A new empirical formula has been developed that describes the $({γ}, n)$ nuclear reaction cross sections for the isotopes with $Z ≥ 60$. The results were supported by calculations using TALYS - 1.6, EMPIRE - 3.2.2 nuclear modular codes. The energy region for incident photon energy have been selected near to the giant dipole resonance (GDR) peak energy. The evaluated empirical data were compared with available data in the experimental data library - EXFOR. The data produced using TALYS - 1.6 and EMPIRE - 3.2.2 were in good agreement with experimental data. We have tested and presented the reproducibility of the present new empirical formula. We observed the reproducibility of the new empirical formula near to GDR peak energy is in good agreement with the experimental data and remarkable dependency on key nuclei properties: the neutron, proton and atomic number of the nuclei. The behavior of nucleus near GDR peak energy, and dependency of GDR peak on the isotopic nature were predicted. An effort has been made to explain the deformation of the GDR peak in $({γ}, n)$ nuclear reaction cross section for some isotopes, which could not reproduce with TALYS - 1.6 and EMPIRE - 3.2.2. The evaluated data have been presented for the isotopes 180W, 183W, 202Pb, 203Pb, 204Pb, 205Pb, 231Pa, 232U, 237U and 239Pu that have no previous measurements. ; Comment: Accepted to be published in Chinese Physics C, 24 pages, 13 figures