连续谱Faddeev积分方程的新解法

在动量空间中具有定域势的Faddeev方程是二维积分方程,在破裂过程和三体散射一类的连续谱情况下,方程的积分核是奇异的。本文根据奇异积分方程一般理论提出一种求解二维方程的数值方法。实践证明数值解是收敛的,全运动学微分截面的计算值与实验数据十分符合。     

Interpolation algorithm of Leverrier–Faddev type for polynomial matrices

We investigated an interpolation algorithm for computing outer inverses of a given polynomial matrix, based on the Leverrier–Faddeev method. This algorithm is a continuation of the finite algorithm for computing generalized inverses of a given polynomial matrix, introduced in [11]. Also, a method for estimating the degrees of polynomial matrices arising from the Leverrier–Faddeev algorithm is given as the improvement of the interpolation algorithm. Based on similar idea, we introduced methods for computing rank and index of polynomial matrix. All algorithms are implemented in the symbolic programming language MATHEMATICA , and tested on several different classes of test examples.     

Constraints on two-neutron separation energy in the Borromean C nucleus

The recently extracted matter radius of carbon isotope ²²C allows us to estimate the mean-square distance of a halo neutron with respect to the center-of-mass of this nucleus. By considering this information, we suggest an energy region for an experimental investigation of the unbound ²¹C virtual state. Our analysis, in a renormalized zero-ranged three-body model, also indicates that the two-neutron separation energy in ²²C is expected to be found below ∼0.4 MeV$\sim 0.4\text{MeV}$, where the ²²C is approximated by a Borromean configuration with a pointlike ²⁰C and two s-wave halo neutrons. A virtual-state energy of ²¹C close to zero, would make the ²²C, within Borromean nuclei configurations, the most promising candidate to present an excited bound Efimov state or a continuum three-body resonance.     

The Faddeev equation and the location of the essential spectrum of a model multi-particle operator

In this paper we consider a model operator which acts in a three-particle cut subspace of the Fock space. We describe “two-particle” and “three-particle” branches of the essential spectrum and obtain an analog of the Faddeev equation for eigenfunctions of this operator.     

On light supernuclei

The possible existence of charmed analogues of the YN and light hypernuclear systems are investigated using phenomenological one-boson-exchange potential and the SU(4) symmetry. Bound light supernuclei such as C₁N (I=3/2, J=0) and C₁NN(I=2, J=1/2) C₀NN (I=1, J=1/2, and I=0, J=1/2 or 3/2) are predicted with reasonable binding energies using Faddeev formalism for the three body systems.     

Nonperturbative, Unitary Quantum-Particle Scattering Amplitudes from Three-Particle Equations

We here use our nonperturbative, cluster decomposable relativistic scattering formalism to calculate photon–spinor scattering, including the related particle–antiparticle annihilation amplitude. We start from a three-body system in which the unitary pair interactions contain the kinematic possibility of single quantum exchange and the symmetry properties needed to identify and substitute antiparticles for particles. We extract from it a unitary two-particle amplitude for quantum–particle scattering. We verify that we have done this correctly by showing that our calculated photon–spinor amplitude reduces in the weak coupling limit to the usual lowest order, manifestly covariant (QED) result with the correct normalization. That we are able to successfully do this directly demonstrates that renormalizability need not be a fundamental requirement for all physically viable models.     

Faddeev–Jackiw quantization of the higher derivative Chern–Simons gauge theory in the first-order formalism

We analyse the physical constraints of the higher derivative Chern–Simons gauge model by means of Faddeev–Jackiw symplectic approach in the first-order formalism. Within such framework, we systematically determine the zero-mode structure of the corresponding symplectic matrix. In addition, we calculate the Faddeev–Jackiw quantum brackets by choosing appropriate gauge-fixing conditions and evaluate the determinant of the non-singular symplectic matrix as well as the transition-amplitude. Finally, we present a detailed Hamiltonian analysis using Dirac–Bergmann algorithm method and show that the Dirac brackets coincide with the FJ brackets when all the second-class constraints are treated as zero equations.     

Faddeev calculations on lambda hypertriton with potentials from Gel'fand-Levitan-Marchenko theory

Effective lambda-proton and lambda-neutron potentials, restored from theoretical scattering phases through Gel'fand-Levitan-Marchenko theory, are tested on a lambda hypertriton through three-body calculations. The lambda hypertriton is treated as a three-body system consisting of lambda-proton, lambda-neutron and proton-neutron subsystems. Binding energy and root mean square radius are computed for the ground state of lambda hypertriton (${J}^{\pi }=1/{2}^{+}$). In coordinate space, the dynamics of the system is described using a set of coupled hyperradial equations obtained from the differential Faddeev equations. By solving the eigenvalue problem derived from this set of coupled hyperradial equations, the binding energy and root mean square matter radius computed are found to be −2.462 MeV and 7.00 fm, respectively. The potentials are also shown to display a satisfactory convergence behaviour.     

Construction of regular solutions of Schrödinger and Faddeev equations in the linear three-particle configuration limit

We study the six-dimensional Schrödinger and Faddeev equations for a three-particle system with central pairwise interactions more general than the Coulomb interactions. The regular general and particular physical solutions of such equations are represented by infinite series in integer powers of the distance from one of the particles to the center of mass of the other two particles and in some functions of the other three-particle coordinates. Constructing such functions in the angular bases formed by spherical and bispherical harmonics or by symmetrized Wigner D-functions reduces to solving simple algebraic recurrence relations. For the projections of physical solutions on the angular basis functions, we introduce the boundary conditions in the linear three-particle configuration limit.     

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.