413 research outputs found
A New Tool for the Lamb Shift Calculation
We solve the Bethe-Salpeter equation for hydrogenic bound states by choosing
an appropriate interaction kernel . We want to use our solution to
calculate up to a higher order the hydrogen Lamb-shift, and as a first
application we present up to order \left(\aa / \pi\right)(\za)^7 the
contribution of the lowest order self-energy graph, calculated {\it exactly}.
The basic formalism is a natural extension to the hydrogenic bound states of
the one previously presented by R. Barbieri and E. Remiddi and used in the case
of positronium.Comment: 21 pages, Latex, Preprint DFUB-94-0
The Instantaneous Bethe-Salpeter Equation and Its Analog: the Breit-like Equation
We take () systems and consider the states with quantum number
as examples, to explore the different contents of the instantaneous
Bethe-Salpeter (BS) equation and its analog, Breit equation, by solving them
exactly. The results show that the two equations are not equivalent, although
they are analogous. Furthermore, we point out that the Breit equation contains
extra un-physical solutions, so it should be abandoned if one wishes to have an
accurate description of the bound states for the instantaneous interacting
binding systems.Comment: 5 pages, no figur
Instantaneous Bethe-Salpeter Equation and Its Exact Solution
We present an approach to solve a Bethe-Salpeter (BS) equation exactly
without any approximation if the kernel of the BS equation exactly is
instantaneous, and take positronium as an example to illustrate the general
features of the solutions. As a middle stage, a set of coupled and
self-consistent integration equations for a few scalar functions can be
equivalently derived from the BS equation always, which are solvable
accurately. For positronium, precise corrections to those of the Schr\"odinger
equation in order (relative velocity) in eigenfunctions, in order in
eigenvalues, and the possible mixing, such as that between () and
() components in () states as well, are
determined quantitatively. Moreover, we also point out that there is a
problematic step in the classical derivation which was proposed first by E.E.
Salpeter. Finally, we emphasize that for the effective theories (such as NRQED
and NRQCD etc) we should pay great attention on the corrections indicated by
the exact solutions.Comment: 4 pages, replace for shortening the manuscrip
Solar Mikheyev-Smirnov-Wolfenstein Effect with Three Generations of Neutrinos
Under the assumption that the density variation of the electrons can be
approximated by an exponential function, the solar Mikheyev-Smirnov-Wolfenstein
effect is treated for three generations of neutrinos. The generalized
hypergeometric functions that result from the exact solution of this problem
are studied in detail, and a method for their numerical evaluation is
presented. This analysis plays a central role in the determination of neutrino
masses, not only the differences of their squares, under the assumption of
universal quark-lepton mixing.Comment: 22 pages, LaTeX, including 2 figure
Majorana solutions to the two-electron problem
A review of the known different methods and results devised to study the
two-electron atom problem, appeared in the early years of quantum mechanics, is
given, with particular reference to the calculations of the ground state energy
of helium. This is supplemented by several, unpublished results obtained around
the same years by Ettore Majorana, which results did not convey in his
published papers on the argument, and thus remained unknown until now.
Particularly interesting, even for current research in atomic and nuclear
physics, is a general variant of the variational method, developed by Majorana
in order to take directly into account, already in the trial wavefunction, the
action of the full Hamiltonian operator of a given quantum system. Moreover,
notable calculations specialized to the study of the two-electron problem show
the introduction of the remarkable concept of an effective nuclear charge
different for the two electrons (thus generalizing previous known results), and
an application of the perturbative method, where the atomic number Z was
treated effectively as a continuous variable, contributions to the ground state
energy of an atom with given Z coming also from any other Z. Instead,
contributions relevant mainly for pedagogical reasons count simple broad range
estimates of the helium ionization potential, obtained by suitable choices for
the wavefunction, as well as a simple alternative to Hylleraas' method, which
led Majorana to first order calculations comparable in accuracy with well-known
order 11 results derived, in turn, by Hylleraas.Comment: amsart, 20 pages, no figure
High-energy expansion of Coulomb corrections to the e+e- photoproduction cross section
First correction to the high-energy asymptotics of the total
photoproduction cross section in the electric field of a heavy atom is derived
with the exact account of this field. The consideration is based on the use of
the quasiclassical electron Green function in an external electric field. The
next-to-leading correction to the cross section is discussed. The influence of
screening on the Coulomb corrections is examined in the leading approximation.
