  CeRhSi$_{3}$ is a superconductor under pressure coexisting with a weakly
antiferromagnetic phase characterized by a Bragg peak at $\vec{q}_{0}$=($\sim$
0.2, 0, 0.5) (N. Aso et al. J. Magn. Magn. Mater. 310, 602 (2007)). The
compound is also a heavy fermion material with a large specific heat
coefficient $\gamma$=110 mJ $\cdot$ mol$^{-1}$ $\cdot$ K$^{-2}$ and a high
Kondo temperature of $T_{K}$=50 K indicative that CeRhSi$_{3}$ is in a strongly
Kondo screened state. We apply high resolution neutron spectroscopy to
investigate the magnetic fluctuations in the normal phase, at ambient
pressures, and at low temperatures. We measure a commensurate dynamic response
centered around the $\vec{Q}$=(0, 0, 2) position that gradually evolves to
H$\sim$ 0.2 with decreasing temperature and/or energy transfers. The response
is broadened both in momentum and energy and not reminiscent of sharp spin wave
excitations found in insulating magnets where the electrons are localized. We
parameterize the excitation spectrum and temperature dependence using a
heuristic model utilizing the random phase approximation to couple relaxing
Ce$^{3+}$ ground state Kramers doublets with a Kondo-like dynamic response.
With a Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction within the
$ab$ plane and an increasing single site susceptibility, we can qualitatively
reproduce the neutron spectroscopic results in CeRhSi$_{3}$ and namely the
trade-off between scattering at commensurate and incommensurate positions. We
suggest that the antiferromagnetic phase in CeRhSi$_{3}$ is driven by weakly
correlated relaxing localized Kramers doublets and that CeRhSi$_{3}$ at ambient
pressures is on the border between a Rudderman-Kittel-Yosida antiferromagnetic
state and a Kondo screened phase where static magnetism is predominately
absent.
