A model for an artificial hydrogen molecule consisting of two positive on-axis Coulombic centers and two electrons coupled to them inside a double concentric quantum ring is considered. Such a nanostructure is assumed to be under the influence of external probes like hydrostatic pressure and magnetic field. By using the adiabatic approximation, the ground state energy is calculated as a function of the outer center line radius and the impurity Coulombic center separation, for different values of the hydrostatic pressure and magnetic field strength. In contrast to the single properties imposed by nature on the actual hydrogen molecule, our model allows us to explore a great variety of properties of the artificial hydrogen molecule by changing the ring dimensions. The artificial hydrogen molecule energy structure may be tuned by changing the external field strengths.
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