Resonant spectra of quadrupolar anions

Abstract

In quadrupole-bound anions, an extra electron is attached at a sufficiently large quadrupole moment of a neutral molecule, which is lacking a permanent dipole moment. The nature of the bound states and low-lying resonances of such anions is of interest for understanding the threshold behavior of open quantum systems in general. In this work, we investigate the properties of quadrupolar anions as extreme halo systems, the formation of rotational bands, and the transition from a subcritical to supercritical electric quadrupole moment. We solve the electron-plus-molecule problem using a non-adiabatic coupled-channel formalism by employing the Berggren ensemble, which explicitly contains bound states, narrow resonances, and the scattering continuum. We demonstrate that binding energies and radii of quadrupolar anions strictly follow the scaling laws for two-body halo systems. Contrary to the case of dipolar anions, ground-state band of quadrupolar anions smoothly extend into the continuum, and many rotational bands could be identified above the detachment threshold. We study the evolution of a bound state of an anion as to dives into the continuum at a critical quadrupole moment and we show that the associated critical exponent is consistent with the second-order phase transition. Everything considered, quadrupolar anions represent a perfect laboratory for the studies of marginally bound open quantum systems

Resonant spectra of multipole-bound anions

“…An alternative to the DIM is the Berggren expansion method (BEM), previously applied in the context of multipole-bound anions [16,17] and nuclear halos [54][55][56]. The Berggren basis [57,58] used in this work is defined in the complex momentum plane; it contains explicitly resonant states (poles of the one-body S-matrix) and scattering states defined along a contour L + in the fourth quadrant of the momentum plane.…”

“…Bound states and decaying resonances entering the Berggren basis for a given partial wave are obtained by a direct integration of the Schrödinger equation for the diagonal term of the potential, while the selected scattering states along the contour L + are discretized in the momentum space using a Gauss-Legendre quadrature as in Refs. [16,17]. The non-resonant continuum is limited by the momentum cutoff k max that has to be sufficiently large to ensure the completeness of the Berggren basis.…”

“…Differentiating resonant states from the nonresonant scattering background requires special treatment. Since resonant states do not depend on a detailed choice of the contour L + , by moving the contour slightly a new spectrum can be obtained, where non-resonant states move according to the contour change and resonant states stay invariant [17]. In this way, resonant states can be located.…”

“…Fermi and Teller, in their pioneering work [5], demonstrated the existence of the minimal dipole moment required to bind an electron in an external point dipolar field. This result stimulated many theoretical and experimental investigations on multipolebound anions using effective potential methods [1,[6][7][8][9][10][11][12][13][14][15][16][17] and ab-initio approaches [18][19][20][21][22][23][24][25][26][27][28][29][30].…”

“…The continuum couplings are included using the Berggren expansion method as in Refs. [15][16][17]. To study the threshold behavior of the system we investigate the pattern of resonant poles as a function of four parameters: the strength and range of the Gaussian form factor, the multipolarity of the potential, and the molecular moment of inertia.…”