  The charge density wave (CDW) phase in 1$T$-TiSe$_2$ is investigated using
angle resolved photoemission spectroscopy (ARPES) and neutron scattering
measurements. Our ARPES results reveal a clear temperature dependence of the
chemical potential of the system. They also demonstrate specific changes
encountered by the Se 4$p$ valence and Ti 3$d$ conduction bands as the
temperature of the system is decreased through $T_{\text{CDW}}$. The valence
band undergoes a downward shift, whereas the conduction band remains
unaffected. The crystal structure in the CDW state shows a distinct split of
the Ti-Se atomic correlations that are reminiscent of Jahn-Teller distortions,
manifested in a breathing-type mode. The ARPES data together with the local
structure analysis support a direct link between Jahn-Teller-like distortions
and the CDW order in 1$T$-TiSe$_2$.
