Bound states of the two-roton Schrodinger equation

Bound states of two rotons are sought by explicit numerical integration of a Schrodinger equation, based on an interaction hamiltonian of dipole-dipole form and self-hamiltonians derived from the modified Landau dispersion relationship. It is found that the most tightly bound state of zero total momentum belongs to the angular momentum quantum number l=3. The binding energy is about 0.43K, and the root mean square separation of the rotons is almost 12 AA. Bound states for other values of l are located. In particular, the greatest binding energy of the l=2 bound state is about 0.29K, in satisfactory agreement with the experimentally determined value of (0.37+or-0.10)K with a root mean square roton separation of just over 14 AA. The largest effective masses of these l=2 and l=3 states are respectively about 2.1 and 2.8 times the mass of the helium atom.