Dirac sea effects in $K^+$ scattering from nuclei

Abstract

The ratio $R_T$ of $K^+-^{12}C$ to $K^+-d$ cross sections has been calculated
microscopically using a boson-exchange $KN$ amplitude in which the $\sigma$ and
$\omega$ mesons are dressed by the modifications of the Dirac sea in nuclear
matter. In spite of the fact that this dressing leads to a scaling of the
mesons effective mass in nuclear matter, the effect on the $R_T$ ratio is found
to be weak.

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arXiv:nucl-th/9306012v1 11 Jun 1993
Dirac sea effects in K+scattering
from nuclei
J.C. CAILLON and J. LABARSOUQUE
Laboratoire de Physique Th´ eorique†, Universit´ e Bordeaux I
rue du Solarium, 33175 Gradignan Cedex, France
Abstract
The ratio RTof K+−12C to K+−d cross sections has been calcu-
lated microscopically using a boson-exchange KN amplitude in which
the σ and ω mesons are dressed by the modifications of the Dirac sea
in nuclear matter. In spite of the fact that this dressing leads to a
scaling of the mesons effective mass in nuclear matter, the effect on
the RT ratio is found to be weak.

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LPTB-93-7
E-mail LABARS@FRCPN11
† Unit´ e associ´ ee au CNRS 764
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These last years, it has been shown that the in-nuclear-medium modifi-
cations of the NN excitations of the Dirac sea might be important in the
understanding of some phenomena like, for example, the quenching of the
Coulomb sum rule in electron-nucleus scattering[1, 2].
It has also been shown that these modifications lead to an increase of the
proton radius and to a decrease of the ω effective mass in nuclear matter[1],
both phenomena often invoked[3, 4, 5] to explain the discrepancies between
the conventional nuclear physics calculations and the experimental data in
K+-nucleus scattering.
The purpose of the present work was to investigate quantitatively in what
extent the K+-nucleus cross sections are sensitive to these modifications of
the Dirac sea.
We have analyzed these effects on the ratio RT of K+−12C to K+− d
total cross sections.
RT=σtot(K+−12C)
6 · σtot(K+− d)
(1)
As emphasized by many authors, this ratio is less sensitive to experimental
and theoretical uncertainties than, for example, differential cross sections,
and thus more transparent to the underlying physics. The ratio RThas been
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calculated from 400MeV/c to 900MeV/c.
In our calculation, we have used the same basic ingredients as in ref[5]: the
K+-nucleus optical potential has been built by folding the density-dependent
K+-nucleon t-matrix by the nuclear densities, these nuclear densities have
been deduced from electron scattering experiments, and the KN amplitude
has been calculated using the Bonn boson exchange model[6]. The K+-
nucleus total cross-section has been deduced from the forward K+-nucleus
elastic scattering amplitude using the optical theorem.
Since in isoscalar nuclear matter the main part of the KN interaction
comes from σ and ω exchange, we have considered only the dressing of these
two mesons, the remaining part beeing kept as in free space. Moreover, since
the K+-nucleus forward amplitude is dominated by forward (q ≃ 0) KN
scattering processes, the modification of the Dirac sea polarization will be
included at the one-loop approximation.
In nuclear matter, the NN excitations of the Dirac sea are modified by
the surrounding medium. The main effect of the nuclear medium on the
nucleon states is the modification of the Dirac spinor which takes the same
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form as in free space but with an effective mass:
M∗(ρ) = M + ΣS(ρ)(2)
where ΣS(ρ) is the scalar part of the nucleon self-energy at density ρ. Up
to now, this self-energy has not been unambiguously determined, but it is
commonly admitted as the most realistic that, at saturation, the effective
mass would be approximately 15% smaller than in free space[7]. Thus, we
have used here a density dependence in this way:
M∗(ρ) = M(1 − 0.15ρ
ρ0)(3)
and we have verified that smooth variations from this linear dependence don’t
change significantly the results.
Since the parameters of the KN interaction have been determined[6] in
order to reproduce the KN data in free space, the polarization of the Dirac
sea in free space has already been taken into account in the KN amplitude,
at least in average. Therefore, in nuclear matter, this free-space polarization
of the Dirac sea must be substracted from the in-medium one. Moreover,
in order to eliminate divergent terms, a renormalization procedure has to be
applied. It has been done as usual[1, 2, 8] by requiring that, in free space, the
three- and four-σ vertices vanish at zero momenta and the corrections to the
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