banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Dimensional scaling treatment with relativistic corrections for stable multiply charged atomic ions in high-frequency super-intense laser fields
Rent this article for


Image of FIG. 1.
FIG. 1.

Non-relativistic effective potential for a 1D particle in a box under different laser intensity, measured by α0.

Image of FIG. 2.
FIG. 2.

Relativistic corrections to the effective potential for different laser fields.

Image of FIG. 3.
FIG. 3.

Effective potential for two alternating electric fields superposed along and , respectively, with different colors.

Image of FIG. 4.
FIG. 4.

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.

Image of FIG. 5.
FIG. 5.

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.

Image of FIG. 6.
FIG. 6.

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.

Image of FIG. 7.
FIG. 7.

Top: Probability distribution for H, a two electron system. Bottom: Probability distribution for He, a three electron system.

Image of FIG. 8.
FIG. 8.

The above displays the relationship between the system's geometry with respect to the electrons and the coordinates use in Eq. (40).

Image of FIG. 9.
FIG. 9.

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.

Image of FIG. 10.
FIG. 10.

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 .

Image of FIG. 11.
FIG. 11.

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.

Image of FIG. 12.
FIG. 12.

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.

Image of FIG. 13.
FIG. 13.

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.

Image of FIG. 14.
FIG. 14.

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.


Generic image for table
Table I.

Results of Mulliken population analysis, note that there are four outer orbitals the table contains one of the four values.

Generic image for table
Table II.

Differences present when relativistic considerations are undertaken for these multiply charged ions. The non-relativistic values were taken from Ref. 14.


Article metrics loading...


Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Dimensional scaling treatment with relativistic corrections for stable multiply charged atomic ions in high-frequency super-intense laser fields