<P> The phenomenon of non-sequential ionization (NSI) of atoms exposed to intense laser fields has been a subject of many theoretical and experimental studies since 1983 . The pioneering work began with the observation of a "knee" structure on the Xe ion signal versus intensity curve by L'Huillier et al . From the experimental point of view, the NS double ionization refers to processes which somehow enhance the rate of production of doubly charged ions by a huge factor at intensities below the saturation intensity of the singly charged ion . Many, on the other hand, prefer to define the NSI as a process by which two electrons are ionized nearly simultaneously . This definition implies that apart from the sequential channel A + L −> A + + L −> A + + (\ displaystyle A + L -> A ^ (+) + L -> A ^ (+ +)) there is another channel A + L −> A + + (\ displaystyle A + L -> A ^ (+ +)) which is the main contribution to the production of doubly charged ions at lower intensities . The first observation of triple NSI in argon interacting with a 1 μm laser was reported by Augst et al. Later, systematically studying the NSI of all rare gas atoms, the quadruple NSI of Xe was observed . The most important conclusion of this study was the observation of the following relation between the rate of NSI to any charge state and the rate of tunnel ionization (predicted by the ADK formula) to the previous charge states; </P> <Dl> <Dd> W N S (A n +) = ∑ i = 1 n − 1 α n (λ) W A D K (A i +) (\ displaystyle W_ (NS) (A ^ (n+)) = \ sum _ (i = 1) ^ (n - 1) \ alpha _ (n) \ left (\ lambda \ right) W_ (ADK) \ left (A ^ (i+) \ right)) </Dd> </Dl> <Dd> W N S (A n +) = ∑ i = 1 n − 1 α n (λ) W A D K (A i +) (\ displaystyle W_ (NS) (A ^ (n+)) = \ sum _ (i = 1) ^ (n - 1) \ alpha _ (n) \ left (\ lambda \ right) W_ (ADK) \ left (A ^ (i+) \ right)) </Dd> <P> where W A D K (A i +) (\ displaystyle W_ (ADK) \ left (A ^ (i+) \ right)) is the rate of quasi-static tunneling to i'th charge state and α n (λ) (\ displaystyle \ alpha _ (n) (\ lambda)) are some constants depending on the wavelength of the laser (but not on the pulse duration). </P>

How does ionization energy demonstrate the shell model of electron structure