Search for resonances in the three-and four-neutron systems in the $^7$Li($^7$Li,$^{11}$C)$3n$ and $^7$Li($^7$Li,$^{10}$C)$4n$ reactions

The spectra of the $^{11}$C and $^{10}$C nuclei from the $^7$Li($^7$Li,$^{11}$C)$3n$ and $^7$Li($^7$Li,$^{10}$C)$4n$ reactions, respectively, have been measured at a $^7$Li energy of $82$ MeV and an angle of $2^\circ$ up to excitation energies of $20$–$30$ MeV of the desired multineutrons. The experiments were carried out with a magnetic separator, which made it possible to significantly increase the intensity of a beam by removing scattered particles and to carry out small-angle measurements. The energy spectra are well described by four-and five-particle phase spaces. No evidence has been found for the existence of nuclear stable and resonance states (with $\Gamma<3$ MeV) of multineutrons. The upper limits have been obtained for the cross sections for the formation of nuclear stable states of $3n$ (1.4 nb/sr) and $4n$ (0.1 nb/sr) in the center-of-mass system.