The aim of this paper is the spectroscopic study of 13 galaxies belonging to the field of the protocluster associated with the radio galaxy (RG) 7C 1756+6520 at z = 1.4156. In particular, we focus on the characterization of the nuclear activity. This analysis has been performed on rest-frame optical spectra taken with LBT-LUCI. The spectral coverage allowed us to observe emission lines such as Halpha, Hbeta, [Oiii]5007 A, and [Nii]6583 A at the z of the central RG. We observed the central part of the protocluster, which is suitable to include the radio galaxy, several spectroscopically confirmed AGN belonging to the protocluster, and other objects that might be members of the protocluster. For four previously identified protocluster members, we derived the redshift by detecting emission lines that have never detected before for these galaxies. The stacked spectrum of the galaxies in which we detected the [Oiii]5007 A emission line revealed the presence of the second line of the [Oiii] doublet at 4959 A and of Hbeta, which confirms that they belong to the protocluster. By collecting all members identified so far in this work and other members from the literature, we defined 31 galaxies, including the central RG, around z = 1.4152 +/- 0.056, corresponding to peculiar velocities <~5000 km/s with respect to the RG. The PV phase-space diagram suggests that 3 protocluster AGN and the central RG might be a virialized population that has been coexisting for a long time in the densest core region of this forming structure. This protocluster is characterized by a high fraction of AGN (23%). For one of them, AGN1317, we produced 2 BPT diagrams. The high fraction of AGN and their distribution within the protocluster seem to be consistent with predictions of some theoretical models on AGN growth and feedback.
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