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    Arbitrary direction incident Gaussian beam scattering by multispheres
    Li Zheng-Jun(李正军), Wu Zhen-Sen(吴振森), Li Huan(李焕), and Li Hai-Ying(李海英)
    Chin. Phys. B, 2011, 20 (8): 081101.   DOI: 10.1088/1674-1056/20/8/081101
    Abstract1430)      PDF (528KB)(1163)      
    Based on spherical vector wave functions and their coordinate rotation theory, the field of a Gaussian beam in terms of the spherical vector wave functions in an arbitrary unparallel Cartesian coordinate system is expanded. The beam shape coefficient and its convergence property are discussed in detail. Scattering of an arbitrary direction Gaussian beam by multiple homogeneous isotropic spheres is investigated. The effects of beam waist width, sphere separation distance, sphere number, beam centre positioning, and incident angle for a Gaussian beam with two polarization modes incident on various shaped sphere clusters are numerically studied. Moreover, the scattering characteristics of two kinds of shaped red blood cells illuminated by an arbitrary direction incident Gaussian beam with two polarization modes are investigated. Our results are expected to provide useful insights into particle sizing and the measurement of the scattering characteristics of blood corpuscle particles with laser diagnostic techniques.
    Low frequency asymptotics for the spin-weighted spheroidal equation in the case of s=1/2
    Dong Kun(董锟), Tian Gui-Hua(田贵花), and Sun Yue(孙越)
    Chin. Phys. B, 2011, 20 (7): 071101.   DOI: 10.1088/1674-1056/20/7/071101
    Abstract1291)      PDF (146KB)(544)      
    The spin-weighted spheroidal equation in the case of s=1/2 is thoroughly studied by using the perturbation method from the supersymmetric quantum mechanics. The first-five terms of the superpotential in the series of parameter β are given. The general form for the n-th term of the superpotential is also obtained, which could also be derived from the previous terms Wk, k < n. From these results, it is easy to obtain the ground eigenfunction of the equation. Furthermore, the shape-invariance property in the series of parameter β is investigated and is proven to be kept. This nice property guarantees that the excited eigenfunctions in the series form can be obtained from the ground eigenfunction by using the method from the supersymmetric quantum mechanics. We show the perturbation method in supersymmetric quantum mechanics could completely solve the spin-weight spheroidal wave equations in the series form of the small parameter β.
    Spin-weighted spheroidal equation in the case of s=1
    Sun Yue(孙越), Tian Gui-Hua(田贵花), and Dong Kun(董锟)
    Chin. Phys. B, 2011, 20 (6): 061101.   DOI: 10.1088/1674-1056/20/6/061101
    Abstract1343)      PDF (244KB)(727)      
    We present a series of studies to solve the spin-weighted spheroidal wave equation by using the method of super-symmetric quantum mechanics. We first obtain the first four terms of super-potential of the spin-weighted spheroidal wave equation in the case of s=1. These results may help summarize the general form for the n-th term of the super-potential, which is proved to be correct by means of induction. Then we compute the eigen-values and the eigen-functions for the ground state. Finally, the shape-invariance property is proved and the eigen-values and eigen-functions for excited states are obtained. All the results may be of significance for studying the electromagnetic radiation processes near rotating black holes and computing the radiation reaction in curved space-time.
    Lie symmetry and Mei conservation law of continuum system
    Shi Shen-Yang(施沈阳) and Fu Jing-Li(傅景礼)
    Chin. Phys. B, 2011, 20 (2): 021101.   DOI: 10.1088/1674-1056/20/2/021101
    Abstract1499)      PDF (151KB)(944)      
    Lie symmetry and Mei conservation law of continuum Lagrange system are studied in this paper. The equation of motion of continuum system is established by using variational principle of continuous coordinates. The invariance of the equation of motion under an infinitesimal transformation group is determined to be Lie-symmetric. The condition of obtaining Mei conservation theorem from Lie symmetry is also presented. An example is discussed for applications of the results.
    Conformal invariance and conserved quantities of Birkhoff systems under second-class Mei symmetry
    Luo Yi-Ping(罗一平) and Fu Jin-Li(傅景礼)
    Chin. Phys. B, 2011, 20 (2): 021102.   DOI: 10.1088/1674-1056/20/2/021102
    Abstract1495)      PDF (197KB)(849)      
    This paper proposes a new concept of the conformal invariance and the conserved quantities for Birkhoff systems under second-class Mei symmetry. The definition about conformal invariance of Birkhoff systems under second-class Mei symmetry is given. The conformal factor in the determining equations is found. The relationship between Birkhoff system's conformal invariance and second-class Mei symmetry are discussed. The necessary and sufficient conditions of conformal invariance, which are simultaneously of second-class symmetry, are given. And Birkhoff system's conformal invariance may lead to corresponding Mei conserved quantities, which is deduced directly from the second-class Mei symmetry when the conformal invariance satisfies some conditions. Lastly, an example is provided to illustrate the application of the result.
    Noether's theory of Lagrange systems in discrete case
    Lü Hong-Sheng(吕洪升), Zhang Hong-Bin(张宏彬), and Gu Shu-Long(顾书龙)
    Chin. Phys. B, 2011, 20 (1): 011101.   DOI: 10.1088/1674-1056/20/1/011101
    Abstract1420)      PDF (172KB)(825)      
    In this paper, Noether theory of Lagrange systems in discrete case are studied. First, we briefly overview the well-known Noether theory of Lagrange system in the continuous case. Then, we introduce some definitions and notations, such as the operators of discrete translation to the right and the left and the operators of discrete differentiation to the right and the left, and give the conditions for the invariance of the difference functional on the uniform lattice and the non-uniform one, respectively. We also deduce the discrete analog of the Noether-type identity. Finally, the discrete analog of Noether's theorem is presented. An example was discussed to illustrate these results.
    Inverse Monte Carlo study on effective interaction potential of Ag--Rh alloy from pair correlation functions
    Zhang Jing-Xiang(张景祥), Li Hui(李辉), Song Xi-Gui(宋西贵), and Zhang Jie(张洁)
    Chin. Phys. B, 2009, 18 (12): 5259-5266.   DOI: 10.1088/1674-1056/18/12/024
    Abstract1740)      PDF (1035KB)(764)      
    This paper presents an inverse Monte Carlo method to reconstruct pair interaction potential from pair correlation function. This approach adopts an iterative algorithm on interaction potential to fit known pair correlation function by compelling deviations of canonical average to meet with Hamiltonian parameters on a basis of statistical mechanism. The effective interaction potential between particles in liquid Ag--Rh alloys has been calculated with the inverse Monte Carlo method. It demonstrates an effective and simple way to obtain the effective potential of complex melt systems.
    Analysis of the decay $B^0 \to \chi_{c1}\pi^0$ with light-cone QCD sum rules
    Wang Zhi-Gang(王志刚)
    Chin. Phys. B, 2009, 18 (9): 3802-3809.   DOI: 10.1088/1674-1056/18/9/031
    Abstract1734)      PDF (209KB)(533)      
    In this article, we calculate the contribution from the nonfactorizable soft hadronic matrix element to the decay $B^0 \to \chi_{c1}\pi^0$ with the light-cone quantum chromo-dynamic (QCD) sum rules. The numerical results show that its contribution is rather large and should not be neglected. The total amplitudes lead to a branching fraction which is in agreement with the experimental data marginally.
    Topological aspects in a two-component Bose condensed system in neutron star
    Ren Ji-Rong(任继荣) and Guo Heng(郭恒)
    Chin. Phys. B, 2009, 18 (8): 3379-3383.   DOI: 10.1088/1674-1056/18/8/043
    Abstract1404)      PDF (165KB)(574)      
    By making use of Duan--Ge's decomposition theory of gauge potential and the topological current theory proposed by Prof. Duan Yi-Shi, we study a two-component superfluid Bose condensed system, which is supposed to be realized in the interior of neutron stars in the form of the coexistence of a neutron superfluid and a protonic superconductor. We propose that this system possesses vortex lines. The topological charges of the vortex lines are characterized by the Hopf indices and the Brower degrees of $\phi$-mapping.
    Experimental sensitivity on searching for CP violation at BES-III
    Zhao Ming-Gang(赵明刚), Rong Gang(荣刚), Ma Hai-Long(马海龙), and Zhang Da-Hua(张达华)
    Chin. Phys. B, 2009, 18 (6): 2213-2216.   DOI: 10.1088/1674-1056/18/6/018
    Abstract1713)      PDF (174KB)(657)      
    The CP violation in the D system is predicted to be an unobserved level in the Standard Model. In this paper, we describe the method of searching for CP violation decay processes with the coherently produced $D^0\bar{D}^0$ mesons from the $\psi$(3770) decay. The CP violation decay processes can be searched for at the BES-III experiment. The experimental sensitivity for searching for the CP violation can reach about a 10-4 level with a $\psi$(3770) data sample of about 20 fb-1.
