# 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

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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

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 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.

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PACS numbers: 25.80.Nv, 21.30.+y, 21.60.Jz, 24.10.Jv

E-mail LABARS@FRCPN11.IN2P3.FR

† UMR CNRS 6426

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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[1] 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[2] 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[3], 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[4]. 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

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decreasing of the nucleon effective mass by the scalar nuclear field in the target,

decreasing which modifies the KN amplitude in the medium[7].

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[10], they seem to lead also to a small improvement[9].

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.

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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

Machleidt[1].

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.

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 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[14] 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[15] which is actually one of the more elaborate descriptions of

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