Abstract. The neutron emission of the β-decay of 74,76,78,80 Ni are studied within the quasiparticle random phase approximation with the Skyrme interaction. The coupling between one-and two-phonon terms in the wave functions of the low-energy 1 + states of the daughter nuclei is taken into account. It is shown that the strength decrease of the neutronproton tensor interaction leads to the increase of the half-life and the neutron-emission probability.Study of the β-decay properties of the nuclei near the doubly magic isotope 78 Ni plays the crucial role in the modeling of the astrophysical r-process [1]. The multi-neutron emission is a multistep process consisting of the β-decay of the parent nucleus (N, Z) which results in feeding the excited states of the daughter nucleus (N -1, Z + 1) followed by the multi-neutron emissions to the ground state or γ-deexcitation to the ground state of the product nucleus (N -1 -X, Z + 1) [2]. The microscopic study of the β-decay half-lives and the β-delayed neutron-emission probabilities of the nuclei with high N/Z ratio asymmetry makes it possible to reconstruct the β-strength function [2,3]. Taking into account the tensor interaction has a substantial effect on the Gamow-Teller (GT) transitions within the β-decay window [4]. A redistribution of the GT strength has been found due to the impact of the tensor correlations and 2p-2h fragmentation of the GT transitions [5].One of the successful tools for studying charge-exchange nuclear modes is the quasiparticle random phase approximation (QRPA) with the self-consistent mean-field derived from a Skyrme energydensity functional (EDF), see e.g., [6][7][8][9]. These QRPA calculations enable one to describe the properties of the ground state and excited charge-exchange states using the same EDF. As proposed in Ref.[10], the study of the multineutron emission, following the β-decay, requires taken into account the phonon-phonon coupling (PPC). The finite rank separable approximation (FRSA) [11][12][13] for the residual interaction allows one to perform the calculations in large configurational spaces.In this paper, we investigate the impact of the tensor correlations on the probability of the neutron emission. As the parameter set in the particle-hole channel, we use the Skyrme EDFs TIJ [14], which take into account the tensor terms. Indices I and J refer to the proton-neutron (β) and like-particle (α) coupling constants that define the contribution to the spin-orbit potential from the J 2 terms: