58,540 research outputs found
Levinson's theorem for the Schr\"{o}dinger equation in two dimensions
Levinson's theorem for the Schr\"{o}dinger equation with a cylindrically
symmetric potential in two dimensions is re-established by the Sturm-Liouville
theorem. The critical case, where the Schr\"{o}dinger equation has a finite
zero-energy solution, is analyzed in detail. It is shown that, in comparison
with Levinson's theorem in non-critical case, the half bound state for
wave, in which the wave function for the zero-energy solution does not decay
fast enough at infinity to be square integrable, will cause the phase shift of
wave at zero energy to increase an additional .Comment: Latex 11 pages, no figure and accepted by P.R.A (in August); Email:
[email protected], [email protected]
Sensitivity of neutron to proton ratio toward the high density behavior of symmetry energy in heavy-ion collisions
The symmetry energy at sub and supra-saturation densities has a great
importance in understanding the exact nature of asymmetric nuclear matter as
well as neutron star, but, it is poor known, especially at supra-saturation
densities. We will demonstrate here that the neutron to proton ratios from
different kind of fragments is able to determine the supra-saturation behavior
of symmetry energy or not. For this purpose, a series of Sn isotopes are
simulated at different incident energies using the Isospin Quantum Molecular
Dynamics (IQMD) model with either a soft or a stiff symmetry energy for the
present study. It is found that the single neutron to proton ratio from free
nucleons as well as LCP's is sensitive towards the symmetry energy, incident
energy as well as isospin asymmetry of the system. However, with the double
neutron to proton ratio, it is true only for the free nucleons. It is possible
to study the high density behavior of symmetry energy by using the neutron to
proton ratio from free nucleons.Comment: 11 Pages, 9 Figure
Melosh rotation: source of the proton's missing spin
It is shown that the observed small value of the integrated spin structure
function for protons could be naturally understood within the naive quark model
by considering the effect from Melosh rotation. The key to this problem lies in
the fact that the deep inelastic process probes the light-cone quarks rather
than the instant-form quarks, and that the spin of the proton is the sum of the
Melosh rotated light-cone spin of the individual quarks rather than simply the
sum of the light-cone spin of the quarks directly.Comment: 5 latex page
Hyperon polarization in e^-p --> e^-HK with polarized electron beams
We apply the picture proposed in a recent Letter for transverse hyperon
polarization in unpolarized hadron-hadron collisions to the exclusive process
e^-p --> e^-HK such as e^-p-->e^-\Lambda K^+, e^-p --> e^-\Sigma^+ K^0, or
e^-p--> e^-\Sigma^0 K^+, or the similar process e^-p\to e^-n\pi^+ with
longitudinally polarized electron beams. We present the predictions for the
longitudinal polarizations of the hyperons or neutron in these reactions, which
can be used as further tests of the picture.Comment: 15 pages, 2 figures. submitted to Phys. Rev.
The Relativistic Levinson Theorem in Two Dimensions
In the light of the generalized Sturm-Liouville theorem, the Levinson theorem
for the Dirac equation in two dimensions is established as a relation between
the total number of the bound states and the sum of the phase shifts
of the scattering states with the angular momentum :
\noindent The critical case, where the Dirac equation has a finite
zero-momentum solution, is analyzed in detail. A zero-momentum solution is
called a half bound state if its wave function is finite but does not decay
fast enough at infinity to be square integrable.Comment: Latex 14 pages, no figure, submitted to Phys.Rev.A; Email:
[email protected], [email protected]
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