1,855 research outputs found
Exponential versus linear amplitude decay in damped oscillators
We comment of the widespread belief among some undergraduate students that
the amplitude of any harmonic oscillator in the presence of any type of
friction, decays exponentially in time. To dispel that notion, we compare the
amplitude decay for a harmonic oscillator in the presence of (i) viscous
friction and (ii) dry friction. It is shown that, in the first case, the
amplitude decays exponentially with time while in the second case, it decays
linearly with time.Comment: 3 pages, 1 figure, accepted in Phys. Teac
Sum Rules for Magnetic Moments and Polarizabilities in QED and Chiral Effective-Field Theory
We elaborate on a recently proposed extension of the Gerasimov-Drell-Hearn
(GDH) sum rule which is achieved by taking derivatives with respect to the
anomalous magnetic moment. The new sum rule features a {\it linear} relation
between the anomalous magnetic moment and the dispersion integral over a
cross-section quantity. We find some analogy of the linearized form of the GDH
sum rule with the `sideways dispersion relations'. As an example, we apply the
linear sum rule to reproduce the famous Schwinger's correction to the magnetic
moment in QED from a tree-level cross-section calculation and outline the
procedure for computing the two-loop correction from a one-loop cross-section
calculation. The polarizabilities of the electron in QED are considered as well
by using the other forward-Compton-scattering sum rules. We also employ the sum
rules to study the magnetic moment and polarizabilities of the nucleon in a
relativistic chiral EFT framework. In particular we investigate the chiral
extrapolation of these quantities.Comment: 24 pages, 7 figures; several additions, published versio
The effects of the small t properties of hadronic scattering amplitude on the determination its real part
Taking into account the different forms of the Coulomb-hadron interference
phase and the possible spin-flip contribution the new analysis of the
experimental data of the proton-antiproton elastic scattering at GeV/c and small momentum transfer is carried out. It is shown that the
size of the spin-flip amplitude can be determined from the form of the
differential cross sections at small , and the deviation of
obtained from the examined experimental data of the scattering from
the analysis \cite{Kroll}, based on the dispersion relations, is conserved in
all xamined assumptions. The analysis of the proton-proton elastic scattering
at GeV/c also shows the impact of the examined effects on the
form of the differential cross sections.Comment: 13 pages, 3 figure
Q^2 Evolution of Generalized Baldin Sum Rule for the Proton
The generalized Baldin sum rule for virtual photon scattering, the
unpolarized analogy of the generalized Gerasimov-Drell-Hearn integral, provides
an important way to investigate the transition between perturbative QCD and
hadronic descriptions of nucleon structure. This sum rule requires integration
of the nucleon structure function F_1, which until recently had not been
measured at low Q^2 and large x, i.e. in the nucleon resonance region. This
work uses new data from inclusive electron-proton scattering in the resonance
region obtained at Jefferson Lab, in combination with SLAC deep inelastic
scattering data, to present first precision measurements of the generalized
Baldin integral for the proton in the Q^2 range of 0.3 to 4.0 GeV^2.Comment: 4 pages, 3 figures, one table; text added, one figure replace
Survey of charge symmetry breaking operators for dd -> alpha pi0
The charge-symmetry-breaking amplitudes for the recently observed d d ->
alpha pi0 reaction are investigated. Chiral perturbation theory is used to
classify and identify the leading-order terms. Specific forms of the related
one- and two-body tree level diagrams are derived. As a first step toward a
full calculation, a few tree-level two-body diagrams are evaluated at each
considered order, using a simplified set of d and alpha wave functions and a
plane-wave approximation for the initial dd state. The leading-order
pion-exchange term is shown to be suppressed in this model because of poor
overlap of the initial and final states. The higher-order one-body and
short-range (heavy-meson-exchange) amplitudes provide better matching between
the initial and final states and therefore contribute significantly and
coherently to the cross section. The consequences this might have for a full
calculation, with realistic wave functions and a more complete set of
amplitudes, are discussed.Comment: REVTeX 4, 35 pages, 8 eps figures, submitted to PR
Mechanisms for High-frequency QPOs in Neutron Star and Black Hole Binaries
We explain the millisecond variability detected by Rossi X-ray Timing
Explorer (RXTE) in the X-ray emission from a number of low mass X-ray binary
systems (Sco X-1, 4U1728-34, 4U1608-522, 4U1636-536, 4U0614+091, 4U1735-44,
4U1820-30, GX5-1 and etc) in terms of dynamics of the centrifugal barrier, a
hot boundary region surrounding a neutron star. We demonstrate that this region
may experience the relaxation oscillations, and that the displacements of a gas
element both in radial and vertical directions occur at the same main
frequency, of order of the local Keplerian frequency. We show the importance of
the effect of a splitting of the main frequency produced by the Coriolis force
in a rotating disk for the interpretation of a spacing between the QPO peaks.
We estimate a magnitude of the splitting effect and present a simple formula
for the whole spectrum of the split frequencies. It is interesting that the
first three lowest-order overtones fall in the range of 200-1200 Hz and match
the kHz-QPO frequencies observed by RXTE. Similar phenomena should also occur
in Black Hole (BH) systems, but, since the QPO frequency is inversely
proportional to the mass of a compact object, the frequency of the
centrifugal-barrier oscillations in the BH systems should be a factor of 5-10
lower than that for the NS systems. The X-ray spectrum formed in this region is
a result of upscattering of a soft radiation (from a disk and a NS surface) off
relatively hot electrons in the boundary layer. We also briefly discuss some
alternative QPO models, including a possibility of acoustic oscillations in the
boundary layer, the proper stellar rotation, and g-mode disk oscillations.Comment: The paper is coming out in the Astrophysical Journal in the 1st of
May issue of 199
Impact of saturation on spin effects in proton-proton scattering
For pomerons described by a sum of two simple-pole terms, a soft and a hard
pomeron, the unitarity bounds from saturation in impact-parameter space are
examined. We consider the effect of these bounds on observables linked with
polarisation, such as the analyzing power in elastic proton-proton scattering,
for LHC energies. We obtain the s and t dependence of the Coulomb-nuclear
interference at small momentum transfer, and show that the effect of the hard
pomeron may be observed at the LHC.Comment: 8 pages, 2 figures, presented by O.V.S. at the Advanced Studies
Institute "Symetries and Spin" (SPIN-Praha-2004), Prague, July 5 - July 10,
200
Importance of Compton scattering to radiation spectra of isolated neutron stars
Model atmospheres of isolated neutron stars with low magnetic field are
calculated with Compton scattering taking into account. Models with effective
temperatures 1, 3 and 5 MK, with two values of surface gravity log(g)g = 13.9
and 14.3), and different chemical compositions are calculated. Radiation
spectra computed with Compton scattering are softer than the computed with
Thomson scattering at high energies (E > 5 keV) for hot (T_eff > 1 MK)
atmospheres with hydrogen-helium composition. Compton scattering is more
significant to hydrogen models with low surface gravity. The emergent spectra
of the hottest (T_eff > 3 MK) model atmospheres can be described by diluted
blackbody spectra with hardness factors ~ 1.6 - 1.9. Compton scattering is less
important for models with solar abundance of heavy elements.Comment: Proceedings of the 363. WE-Heraeus Seminar on: Neutron Stars and
Pulsars (Posters and contributed talks) Physikzentrum Bad Honnef, Germany,
May.14-19, 2006, eds. W.Becker, H.H.Huang, MPE Report 291, pp.173-17
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