Context. Cosmic rays (CRs), which are energetic particles mainly composed of protons and electrons, play an important role in the chemistry and dynamics of the interstellar medium. In dense environments, they represent the main ionising agent, hence driving the rich chemistry of molecular ions. Furthermore, they determine the ionisation fraction, which regulates the degree of coupling between the gas and the interstellar magnetic fields, and the heating of the gas. Estimates of the CR ionisation rate of molecular hydrogen (ζ₂) span several orders of magnitude, depending on the targeted sources and on the method used. Aims. Recent theoretical models have characterised the CR attenuation with increasing density. We aim to test these models for the attenuation of CRs in the low-mass pre-stellar core L1544. Methods. We used a state-of-the-art gas-grain chemical model, which accepts the CR ionisation rate profile as input, to predict the abundance profiles of four ions: N₂H⁺, N₂D⁺, HC¹⁸O⁺, and DCO⁺. Non-local thermodynamic equilibrium radiative transfer simulations were run to produce synthetic spectra based on the derived abundances. These were compared with observations obtained with the Institut de Radioastronomie Millimétrique 30 m telescope. Results. Our results indicate that a model with high ζ₂ (>10⁻¹⁶ s⁻¹) is excluded by the observations. Also the model with the standard ζ₂ = 1.3 × 10⁻¹⁷ s⁻¹ produces a worse agreement with respect to the attenuation model based on Voyager observations, which is characterised by an average ⟨ ζ₂ ⟩ = 3 × 10⁻¹⁷ s⁻¹ at the column densities typical of L1544. The single-dish data, however, are not sensitive to the attenuation of the CR profile, which changes only by a factor of two in the range of column densities spanned by the core model (N = 2−50 × 10²¹ cm⁻²). Interferometric observations at higher spatial resolution, combined with observations of transitions with lower critical density – hence tracing the low-density envelope – are needed to observe a decrease in the CR ionisation rate with density.

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