Direct measurements of solar energetic particles (SEP) cover the space era of several decades, but indirectly they can be studied for thousands and millions of years backward using cosmogenic nuclides in lunar rocks and soil. With a proper nuclide production model, it is possible to estimate the mean energy spectrum of SEP, as well as of
galactic cosmic rays (GCR) from a depth profile of the measured nuclide content.

Here we used aluminium-26 (lifetime 1.03 Myr) measurements in Apollo-mission lunar samples. Previous estimates of the SEP spectrum from lunar data were based on the assumed specific shape and only provided reconstructed spectral parameters. We report a different approach to use a lunar rock as an integral spectrometer within 20--80 MeV. With that, one can reconstruct the particle spectrum directly without any a-priori assumptions on its exact shape.

For each studied lunar sample, we have developed an accurate Geant4 odel. We estimated the average GCR spectrum over the last million years (the modulation potential 496$\pm$40 MV), which is consistent with that for the Holocene (449$\pm$70 MV), but significantly lower than that for the modern epoch (660$\pm$20 MV). We also made a true reconstruction of the mean SEP spectrum over the last million years. The integral flux $>$30 MeV was estimated as 37.4 particles/(cm$^2$ s), which is consistent with that for the modern epoch. The estimated occurrence probability of SEP events shows no expected events with fluence $>$30 MeV over $5\times10^{10}$ and $1\times10^{11}$ particles/cm$^2$ on millennial and Mega-year time scales, respectively.