It turns out that the high-energy asymptotics of the corresponding correction
is independent of the photon energy. In the region where both produced
particles are relativistic, the corrections to the high-energy asymptotics of
the electron (positron) spectrum are derived. Our results for the total cross
section are in good agreement with experimental data for photon energies down
to a few . In addition, the corrections to the bremsstrahlung spectrum are
obtained from the corresponding results for pair production.Comment: 22 pages, 7 figures, RevTeX.Typos are corrected. The numerical
results, figures and conclusions remain unchanged as they were obtained using
correct formula
Wavelength dependent ac-Stark shift of the 1S0 - 3P1 transition at 657 nm in Ca
We have measured the ac-Stark shift of the 4s2 1S0 - 4s4p 3P1 line in 40Ca
for perturbing laser wavelengths between 780 nm and 1064 nm with a time domain
Ramsey-Borde atom interferometer. We found a zero crossing of the shift for the
mS = 0 - mP = 0 transition and \sigma polarized perturbation at 800.8(22) nm.
The data was analyzed by a model deriving the energy shift from known
transition wavelengths and strengths. To fit our data, we adjusted the Einstein
A coefficients of the 4s3d 3D - 4s4p 3P and 4s5s 3S - 4s4p 3P fine structure
multiplets. With these we can predict vanishing ac-Stark shifts for the 1S0 m =
0 - 3P1 m = 1 transition and \sigma- light at 983(12) nm and at 735.5(20) nm
for the transition to the 3P0 level.Comment: 8 pages, 5 figures, 2 table
Observation of Enhanced Beaming from Photonic Crystal Waveguides
We report on the experimental observation of the beaming effect in photonic
crystals enhanced via surface modes. We experimentally map the spatial field
distribution of energy emitted from a subwavelength photonic crystal waveguide
into free-space, rendering with crisp clarity the diffractionless beaming of
energy. Our experimental data agree well with our numerical studies of the
beaming enhancement in photonic crystals with modulated surfaces. Without loss
of generality, we study the beaming effect in a photonic crystal scaled to
microwave frequencies and demonstrate the technological capacity to deliver
long-range, wavelength-scaled beaming of energy.Comment: 4 pages, 6 figure
New Way to Produce Dense Double-Antikaonic Dibaryon System, \bar{K}\bar{K} NN, through Lambda(1405)-Doorway Sticking in p+p Collisions
A recent successful observation of a dense and deeply bound \bar{K} nuclear
system, K^-pp, in the p + p \rightarrow K^+ + K^-pp reaction in a DISTO
experiment indicates that the double-\bar{K} dibaryon, K^-K^-pp, which was
predicted to be a dense nuclear system, can also be formed in p+p collisions.
We find theoretically that the K^- -K^- repulsion plays no significant role in
reducing the density and binding energy of K^-K^-pp and that, when two
\Lambda(1405) resonances are produced simultaneously in a short-range p+p
collision, they act as doorways to copious formation of K^-K^-pp, if and only
if K^-K^-pp is a dense object, as predicted.Comment: 8 pages, 9 figures, Accepted Apr. 19, 201
A Perturbative Calculation of the Electromagnetic Form Factors of the Deuteron
Making use of the effective field theory expansion recently developed by the
authors, we compute the electromagnetic form factors of the deuteron
analytically to next-to-leading order (NLO). The computation is rather simple,
and involves calculating several Feynman diagrams, using dimensional
regularization. The results agree well with data and indicate that the
expansion is converging. They do not suffer from any ambiguities arising from
off-shell versus on-shell amplitudes.Comment: 22 pages, 8 figures. Discussion of effective range theory added,
typos correcte
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