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We study the exact solution for a two-mode model describing coherent couplingbetween atomic and molecular Bose-Einstein condensates (BEC), in the context ofthe Bethe ansatz. By combining an asymptotic and numerical analysis, weidentify the scaling behaviour of the model and determine the zero temperatureexpectation value for the coherence and average atomic occupation. Thethreshold coupling for production of the molecular BEC is identified as thepoint at which the energy gap is minimum. Our numerical results indicate aparity effect for the energy gap between ground and first excited statedepending on whether the total atomic number is odd or even. The numericalcalculations for the quantum dynamics reveals a smooth transition from theatomic to the molecular BEC.Comment: 5 pages, 4 figure

EXACT SOLUTION, SCALING BEHAVIOUR AND QUANTUM DYNAMICS OF A MODEL OF AN ATOM-MOLECULE BOSE–EINSTEIN CONDENSATE