Fig. 1: J-spectra and energy levels of the ammonium isotopologues studied in this work.

a Zero-field NMR J-spectra of the mixture of [¹⁵N]- and [¹⁴N]-ammonium cations (¹⁵\({{{{{\rm{N}}}}}}{{{{{{\rm{H}}}}}}}_{4}^{+}\) and ¹⁴\({{{{{\rm{N}}}}}}{{{{{{\rm{H}}}}}}}_{4}^{+}\)) in aqueous solution of H₂SO₄ (2 M). The asterisk depicts the third harmonic of the 60 Hz power-line frequency. b, c Molecular diagram and nuclear spin energy-level structure of the [¹⁵N]-ammonium and [¹⁴N]-ammonium cation, respectively. Observable transitions correspond to spin flips in the manifolds conserving the total proton spin K_A = 0, 1, and 2. The main interaction in the system is heteronuclear J_NH-coupling (in the simulation, we used J_HH = 0 since it does not affect transition frequencies and, thus, does not manifest in spectra).