Antisymmetrized four-body wave function and coexistence of single particle and cluster structures

1979 ◽  
Vol 19 (4) ◽  
pp. 1498-1503 ◽  
Author(s):  
Tatuya Sasakawa
Keyword(s):  
Wave Function ◽  
Single Particle ◽  
Body Wave

A COMPLETE VARIATIONAL WAVE FUNCTION FOR THE GROUND STATE OF 3H AND 3He

1966 ◽  
Vol 44 (9) ◽  
pp. 2095-2110 ◽  
Author(s):  
Marcel Banville ◽  
P. D. Kunz
Keyword(s):  
Wave Function ◽  
Coordinate System ◽  
Body Wave ◽  
Center Of Mass ◽  
Minimum Energy ◽  
Equal Mass ◽  
Radial Coordinate ◽  
Orthogonal Functions ◽  
Gaussian Shape ◽  
Three Body

The three-body wave function for particles of equal mass is expanded in a systematic way by making use of a hyperspherical coordinate system. Apart from the center-of-mass coordinates, three of the variables are the usual Euler angles describing the orientation of the plane defined by the three particles. The other three variables, which describe the shape of the triangle, are represented in terms of a radial coordinate and two angular coordinates. The kinetic energy for these last three coordinates is separable and allows one to expand the three-body wave function in a complete set of orthogonal functions based upon the angular variables. The particular symmetry of the internal part of the wave function under permutations of the three particles is easily represented in terms of the set of functions for one of the angular variables. By choosing a particular set of radial functions one can then obtain the upper limit on the binding energy for the three-body system through the Rayleigh–Ritz variational procedure. The advantage of this particular coordinate system is that all but a few of the variational parameters occur linearly in the wave function, and the minimum energy can be obtained by diagonalizing a small number of the energy matrices. The method is applied to find the lower limit to a standard spin-independent potential of Gaussian shape.

The 1S0 two-nucleon T matrix and the interior wave function

1976 ◽  
Vol 54 (22) ◽  
pp. 2225-2239 ◽  
Author(s):  
R. J. W. Hodgson ◽  
J. Tan
Keyword(s):  
Wave Function ◽  
Nuclear Matter ◽  
Symmetric Function ◽  
Body Wave ◽  
Binding Energies ◽  
Strongly Correlated ◽  
Scattering Wave ◽  
T Matrix

The fully off-shell T matrix is generated from a real symmetric function σ(k,k′) which in turn can be obtained from a knowledge of the two-body wave function in the interaction interior. The resulting T matrices are employed to compute the binding energies of 16O, 40Ca, and nuclear matter. Limiting the two-body wave function to physically acceptable forms limits the allowed σ functions. A 'difference integral' is defined in terms of the two-body scattering wave function, which seems to be strongly correlated with the binding energies.

Quality of the three - body wave function obtained with the unitary pole approximation

1972 ◽  
Vol 40 (1) ◽  
pp. 61-64 ◽  
Author(s):  
E. Hadjimichael ◽  
E. Harms ◽  
V. Newton
Keyword(s):  
Wave Function ◽  
Body Wave ◽  
Pole Approximation ◽  
Unitary Pole ◽  
Three Body

Electron correlation and many-body wave function of semiconductor heterojunction

1989 ◽  
Vol 6 (8) ◽  
pp. 370-373
Author(s):  
Wang Hongwei ◽  
Feng Weiguo ◽  
Mao Huiming ◽  
Sun Xin
Keyword(s):  
Wave Function ◽  
Electron Correlation ◽  
Body Wave ◽  
Many Body

ON THE SEPARATION METHOD FOR THE NUCLEAR MANY-BODY PROBLEM

1965 ◽  
Vol 43 (4) ◽  
pp. 605-618 ◽  
Author(s):  
M. Razavy ◽  
S. J. Stack
Keyword(s):  
Wave Function ◽  
Long Range ◽  
Body Wave ◽  
Outer Part ◽  
Separation Distance ◽  
Many Body ◽  
Range Interaction ◽  
Method Of Calculation ◽  
Reaction Matrix ◽  
Range Part

A method of calculation of the nuclear reaction matrix is proposed in which the interaction is divided into two parts. The long-range part of the interaction together with the kinetic energy forms the unperturbed Hamiltonian and the short-range interaction is treated as a perturbation. The separation distance is so chosen that the perturbation produces no energy shift, but modifies the many-body wave function. For the special case where the outer part of the interaction is sufficiently weak, a plane-wave approximation is used for the unperturbed wave function, with the result that the diagonal elements of the reaction matrix are given by the first Born approximation of the long-range part of the potential. An iteration scheme is set up to compute the dividing point of the interaction. Such properties of nuclear matter as saturation, binding energy, and rearrangement energy are discussed in terms of the separation distance and its derivatives. Finally, this method is compared with those of Moszkowski and Scott (1960) and Bethe et al. (1963).

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