Calculations on the three-nucleon system using a separable expansion of local potentials

A separable expansion for local potentials called the unitary pole expansion (UPE) has been applied to the singlet-S soft-core Reid potential. The separable potentials obtained are used in conjunction with a separable tensor potential to calculate the triton binding energy, the nd doublet scattering length and the nd phase shifts in the state above and below break up. The convergence of the UPE is good especially for repulsive terms. The one term approximation (UPA) gives a triton energy differing by 0.04 MeV and a doublet scattering length differing by 0.14 fm from the values found for the local potential. The calculated phase shifts are in good agreement with the phase-shift analysis of Van Oers and Seagrave.     

Off-energy-shell variations of two-nucleon transition matrix and three-nucleon problem

For a schematic three-nucleon problem, we derive approximate analytic expressions for the functional derivatives of measurable three-particle quantities with respect to off-shell variations of the triplet-s, two-nucleon transition matrix. Those quantities include neutron-deuteron scattering lengths, trinucleon binding energies, and the ³He charge form-factor minimum; correlations between off-shell changes in the latter two are discussed. We indicate how results of this kind may be used to decide whether or not a given set of discrepancies between calculated and experimental three-nucleon observables can be reconciled in terms of off-shell variations of a nonretarded hermitean two-nucleon interaction. The treatment is not restricted to special classes of phase-shift equivalent potentials or phase-shift preserving transformations but instead makes use of a systematic parameterization of off-shell variations in terms of symmetric rational approximants of increasing order.     

Effective three-nucleon forces from the folded diagram expansion

The folded diagram expansion for the effective hamiltonian of a system of three valence nucleons in the 1s0d shell is investigated. Beside the one-body and two-body operators, which already occur in the folded diagram expansion for systems with one and two valence nucleons, also folded diagrams involving three nucleons are obtained. These terms, which can be interpreted as a contribution to an effective three-nucleon force, yield a non-negligible contribution which is repulsive for the low-lying states. Two different techniques are studied for the summation of the folded diagrams. A very good convergence is obtained using the Lee-Suzuki iteration scheme.     

Euler and correlated harmonic-oscillator wave function for the trinucleon bound-state

The trinucleon bound-state properties have been calculated by means of an Euler variational procedure, subsequently improved by the addition of correlated harmonic-oscillator wave functions. Three realistic model interactions containing only two-body forces have been considered. The results obtained show a satisfactory accuracy when compared with the corresponding estimates from Faddeev theory. The extension to larger nuclei of the method here investigated is a possible goal.Dedicated to Profs. Erich Schmid and Ivo laus on the occasion of their 60th birthdays     

On the separable expansion method in an optical potential scattering

Potential separable expansion method (PSE) in harmonic oscillator basis is applied to the two-body scattering problem with a complex optical potential. The introduction of smoothing Lanczos-factors considerably improves the convergence. The efficiency of the PSE method is demonstrated on model example.     

长短波相互作用方程的Jacobi椭圆函数求解

推广了Jacobi椭圆函数展开方法,研究了复非线性演化方程组的求解问题,得到了长短波相互作用方程的准确包络周期解.该结果在一定条件下包含了相应的孤波解. 关键词： Jacobi椭圆函数方法 长短波相互作用方程 孤波解     

Usefulness of the distorted wave bound-state approximation in reaction theory

The bound state approximation (BSA) restricts the intermediate state propagation of a manybody system to specified two-cluster configurations. This approximation was tested recently by applying it to the calculation of the binding energy of the three-boson Amado model. The method was found to give poor results. We have tested the distorted wave BSA on the same model and found that the distortion can produce a great improvement.     

A separable parametrization of the trinucleon wave function with the Reid soft-core potential

We present a useful analytical parametrization of the bound trinucleon wave function obtained from solving the Faddeev equations with the Reid soft-core potential. The partial wave components of the wave function are expanded in separable terms having rational fraction forms which incorporate the appropriate asymptotic behaviors. Both momentum and configuration space representations of the parametrized partial wave components are presented.     

Direct application of the quasiparticle method to a three-nucleon system

The energy dependence of the expectation values of powers of the Lippmann-Schwinger operator,I _k (W)=〈γ|V(G ₀(W)·V) ^k |γ〉, is used to calculate the ground-state energy of the triton for a simple central two-nucleon interaction of Gaussian type. This method allows to calculate the exact energy eigenvalueE ₀ of a three-nucleon-system in principle with any desired precision. The calculations are performed untilk=3. In this approximation the valueE ₀ ⁽³=?13.25 MeV is obtained which is simultaneously an upper bound of the true groundstate energyE ₀ of the system.     

