161 research outputs found
Differential cross sections for muonic atom scattering from hydrogenic molecules
The differential cross sections for low-energy muonic hydrogen atom
scattering from hydrogenic molecules are directly expressed by the
corresponding amplitudes for muonic atom scattering from hydrogen-isotope
nuclei. The energy and angular dependence of these three-body amplitudes is
thus taken naturally into account in scattering from molecules, without
involving any pseudopotentials. Effects of the internal motion of nuclei inside
the target molecules are included for every initial rotational-vibrational
state. These effects are very significant as the considered three-body
amplitudes often vary strongly within the energy interval eV.
The differential cross sections, calculated using the presented method, have
been successfully used for planning and interpreting many experiments in
low-energy muon physics. Studies of nuclear capture in and the
measurement of the Lamb shift in atoms created in H gaseous targets
are recent examples.Comment: 21 pages, 13 figures, submitted to Phys. Rev.
Intrinsic symmetries
In this paper a concept of symmetry in the parameter space of the parameter dependent Hamiltonians is considered. The three different ways of realization of this symmetry is introduced. The example of analysis of this kind of symmetries is made in case of spherical harmonic oscillator. Some consequences of this symmetry for the electric type transition amplitudes of the electromagnetic nuclear radiation is shown
An infinite family of superintegrable Hamiltonians with reflection in the plane
We introduce a new infinite class of superintegrable quantum systems in the
plane. Their Hamiltonians involve reflection operators. The associated
Schr\"odinger equations admit separation of variables in polar coordinates and
are exactly solvable. The angular part of the wave function is expressed in
terms of little -1 Jacobi polynomials. The spectra exhibit "accidental"
degeneracies. The superintegrability of the model is proved using the
recurrence relation approach. The (higher-order) constants of motion are
constructed and the structure equations of the symmetry algebra obtained.Comment: 19 page
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