86 research outputs found
New representation of orbital motion with arbitrary angular momenta
A new formulation is presented for a variational calculation of -body
systems on a correlated Gaussian basis with arbitrary angular momenta. The
rotational motion of the system is described with a single spherical harmonic
of the total angular momentum , and thereby needs no explicit coupling of
partial waves between particles. A simple generating function for the
correlated Gaussian is exploited to derive the matrix elements. The formulation
is applied to various Coulomb three-body systems such as , and up to in order to show its usefulness and
versatility. A stochastic selection of the basis functions gives good results
for various angular momentum states.Comment: Revte
Second bound state of the positronium molecule and biexcitons
A new, hitherto unknown bound state of the positronium molecule, with orbital
angular momentum L=1 and negative parity is reported. This state is stable
against autodissociation even if the masses of the positive and negative
charges are not equal. The existence of a similar state in two-dimension has
also been investigated. The fact that the biexcitons have a second bound state
may help the better understanding of their binding mechanism.Comment: Latex, 8 pages, 2 Postscript figure
Analytic Evaluation of Four-Particle Integrals with Complex Parameters
The method for analytic evaluation of four-particle integrals, proposed by
Fromm and Hill, is generalized to include complex exponential parameters. An
original procedure of numerical branch tracking for multiple valued functions
is developed. It allows high precision variational solution of the Coulomb
four-body problem in a basis of exponential-trigonometric functions of
interparticle separations. Numerical results demonstrate high efficiency and
versatility of the new method.Comment: 13 pages, 4 figure
Absorption spectrum of a weakly n-doped semiconductor quantum well
We calculate, as a function of temperature and conduction band electron
density, the optical absorption of a weakly n-doped, idealized semiconductor
quantum well. In particular, we focus on the absorption band due to the
formation of a charged exciton. We conceptualize the charged exciton as an
itinerant excitation intimately linked to the dynamical response of itinerant
conduction band electrons to the appearance of the photo-generated valence band
hole. Numerical results for the absorption in the vicinity of the exciton line
are presented and the spectral weights associated with, respectively, the
charged exciton band and the exciton line are analyzed in detail. We find, in
qualitative agreement with experimental data, that the spectral weight of the
charged exciton grows with increasing conduction band electron density and/or
decreasing temperature at the expense of the exciton.Comment: 5 pages, 4 figure
Global-Vector Representation of the Angular Motion of Few-Particle Systems II
The angular motion of a few-body system is described with global vectors
which depend on the positions of the particles. The previous study using a
single global vector is extended to make it possible to describe both natural
and unnatural parity states. Numerical examples include three- and four-nucleon
systems interacting via nucleon-nucleon potentials of AV8 type and a 3
system with a nonlocal potential. The results using the
explicitly correlated Gaussian basis with the global vectors are shown to be in
good agreement with those of other methods. A unique role of the unnatural
parity component, caused by the tensor force, is clarified in the state
of He. Two-particle correlation function is calculated in the coordinate
and momentum spaces to show different characteristics of the interactions
employed.Comment: 39 pages, 4 figure
Four-Body Bound State Calculations in Three-Dimensional Approach
The four-body bound state with two-body interactions is formulated in
Three-Dimensional approach, a recently developed momentum space representation
which greatly simplifies the numerical calculations of few-body systems without
performing the partial wave decomposition. The obtained three-dimensional
Faddeev-Yakubovsky integral equations are solved with two-body potentials.
Results for four-body binding energies are in good agreement with achievements
of the other methods.Comment: 29 pages, 2 eps figures, 8 tables, REVTeX
Benchmark Test Calculation of a Four-Nucleon Bound State
In the past, several efficient methods have been developed to solve the
Schroedinger equation for four-nucleon bound states accurately. These are the
Faddeev-Yakubovsky, the coupled-rearrangement-channel Gaussian-basis
variational, the stochastic variational, the hyperspherical variational, the
Green's function Monte Carlo, the no-core shell model and the effective
interaction hyperspherical harmonic methods. In this article we compare the
energy eigenvalue results and some wave function properties using the realistic
AV8' NN interaction. The results of all schemes agree very well showing the
high accuracy of our present ability to calculate the four-nucleon bound state.Comment: 17 pages, 1 figure
Four-nucleon scattering with a correlated Gaussian basis method
Elastic-scattering phase shifts for four-nucleon systems are studied in an
- type cluster model in order to clarify the role of the tensor
force and to investigate cluster distortions in low energy and
scattering. In the present method, the description of the cluster wave function
is extended from a simple (0) harmonic-oscillator shell model to a few-body
model with a realistic interaction, in which the wave function of the
subsystems are determined with the Stochastic Variational Method. In order to
calculate the matrix elements of the four-body system, we have developed a
Triple Global Vector Representation method for the correlated Gaussian basis
functions. To compare effects of the cluster distortion with realistic and
effective interactions, we employ the AV8 potential as a realistic
interaction and the Minnesota potential as an effective interaction. Especially
for , the calculated phase shifts show that the and channels
are strongly coupled to the channel for the case of the realistic
interaction. On the contrary, the coupling of these channels plays a relatively
minor role for the case of the effective interaction. This difference between
both potentials originates from the tensor term in the realistic interaction.
Furthermore, the tensor interaction makes the energy splitting of the negative
parity states of He consistent with experiments. No such splitting is
however reproduced with the effective interaction
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