36 research outputs found
Relativistic Coulomb Sum Rules for
A Coulomb sum rule is derived for the response of nuclei to
scattering with large three-momentum transfers. Unlike the nonrelativistic
formulation, the relativistic Coulomb sum is restricted to spacelike
four-momenta for the most direct connection with experiments; an immediate
consequence is that excitations involving antinucleons, e.g., pair
production, are approximately eliminated from the sum rule. Relativistic recoil
and Fermi motion of target nucleons are correctly incorporated. The sum rule
decomposes into one- and two-body parts, with correlation information in the
second. The one-body part requires information on the nucleon momentum
distribution function, which is incorporated by a moment expansion method. The
sum rule given through the second moment (RCSR-II) is tested in the Fermi gas
model, and is shown to be sufficiently accurate for applications to data.Comment: 32 pages (LaTeX), 4 postscript figures available from the author
Transmission Properties of the oscillating delta-function potential
We derive an exact expression for the transmission amplitude of a particle
moving through a harmonically driven delta-function potential by using the
method of continued-fractions within the framework of Floquet theory. We prove
that the transmission through this potential as a function of the incident
energy presents at most two real zeros, that its poles occur at energies
(), and that the
poles and zeros in the transmission amplitude come in pairs with the distance
between the zeros and the poles (and their residue) decreasing with increasing
energy of the incident particle. We also show the existence of non-resonant
"bands" in the transmission amplitude as a function of the strength of the
potential and the driving frequency.Comment: 21 pages, 12 figures, 1 tabl
Nuclear Medium Effects in the Relativistic Treatment of Quasifree Electron Scattering
Non-relativistic reduction of the S-matrix for the quasifree electron
scattering process is studied in order to
understand the source of differences between non-relativistic and relativistic
models. We perform an effective Pauli reduction on the relativistic expression
for the S-matrix in the one-photon exchange approximation. The reduction is
applied to the nucleon current only; the electrons are treated fully
relativistically. An expansion of the amplitude results in a power series in
the nuclear potentials. The series is found to converge rapidly only if the
nuclear potentials are included in the nuclear current operator. The results
can be cast in a form which reproduces the non-relativistic amplitudes in the
limit that the potentials are removed from the nuclear current operator. Large
differences can be found between calculations which do and do not include the
nuclear potentials in the different orders of the nuclear current operator. In
the high missing momentum region we find that the non-relativistic calculations
with potentials included in the nuclear current up to second order give results
which are close to those of the fully relativistic calculation. This behavior
is an indication of the importance of the medium modifications of the nuclear
currents in this model, which are naturally built into the relativistic
treatment of the reaction.Comment: Latex, 26 pages including 5 uuencoded postscript figures. accepted
for publication in Phys. Rev. C
Resonant structure of space-time of early universe
A new fully quantum method describing penetration of packet from internal
well outside with its tunneling through the barrier of arbitrary shape used in
problems of quantum cosmology, is presented. The method allows to determine
amplitudes of wave function, penetrability and reflection relatively the barrier (accuracy of the method: ), coefficient of penetration (i.e. probability of
the packet to penetrate from the internal well outside with its tunneling),
coefficient of oscillations (describing oscillating behavior of the packet
inside the internal well). Using the method, evolution of universe in the
closed Friedmann--Robertson--Walker model with quantization in presence of
positive cosmological constant, radiation and component of generalize Chaplygin
gas is studied. It is established (for the first time): (1) oscillating
dependence of the penetrability on localization of start of the packet; (2)
presence of resonant values of energy of radiation , at which the
coefficient of penetration increases strongly. From analysis of these results
it follows: (1) necessity to introduce initial condition into both
non-stationary, and stationary quantum models; (2) presence of some definite
values for the scale factor , where start of expansion of universe is the
most probable; (3) during expansion of universe in the initial stage its radius
is changed not continuously, but passes consequently through definite discrete
values and tends to continuous spectrum in latter time.Comment: 18 pages, 14 figures, 4 table
Unitarity and Interfering Resonances in pipi Scattering and in Pion Production piN->pipiN
Additivity of Breit-Wigner phases has been proposed to describe interfering
resonances in partial waves in scattering. This assumption leads to an
expression for partial wave amplitudes that involves products of Breit-Wigner
amplitudes. We show that this expression is equivalent to a coherent sum of
Breit-Wigner amplitudes with specific complex coefficients which depend on the
resonance parameters of all contributing resonances. We use analyticity of
partial wave amplitudes to show that they must have the form of a
coherent sum of Breit-Wigner amplitudes with complex coefficients and a complex
coherent background. The assumption of additivity of Breit-Wigner phases
restricts the partial waves to analytical functions with very specific form of
residues of Breit-Wigner poles. We argue that the general form provided by the
analyticity is more appropriate in fits to data to determine resonance
parameters. The partial wave unitarity can be imposed using the modern methods
of constrained optimization. We discuss unitarity and the production amplitudes
in and use analyticity in the dipion mass variable to
justify the common practice of writing the production amplitudes as a coherent
sum of Breit-Wigner amplitudes with free complex coefficients and a complex
coherent background in fits to mass spectra with interfering resonances.Comment: 31 page