall into three types: i)Φ(r)=√-1/c 1/r; ii)Φ(r)=a/(r2+A2); iii)Φ(r)=a′/(r2-A2).
In this paper, using the method of power series expansion, all spherical symme-tric exact solutions of the non-linear equation∂2Φ(x)=cΦ3(x) are given. These solu-tions fall into three types: i)Φ(r)=√-1/c 1/r; ii)Φ(r)=a/(r2+A2); iii)Φ(r)=a′/(r2-A2).
Abstract:
A mistake in derivation of a quasipotential equation from an equation of the B-SType given by Zirov and Todorov has been pointed out and a new derivation is sug-gested.
A mistake in derivation of a quasipotential equation from an equation of the B-SType given by Zirov and Todorov has been pointed out and a new derivation is sug-gested.
Abstract:
The sponstaneous breakdown of a continuous symmetry implies the infinite de-generacy of continuous vacuum states, while Goldstone theorem implies the existenceof zero mass Goldstone bosons. When a particular vacuum state satisfying ak|vac>=0 , bk|vac>=0 is chosen, other degenerate vacuum states|vac>' of the broken symmetry are usuallyviewed as the superposition of states containing different number of zero energy andzero momentum Goldstone bosons, i.e.,
with ak and ak+ representing annihilation and creation operators of Goldstone bosonscarrying momentumk, while bk representing the annihilation operator of other par-ticles. But actually such a consideration is not correct, because the zero frequencypart of a free hermitian massless scalar field φ（T） can be written as V-(1/2)∫Vd3xφ(xt)=Q+Pt where V is the size of the normalization box and Q, P are space-time independentoperators. Due to cannonical quantization, they satisfy [Q, P]=i. Thus no zerofrequency annihilation and creation operators ak=0, ak+=0 can be defined. The freeHamiltonian becomes 
with Nk=ak+ak，k=|K|.Thus P and Nk form a complete commuting set of opera-tors describing the eigenstates. Since the eigenvalues of P are continuous all theseeigenstates are not normalizable and all calculation has to be done with the aid ofdistribution (i.e., the delta function.) It can be shown that there is no transition between states with different eigen-values of P, if φ(x) is to remain massless. Thus the vacuum state is not degenerate,but can be chosen as any one state in an mfinitely wide energy band. As a resultthe eigenvalues of P are not measurable. The free Lagrangian of φ(x) has the continuous symmetry φ(x)→φ(x)+η where η is any number, the generator being Z=∫Vd3xφ(x) We discover that eiηz |vac> is not orthogonal to |vac>; thus there is no sponstaneously breaking of this sym-metry. Using distribution, the difficulty of (﹤vac|eiηz)φ(x)(e-iηz |vac>)-﹤vac|φ(x)|vac>=η﹤vac|vac> can easily be resolved. When φ(x) is complex, each chosen vacuum state is infinitelybut discretely degenerate. Thus there is still no spontaneously broken symmetry. Using these vacuum states, it is easy to verify that in proving Goldstone theorem,the inserted zero momentum and zero energy states do not represent the coherentsuperposition of states containing different number of Goldstone bosons, and do notnecessarily orthogonal to the chosen vacuum state.
