RPA calculation of $K^+$-nucleus cross-sections with a density-dependent Brueckner-Hartree-Fock NN interaction
ABSTRACT In the calculation of the $K^+$-nucleus cross sections, the coupling of the mesons exchanged between the $K^+$ and the target nucleons to the polarization of the Fermi and Dirac seas has been taken into account. This polarization has been calculated in the one-loop approximation but summed up to all orders (RPA approximation). For this calculation a density-dependent Brueckner-Hartree-Fock NN interaction providing a good description of both nuclear matter and finite nuclei has been used. The agreement with experiment is considerably improved. Comment: 7 pages, LaTeX, 1 figure available upon request, preprint CENBG-94-th1
arXiv:nucl-th/9406024v1 21 Jun 1994
RPA calculation of K+-nucleus
cross-sections with a density-dependent
Brueckner-Hartree-Fock NN interaction
J.C. CAILLON and J. LABARSOUQUE
Centre d’Etudes Nucl´ eaires de Bordeaux-Gradignan†
Universit´ e Bordeaux I
rue du Solarium, 33175 Gradignan Cedex, France
In the calculation of the K+-nucleus cross sections, the coupling of the
mesons exchanged between the K+and the target nucleons to the polariza-
tion of the Fermi and Dirac seas has been taken into account. This polariza-
tion has been calculated in the one-loop approximation but summed up to
all orders (RPA approximation). For this calculation a density-dependent
Brueckner-Hartree-Fock NN interaction providing a good description of
both nuclear matter and finite nuclei has been used. The agreement with
experiment is considerably improved.
PACS numbers: 25.80.Nv, 21.30.+y, 21.60.Jz, 24.10.Jv
† UMR CNRS 6426
These last years, significant progress have been made towards a better un-
derstanding of the properties of both nuclear matter and finite nuclei starting
from a free-space nucleon-nucleon interaction. Using a relativistic Brueckner-
Hartree-Fock theory with a one-boson-exchange potential where coupling con-
stants and form factors were obtained from the NN scattering data, Brockmann
and Machleidt reproduced the saturation properties of nuclear matter nearly
quantitatively. The scalar and vector fields they obtained have then been in-
troduced as input in a relativistic density-dependent Hartree approach for finite
nuclei by Brockmann and Toki who obtained a good agreement with experi-
ment for both the binding energy and the mean-square radius in16O and40Ca.
This result solves an old outstanding problem of nuclear physics.
Another longstanding problem is the continuing discrepancy between exper-
imental results and theoretical predictions for K+-nucleus total cross-sections.
Since the K+interact very weakly (at the hadronic scale) with nucleons, they
reach the dense central regions of nuclei and thus should be sensitive to the in-
medium modifications of the nucleons and mesons.
Different types of such medium effects have been studied. Historically, the
first one has been the swelling of the nucleons in nuclear matter. This possible
swelling has then been related to a decreasing of the mesons effective mass in
the cloud around the nucleon core. This scaling of the mesons mass with density
leads to improved K+-nucleus cross sections[5, 6]. Let us mention that an im-
provement has also been obtained, but to a lesser extent, taking into account the
decreasing of the nucleon effective mass by the scalar nuclear field in the target,
decreasing which modifies the KN amplitude in the medium.
The second type of medium effects which has been considered is the possibility
for the K+to scatter on the mesons exchanged between the target nucleons[8, 9].
Although these calculations seem not completely under control since the ex-
changed mesons are well off-shell, they seem to lead also to a small improvement.
About these medium effects, the most important arises from the modification
of the properties of the mesons exchanged between the K+and the target nu-
cleons. Since they are well off-mass-shell, it is not sufficient to consider that the
only modification in their propagation is the change of their effective mass. For
example, since they are space-like, they can produce particle-hole excitations, and
thus acquire also a width. To go beyond this effective mass approximation, we
can consider that, at the hadronic level, this modification of the mesons propaga-
tion in nuclear matter arises from the coupling of these mesons with particle-hole
and nucleon-antinucleon excitations. Since the interaction is strong, this coupling
must be summed up to all orders and thus the choice of the NN interaction which
will be used is very important if we want the final result might have a chance to
be realistic. The question arises if the relativistic Brueckner-Hartree-Fock inter-
action we spoke about, which reproduces the properties of nuclear matter and
finite nuclei, could also give a good description of the polarization of nuclear
matter (at least in the region of small energy-momentum transfer) and thus lead
to improved K+-nucleus cross-sections.
In this work, we have calculated the K+-nucleus cross-sections using a KN
amplitude in which the mesons exchanged are coupled to the polarization of the
medium in the RPA approximation. This polarization has been obtained us-
ing the relativistic Brueckner-Hartree-Fock NN interaction of Brockmann and
We have analyzed these effects on the ratio RT of K+−12C to K+− d total
cross sections which has been measured[11, 12, 13] from 400MeV/c to 900MeV/c.
6 · σtot(K+− d)
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 total K+-nucleus cross section has been obtained from the forward scat-
tering amplitude using the optical theorem. The optical potential we used to
calculate the K+-nucleus amplitude has been built by folding the in-medium
KN amplitude by the nuclear density. The point-like proton distribution of the
12C nucleus required in the present analysis is that deduced, after the proton
finite-size correction has been made, from the electron-scattering charge density
of Sick and McCarthy and we have chosen equal n and p-distributions. For
the K+-nucleon amplitude in free space, we have used here the full Bonn boson
exchange model which is actually one of the more elaborate descriptions of