4,789 research outputs found

### Generalized Hamilton-Jacobi equations for nonholonomic dynamics

Employing a suitable nonlinear Lagrange functional, we derive generalized
Hamilton-Jacobi equations for dynamical systems subject to linear velocity
constraints. As long as a solution of the generalized Hamilton-Jacobi equation
exists, the action is actually minimized (not just extremized)

### Screening and finite size corrections to the octupole and Schiff moments

Parity (P) and time reversal (T) violating nuclear forces create P, T -odd
moments in expansion of the nuclear electrostatic potential. We derive
expression for the nuclear electric octupole field which includes the electron
screening correction (similar to the screening term in the Schiff moment). Then
we calculate the Z alpha corrections to the Schiff moment which appear due to
the finite nuclear size. Such corrections are important in heavy atoms with
nuclear charge Z > 50. The Schiff and octupole moments induce atomic electric
dipole moments (EDM) and P, T -odd interactions in molecules which are measured
in numerous experiments to test CP-violation theories

### Enhancement of the electric dipole moment of the electron in the YbF molecule

We calculate an effective electric field on the unpaired electron in the YbF
molecule. This field determines sensitivity of the molecular experiment to the
electric dipole moment of the electron. We use experimental value of the
spin-doubling constant to estimate the admixture of the configuration with the
hole in the 4f-shell of Ytterbium to the ground state of the molecule. This
admixture reduces the field by 7%. Our value for the effictive field is 5.1
a.u. = 2.5 10^{10} V/cm.Comment: 5 pages, LATEX, uses revtex.st

### Fermi acceleration in time-dependent rectangular billiards due to multiple passages through resonances

We consider a slowly rotating rectangular billiard with moving boundaries and
use the canonical perturbation theory to describe the dynamics of a billiard
particle. In the process of slow evolution certain resonance conditions can be
satisfied. Correspondingly, phenomena of scattering on a resonance and capture
into a resonance happen in the system. These phenomena lead to destruction of
adiabatic invariance and to unlimited acceleration of the particle.Comment: 20 pages. Presented on School-Conference "Mathematics and Physics of
Billiard-Like Systems" (Ubatuba, 2011). Accepted to Chao

### Using Molecules to Measure Nuclear Spin-Dependent Parity Violation

Nuclear spin-dependent parity violation arises from weak interactions between
electrons and nucleons, and from nuclear anapole moments. We outline a method
to measure such effects, using a Stark-interference technique to determine the
mixing between opposite-parity rotational/hyperfine levels of ground-state
molecules. The technique is applicable to nuclei over a wide range of atomic
number, in diatomic species that are theoretically tractable for
interpretation. This should provide data on anapole moments of many nuclei, and
on previously unmeasured neutral weak couplings

### Extension of the Schiff theorem to ions and molecules

According to the Schiff theorem the nuclear electric dipole moment (EDM) is
screened in neutral atoms. In ions this screening is incomplete. We extend a
derivation of the Schiff theorem to ions and molecules. The finite nuclear size
effects are considered including Z^2 alpha^2 corrections to the nuclear Schiff
moment which are significant in all atoms and molecules of experimental
interest. We show that in majority of ionized atoms the nuclear EDM
contribution to the atomic EDM dominates while in molecules the contribution of
the Schiff moment dominates. We also consider the screening of electron EDM in
ions

### Enhancement of the electric dipole moment of the electron in BaF molecule

We report results of ab initio calculation of the spin-rotational Hamiltonian
parameters including P- and P,T-odd terms for the BaF molecule. The ground
state wave function of BaF molecule is found with the help of the Relativistic
Effective Core Potential method followed by the restoration of molecular
four-component spinors in the core region of barium in the framework of a
non-variational procedure. Core polarization effects are included with the help
of the atomic Many Body Perturbation Theory for Barium atom. For the hyperfine
constants the accuracy of this method is about 5-10%.Comment: 8 pages, REVTEX, report at II International Symposium on Symmetries
in Subatomic Physics, Seattle 199

### A Necessary Condition for existence of Lie Symmetries in Quasihomogeneous Systems of Ordinary Differential Equations

Lie symmetries for ordinary differential equations are studied. In systems of
ordinary differential equations, there do not always exist non-trivial Lie
symmetries around equilibrium points. We present a necessary condition for
existence of Lie symmetries analytic in the neighbourhood of an equilibrium
point. In addition, this result can be applied to a necessary condition for
existence of a Lie symmetry in quasihomogeneous systems of ordinary
differential equations. With the help of our main theorem, it is proved that
several systems do not possess any analytic Lie symmetries.Comment: 15 pages, no figures, AMSLaTe

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