Three-body interactions in a homonuclear van der Waals bound trimer (the 1 (4)A(2)＇ state of Na-3) are studied spectroscopically for the first time using laser induced emission spectroscopy on a liquid helium nanodroplet coupled with ab initio calculations. The van der Waals bound, spin polarized sodium trimers are prepared via pickup by, and selective survival in, a beam of helium clusters. Laser excitation from the 1 (4)A(2)＇ to the 2 E-4＇ state, followed by dispersion of the fluorescence emission, allows for the resolution of the structure due to the vibrational levels of the lower state and for the gathering of precise information on the three-body interatomic potential. From previous experiments on Na-2 we know that the presence of the liquid helium perturbs the spectra by a very small amount [see J. Higgins , J. Phys. Chem. 102, 4952 (1998)]. Ab initio potential energy calculations are carried out at 42 geometries of the lowest quartet state using the coupled cluster method at the single, double, and noniterative triple excitations level [CCSD(T)]. The full potential energy surface is obtained from the ab initio points using an interpolation procedure based on a Reproducing Kernel Hilbert Space (RKHS) methodology. This surface is compared to a second, constructed using an analytical model function for both the two-body interaction and the nonadditivity correction. The latter is calculated as the difference between the CCSD(T) points and the sum of the two-body interactions. The bound vibrational states are calculated using the two potential energy surfaces and are compared to the experimentally determined levels. The calculated bound levels are combined with an intensity calculation of the nu(2)" mode of E＇ symmetry derived from a Jahn-Teller analysis of the excited electronic state. The calculated frequencies of nu(1)" and nu(2)" are found to be 37.1 cm(-1) and 44.7 cm(-1), respectively, using the RKHS potential surface while values of 37.1 cm(-1) and 40.8 cm(-1) are obtained from the analytical potential. These values are found to be in good to fair agreement with those obtained from the emission spectrum and to be significantly different from any values calculated from additive potential energy surfaces. The 1 (4)A(2)＇ Na-3 potential energy surface is characterized by a D-3h symmetry minimum of -850 cm(-1) (relative to the three 3 S-2 Na atom dissociation limit) with a bond distance of 4.406 Angstrom. This bond distance differs by about 0.8 Angstrom from the value of 5.2 Angstrom found for the sodium triplet dimer. This means that approximately 80% of the binding energy at the potential minimum is due to three-body effects. This strong nonadditivity is overwhelmingly due to the deformability of the valence electron density of the Na atoms which leads to a significant decrease of the exchange overlap energy in the trimer. (C) 2000 American Institute of Physics. [S0021-9606(00)01813-4].