The radiation spectra in the CERN Large Hadron Collider (LHC) ranges from gigaelectronvolts down to thermal neutron levels. It is known that the thermal neutrons can significantly affect the electronic devices and systems exposed to the radiation environment of the tunnel and the shielded areas of the LHC. CERN's radiation monitoring (RadMon) system uses static random access memories (SRAMs) to measure the contributions to the spectrum from both the high-energy hadrons (>20 MeV) and thermal neutrons. The knowledge of the SRAM thermal neutron cross section is required for evaluating their contribution to the particle spectra and thus identifying the thermal neutron critical area. This paper describes a procedure to acquire, by means of RadMon system, the thermal neutron cross section of SRAM memories in a mixed-field environment. The capabilities of the CERN High AcceleRator Mixed-field facility (CHARM) to measure the thermal neutron sensitivity are then investigated. The procedure is evaluated by comparing the thermal neutron cross sections obtained at CHARM and the one measured using a pure thermal neutron beam. The same procedure could be applied to other devices to understand their susceptibility.