Scattering States of Three-Body Systems with the Hyperspherical Adiabatic Method

In this paper, we investigate the feasibility of employing the Hyperspherical Adiabatic (HA) basis set to describe continuum states of the Helium trimer molecule.     

A Simple Approach to Study the Isospin Effect in Mass Splitting of Three-Nucleon Systems by Using Hyperspherical Functions

In this work, the binding energy and wavefunctions of three-nucleon systems are obtained by using hy-perspherical harmonic approach. We have used a mathematical modification method to obtain the eigenvalues and eigenfunctions of Schrdinger equation for three-nucleon systems in calculation. Next, we have used a simple approach to obtain the difference between binding energy of 3H and 3He where gives us mass splitting of three-nucleon systems. We have compared our results with the other works and experimental values.     

Adiabatic Hyperspherical Approach to the Problems of Muon Catalyzed Fusion

The adiabatic hyperspherical approach (AHSA) is applied for the numerical investigation of the scattering processes and resonances in Coulomb three-body mesic atomic systems. The results of the calculations of elastic and inelastic cross sections in low-energy collisions aμ + b (a, b = p, d, t), energies, lifetimes and local characteristics of resonant states of mesic molecular ions ⁿ Heaμ⁺ (n = 3, 4) are presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

Six-Bodies Calculations Using the Hyperspherical Harmonics Method

In this work we show results for light nuclear systems and small clusters of helium atoms using the hyperspherical harmonics basis. We use the basis without previous symmetrization or antisymmetrization of the state. After the diagonalization of the Hamiltonian matrix, the eigenvectors have well defined symmetry under particle permutation and the identification of the physical states is possible. We show results for systems composed up to six particles. As an example of a fermionic system, we consider a nucleon system interacting through the Volkov potential, used many times in the literature. For the case of bosons, we consider helium atoms interacting through a potential model which does not present a strong repulsion at short distances. We have used an attractive gaussian potential to reproduce the values of the dimer binding energy, the atom-atom scattering length, and the effective range obtained with one of the most widely used He–He interaction, the LM2M2 potential. In addition, we include a repulsive hypercentral three-body force to reproduce the trimer binding energy.     

Beyond the first order of the Hyperspherical Harmonic Expansion Method

In this paper we demonstrate the inadequacy of the first order of the Hyperspherical Harmonic Expansion Method, the L_m approximation, for the calculation of the binding energies, charge form factors and charge densities of doubly magic nuclei like ¹⁶O and ⁴⁰Ca. We then extend the Hyperspherical Expansion Method to many-fermion systems, consisting of an arbitrary number of fermions, and develop an exact formalism capable of generating the complete optimal subset of the hyperspherical harmonic basis functions. This optimal subset consists of those hyperspherical harmonic basis functions directly connected to the dominant first term in the expansion, the hyperspherical harmonic of minimal order L_m, through the total interaction between the particles. The required many-body coefficients are given using either the Gogny or Talmi-Moshinsky coefficients for the two-body operators. Using the two-body coefficients the weight function generating the orthogonal polynomials associated with the optimal subset is constructed.     

Improved Method for Partial-Wave Decomposition of Two-Pion Exchange Three-Nucleon Force

In this article an efficient method to calculate the matrix elements of three-nucleon force is presented. The new method is improved version of partial-wave decomposition of Hüber et al. (Few-Body Syst 22:107, 1997), which simplifies expression to be evaluated as well as permits to reduce computational effort. Proposed method naturally applies to Faddeev-type calculations.     

Reworking the Tucson-Melbourne Three-Nucleon Potential

 We introduce new values of the strength constants (i.e., a, b, c, and d coefficients) of the Tucson-Melbourne (TM) 2π-exchange three-nucleon potential. The new values come from contemporary dispersion-relation analyses of meson-factory πN-scattering data. We make variational Monte-Carlo calculations of the triton with the original and updated three-body forces to study the effects of this update. We remove a short-range–π-range part of the potential due to the c coefficient and discuss the effect on the triton binding energy. Received September 11, 1999; revised November 2, 1999; accepted February 23,     

Calculations of Three-Nucleon Reactions

Faddeev calculations using the chiral three-nucleon force in next-to-next-to-next-to-leading-order show that this force is too weak to provide an explanation for the low-energy A _y puzzle. The large discrepancy between data and theory for the neutron–neutron quasi-free-scattering cross section in low energy neutron–deuteron breakup requires a modification of the ${^{1}S_0}$ neutron–neutron force. We discuss the consequences that a bound ${^{1}S_0}$ state of two neutrons has on neutron–deuteron scattering observables. At higher energies we compare the solutions of the non-relativistic three-nucleon Faddeev equations with three-nucleon force included to the solutions of its Poincaré invariant version.     

