53,436 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]
Nuclear modification factor in intermediate-energy heavy-ion collisions
The transverse momentum dependent nuclear modification factors (NMF), namely
, is investigated for protons produced in Au + Au at 1 GeV within
the framework of the isospin-dependent quantum molecular dynamics (IQMD) model.
It is found that the radial collective motion during the expansion stage
affects the NMF at low transverse momentum a lot. By fitting the transverse
mass spectra of protons with the distribution function from the Blast-Wave
model, the magnitude of radial flow can be extracted. After removing the
contribution from radial flow, the can be regarded as a thermal one
and is found to keep unitary at transverse momentum lower than 0.6 GeV/c and
enhance at higher transverse momentum, which can be attributed to Cronin
effect.Comment: 8 pages, 5 figures; aceepted by Physics Letters
QCD Evolutions of Twist-3 Chirality-Odd Operators
We study the scale dependence of twist-3 distributions defined with
chirality-odd quark-gluon operators. To derive the scale dependence we
explicitly calculate these distributions of multi-parton states instead of a
hadron. Taking one-loop corrections into account we obtain the leading
evolution kernel in the most general case. In some special cases the evolutions
are simplified. We observe that the obtained kernel in general does not get
simplified in the large- limit in contrast to the case of those twist-3
distributions defined only with chirality-odd quark operators. In the later,
the simplification is significant.Comment: 9 pages, 2 figure
- …