强子物质中的介子-介子散射(英文)

建立了一个夸克交换模型和提出了一个夸克-反夸克湮灭模型来研究介子-介子散射。从量子色动力学我们得到一个依赖于温度的夸克作用势。从微扰量子色动力学推导对应于夸克-反夸克湮灭和产生的跃迁势。模型给出基态介子质量的实验值,并且在玻恩近似下能说明真空中阈能附近的π-π弹性散射相移的实验值。从S矩阵元出发,推导散射的跃迁振幅和截面公式。计算出涉及π,ρ,K,K*的反应的非极化截面。发现这些截面具有强烈的温度依赖性。We have established a quark-interchange model and have proposed a quark-antiquark annihilation model to study meson-meson scattering. From QCD we obtain a temperature-dependent quark potential. The transition potential corresponding to quark-antiquark annihilation and creation is derived in perturbative QCD. The experimental ground-state meson masses are reproduced and the experimental data of elastic phase shifts for ππ scattering near the threshold energy in vacuum can be accounted for in the Born approximation. Starting from S-matrix element, we derive the transition amplitude and the cross section for the scattering. Unpolarised cross sections for reactions involving π, ρ, K and K* are calculated. Remarkable temperature dependence of the cross sections is found.     

Role of quark-interchange processes in evolution of mesonic matter

We divide the cross-section for a meson-meson reaction into three parts. The first part is for the quark-interchange process, the second for quark-antiquark annihilation processes and the third for resonant processes. Master rate equations are established to yield time dependence of fugacities of pions, rhos, kaons and vector kaons. The equations include cross-sections for inelastic scattering of pions, rhos, kaons and vector kaons. Cross-sections for quark-interchange-induced reactions, that were obtained in a potential model, are parametrized for convenient use. The number densities of π and ρ (K and K ^* are altered by quark-interchange processes in equal magnitudes but opposite signs. The master rate equations combined with the hydrodynamic equations for longitudinal and transverse expansion are solved with many sets of initial meson fugacities. Quark-interchange processes are shown to be important in the contribution of the inelastic meson-meson scattering to the evolution of mesonic matter.     

Quark-gluon amplitudes in the dual expansion

The dual representation, which gives a simple analytical form for purely gluonic amplitudes, is extended to amplitudes which include a quark-antiquark pair. To minimize the calculations, supersymmetry is used to relate the purely gluonic amplitudes to those including a gluino pair from which the quark-antiquark amplitudes are easily deduced. We explicitly give simple analytical forms for the full amplitudes for those multi-parton processes which involve a quark-antiquark pair plus two, three and four gluons.     

Relativistic scattering theory of two bound quark-antiquark systems in the low- and intermediate-energy region

Relativistic three-dimensional equations for meson-meson scattering amplitudes are constructed considering the mesons as bound quark-antiquark systems. The resulting equations have a form identical with the field-theoretical Low equations for the meson-meson scattering amplitude without quark degrees of freedom. Therefore the solution of these equations and their linearized representations satisfy the unitarity condition and the low-energy theorems. In order to build the effective potential of the proposed equations one uses meson-quark-antiquark bound-state wave functions and transition matrices. Also these quark-antiquark bound-state wave functions satisfy the relativistic three-dimensional integral equation, which contains all retardation effects.Supported by Deutsche Forschungsgemeinschaft under contract no. Fa. 67/10-5     

Calculation of the differential cross sections of excitation and ionization of a helium atom by electrons

Equations for the amplitudes and differential cross sections of electronic excitation and ionization of a helium atom are derived in the approximation of a frozen ion core. The wave functions of the discrete states are chosen in the form of generalized hydrogenlike orbitals. The radial wave functions of the continuous spectrum are determined by solving the equation of motion numerically. The differential excitation cross sections of excitation of the 2p, 3p, and 4p levels and ionization of a helium atom by electrons are calculated in the energy range up to 50 eV. Estimates are obtained for the nonorthogonal wave functions in the amplitudes of the excitation and ionization processes. It is shown that the given method is more compatible with experiment than the Born method.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 48–57, December, 1994.     

ns → n′s transition of hydrogen atom by positron impact with screened Coulomb interactions

We have made an investigation on H(ns) → H(n′ s) transition processes by positron impact with screened Coulomb potentials (SCP) by employing a distorted-wave formalism in the momentum space. Making use of simple variational wave functions of the hydrogen atom interacting with SCP we have been able to obtain the partial-wave scattering amplitudes in closed analytical forms. We have then used these distorted-wave scattering amplitudes to make a detailed study on differential and total cross sections in the energy range 20–300 eV. This study reveals some hitherto unknown features of the differential and total cross section. To the best of our knowledge such a study on the differential and total cross sections for inelastic positron-hydrogen collisions with SCP is reported for the first time in the literature.     

