Structure of $^{83}$As, $^{85}$As and $^{87}$As: from semi-magicity to $\gamma$-softness

The structure of $^{83}$As, $^{85}$As and $^{87}$As have been studied in fusion-fission reaction $^{238}$U+$^9$Be. Fission fragments were identified in mass and atomic number using the VAMOS++ spectrometer and the coincident $\gamma$-rays were detected in the $\gamma$-ray tracking array AGATA. New transitions in $^{83}$As and $^{85}$As are reported and placed in the level schemes. A level scheme of the excited states in $^{87}$As is proposed for the first time. The data are interpreted in frame of Large-Scale Shell-Model calculations, SU3 symmetries and Beyond Mean-Field frameworks. A spherical regime at magic number $N$=50 is predicted and the location of the proton $g_{9/2}$ orbital is proposed for the first time. Development of collectivity in a prolate deformed, $\gamma$-soft regime in the open shell cases $^{85}$As and $^{87}$As, most neutron-rich isotopes beyond $N$=50, is concluded. Data and theoretical calculations give confidence to a relatively high extrapolated excitation energy about 4 MeV of the $9/2^+$ state in $^{79}$Cu, one proton above $^{78}$Ni.