The sponstaneous breakdown of a continuous symmetry implies the infinite de-generacy of continuous vacuum states, while Goldstone theorem implies the existenceof zero mass Goldstone bosons. When a particular vacuum state satisfying ak|vac>=0 , bk|vac>=0 is chosen, other degenerate vacuum states|vac>' of the broken symmetry are usuallyviewed as the superposition of states containing different number of zero energy andzero momentum Goldstone bosons, i.e.,
with ak and ak+ representing annihilation and creation operators of Goldstone bosonscarrying momentumk, while bk representing the annihilation operator of other par-ticles. But actually such a consideration is not correct, because the zero frequencypart of a free hermitian massless scalar field φ（T） can be written as V-(1/2)∫Vd3xφ(xt)=Q+Pt where V is the size of the normalization box and Q, P are space-time independentoperators. Due to cannonical quantization, they satisfy [Q, P]=i. Thus no zerofrequency annihilation and creation operators ak=0, ak+=0 can be defined. The freeHamiltonian becomes with Nk=ak+ak，k=|K|.Thus P and Nk form a complete commuting set of opera-tors describing the eigenstates. Since the eigenvalues of P are continuous all theseeigenstates are not normalizable and all calculation has to be done with the aid ofdistribution (i.e., the delta function.) It can be shown that there is no transition between states with different eigen-values of P, if φ(x) is to remain massless. Thus the vacuum state is not degenerate,but can be chosen as any one state in an mfinitely wide energy band. As a resultthe eigenvalues of P are not measurable. The free Lagrangian of φ(x) has the continuous symmetry φ(x)→φ(x)+η where η is any number, the generator being Z=∫Vd3xφ(x) We discover that eiηz |vac> is not orthogonal to |vac>; thus there is no sponstaneously breaking of this sym-metry. Using distribution, the difficulty of (﹤vac|eiηz)φ(x)(e-iηz |vac>)-﹤vac|φ(x)|vac>=η﹤vac|vac> can easily be resolved. When φ(x) is complex, each chosen vacuum state is infinitelybut discretely degenerate. Thus there is still no spontaneously broken symmetry. Using these vacuum states, it is easy to verify that in proving Goldstone theorem,the inserted zero momentum and zero energy states do not represent the coherentsuperposition of states containing different number of Goldstone bosons, and do notnecessarily orthogonal to the chosen vacuum state.
Abstract:
This article gives an approach to the calculation of the scattering phase shift tak-mg into account the effect of the size change of scattering nuclei. As an example,we have calculated the phase shift of a-a scattering. Firstly, we calculate the sizechange of the a particle with the generator coordinate (the mean distance betweenthe two particles by the variations method based on the microscopic many body the-ory of the double well centre shell model, and secondly, calculate the phase shift byKohn variational method choosing such trial wave function so that we can use therelation of the GCM and the RGM. The results shows that there are considerable af-fection of the size change of the a particle on the phase shift and some improvementsfor the theoretical values of the phase shift has been obtained.
This article gives an approach to the calculation of the scattering phase shift tak-mg into account the effect of the size change of scattering nuclei. As an example,we have calculated the phase shift of a-a scattering. Firstly, we calculate the sizechange of the a particle with the generator coordinate (the mean distance betweenthe two particles by the variations method based on the microscopic many body the-ory of the double well centre shell model, and secondly, calculate the phase shift byKohn variational method choosing such trial wave function so that we can use therelation of the GCM and the RGM. The results shows that there are considerable af-fection of the size change of the a particle on the phase shift and some improvementsfor the theoretical values of the phase shift has been obtained.
Abstract:
The excitation functions at several angles and the angular distributions at someenergies were measured for the reactions C12(d,d)C12,C12(d,p0)C13 g.s., C12(d,p1)C131st ,C12(d,p2)C132nd and C12(d,p3)C133rd over the energy range from 0.5 to 2.5 MeV. Around Ed = 1.73 MeV, there was regular variation in the angular distributionsand excitation functions. The interference effect of various nuclear reaction mecha-nisms was discussed, and the possibility of the existence of an isolated "doorwaystate" was studied.
The excitation functions at several angles and the angular distributions at someenergies were measured for the reactions C12(d,d)C12,C12(d,p0)C13 g.s., C12(d,p1)C131st ,C12(d,p2)C132nd and C12(d,p3)C133rd over the energy range from 0.5 to 2.5 MeV. Around Ed = 1.73 MeV, there was regular variation in the angular distributionsand excitation functions. The interference effect of various nuclear reaction mecha-nisms was discussed, and the possibility of the existence of an isolated "doorwaystate" was studied.
