644 research outputs found
Microscopic Model versus Systematic Low-Energy Effective Field Theory for a Doped Quantum Ferromagnet
We consider a microscopic model for a doped quantum ferromagnet as a test
case for the systematic low-energy effective field theory for magnons and
holes, which is constructed in complete analogy to the case of quantum
antiferromagnets. In contrast to antiferromagnets, for which the effective
field theory approach can be tested only numerically, in the ferromagnetic case
both the microscopic and the effective theory can be solved analytically. In
this way the low-energy parameters of the effective theory are determined
exactly by matching to the underlying microscopic model. The low-energy
behavior at half-filling as well as in the single- and two-hole sectors is
described exactly by the systematic low-energy effective field theory. In
particular, for weakly bound two-hole states the effective field theory even
works beyond perturbation theory. This lends strong support to the quantitative
success of the systematic low-energy effective field theory method not only in
the ferromagnetic but also in the physically most interesting antiferromagnetic
case.Comment: 34 pages, 1 figur
Coulomb corrections and multiple e+e- pair production in ultra-relativistic nuclear collisions
We consider the problem of Coulomb corrections to the inclusive cross
section. We show that these corrections in the limiting case of small charge
number of one of the nuclei coincide with those to the exclusive cross section.
Within our approach we also obtain the Coulomb corrections for the case of
large charge numbers of both nuclei.Comment: 7 pages, REVTeX
Relativistic Reduced-Mass and Recoil Corrections to Vacuum Polarization in Muonic Hydrogen, Muonic Deuterium and Muonic Helium Ions
The reduced-mass dependence of relativistic and radiative effects in simple
muonic bound systems is investigated. The spin-dependent nuclear recoil
correction of order (Zalpha)^4 mu^3/m_N^2 is evaluated for muonic hydrogen and
deuterium, and muonic helium ions (mu is the reduced mass and m_N is the
nuclear mass). Relativistic corrections to vacuum polarization of order alpha
(Zalpha)^4 mu are calculated, with a full account of the reduced-mass
dependence. The results shift theoretical predictions. The radiative-recoil
correction to vacuum polarization of order alpha (Z\alpha)^5 ln^2(Zalpha)
mu^2/m_N is obtained in leading logarithmic approximation. The results
emphasize the need for a unified treatment of relativistic corrections to
vacuum polarization in muonic hydrogen, muonic deuterium and muonic helium
ions, where the mass ratio of the orbiting particle to the nuclear mass is
larger than the fine-structure constant.Comment: 6 pages; RevTe
Effective Field Theory for Short-Range Forces
The method of effective field theories (EFTs) is developed for the scattering
of two particles at wavelengths which are large compared to the range of their
interaction. It is shown that the renormalized EFT is equivalent to the
effective range expansion, to a Schroedinger equation with a pseudo-potential,
and to an energy expansion of a generic boundary condition at the origin. The
roles of regulators and potentials are also discussed. These ideas are
exemplified in a toy model.Comment: 38 pages, 6 figure
Exact solution of the Zeeman effect in single-electron systems
Contrary to popular belief, the Zeeman effect can be treated exactly in
single-electron systems, for arbitrary magnetic field strengths, as long as the
term quadratic in the magnetic field can be ignored. These formulas were
actually derived already around 1927 by Darwin, using the classical picture of
angular momentum, and presented in their proper quantum-mechanical form in 1933
by Bethe, although without any proof. The expressions have since been more or
less lost from the literature; instead, the conventional treatment nowadays is
to present only the approximations for weak and strong fields, respectively.
However, in fusion research and other plasma physics applications, the magnetic
fields applied to control the shape and position of the plasma span the entire
region from weak to strong fields, and there is a need for a unified treatment.
