Application of parametric equations of motion to study the resonance coalescence in $\text{H}_{2}^{+}$H2+

Abstract

Recently, occurrence of coalescence point was reported in H(2)(+) undergoing multiphoton dissociation in strong laser field. We have applied parametric equations of motion and smooth exterior scaling method to study the coalescence phenomenon of H(2)(+). The advantage of this method is that one can easily trace the different states that are changing as the field parameters change. It was reported earlier that in the parameter space, only two bound states coalesce [R. Lefebvre, O. Atabek, M. Sindelka, and N. Moiseyev, Phys. Rev. Lett. 103, 123003 (2009)]. However, it is found that increasing the accuracy of the calculation leads to the coalescence between resonance states originating from the bound and the continuum states. We have also reported many other coalescence points.

Use of the dilated electron propagator in conjunction with the modified smooth exterior scaling method to characterize 2S Be+ (1s−1), 2S Ne+ (1s−1) Auger and 2P Be− shape resonances

“…The value of g(x) is varied from 0 to 1 around the point x = x 0 . 9 A method called modified smooth exterior scaling (MSES) [25][26][27] is developed by modifying the scaling path of the SES method. In MSES, the scaling path F(x) is defined as…”

“…The value of g ( x ) is varied from 0 to 1 around the point x = x 0 . 9 A method called modified smooth exterior scaling (MSES) 25–27 is developed by modifying the scaling path of the SES method. In MSES, the scaling path F ( x ) is defined as F ( x ) = x e iθ ( x ) = x e iθ 0 a ( x ) where θ ( x ) goes smoothly from 0 to θ 0 and the value of a ( x ) varies from 0 to 1 around the point x = x 0 .…”

An Innovative Approach for Precise Identification of the Lowest Unoccupied Molecular Orbital Using the Parametric Equation of Motion

“…Further, Gupta et al applied PEM to obtain the 3D plots of population dynamics as a function of frequency and phase (or amplitude and phase) and to study the laser-induced multiphoton dissociation dynamics of H 2 + as a function of the laser field amplitude and frequency . The PEM method in conjunction with modified smooth exterior scaling method was also used to study the resonance coalescence in H 2 + …”

Particular spectral singularity in the continuum energies: a manifestation as resonances

“…In recent years the development and progress of quantum physics with non-Hermitian operators has given rise to important accomplishments in different fields [1][2][3][4][5][6][7][8][9], and in particular in the study of the physics of exceptional points [2,7,[10][11][12][13] and spectral singularities [14][15][16][17][18][19]. Many theoretical [11,[20][21][22][23][24][25][26][27][28][29][30][31][32][33] and experimental [34][35][36][37][38][39][40][41] works are related to exceptional points produced by an accidental degeneracy of resonant states. Exceptional points in the real and continuous spectrum of a Hamiltonian of infinite dimension [42][43][44] have received much less attention than the case o...…”