    Knot solitons in AFZ model
    Ren Ji-Rong(任继荣), Mo Shu-Fan(墨淑凡), and Zhu Tao(朱涛)
    Chin. Phys. B, 2009, 18 (5): 1814-1820.   DOI: 10.1088/1674-1056/18/5/016
    Abstract1219)      PDF (143KB)(540)      
    This paper studies the topological properties of knotted solitons in the (3+1)-dimensional Aratyn--Ferreira--Zimerman (AFZ) model. Topologically, these solitons are characterized by the Hopf invariant I, which is an integral class in the homotopy group $\pi$3(S3)=Z. By making use of the decomposition of U(1) gauge potential theory and Duan's topological current theory, it is shown that the invariant is just the total sum of all the self-linking and linking numbers of the knot family while only linking numbers are considered in other papers. Furthermore, it is pointed out that this invariant is preserved in the branch processes (splitting, merging and intersection) of these knot vortex lines.
    Infinite series symmetry reduction solutions to the modified KdV--Burgers equation
    Yao Ruo-Xia(姚若侠), Jiao Xiao-Yu(焦小玉), and Lou Sen-Yue(楼森岳)
    Chin. Phys. B, 2009, 18 (5): 1821-1827.   DOI: 10.1088/1674-1056/18/5/017
    Abstract1284)      PDF (131KB)(659)      
    From the point of view of approximate symmetry, the modified Korteweg--de Vries--Burgers (mKdV--Burgers) equation with weak dissipation is investigated. The symmetry of a system of the corresponding partial differential equations which approximate the perturbed mKdV--Burgers equation is constructed and the corresponding general approximate symmetry reduction is derived; thereby infinite series solutions and general formulae can be obtained. The obtained result shows that the zero-order similarity solution to the mKdV--Burgers equation satisfies the Painlevé II equation. Also, at the level of travelling wave reduction, the general solution formulae are given for any travelling wave solution of an unperturbed mKdV equation. As an illustrative example, when the zero-order tanh profile solution is chosen as an initial approximate solution, physically approximate similarity solutions are obtained recursively under the appropriate choice of parameters occurring during computation.
    Regarding the 21S0 and 23S1 multiplets
    Liu Yun-Hu(刘云虎)
    Chin. Phys. B, 2009, 18 (5): 1828-1832.   DOI: 10.1088/1674-1056/18/5/018
    Abstract1538)      PDF (113KB)(485)      
    This paper discusses the masses and possible members of $2^1S_0$ and $2^3S_1$ meson multiplets in the framework of meson--meson mixing and Regge phenomenology. For the $2^1S_0$ meson nonet, $K^*(1460)$ may be the observed  state of the $2^1S_0$ isodoublet with a mass of 1400~MeV and the mass of $\omega(1420)$ is 1412 MeV. For the $2^3S_1$ meson nonet, $K^*(1410)$ seems too light to be the $2^3S_1$ $n\overline{s}$ member. The fact that the  agreement between the present findings and those given by experiments and other different approaches is satisfactory implies that the assignments in this paper may be reasonable.
    Topological aspect of disclinations in two-dimensional crystals
    Qi Wei-Kai(齐维开), Zhu Tao(朱涛), Chen Yong(陈勇), and Ren Ji-Rong(任继荣)
    Chin. Phys. B, 2009, 18 (3): 1002-1008.   DOI: 10.1088/1674-1056/18/3/026
    Abstract1173)      PDF (452KB)(1048)      
    By using topological current theory, this paper studies the inner topological structure of disclinations during the melting of two-dimensional systems. From two-dimensional elasticity theory, it finds that there are topological currents for topological defects in homogeneous equation. The evolution of disclinations is studied, and the branch conditions for generating, annihilating, crossing, splitting and merging of disclinations are given.
    Towards the understanding of 11P1 meson mass spectrum
    Feng Xue-Chao (冯学超), Jiang Feng-Chun(蒋逢春), Chang Tong-Qin (常同钦), Feng Jun-Lan(冯军兰)
    Chin. Phys. B, 2008, 17 (12): 4472-4475.   DOI: 10.1088/1674-1056/17/12/023
    Abstract1722)      PDF (170KB)(691)      
    Based on the meson-meson mixing and Regge trajerory, this paper establishes the mass relations which can describe the mass spectrum of 11P1 meson state. Using these mass relations, it obtains the mass of K1B, h1(1380) and hc(1P) to be 1358.5MeV, 1468MeV and 3543.9MeV, respectively. The results are compared with other theoretical results and should be tested by experiments in the future.
