4,401 research outputs found
Recurrence Formulas for Fully Exponentially Correlated Four-Body Wavefunctions
Formulas are presented for the recursive generation of four-body integrals in
which the integrand consists of arbitrary integer powers (>= -1) of all the
interparticle distances r_ij, multiplied by an exponential containing an
arbitrary linear combination of all the r_ij. These integrals are
generalizations of those encountered using Hylleraas basis functions, and
include all that are needed to make energy computations on the Li atom and
other four-body systems with a fully exponentially correlated Slater-type basis
of arbitrary quantum numbers. The only quantities needed to start the recursion
are the basic four-body integral first evaluated by Fromm and Hill, plus some
easily evaluated three-body "boundary" integrals. The computational labor in
constructing integral sets for practical computations is less than when the
integrals are generated using explicit formulas obtained by differentiating the
basic integral with respect to its parameters. Computations are facilitated by
using a symbolic algebra program (MAPLE) to compute array index pointers and
present syntactically correct FORTRAN source code as output; in this way it is
possible to obtain error-free high-speed evaluations with minimal effort. The
work can be checked by verifying sum rules the integrals must satisfy.Comment: 10 pages, no figures, accepted by Phys. Rev. A (January 2009
QED calculation of the n=1 and n=2 energy levels in He-like ions
We perform ab initio QED calculations of energy levels for the and
states of He-like ions with the nuclear charge in the range -100.
The complete set of two-electron QED corrections is evaluated to all orders in
the parameter \aZ. Uncalculated contributions to energy levels come through
orders \alpha^3 (\aZ)^2, \alpha^2 (\aZ)^7, and higher. The calculation
presented is the first treatment for excited states of He-like ions complete
through order \alpha^2 (\aZ)^4. A significant improvement in accuracy of
theoretical predictions is achieved, especially in the high- region.Comment: 23 pages, 5 figure
Recursion relations for Hylleraas three-electron integral
Recursion relations for Hylleraas three-electron integral are obtained in a
closed form by using integration by parts identities. Numerically fast and well
stable algorithm for the calculation of the integral with high powers of
inter-electronic coordinates is presented.Comment: 12 pages, requires RevTeX4, submitted to Phys. Rev.
Calculations of polarizabilities and hyperpolarizabilities for the Be ion
The polarizabilities and hyperpolarizabilities of the Be ion in the
state and the state are determined. Calculations are performed
using two independent methods: i) variationally determined wave functions using
Hylleraas basis set expansions and ii) single electron calculations utilizing a
frozen-core Hamiltonian. The first few parameters in the long-range interaction
potential between a Be ion and a H, He, or Li atom, and the leading
parameters of the effective potential for the high- Rydberg states of
beryllium were also computed. All the values reported are the results of
calculations close to convergence. Comparisons are made with published results
where available.Comment: 18 pp; added details to Sec. I
Proton radii of 4,6,8He isotopes from high-precision nucleon-nucleon interactions
Recently, precision laser spectroscopy on 6He atoms determined accurately the
isotope shift between 4He and 6He and, consequently, the charge radius of 6He.
A similar experiment for 8He is under way. We have performed large-scale ab
initio calculations for 4,6,8He isotopes using high-precision nucleon-nucleon
(NN) interactions within the no-core shell model (NCSM) approach. With the
CD-Bonn 2000 NN potential we found point-proton root-mean-square (rms) radii of
4He and 6He 1.45(1) fm and 1.89(4), respectively, in agreement with experiment
and predict the 8He point proton rms radius to be 1.88(6) fm. At the same time,
our calculations show that the recently developed nonlocal INOY NN potential
gives binding energies closer to experiment, but underestimates the charge
radii.Comment: 5 pages, 9 figure
Long-range interactions of metastable helium atoms
Polarizabilities, dispersion coefficients, and long-range atom-surface
interaction potentials are calculated for the n=2 triplet and singlet states of
helium using highly accurate, variationally determined, wave functions.Comment: RevTeX, epsf, 4 fig
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