190 research outputs found
Symbolic-Numeric Algorithms for Computer Analysis of Spheroidal Quantum Dot Models
A computation scheme for solving elliptic boundary value problems with
axially symmetric confining potentials using different sets of one-parameter
basis functions is presented. The efficiency of the proposed symbolic-numerical
algorithms implemented in Maple is shown by examples of spheroidal quantum dot
models, for which energy spectra and eigenfunctions versus the spheroid aspect
ratio were calculated within the conventional effective mass approximation.
Critical values of the aspect ratio, at which the discrete spectrum of models
with finite-wall potentials is transformed into a continuous one in strong
dimensional quantization regime, were revealed using the exact and adiabatic
classifications.Comment: 6 figures, Submitted to Proc. of The 12th International Workshop on
Computer Algebra in Scientific Computing (CASC 2010) Tsakhkadzor, Armenia,
September 5 - 12, 201
Nonrelativistic ionization energy for the helium ground state
The helium ground state nonrelativistic energy with 24 significant digits is
presented. The calculations are based on variational expansion with randomly
chosen exponents. This data can be used as a benchmark for other approaches for
many electron and/or three-body systems.Comment: 3 pages, 0 figure
Relationship between the inexact Newton method and the continuous analogy of Newton's method
In this paper we propose two new strategies to determine the forcing terms that allow one to improve the efficiency and robustness of the inexact Newton method. The choices are based on the relationship between the inexact Newton method and the continuous analogy of Newton's method. With the new forcing terms, the inexact Newton method is locally -superlinearly and quadratically convergent. Numerical results are presented to support the effectiveness of the new forcing terms
Effects of nonzero photon momentum in (\gamma,2e) processes
We study the effects of nonzero photon momentum on the triply-differential
cross section for (\gamma,2e) processes. Due to the low value of the photon
momentum, these effects are weak and manifest only in special kinematical
conditions like the back-to-back emission of the electrons with equal energy
sharing. Helium and a few light helium-like ions are treated in detail. Quite
unexpectedly, the magnitude of these effects is maximal for relatively small
photon energies. However, although this effect on the TDCS remains rather
small, of the order of a few mbarn eV^{-1} sr^{-2}, it is sufficient to be
observed experimentally.Comment: 8 pages, 7 figures, 1 tabl
Transfer ionization and its sensitivity to the ground-state wave function
We present kinematically complete theoretical calculations and experiments
for transfer ionization in HHe collisions at 630 keV/u. Experiment and
theory are compared on the most detailed level of fully differential cross
sections in the momentum space. This allows us to unambiguously identify
contributions from the shake-off and two-step-2 mechanisms of the reaction. It
is shown that the simultaneous electron transfer and ionization is highly
sensitive to the quality of a trial initial-state wave function
Unusual chemical bond and spectrum of beryllium dimer in ground state
This review outlines the main results which show the dual nature of the
chemical bond in diatomic beryllium molecule in the ground
state. It has been shown that the beryllium atoms are covalently bound at
low-lying vibrational energy levels ({\nu}=0-4), while at higher ones
({\nu}=5-11) they are bound by van der Waals forces near the right turning
points. High precision ab initio quantum calculations of Be resulted in the
development of the modified expanded Morse oscillator potential function which
contains all twelve vibrational energy levels [A.V. Mitin, Chem. Phys. Lett.
682, 30 (2017)]. The dual nature of chemical bond in Be is evidenced as a
sharp corner on the attractive branch of the ground state potential curve.
Moreover, it has been found that the Douglas-Kroll-Hess relativistic
corrections also show a sharp corner when presented in dependence on the
internuclear separation. The difference in energy between the extrapolated and
calculated multi-reference configuration interaction energies in dependence on
the internuclear separation also exhibits singular point in the same region.
The other problems of ab initio quantum calculations of the beryllium dimer are
also discussed. Calculated spectrum of vibrational-rotational bound states and
new metastable states of the beryllium dimer in the ground state important for
laser spectroscopy are presented. The vibration problem was solved for the
modified expanded Morse oscillator potential function and for the potential
function obtained with Slater-type orbitals [M. Lesiuk et al, Chem. Theory
Comput. 15, 2470 (2019)]. The theoretical upper and lower estimates of the
spectrum of vibrational-rotational bound states and the spectrum of
rotational-vibrational metastable states with complex-valued energy eigenvalues
and the scattering length in the beryllium dimer are presented
- …