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In the paper, the results of analysis of elastic scattering and breakupprocesses in interactions of the $^{11}$Li nucleus with protons are presented.The hybrid model of the microscopic optical potential (OP) is applied. This OPincludes the single-folding real part, while its imaginary part is derivedwithin the high-energy approximation (HEA) theory. For the $^{11}$Li$+p$elastic scattering, the microscopic large-scale shell model (LSSM) density of$^{11}$Li is used. The depths of the real and imaginary parts of OP are fittedto the elastic scattering data at 62, 68.4, and 75 MeV/nucleon, beingsimultaneously adjusted to reproduce the true energy dependence of thecorresponding volume integrals. The role of the spin-orbit potential is studiedand predictions for the total reaction cross sections are made. Also, thecluster model, in which $^{11}$Li consists of $2n$-halo and the $^{9}$Li corehaving its own LSSM form of density, is adopted. The respective microscopicproton-cluster OP's are calculated and folded with the density probability ofthe relative motion of both clusters to get the whole $^{11}$Li$+p$ opticalpotential. The breakup cross sections of $^{11}$Li at 62 MeV/nucleon andmomentum distributions of the cluster fragments are calculated. An analysis ofthe single-particle density of $^{11}$Li within the same cluster modelaccounting for the possible geometric forms of the halo-cluster densitydistribution is performed.

Microscopic analysis of $^{11}$Li elastic scattering on protons and breakup processes within $^{9}$Li+$2n$ cluster model