New method for calculating helicity amplitudes of jet-like QED processes for high-energy colliders

Inelastic QED processes, the cross sections of which do not drop with increasing energy, play an important role at high-energy colliders. Such reactions have the form of two-jet processes with the exchange of a virtual photon in the t-channel. We consider them in the region of small scattering angles , which yields the dominant contribution to their total cross sections. A new effective method is presented and applied to QED processes with emission of real photons to calculate the helicity amplitudes of these processes. Its basic idea is similar to the well-known equivalent-lepton method. Compact analytical expressions for those amplitudes up to are derived omitting only terms of the order of and higher order. The helicity amplitudes are presented in a compact form in which large compensating terms are already cancelled. Some common properties for all jet-like processes are found and we discuss their origin. Received: 19 December 2001 / Published online: 5 April 2002     

The Q2 evolution of flavour singlet wave functions in QCD

We calculate the Q² evolution of the quark-antiquark and gluon-gluon components of helicity-zero, flavour and colour singlet wave functions by summing diagrams to all orders in axial gauge QCD perturbation theory in the leading logarithm approximation. We find that Gegenbauer moments of these components have exactly the same scale-breaking behaviour as moments of singlet quark and gluon distribution functions in leptoproduction. The resulting singlet wave function is used to calculate the amplitudes for quark-antiquark and gluon-gluon jet production in off-shell photon-photon collisions.     

On Fliessbach's approaches to direct reactions

The conventional models of direct cluster reactions treat the nuclear wave-function overlaps or reduced-width amplitudes as single-particle wave functions, which is contrary to the Pauli principle. The motivation of Fliessbach's two approaches reviewed in this paper is to improve on these models by a proper treatment of antisymmetrization. Fliessbach's approaches involve redefined reduced-width amplitudes, which can be regarded as single-particle wave functions. We show, however, that in the approach specialized to transfer reactions the antisymmetrization is in fact treated incorrectly, and the more general approach seems applicable only to processes that involve just two nuclear fragments, like a decay or radiative capture. We outline how single-particle wave functions can be used correctly in approximating reduced-width amplitudes. We show that our approach helps to bring the phenomenological spectroscopic factors into agreement with the nuclear structure models.     

Jets production in peripheral interactions of high energy leptons,quarks, photons,and gluons with the proton

The paper presents short historical reviews of the processes of lepton pairs production in peripheral interaction of leptons and ions at high energies. The orders of magnitude of the QED and QCD cross sections with the production of two and three jets are given. The technique of the analysis is described in detail based on the parameterization of Sudakov 4-momentum tasks and writing the amplitude in an explicit gaugeinvariant form. Based on this formalism the differential cross sections of QCD processes \(gp \to (ggg)p;qp \to (q\bar QQ)p;gp \to (gQ\bar Q)P\) were obtained, including the distribution on transverse momentum component of jets fragments. It was shown that the role of the contribution of “non-Abelian” nature may become dominant in a particular kinematics of the final particles. The kinematics, in which the initial particle changes the direction of movement to the opposite one, was considered in the case of heavy quark-antiquark pair production. In the appendices, the details of the calculations and the explicit form of the differential cross sections are given. Some extended comments on the frequently used cross sections of the pair production in the case of two-photon scattering are presented. In particular, the degree of the longitudinal polarization of the positron, the interaction polarized initial electron, was calculated. The method of calculating the cross sections of the 2 → 2 processes in QCD, based on the isolation of irreducible color structures and the method CALCUL of spiral amplitudes, was discussed in detail.     

Calculation of spectroscopic amplitudes using boson expansion wave functions

A formalism is derived which allows the evaluation of spectroscopic amplitudes for two-nucleon transfer reactions. The transfer is assumed to take place between low-lying collective states described by boson expansion wave functions. Numerical calculations have been performed for (t, p) reactions on^{148, 150, 152}Sm. Excellent agreement is obtained for cross sections leading to the ground state in the residual nucleus.     

Analytical Solution of Partial-Wave Faddeev Equations with Application to Scattering and Statistical Mechanical Properties

In this work, the Faddeev equations for three-body scattering at arbitrary angular momentum are exactly solved and the transition matrices for some transition processes, including scattering and rearrangement channels are formulated in terms of free-particle resolvent matrix. A generalized Yamaguchi rank-two nonlocal separable potential has been used to obtain the analytical expressions for partial wave scattering properties of a three-particle system. The partial-wave analysis for some transition processes in a three-particle system is suggested. The partial-wave three-particle transition matrix elements have been constructed via knowledge of the matrix elements of the free motion resolvent. The calculation of a number of scattering properties of interest of the system such as transition matrix and its poles (bound states and resonances) and consequently other related quantities like scattering amplitudes, scattering length, phase shifts and cross sections are feasible in a straightforward manner. Moreover, we obtain a new analytical expression for the third virial coefficient in terms of three-body transition matrix.     

The impact of vibrational wave function on low energy electron vibrational scattering from nitrogen molecule

The vibrational wave function of the target theoretically plays an important role in the calculation of vibrational excitation cross sections. By a careful study of the differential cross sections resulting from different vibrational wave functions we find that cross sections are susceptible to vibrational wave functions. Minor changes in the vibration wave function may cause a significant change in the cross section. Even more surprising is that by selecting a few numbers of potential models(which determine the vibrational wave functions) we can often calculate the differential scattering cross section in much closer agreement with experiment in the framework of body-frame vibrational close-coupling theory, which suggest that an accurate potential energy may play a more important role in scattering than we thought before.     

