  The results of experimental studies of the low-energy isomeric state in the
$^{229}$Th nucleus are presented. The work is consisted of several stages.
During the first stage $^{229}$Th nuclei were excited with the inverse internal
conversion to the low-lying isomeric level in plasma that was formed by laser
pulse at the $^{229}$Th-containing target surface. Then thorium ions having
excited nuclei were extracted from the plasma by an external electrical field
and implanted into thin SiO$_2$ film grown on a silicon substrate (that is a
dielectric material with about 9 eV band-gap). Gamma decay of isomeric nuclei
was registered during the second stage by the general methods of the electron
spectroscopy after the photon-electron emission from the silicon substrate.
Substitution of the photon registration with the electron one allowed us to
increase the desired signal by several orders of magnitude and detect the
$^{229}$Th nuclei decay. During the third stage the electron spectra from
standard Xe VUV source was obtained that allowed determining the energy of
photons. In order to prove that the detected signal is caused by isomeric
$^{229}$Th nuclei decay a series of experiments was carried. The analysis of
electron spectra gives the following results: the energy of the nuclear
transition is $E_{\text{is}}=7.1(^{+0.1}_{-0.2})$~eV, the half-life of the
isomeric level in bare nucleus in vacuum is $T_{1/2}=1880\pm170$~s, the reduced
probability of the isomeric nuclear transition is
$B_{\text{W.u.}}(M1;3/2^+\rightarrow 5/2^+)=(3.3\pm0.3)\times10^{-2}$.
