Abstract
A simple three-body oscillator cluster shell model is proposed as an approximation for wave functions of neutron-rich nuclei, having a (core+2n) structure. The model is applied to the $^{11}\mathrm{Li}$ nucleus. With a few free parameters the model reproduces the experimental rms matter radius of $^{11}\mathrm{Li}$, as well as the experimental transverse momentum distribution of the $^{9}\mathrm{Li}$ nucleus resulting from $^{11}\mathrm{Li}$ fragmentation on a carbon target at an energy of 790 MeV/nucleon. The transverse momentum distributions of the neutrons from this reaction have also been calculated without any additional parameters. All geometric parameters of the $^{11}\mathrm{Li}$ nucleus are also calculated within the framework of this three-body model.
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