  In the mean-field approximation, the well-known effect of the critical
quantum collapse in a 3D gas of particles pulled to the center by potential
U(r) = -U_0/r^2 is suppressed by repulsive interparticle interactions, which
create the otherwise non-existing s-wave ground state. Here, we address excited
bound states carrying angular momentum, with the orbital and magnetic quantum
numbers, l and m. They exist above a threshold value of the potential's
strength, U_0 > l(l+1). The sectoral, tesseral, and zonal modes, which
correspond to m = l, 0 < m < l, and m = 0, respectively, are found in an
approximate analytical form for relatively small values of U_0 - l(l+1).
Explicit results are produced for the p- and d-wave states, with l = 1 and 2,
respectively. In the general form, the bound states are obtained numerically,
confirming the accuracy of the analytical approximation.
