234 research outputs found
Equivalence of the long-wavelength approximation and the truncated Taylor expansion in relativistic Coulomb excitation
The long-wavelength approximation and the truncated Taylor expansion are
frequently used in the theory of relativistic Coulomb excitation to obtain
multipole expansions of the interaction. It is shown in this note that these
two approximations are exactly equivalent.Comment: 5 page
Gauge dependence of calculations in relativistic Coulomb excitation
Before a quantum-mechanical calculation involving electromagnetic
interactions is performed, a choice must be made of the gauge to be used in
expressing the potentials. If the calculation is done exactly, the observable
results it predicts will be independent of the choice of gauge. However, in
most practical calculations approximations are made, which can destroy the
gauge invariance of the predictions. We compare here the results of
coupled-channel time-dependent relativistic Coulomb excitation calculations, as
performed in either Lorentz or Coulomb gauges. We find significant differences
when the bombarding energy per nucleon is 2 GeV, which indicates that
the common practice of relying completely on the Lorentz gauge can be
dangerous.Comment: 23 pages, 3 figure
Coulomb Excitation of Multi-Phonon Levels of the Giant Dipole Resonance
A closed expression is obtained for the cross-section for Coulomb excitation
of levels of the giant dipole resonance of given angular momentum and phonon
number. Applications are made to the Goldhaber-Teller and Steinwedel-Jensen
descriptions of the resonance, at non-relativistic and relativistic bombarding
energies.Comment: 16 pages, 5 figure
Quantum derivation of the use of classical electromagnetic potentials in relativistic Coulomb excitation
We prove that a relativistic Coulomb excitation calculation in which the
classical electromagnetic field of the projectile is used to induce transitions
between target states gives the same target transition amplitudes, to all
orders of perturbation theory, as would a calculation in which the interaction
between projectile and target is mediated by a quantized electromagnetic field.Comment: 1 .zip file containing LaTex source plus three figures as .eps file
Phase transitions in the Interacting Boson Fermion Model: the gamma-unstable case
The phase transition around the critical point in the evolution from
spherical to deformed gamma-unstable shapes is investigated in odd nuclei
within the Interacting Boson Fermion Model. We consider the particular case of
an odd j=3/2 particle coupled to an even-even boson core that undergoes a
transition from spherical U(5) to gamma-unstable O(6) situation. The particular
choice of the j=3/2 orbital preserves in the odd case the condition of
gamma-instability of the system. As a consequence, energy spectrum and
electromagnetic transitions, in correspondence of the critical point, display
behaviours qualitatively similar to those of the even core. The results are
also in qualitative agreement with the recently proposed E(5/4) model, although
few differences are present, due to the different nature of the two schemes.Comment: In press in PRC as rapid communication. 7 pages, 4 figure
Degeneracies when only T=1 two-body interactions are present
In the nuclear f_7/2 shell, the nucleon-nucleon interaction can be
represented by the eight values E(J)=,
J=0,1,...,7, where for even J the isospin is 1, and for odd J it is 0. If we
set the T=0 (odd J) two-body matrix elements to 0 (or to a constant), we find
several degeneracies which we attempt to explain in this work. We also give
more detailed expressions than previously for the energies of the states in
question. New methods are used to explain degeneracies that are found in {45}Ti
(I=25/2- and 27/2-), {46}V (I=12^+_1 and 13^+_1, as well as I=13^+_2 and 15+),
and {47}V (I=29/2- and 31/2-).Comment: 21 pages; RevTeX4. We have filled in some holes, mainly including
more equations for the 44Ti Sectio
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