  Whether it is for shielding applications or for safety criticality studies,
numerically solving the neutron transport equation with a good accuracy
requires to precisely estimate the Doppler broadened elastic scattering kernel
in the thermal and epithermal energy range of neutrons travelling in a free
gas. In Geant4, low energy neutrons are transported using evaluated data
libraries handled by the Neutron High-Precision (Neutron-HP) package. Version
11.00.p03 of the code features in particular the Doppler broadened elastic
scattering kernel, provided by the so-called 'Sampling of the Velocity of the
Target' (SVT) method. However this latter fails for resonant heavy nuclei such
as 238U and can severely impact the solving of the Boltzmann equation in
fissile media. To overcome this shortcoming, the Doppler Broadened Rejection
Correction (DBRC) method has been implemented in Geant4 and successfully
validated with the reference Monte Carlo neutron transport code Tripoli4
(version 11). This development will be taken into account in the next release
of the code. The cross section Doppler broadening process, which is performed
on-the-fly, is also carefully investigated and ways to improve it on a
simulation-by-simulation basis are presented. All the validations have been
performed with an automated benchmark tool which has been designed to support
the quality assurance of the Geant4 Neutron-HP package. This tool is currently
available on an ad hoc Gitlab repository and will be included in Geant4.