In this paper we present the detailed quantum-mechanical derivation of the
exact eigenenergies and eigenstates of hydrogen-like atoms and ions in a static
magnetic field. Notably, these formulas are not much more complicated than the
better-known approximations. Moreover, the derivation allows the value of the
electron spin gyromagnetic ratio to be different from 2. For
completeness, we then review the details of dipole transitions between two
hydrogenic levels, and calculate the corresponding Zeeman spectrum. The various
approximations made in the derivation are also discussed in details.Comment: 18 pages, 4 figures. Submitted to Physica Script
Hypercritical Advection Dominated Accretion Flow
In this note we study the accretion disc that arises in hypercritical
accretion of onto a neutron star while it is in
common envelope evolution with a massive companion. In order to raise the
temperature high enough that the disc might cool by neutrino emission,
Chevalier found a small value of the -parameter, where the kinematic
coefficient of shear viscosity is , with the velocity
of sound and the disc height; namely, was necessary
for gas pressure to dominate. He also considered results with higher values of
, pointing out that radiation pressure would then predominate. With
these larger 's, the temperatures of the accreting material are much
lower, \lsim 0.35 MeV. The result is that neutrino cooling during the flow is
negligible, satisfying very well the advection dominating conditions. The low
temperature of the accreting material means that it cannot get rid of its
energy rapidly by neutrino emission, so it piles up, pushing its way through
the accretion disc. An accretion shock is formed, far beyond the neutron star,
at a radius \gsim 10^8 cm, much as in the earlier spherically symmetric
calculation, but in rotation. Two-dimensional numerical simulation shows that
an accretion disc is reformed inside of the accretion shock, allowing matter to
accrete onto the neutron star with pressure high enough so that neutrinos can
carry off the energy.Comment: 6 pages, ApJ, submitte
Wire scanners in low energy accelerators
Fast wire scanners are today considered as part of standard instrumentation
in high energy synchrotrons. The extension of their use to synchrotrons working
at lower energies, where Coulomb scattering can be important and the transverse
beam size is large, introduces new complications considering beam heating of
the wire, composition of the secondary particle shower and geometrical
consideration in the detection set-up. A major problem in treating these
effects is that the creation of secondaries in a thin carbon wire by a
energetic primary beam is difficult to describe in an analytical way. We are
here presenting new results from a full Monte Carlo simulation of this process
yielding information on heat deposited in the wire, particle type and energy
spectrum of secondaries and angular dependence as a function of primary beam
energy. The results are used to derive limits for the use of wire scanners in
low energy accelerators.Comment: 20 pages, 8 Postscript figures, uses elsart.cl
Two-Photon Decays Reexamined: Cascade Contributions and Gauge Invariance
The purpose of this paper is to calculate the two-photon decay rate
corresponding to the two-photon transitions nS->1S and nD->1S in hydrogenlike
ions with a low nuclear charge number Z (for principal quantum numbers n =
2,...,8. Numerical results are obtained within a nonrelativistic framework, and
the results are found to scale approximately as (Z alpha)^6/n^3, where alpha is
the fine-structure constant. We also attempt to clarify a number of subtle
issues regarding the treatment of the coherent, quasi-simultaneous emission of
the two photons as opposed to one-photon cascades. In particular, the gauge
invariance of the decay rate is shown explicitly.Comment: 10 pages, LaTe
On the nature of Coulomb corrections to the e^+e^- pair production in ultrarelativistic heavy-ion collisions
We manifest the origin of the wrong conclusion made by several groups of
authors on the absence of Coulomb corrections to the cross section of the
e^+e^- pair production in ultrarelativistic heavy-ion collisions. The source of
the mistake is connected with an incorrect passage to the limit in the
expression for the cross section. When this error is eliminated, the Coulomb
corrections do not vanish and agree with the results obtained within the
Weizs\"acker-Williams approximation.Comment: 7 pages, LaTe
Enhancement of Blackbody Friction due to the Finite Lifetime of Atomic Levels
The thermal friction force acting on an atom moving relative to a thermal
photon bath is known to be proportional to an integral over the imaginary part
of the frequency-dependent atomic (dipole) polarizability. Using a numerical
approach, we find that blackbody friction on atoms either in dilute
environments or in hot ovens is larger than previously thought by orders of
magnitude. This enhancement is due to far off-resonant driving of transitions
by low-frequency thermal radiation. At typical temperatures, the blackbody
radiation maximum lies far below the atomic transition wavelengths.
Surprisingly, due to the finite lifetime of atomic levels, which gives rise to
Lorentzian line profiles, far off-resonant excitation leads to the dominant
contribution to the blackbody friction.Comment: 4 pages; RevTe
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