Non-relativistic effective potential for a 1D particle in a box under different laser intensity, measured by α0.
Relativistic corrections to the effective potential for different laser fields.
Effective potential for two alternating electric fields superposed along and , respectively, with different colors.
Contour plots of dressed potential for (clockwise) α0 = 0, 25, 100, 50. Note both the shift in regime as α0 grows and the key below the plots for the interpretation of the intensity of the contours.
Three dimensional plots of the potential energy, , as a function of x and z coordinates for the case α0 = 100. Left and right of above are two different angles of the same surface.
Plots of both molecular energies and binding energy for (clockwise): with non-relativistic trajectory; , relativistic trajectory; , relativistic trajectory; and with non-relativistic trajectory. All may be read as yellow: Binding energy; blue: Hydrogen energy; purple: H− energy.
Top: Probability distribution for H−, a two electron system. Bottom: Probability distribution for He−, a three electron system.
The above displays the relationship between the system's geometry with respect to the electrons and the coordinates use in Eq. (40).
Above are plots of the binding energies of, from left to right and top to bottom: H−, H−2, He−, He−2, and He−3.
Plots of binding energy comparisons for (clockwise): comparison plot of versus , non-relativistic trajectory; with relativistic trajectory m0 and m r , differences value of Hydrogen energy between use of m0 and m r ; and a comparison of relativistic trajectory (both m0 and m r ) with non-relativistic trajectory both using .
Plots of binding energy for the H− (left) and He− (right) systems. Top, Non-normalized plots of the calculation data showing agreement between the methods. Bottom, -B.E./B.E. max to emphasis the qualitative similarity between the methods as they share minima for the B.E. curves.
Top row: Plots of the probabiltiy distribution for the corrected (left) and non-corrected (right) H− system, directly below is a superimposition of the trajectory upon the probability density function plot to emphasis their relation. Bottom row: Contour plots of the H− system, both corrected (left) and non-corrected (right), note the different scales on the vertical (z) axis and the more diffuse behavior of the corrected system.
The electronic elliptical contribution can be seen as the function whose major axis lies in the z-direction (vertical) and the magnetic contribution has an orthogonal orientation.
Within the above plot, the total trajectory can be seen, the amplitude of the major and minor axes are mediated in value between those from the electronic and magnetic components and the orientation is set off by an angle whose value respects the same coefficients as the relative amplitudes.
Results of Mulliken population analysis, note that there are four outer orbitals the table contains one of the four values.
Differences present when relativistic considerations are undertaken for these multiply charged ions. The non-relativistic values were taken from Ref. 14.
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