Abstract:
The p-h calculation of 1- states and its E1 transition probabilities in Pb208 ismade with different types of two-body forces. The same, calculation is made for Hg200,Pt194, W184 using BCS wave function as basis vectors. The agreement between ob-servation and calculation is quite well in the general trend. In addition the calcu-lations demonstrate the de-coupling of E1 transitions of low l-configurations fromthe giant dipole resonance, the spin-isospin oscillation at lower energy and the effectof spin-orbit coupling force on the pygmy resonance.
The p-h calculation of 1- states and its E1 transition probabilities in Pb208 ismade with different types of two-body forces. The same, calculation is made for Hg200,Pt194, W184 using BCS wave function as basis vectors. The agreement between ob-servation and calculation is quite well in the general trend. In addition the calcu-lations demonstrate the de-coupling of E1 transitions of low l-configurations fromthe giant dipole resonance, the spin-isospin oscillation at lower energy and the effectof spin-orbit coupling force on the pygmy resonance.
Abstract:
From the viewpoint of the self-consistent field theory of statistical thermody-namics, the shell effects and pairing effects on nuclear level densities and their rela-tions with excitation energies are analyed. On the basis of the above analysis, aSemi-empirical formula of nuclear level density is proposed. Three empirical para-meters are used, and the results for about 200 nuclei are satisfied.
From the viewpoint of the self-consistent field theory of statistical thermody-namics, the shell effects and pairing effects on nuclear level densities and their rela-tions with excitation energies are analyed. On the basis of the above analysis, aSemi-empirical formula of nuclear level density is proposed. Three empirical para-meters are used, and the results for about 200 nuclei are satisfied.
Abstract:
A complete automatic program for fission products Ge(Li) Gamma-ray spectraanalysis-GSAP is presented. The computational methods of the program are brieflydescribed. A modified Levenberg algorithm with suitable argument constraints isused to solve the least-square peak fitting problem. 8 overlapping peaks can be an-alysed by this program. An unsymmetrical Gaussian superimposed on a parabolicbackground is selected as the fitting function which usually gives a good fit to mostof the peaks in a spectrum. Various experimental tests are described for proving thereliability and accuracy of the program. Satisfactory results for fission yield measu-rements have been obtained with this program. In fact, this program is a general-purpose program, which can be applied to analyse the Ge (Li) Gamma-ray spectrafrom other kinds of experiments.
A complete automatic program for fission products Ge(Li) Gamma-ray spectraanalysis-GSAP is presented. The computational methods of the program are brieflydescribed. A modified Levenberg algorithm with suitable argument constraints isused to solve the least-square peak fitting problem. 8 overlapping peaks can be an-alysed by this program. An unsymmetrical Gaussian superimposed on a parabolicbackground is selected as the fitting function which usually gives a good fit to mostof the peaks in a spectrum. Various experimental tests are described for proving thereliability and accuracy of the program. Satisfactory results for fission yield measu-rements have been obtained with this program. In fact, this program is a general-purpose program, which can be applied to analyse the Ge (Li) Gamma-ray spectrafrom other kinds of experiments.
Abstract:
Starting from the straton model, we discuss the possibility of slassifying the isos-pin of both mesons and baryons by one and the same finite group. We find that thefinite group Td can be used for the purpose.
Starting from the straton model, we discuss the possibility of slassifying the isos-pin of both mesons and baryons by one and the same finite group. We find that thefinite group Td can be used for the purpose.
Abstract:
The microscopic description of the π nucleus scattering is generalized to studythe (p,π) reactions. The differential cross section of the 3He(p,π+）4He at Tplab=415 MeV is calculated by using this method. The shape of the theoretical angulardistribution coincides with the experimental data, but the absolute value is about 3-5 times larger than the experimental value.
The microscopic description of the π nucleus scattering is generalized to studythe (p,π) reactions. The differential cross section of the 3He(p,π+）4He at Tplab=415 MeV is calculated by using this method. The shape of the theoretical angulardistribution coincides with the experimental data, but the absolute value is about 3-5 times larger than the experimental value.
Abstract:
In this paper, the reduced transition probabilities B(E2) between the clusterstructure states and √<r2>
In this paper, the reduced transition probabilities B(E2) between the clusterstructure states and √<r2>
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