49 research outputs found

### Forbidden transitions in the helium atom

Nonrelativistically forbidden, single-photon transition rates between low
lying states of the helium atom are rigorously derived within quantum
electrodynamics theory. Equivalence of velocity and length gauges, including
relativistic corrections is explicitly demonstrated. Numerical calculations of
matrix elements are performed with the use of high precision variational wave
functions and compared to former results.Comment: 11 pages, 1 figure, submitted to Phys. Rev.

### Asymptotic Energies and QED Shifts for Rydberg States of Helium

This paper reviews progress that has been made in obtaining essentially exact solutions to the nonrelativistic three-body problem for helium by a combination of variational and asymptotic expansion methods. The calculation of relativistic and quantum electrodynamic corrections by perturbation theory is discussed, and in particular, methods for the accurate calculation of the Bethe logarithm part of the electron self energy are presented. As an example, the results are applied to the calculation of isotope shifts for the short-lived 'halo' nucleus He-6 relative to He-4 in order to determine the nuclear charge radius of He-6 from high precision spectroscopic measurements carried out at the Argonne National Laboratory. The results demonstrate that the high precision that is now available from atomic theory is creating new opportunities to create novel measurement tools, and helium, along with hydrogen, can be regarded as a fundamental atomic system whose spectrum is well understood for all practical purposes

### Two-photon E1M1 decay of 2 3P0 states in heavy heliumlike ions

Two-photon E1M1 transition rates are evaluated for heliumlike ions with
nuclear charges in the range Z = 50-94. The two-photon rates modify previously
published lifetimes/transition rates of 2 3P0 states. For isotopes with nuclear
spin I not equal 0, where hyperfine quenching dominates the 2 3P0 decay,
two-photon contributions are significant; for example, in heliumlike 187 Os the
two-photon correction is 3% of the total rate. For isotopes with I= 0, where
the 2 3P0 decay is unquenched, the E1M1 corrections are even more important
reaching 60% for Z=94. Therefore, to aid in the interpretation of experiments
on hyperfine quenching in heliumlike ions and to provide a more complete
database for unquenched transitions, a knowledge of E1M1 rates is important.Comment: 6 pages, 3 figures, 3 table

### Radiative Corrections to One-Photon Decays of Hydrogenic Ions

Radiative corrections to the decay rate of n=2 states of hydrogenic ions are
calculated. The transitions considered are the M1 decay of the 2s state to the
ground state and the E1(M2) decays of the $2p_{1/2}$ and $2p_{3/2}$ states to
the ground state. The radiative corrections start in order $\alpha (Z
\alpha)^2$, but the method used sums all orders of $Z\alpha$. The leading
$\alpha (Z\alpha)^2$ correction for the E1 decays is calculated and compared
with the exact result. The extension of the calculational method to parity
nonconserving transitions in neutral atoms is discussed.Comment: 22 pages, 2 figure

### Search for Possible Variation of the Fine Structure Constant

Determination of the fine structure constant alpha and search for its
possible variation are considered. We focus on a role of the fine structure
constant in modern physics and discuss precision tests of quantum
electrodynamics. Different methods of a search for possible variations of
fundamental constants are compared and those related to optical measurements
are considered in detail.Comment: An invited talk at HYPER symposium (Paris, 2002

### Independent Eigenstates of Angular Momentum in a Quantum N-body System

The global rotational degrees of freedom in the Schr\"{o}dinger equation for
an $N$-body system are completely separated from the internal ones. After
removing the motion of center of mass, we find a complete set of $(2\ell+1)$
independent base functions with the angular momentum $\ell$. These are
homogeneous polynomials in the components of the coordinate vectors and the
solutions of the Laplace equation, where the Euler angles do not appear
explicitly. Any function with given angular momentum and given parity in the
system can be expanded with respect to the base functions, where the
coefficients are the functions of the internal variables. With the right choice
of the base functions and the internal variables, we explicitly establish the
equations for those functions. Only (3N-6) internal variables are involved both
in the functions and in the equations. The permutation symmetry of the wave
functions for identical particles is discussed.Comment: 24 pages, no figure, one Table, RevTex, Will be published in Phys.
Rev. A 64, 0421xx (Oct. 2001

### Extension of the sum rule for the transition rates between multiplets to the multiphoton case

The sum rule for the transition rates between the components of two
multiplets, known for the one-photon transitions, is extended to the
multiphoton transitions in hydrogen and hydrogen-like ions. As an example the
transitions 3p-2p, 4p-3p and 4d-3d are considered. The numerical results are
compared with previous calculations.Comment: 10 pages, 4 table

### Majorana solutions to the two-electron problem

A review of the known different methods and results devised to study the
two-electron atom problem, appeared in the early years of quantum mechanics, is
given, with particular reference to the calculations of the ground state energy
of helium. This is supplemented by several, unpublished results obtained around
the same years by Ettore Majorana, which results did not convey in his
published papers on the argument, and thus remained unknown until now.
Particularly interesting, even for current research in atomic and nuclear
physics, is a general variant of the variational method, developed by Majorana
in order to take directly into account, already in the trial wavefunction, the
action of the full Hamiltonian operator of a given quantum system. Moreover,
notable calculations specialized to the study of the two-electron problem show
the introduction of the remarkable concept of an effective nuclear charge
different for the two electrons (thus generalizing previous known results), and
an application of the perturbative method, where the atomic number Z was
treated effectively as a continuous variable, contributions to the ground state
energy of an atom with given Z coming also from any other Z. Instead,
contributions relevant mainly for pedagogical reasons count simple broad range
estimates of the helium ionization potential, obtained by suitable choices for
the wavefunction, as well as a simple alternative to Hylleraas' method, which
led Majorana to first order calculations comparable in accuracy with well-known
order 11 results derived, in turn, by Hylleraas.Comment: amsart, 20 pages, no figure

### Entanglement in helium

Using a configuration-interaction variational method, we accurately compute
the reduced, single-electron von Neumann entropy for several low-energy,
singlet and triplet eigenstates of helium atom. We estimate the amount of
electron-electron orbital entanglement for such eigenstates and show that it
decays with energy.Comment: 5 pages, 2 figures, added references and discussio