A simple model of triton

A model of triton has been considered in which three interactions between nucleons have been approximated by harmonic oscillator forces of different strengths. The parameters have been determined by fitting the mass radius, the charge radius and the binding energy of the triton. The model involves an exact solution of the threebody problem. The wave function parameters and various physical parameters of the triton have been calculated. The assessment of the neutron-neutron interaction has been obtained irrespectively of the charge independence of nuclear forces. The model provides the possibility of testing the fulfilment of charge independence using the neutron-proton interaction only.     

A simple and realistic triton wave function

We propose a simple triton wave function that consists of a product of three correlation operators operating on a three-body spin-isospin state. This wave function is formally similar to that used in the recent variational theories of nuclear matter, the main difference being in the long-range behavior of the correlation operators. Variational calculations are carried out with the Reid potential, using this wave function in the so-called “symmetrized product” and “independent pair” forms. The triton energy and density distributions obtained with the symmetrized product wave function agree with those obtained in Faddeev and other variational calculations using harmonic oscillator states. The proposed wave function and calculational methods can be easily generalized to treat the four-nucleon α-particle.     

Continuum three-body states using the hyperspherical adiabatic basis set

In this paper we investigate the feasibility of employing the hyperspherical adiabatic (HA) basis set to describe continuum three-nucleon states. In particular, the HA expansion is compared with the simpler expansion on hyperspherical harmonics (HH). A practical numerical application is presented using the MT-III potential.     

Low-energy three-body scattering in a hyperspherical adiabatic basis

We propose a hyperspherical adiabatic formalism for the calculation of the 3-to-3S-matrix at low energy, for repulsive potentials, and use it then in a model calculation. That is for McGuire's model (3 particles in one dimension subject to repulsive delta-function interactions), we use analytical expressions for the hyperspherical adiabatic basis, the adiabatic coupling matrix elements, and eigenpotentials to obtain the first terms of the exactS-matrix analytically, in an expansion in powers of the wave number. We were able to associate the definite powers ofq in the expansion of theS-matrix to the corresponding inverse powers of in the expansions of the adiabatic eigenpotentials and coupling matrix elements. We investigate the effect of making the usual approximations found in the literature (extreme and uncoupled adiabatic approximations), when calculating the diagonal and off-diagonalS-matrix elements. Finally, we show that the coupled adiabatic equations uncouple as the energy goes to zero.     

He和类He离子基态能量与波函数的变分计算

在研究Pekeris模型的基础上,提出了一种包含坐标张弛系数的试探波函数,同时利用Matlab(或者Mathematica)语言,开发了一个运用变分法对三体问题进行计算的软件程序.在此基础上对He原子和类He离子的基态能量和解析波函数进行了变分计算,得到了比较理想的结果.这表明,采用Matlab或Mathematica设计的软件,在处理变分法问题时,在运算功能、数据的可靠性和准确度方面都是很具潜力的.     

Construction scheme of four-body wave functions in a hyperspherical basis

The problem of symmetrization of four-body hyperspherical functions is discussed. A construction scheme is given for the symmetrized hyperspherical asis in the (3+1)-configuration. The transformation between hyperspherical functions corresponding to the (2+2)- and (3+1)-configurations is considered.     

Many-body calculations of molecular electric polarizabilities in asymptotically complete basis sets

The static dipole polarizabilities of Ne, CO, N₂, F₂, HF, H₂O, HCN, and C₂H₂ (acetylene) have been determined close to the Full-CI limit along with an asymptotically complete basis set (CBS), according to the principles of a Focal Point Analysis. For this purpose the results of Finite Field calculations up to the level of Coupled Cluster theory including Single, Double, Triple, Quadruple and perturbative Pentuple excitations [CCSDTQ(P)] were used, in conjunction with suited extrapolations of energies obtained using augmented and doubly-augmented Dunning's correlation consistent polarized valence basis sets of improving quality. The polarizability characteristics of C₂H₄ (ethylene) and C₂H₆ (ethane) have been determined on the same grounds at the CCSDTQ level in the CBS limit. Comparison is made with results obtained using lower levels in electronic correlation, or taking into account the relaxation of the molecular structure due to an adiabatic polarization process. Vibrational corrections to electronic polarizabilities have been empirically estimated according to Born–Oppenheimer Molecular Dynamical simulations employing Density Functional Theory. Confrontation with experiment ultimately indicates relative accuracies of the order of 1 to 2%.     

A simple model for planar dechanneling calculations

In this letter a simple procedure for calculating the initial dechanneling of ion is presented. The calculations show good agreement with both experimental data and computer simulation data on planar dechanneling.     

Diffuseness effect and radial basis function network for optimizing a decay calculations

A radial basis function network(RBFN)approach is adopted for the first time to optimize the calcula-tion of a decay half-life in the generalized liquid drop mod...     

Effect of the three-body force on triton asymptotic normalization constants by the hyperspherical harmonics expansion method

We investigate the change in the calculated value of asymptotic normalization constant (ANC) by the hyperspherical harmonics expansion method with the inclusion of three nucleon force (3BF) in addition to two nucleon force. We see that ANC does not change very much with the inclusion of 3BF indicating that the 3BF does not alter the asymptotic behaviours of HHE wavefunction significantly.     

Variational calculations on the hydrogen molecular ion

We present high-precision non-relativistic variational calculations of bound vibrational—rotational state energies for the H⁺ ₂ and D⁺ ₂ molecular ions in each of the lowest electronic states of Σ _g , Σ _u , and Π _u symmetry. The calculations are carried out including coupling between Σ and Π states but without using the Born—Oppenheimer or any adiabatic approximation. Convergence studies are presented which indicate that the resulting energies for low-lying levels are accurate to about 10^?13. Our procedure accounts naturally for the lambda-doubling of the Π _u state.     

Variational calculations on the three-body scattering problem

An extended resonating-group method is used to calculate the elastic scattering amplitudes (up to L = 2 for a system of three identical bosons interacting through local Yukawa potentials. The results are compared to approximate solutions of the Faddeev equations.     

Faddeev partial-wave calculations with a three-nucleon potential for the triton ground state

The triton binding energy, the percentages ofS, S, andD states, and the asymptotic normalization constants are presented for 5-, 18-, 26-, and 34-channel Faddeev calculations with some realistic two-nucleon potentials and the Tucson-Melbourne three-nucleon potential. For the two-nucleon interaction, we take the Reid soft-core, the Argonne, the Paris, and the de-Tourreil-Rouben-Sprung potentials. The convergence properties of these calculations are discussed in detail. It turns out that five-channel calculations are decisively insufficient. We also discuss some asymptotic properties, such as the asymptotic normalization constants, the charge radius, and the momentum distribution in the long-wave-length region. It is shown that these quantities do not depend on the specific dynamics of the system, but only on the binding energy.     

Semiempirical model calculations for chemisorption on transition metals: I. Exact solution and discussion of a simple model

A specially parameterized model Hamiltonian for chemisorption is proposed, which treats the interaction between adsorbate and metal electrons in some detail. The exact solution is obtained for the case of an electron band with zero width. It is identical with the Hartree-Fock solution. There are no relaxation effects on the ionization energies within this model. A formalism for performing semiempirical calculations is shown to yield a good approximate solution to the model Hamiltonian for the simple case treated in this paper. Qualitative features of wavefunctions, charge transfer, adsorption energy and ionization energies are discussed.