"Low-energy alpha particle and proton heavy charged particle (HCP) relative thermoluminescence (TL) efficiencies are calculated for the major dosimetric glow peak in LiF:Mg,Cu,P (MCP-N) in the framework of track structure theory (TST). The calculations employ previously published TRIPOS-E Monte Carlo track segment values of the radial dose in condensed phase LiF calculated at the Instituto National de Investigaciones Nucleares (Mexico) and experimentally measured normalised Co-60 gamma-induced TL doseresponse functions, f(D), carried out at the Institute of Nuclear Physics (Poland). The motivation for the calculations is to test the validity of TST in a TL system in which f(D) is not supralinear (f(D) 1) and is not significantly dependent on photon energy contrary to the behaviour of the doseresponse of composite peak 5 in the glow curve of LiF:Mg,Ti (TLD-100). The calculated HCP relative efficiencies in LiF:MCP-N are 2387 lower than the experimentally measured values, indicating a weakness in the major premise of TST which exclusively relates HCP effects to the radiation action of the secondary electrons liberated by the HCP slowing down. However, an analysis of the uncertainties involved in the TST calculations and experiments (i.e. experimental measurement of f(D) at high levels of dose, sample light self-absorption and accuracy in the estimation of D(r), especially towards the end of the HCP track) indicate that these may be too large to enable a definite conclusion. More accurate estimation of sample light self-absorption, improved measurements of f(D) and full-track Monte Carlo calculations of D(r) incorporating improvements of the low-energy electron transport are indicated in order to reduce uncertainties and enable a final conclusion."