We determine the energies of the excited states of a heavy-light meson Qq , with a static heavy quark and light quark with mass approximately that of the strange quark from both quenched lattices and with dynamical fermions. We are able to explore the energies of orbital excitations up to Lϭ3, the spin-orbit splitting up to Lϭ2 and the first radial excitation. These bs mesons will be very narrow if their mass is less than 5775 MeV-the BK threshold. We investigate this in detail and present evidence that the scalar meson (Lϭ1) will be very narrow and that altogether 6 bs excited states will have energies close to the BK threshold and all will be relatively narrow.

Deeply bound KNN, KNNN and KNNNN states are discussed. The effective force exerted by the K meson on the nucleons is calculated with static nucleons. Next the binding energies are obtained by solving the Schrödinger equation or by variational calculations.The dominant attraction comes from the S-wave Λ(1405) and an additional contribution is due to Σ(1385). The latter state is formed at the nuclear peripheries and absorbs a sizable piece of the binding energy. It also generates new branches of quasi-bound states. The lowest binding energies based on a phenomenological KN input fall into the 40-80 MeV range for KNN, 90-150 MeV for KNNN and 120-220 MeV for Kα systems. The uncertainties are due to unknown KN interactions in the distant subthreshold energy region.

Eta-deuteron scattering lengths are calculated. A summation of the multiple scattering series is carried out and the result is checked against more involved calculations. The necessity to go beyond the fixed nucleon approximation is emphasized. It is shown that a quasibound or virtual state in the η-deuteron system may occur within the range of η-nucleon scattering lengths suggested by other experiments.