Adiabatic approximation in few-body molecular and nuclear systems

Abstract

In this work we critically reexamine an approximation method, called the adiabatic approximation (AA), based more on a mathematical foundation than on a phenomenological physical basis. We extend it to many-body systems and investigate the application of AA to simple molecular and nuclear systems in order to extract insights into the criterion of validity of this approximation method. The validity criterion is in part established by introducing a meaningful dimensionless parameter that indicates the ``goodness'' of AA. We also analyze the Born-Oppenheimer approximation and see if a correlation can be established between the two approximation schemes.