  Background: The existence of a tetraneutron comprising four neutrons has long
been debated.
  Purpose: Motivated by a recent observation of particle-stable tetraneutrons,
we investigated potential particle-stable tetraneutron emission in thermal
neutron-induced $^{235}$U fission using a nuclear research reactor.
  Methods: We performed $\gamma$-ray spectroscopy for a $^{88}$SrCO$_3$ sample
irradiated in a reactor core. Stable $^{88}$Sr was expected to produce
$^{91}$Sr by a tetraneutron-induced ($^4n$,n) reaction; hence, observation of
$\gamma$-rays followed by $\beta$ decay of $^{91}$Sr would indicate
particle-stable tetraneutron emission.
  Results: The $\gamma$-ray spectrum of an irradiated $^{88}$SrCO$_3$ sample
did not show any photopeak for $^{91}$Sr.
  Conclusion: The emission rate of particle-stable tetraneutrons, if they
exist, is estimated to be lower than $8\times 10^{-7}$ per fission at the 95%
confidence level, assuming the cross-sections of reactions induced by
hypothetical particle-stable tetraneutrons.
