Bethe-Salpeter wave functions and transition amplitudes for heavy mesons

The most general form of covariant B-S wave functions and the corresponding integral equations for heavy mesons with arbitrary spin and parity are obtained in the infinite mass limit. A general formula for the I-W functions for transitions between states with arbitrary spin-parity and the ground state is given in terms of these wave functions. Using the covariant instantaneous approximation we apply this formulism to calculate I-W functionsr _1/2,r _3/2 and rates of processes in which a or is emitted in the transitions 1^–0^–, 0⁺0^–, 1⁺1^–.     

Calculation of graviton scattering amplitudes using string-based methods

Techniques based upon the string organisation of amplitudes may be used to simplify field theory calculations. We apply these techniques to perturbative gravity and calculate all one-loop amplitudes for four-graviton scattering with arbitrary internal particle content. Decomposing the amplitudes into contributions arising from supersymmetric multiplets greatly simplifies these calculations. We also discuss how unitarity may be used to constrain the amplitudes.     

Calculation of norms of Bethe wave functions

A class of two dimensional completely integrable models of statistical mechanics and quantum field theory is considered. Eigenfunctions of the Hamiltonians are known for these models. Norms of these eigenfunctions in the finite box are calculated in the present paper. These models include in particular the quantum nonlinear Schrödinger equation and the HeisenbergXXZ model.     

Asymptotic expansion of Feynman amplitudes

Employing the technique of Mellin transforms to scalar convergent Feynman amplitude in the Schwinger integral representation, we determine its asymptotic expansion for large Euclidean momenta. The determination of the coefficients of the expansion is effected via the use of generalized Taylor operators.     

Photoionisation using Kohn-Sham wave functions

The determination of photoionisation cross-sections using the Kohn-Sham wave functions from accurate density functional theory (DFT) calculations is considered. The continuum electrons wave function is specified by its momentum measurable in the detector rather than fixed angular momentum and energy. The method is applied to the test case of a water molecule, where the DFT calculations show excellent agreement to experiment in the ionisation energies if a vertical transition is considered. The continuum electron is described by an analytical wave function and the matrix elements are calculated in both in length and velocity form of the dipole operator. The cross-sections agree well with the experiment in particular for the velocity form.     

半空间球面波函数叠加法重构声源直接辐射声场

提出了基于半空间球面波函数叠加的声场重构方法,以重构含有限声阻抗边界半空间中声源直接辐射的声场。在半空间中多极子声源声压场的解析解的基础上,构造出以边界声阻抗为参量的半空间球面波函数的正交基;通过求逆获得半空间总声压解的基函数系数,同时也获得声源直接辐射声场即自由空间中的基函数系数,进而重构出声源直接辐射的声场。在边界声阻抗已知和边界声阻抗未知两种条件下,对该方法进行了仿真验证和参数分析,并在全消声室内进行了实验验证。结果表明,所提方法能重构出半空间中典型声源即球形声源和平面声源的直接辐射声场;该方法在边界声阻抗已知时的重构精度与稳定性高于在边界声阻抗未知时的情形。     

Linearized augmented plane wave method utilizing the quadratic energy expansion of radial wave functions

Conclusions The developed version of the augmented plane wave method yields eigenvalues and eigenfunctions with higher accuracy than the standard LAPW, preserving its computational efficiency.The approximation of the exact radial solution by the Taylor expansion involving also the second energy derivative of the radial function, except for the first derivative, has two advantages. First, the energy dependence of the logarithmic derivatives atr=R is better described and, therefore, the method is less sensitive to the choice of the centre of expansionE ₀ or, equivalently, acceptably accurate eigenvalues are obtained for the broader energy region aroundE ₀. The other and probably more important advantage is that the approximate radial solutions are remarkably closer to the exact radial functions inside the muffin-tin sphere. This can be of use when evaluating the measurable quantities depending on the wave functions.     

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.     

An expansion of continuum wave functions in terms of resonant states

The poles and residues of the complete outgoing Green function in the complex momentum plane are used to obtain, in the case of finite range potentials, an eigenfunction expansion of the continuum wave solution. It is found that in the region r<a the wave solution may be expressed as an infinite sum of discrete terms involving the bound, antibound and resonant states of the problem. At the boundary radius r = a a different expansion is obtained. In this case, in order to get an infinite discrete sum, one has to introduce two subtraction terms. Otherwise the expansion is given by a finite sum of discrete terms and an     

Five-nucleon spectroscopic amplitudes for 1p-shell nuclei

Spectroscopic amplitudes of the ⁵He or ⁵Li cluster in the ground and first excited states are given for lp-shell nuclei. These Spectroscopic amplitudes are calculated with the aid of intermediate-coupling wave functions of initial and final nuclei. Sum rules for pickup and stripping reactions are presented. The selectivity in excitation of the final states in pickup and stripping reactions of the ⁵He or ⁵Li cluster for some targets are discussed.     

Calculation of electron wave functions and refractive index of Ne

The radial wave functions of inner electron shell and outer electron shell of a Ne atom were obtained by the approximate analytical method and tested by calculating the ground state energy of the Ne atom. The equivalent volume of electron cloud and the refractive index of Ne were calculated. The calculated refractive index agrees well with the experimental result. Relationship between the refractive index and the wave function of Ne was discovered. Supported by the New Star Program of Beijing Science and Technology, China (Grant No. 952870400), the Beijing Municipal Commission of Education, and the Excellent Young Teachers Program of Ministry of Education, China     

A new boson expansion for odd-particle systems

The Beliaev-Zelevinsky boson expansion is extended to include systems with odd particle number. Closed forms, valid to all orders, are given for the particle-boson as well as boson-boson interaction.     

Calculation of the Peierls-Yoccoz translational mass for Hartree-Fock wave functions

The Peierls-Yoccoz projection method for translation is applied to Hartree-Fock wave functions constructed on a mesh for ${}^4\text{He}$ and ${}^{16}\text{O}$. As expected, the mass parameters differ from the nuclear masses, indicating a breaking of galilean invariance.     

Hadronic wave functions at short distances and the operator product expansion

The operator product expansion, of appropriate products of quark fields, is used to find the anomalous dimensions which control the short distance behavior of hadronic wave functions. This behavior in turn controls the high-Q² limit of hadronic form factors. In particular, we relate each anomalous dimension of the nonsinglet structure functions to a corresponding logarithmic correction factor to the nominal α_S(Q²)/Q² fall off of meson form factors. Unlike the case of deep inelastic lepton-hadron scattering, the operator product necessary here involves extra terms which do not contribute to forward matrix elements.     

A theorem on asymptotic expansion of Feynman amplitudes

For any Feynman amplitude, where any subset of invariants and/or squared masses is scaled by a real parameter going to zero or infinity, the existence of an expansion in powers of and ln is proved, and a method is given for determining such an expansion. This is shown quite generally in euclidean metric, whatever the external momenta (exceptional or not) and the internal masses (vanishing or not) may be, and for some simple cases in minkowskian metric, assuming only finiteness of the — eventually renormalized — amplitude before scaling. The method uses what is called Multiple Mellin representation, the validity of which is related to a generalized power-counting theorem.On leave of absence from University of Bahia (Brazil). Fellow of CAPES, Brazil