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Nuclear-structure calculations for the description of low-energy neutral-current neutrino scattering off the stable Tl isotopes are performed in the context of the nuclear shell model using the model space jj56pn. Cross-section and event-rate calculations focusing on inelastic solar-neutrino scattering off Tl are performed. The individual contributions of the various nuclear responses are presented and discussed, and the results are also illustrated in terms of the nuclear recoil energy. Analytical expressions entering the cross sections are given in order to achieve a direct connection with experimental observables.

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