    Classical integrability of strings in $\gamma$-deformed backgrounds
    Xie Xiao-Ning (解小宁), Yue Rui-Hong (岳瑞宏)
    Chin. Phys. B, 2008, 17 (11): 4153-4157.   DOI: 10.1088/1674-1056/17/11/032
    Abstract1432)      PDF (175KB)(621)      
    This paper considers classical strings propagating in $\gamma$-deformed $AdS_3\times S^3$ backgrounds generated by certain shift T-dualities accompanied (TsT) transformations on $S^3$ and $AdS_3$, respectively. It finds that the $U(1)$ currents of strings with the twisted boundary conditions are equal to those in $\gamma$-deformed backgrounds generated by TsT transformations on both $S^3$ and $AdS_3$. Applying the TsT transformations, it derives the local Lax connections and the monodromy matrices in $\gamma$-deformed backgrounds with the spectral parameter which ensure the classical integrability of the string theories.
    Time-domain analytic solutions of two-wire transmission line excited by a plane-wave field
    Ni Gu-Yan(倪谷炎), Yan Li(颜力), and Yuan Nai-Chang(袁乃昌)
    Chin. Phys. B, 2008, 17 (10): 3629-3634.   DOI: 10.1088/1674-1056/17/10/016
    Abstract1188)      PDF (317KB)(679)      
    This paper reports that an analytic method is used to calculate the load responses of the two-wire transmission line excited by a plane-wave directly in the time domain. By the frequency-domain Baum--Liu--Tesche (BLT) equation, the time-domain analytic solutions are obtained and expressed in an infinite geometric series. Moreover, it is shown that there exist only finite nonzero terms in the infinite geometric series if the time variate is at a finite interval. In other word, the time-domain analytic solutions are expanded in a finite geometric series indeed if the time variate is at a finite interval. The computed results are subsequently compared with transient responses obtained by using the frequency-domain BLT equation via a fast Fourier transform, and the agreement is excellent.
    The He--McKellar--Wilkens effect for spin-1 particles on non-commutative space
    Li Kang(李康), Sayipjamal Dulat (沙依甫加马力 $\cdot$ 达吾来提), and Wang Jian-Hua(王剑华)
    Chin. Phys. B, 2008, 17 (5): 1716-1719.   DOI: 10.1088/1674-1056/17/5/030
    Abstract1287)      PDF (170KB)(707)      
    By using star product method, the He--McKellar--Wilkens (HMW) effect for spin-one neutral particle on non-commutative (NC) space is studied. After solving the Kemmer-like equations on NC space, we obtain the topological HMW phase on NC space where the additional terms related to the space--space non-commutativity are given explicitly.
    Interference nature of light
    Yao Zhi-Xin(姚志欣), Zhong Jian-Wei(钟建伟), Mao Bang-Ning(毛邦宁), and Pan Bai-Liang(潘佰良)
    Chin. Phys. B, 2008, 17 (2): 578-584.   DOI: 10.1088/1674-1056/17/2/037
    Abstract1276)      PDF (169KB)(619)      
    Interference of light has been reinvestigated theoretically by linear superposition of two different state-vector functions, of which each describes the photons from one of two different light sources in both polarization and intensity. By the use of microscopic parameters for a photon, namely probability amplitude and phase, it is again validated that interference of light occurs only between the same photons possessing a set of the selfsame eigenvalues.
    Neutrino energy loss by electron capture on strongly screened iron group nuclei
    Liu Jing-Jing(刘晶晶) and Luo Zhi-Quan(罗志全)
    Chinese Physics, 2007, 16 (12): 3624-3630.   DOI: 10.1088/1009-1963/16/12/012
    Abstract1267)      PDF (868KB)(496)      
    The influences on the neutrino energy loss rates in iron group nuclei at the same density are investigated in the presence of strong electron screening and in the absence of electron screening. The results show that at a temperature of $15\times10^9$ K, the neutrino energy loss rates which come from the electron capture process for most iron group nuclei decrease no more than 2 orders of magnitude but for the others (such as $^{53,55,56,57,58,59,60}$Co, $^{56,59}$Ni) they can decrease about 3 orders of magnitude due to strong electron screening (SES), whereas, at a temperature of $10^9K$ the neutrino energy loss rates of the most iron group nuclei can be diminished greatly due to the SES. For example, $^{61}$Fe, $^{60}$Fe, and $^{62}$Ni the neutrino energy loss rates decrease about 4, 15 and 16 orders of magnitude and for $^{57}$Cr, $^{58}$Cr, and $^{60}$Cr decrease about 18, 12, and 10 orders of magnitude respectively. According to our calculations the neutrino energy loss rates of nuclei $^{58}$Mn, $^{59}$Mn, $^{60}$Mn, and $^{62}$Mn may decrease about 13 orders of magnitude at a temperature of $10^9$ K due to the SES.
ISSN 1674-1056   CN 11-5639/O4

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