Four-Nucleon States in the Continuum: A Means to Probe the Nucleon-Nucleon Interaction

 Four-nucleon states in the continuum are studied through exact microscopic calculations based on the solution of the AGS equations for four nonrelativistic quantum particles. Our studies include calculations of cross sections and analyzing powers for all two-body reactions of interest, but here we only show results for n ³He → n ³He. The NN interactions we use are Bonn-CD, Nijmegen II, and Bonn-B. Compared to existing quality data, one finds large discrepancies and some sensitivity to the choice of NN force model. The calculated n + ³He elastic phase shifts show a very strong inelastic resonance at about 0.3 MeV which is not supported by the total cross-section data. This result is due to the existence of a ³ P ₀ (0⁻) resonance in isospin I = 0 at this energy and the undesirable coincidence of n + ³He and p + ³H thresholds in our calculation due to lack of Coulomb repulsion between protons. This interpretation is supported by R-matrix analyses of the data on the basis of coincident thresholds. Calculated 0⁺ and 0⁻ states are compared with modified R-matrix analyses. Received October 30, 2001; accepted for publication November 7, 2001     

A Three-Dimensional Treatment of the Three-Nucleon Bound State

Recently a formalism for a direct treatment of the Faddeev equation for the three-nucleon bound state in three dimensions has been proposed. It relies on an operator representation of the Faddeev component in the momentum space and leads to a finite set of coupled equations for scalar functions which depend only on three variables. In this paper we provide further elements of this formalism and show the first numerical results for chiral NNLO nuclear forces.     

伏安法测电阻

电阻的测量是近年来高考中的热点，也是高考中的难点．在很多复杂多变的测量电阻的电路设计中，其本质思想都是伏安法测电阻．本文从伏安法测电阻实验原理出发，给出伏安法测电阻实验电路，拓展一些常用的测量电阻的方法．     

Novel Three-Nucleon-Force Terms in the Three-Nucleon System

 We include two specific three-nucleon-force terms of pion-range–short-range form in our momentum-space calculations for the three-nucleon continuum. These two terms are expected by chiral perturbation theory to be non-negligible. We study the effects of these terms in elastic neutron-deuteron scattering and pay special attention to the neutron vector-analyzing power A _y . Received September 16, 1999; accepted for publication October 20, 1999     

Incorporation of Three-Nucleon Force in the Effective-Interaction Hyperspherical-Harmonic Approach

It is shown how a bare three-nucleon force is incorporated into the formalism of the effective interaction approach for hyperspherical harmonics. As a practical example we calculate the ground-state properties of ³H and ³He using the Argonne V18 nucleon-nucleon potential and the Urbana IX three-nucleon force. A very good convergence of binding energies and matter radii is obtained. We also find a very good agreement of our results compared to other high-precision calculations.     

Analysis of Adiabatic Approximation Using Stable Hamiltonian Method

In this paper, we deal with the adiabatic approximation of general Hamiltonians by splitting it into two parts, with one part a Hamiltonian that has at least one time-independent eigenstate up to a phase factor. We first develop the method of finding this kind of Hamiltonians. Then the relationship between adiabatic approximation and these Hamiltonians is discussed. Applying this to a general case, we give both a necessary condition and a sufficient condition for adiabatic approximation, followed by a spin-half example to illustrate.     

电测法测量透镜焦距

传统测量透镜焦距的方法通过肉眼读数粗测,误差较大.电测法测量透镜焦距通过光电传感器将光信号转变成电信号,结合电阻率定义及欧姆定律推导出利用电信号直接计算透镜焦距的公式.该方法设计思路简单,操作方便,且能准确有效地测量透镜的焦距.