A multi-reference exponential expansion for the electronic wave function

The expansion structure of a CI vector as combination of excitations from a model-space reference determinant is investigated. It is shown that between the linear and the exponential expansions there is a relation which is similar to the single-reference case, if the internal excitations are adsorbed into the reference vector. Moreover, expansions with respect to different determinants are related by a set of linear equations. By using these two properties, a State-Specific Coupled-Cluster formalism is proposed. Received 2 November 2000 / Received in final form 1st March 2002 Published online 28 June 2002     

Plane-wave approximation in theS-matrix and the construction of bound-state wave functions

Three inversion problem approaches — byGelfand-Levitan, Marchenko andPetrá? [5] —in both non-relativistic and relativistic (Klein-Gordon) variants are used in an approximation scheme selected to construct bound-state wave functions which are advantageous for purposes of model hadron physics. This family of wave functions is created exclusively by theS-matrix quantities and derived in the approximation which requires the Jost function to be equal to the unity throughout the continuous spectrum (the plane-wave approximation). As a consequence of the difference in boundary conditions of the mentioned approaches, the resulting approximate wave functions are not identical, but it is shown that there exists a parallelism as to the form among them. This parallelism is explained more extensively in the non-relativistic case, where the transformation properties of alternative sets of functions are treated. In the present paper it is demonstrated that in the relativistic variants of the above approaches the non-relativistic plane-wave-approximation form of the constructed wave functions for a given bound state is preserved.     

The effective Hamiltonian approach for the two-nucleon distribution function

The microscopic two-body effective Hamiltonian equation satisfied by the two-nucleon distribution function needed for two-particle transfer processes is derived. The usual approximations made in order to obtain a partial solution to this equation are discussed and compared. It is concluded that contributions to the distribution function from both core state and channel coupling terms are likely to be comparable to continuum configurations in importance. Such contributions must certainly be included if an unambiguous normalization for the distribution function is desired.     

1/c expansion of bound-state energies in QED

A new method for calculating bound-state energies in quantum electrodynamics is proposed. It starts from a non-relativistic Schrödinger equation as a zeroth approximation and treats the relativistic corrections by a systematic expansion. The result is expressed as a sum over Feynman-like graphs. No relativistic bound-state equations are used. Only the case of positronium is considered explicitly, but the method generalizes easily to other cases.     

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.     

Improved fake mode free plane wave expansion method

We analyze the origin of the fake modes introduced by the plane wave expansion method with three-dimension (3D) supercell approximation. Through the detailed analysis of the energy distribution of fake modes and real modes, we propose the plane wave expansion-three planar-slab waveguides method to remove the fake modes and obtain the fake mode free band structure of a two-dimensional air hole photonic crystal slab. To the best of our knowledge, this is the first time that such a fake mode free photonic crystal band structure is presented. Our method is also definitely useful in designing other 3D devices.     

Colliding Einstein-Maxwell waves that admit a separable wave equation

We show that the massive wave equation is separable in two particular colliding Einstein-Maxwell waves space-times. The first is the type D metric of Chandrasekhar and Xanthopoulos whereas the second is the doubly polarized Bell-Szekeres solution which is of Petrov type General.     

Determining a Skyrme-type effective interaction from realistic two-nucleon interaction

The Variational Monte Carlo (VMC) method is employed to determine characteristics of symmetric and asymmetric nuclearmatter. The realistic Urbana v14 nucleon-nucleon interaction potential of Lagaris and Pandharipande was used in the VMC calculations with addition of a phenomenological density-dependent term to simulate many-body interactions. A new Skyrme parameter set SKaan-U14 is found to consistently reproduce the characteristics of the nuclear matter obtained from VMC calculations. The properties of symmetric and asymmetric nuclear matter are calculated by the new Skyrme parameter set. The results obtained by using the new Skyrme parameter set are compared with results obtained by different Skyrme parameter sets in the literature.     

一般变换下的Jacobi椭圆函数展开法及应用

将在行波变换下的Jacobi椭圆函数展开法推广到范围非常广泛的一般函数变换下进行，利用这一方法求得了一些非线性发展方程的精确周期解，这些解包括了在行波变换下所求得的周期解. 证明了一些非线性发展方程的周期解一定是行波解. 关键词： 非线性发展方程 周期解 行波解 Jacobi椭圆函数