Analytical Solution of Partial-Wave Faddeev Equations with Application to Scattering and Statistical Mechanical Properties

In this work, the Faddeev equations for three-body scattering at arbitrary angular momentum are exactly solved and the transition matrices for some transition processes, including scattering and rearrangement channels are formulated in terms of free-particle resolvent matrix. A generalized Yamaguchi rank-two nonlocal separable potential has been used to obtain the analytical expressions for partial wave scattering properties of a three-particle system. The partial-wave analysis for some transition processes in a three-particle system is suggested. The partial-wave three-particle transition matrix elements have been constructed via knowledge of the matrix elements of the free motion resolvent.The calculation of a number of scattering properties of interest of the system such as transition matrix and its poles(bound states and resonances) and consequently other related quantities like scattering amplitudes, scattering length,phase shifts and cross sections are feasible in a straightforward manner. Moreover, we obtain a new analytical expression for the third virial coefficient in terms of three-body transition matrix.     

推广的Glauber理论及其在晕核散射中的应用

介绍了推广到晕核散射的Glauber理论,并用其研究晕核¹⁴Be的散射问题.弹核的密度分布分别采用谐振子密度分布和相对论平均场理论计算得到具有两个晕中子结构的密度分布,对晕核模型的多重积分采用蒙特卡洛数值积分方法.计算了不同能量下¹⁴Be,¹²Be与靶核¹²C散射的反应截面,并与实验结果进行比较,¹⁴Be的两个中子采用具有晕中子密度分布的理论计算与实验符合较好,而采用不具有晕中子密度分布的结果与实验值相差较大.     

Asymmetries of various <Emphasis Type="Italic">P</Emphasis>- and <Emphasis Type="Italic">T</Emphasis>-parities in angular distributions of products of cold-polarized-neutron-induced binary and ternary fission of oriented nuclei and <Emphasis Type="Italic">T</Emphasis>-invariance

It is shown that a quantum system whose Hamiltonian is independent of time is T -invariant if this Hamiltonian contains only those terms that do not change sign upon time reversal. It is also shown that the coincidence of the amplitudes for multistep direct and statistical nuclear reactions with the timereversed amplitudes for the reactions being studied is a condition that ensures the T -invariance of the amplitudes in question, the transition from the original amplitudes to their time-reversed counterparts being accomplished, first, upon introducing the inverse-reactionmatrices T instead of the original-reaction matrix T and, second, upon replacing the wave functions for the initial, final, and intermediate states of the system by the respective time-reversed functions. It is found that the T -even (T -odd) asymmetries in cross sections for nuclear reactions stem from the interference between the amplitudes characterizing these reactions and having identical (opposite) T -parities. It is shown that the T -invariance condition for the above T -even (T -odd) asymmetries is related to the conservation of (change in) the sign of these asymmetries upon going over from original to inverse nuclear reactions. Mechanisms underlying the appearance of possible T -even and T-odd asymmetries in the cross sections for the cold-polarizedneutron- induced binary and ternary fission of oriented target nuclei are analyzed for the case of employing T -invariant Hamiltonians for the systems under study. It is also shown that the asymmetries in question satisfy the T -invariance condition if the reactions being considered have a sequential multistep statistical character. It is concluded that T -invariance is violated in the limiting case where, in ternary nuclear fission, the emission of a light third particle froma fissile compound nucleus formed upon incident-neutron capture by a target nucleus and its separation to two fission fragments are simultaneous events.     

Core exchange symmetries in heavy ion reactions

The general symmetry properties of theT-matrix due to the exchange of identical cores in nuclear reactions between composite particles are given. For the case of direct transfer reactions an explicit expression for the cross section is derived in the distorted wave Born approximation. In this model the cross section is the coherent sum of two indistinguishable transfer processes. The relative phase between the corresponding transfer amplitudes is obtained from the Pauli principle and depends on the signs of the spectroscopic amplitudes which may, therefore, be determined experimentally.     

Exact finite range calculations of light-ion induced two-neutron transfer reactions

Exact finite-range (EFR) distorted-wave Born approximation calculations were performed for light-ion induced two-neutron transfer reactions, by using a technique to calculate the form factors rather fast. The use of this method made it possible to carry out calculations even when realistic light-ion wave functions and multi-configurational two-neutron wave functions were used and large transferred angular momenta were considered. It was found that, at lower bombarding energies, the predictions of the EFR and zero-range calculations agree very closely both in angular distributions and relative magnitudes of the cross sections, though they differ significantly in absolute magnitude. As the bombarding energy increases, the discrepancy between the predicted absolute magnitude becomes still larger, and noticeable differences are seen even in relative cross sections. For all the energies considered, the EFR calculations predicted the absolute magnitudes of the experimental cross sections to within a factor of several units.