Numerical calculation of supercritical Dirac resonance parameters by analytic continuation methods

Ackad, Edward; Horbatsch, Marko

doi:10.1103/physreva.75.022508

Cited by 29 publications

(37 citation statements)

References 31 publications

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“…Calculations [5][6][7] for collision systems like U-U predict widths in the kilo-electron volt range, which correspond to lifetimes of the order of 10 −19 s. While this is relatively long-lived compared to the collision time, there is a finite probabilty that the resonance will decay while the nuclei are within a supercritical distance. It is also possible that "sticky" (inelastic) collisions extend the collision time before the decay of a compound nucleus [8].…”

Section: Introductionmentioning

confidence: 99%

“…The stationary eigenvalue problem has been solved using a matrix representation of the Hermitian two-center Hamiltonian [5,9]. The electronic states are expanded in terms of a sine basis sampled on a discrete spatial mesh, and diagonalization of the supercritical Dirac Hamiltonian yields a set of discretized quasicontinuum states.…”

Section: Introductionmentioning

confidence: 99%

“…The supercritical resonance is thus represented as a superposition of these continuum states. The mean energy and width of the resonance can then be obtained by fitting a Breit-Wigner shape to the density of states or to the overlap of the continuum states with a reference 1Sσ subcritical bound state [5].…”

Section: Introductionmentioning

confidence: 99%

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Calculation of supercritical Dirac resonance parameters for heavy-ion systems from a coupled-differential-equation approach

Marsman

Horbatsch

2011

Phys. Rev. A

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Previous work [E. Ackad and M. Horbatsch, Phys. Rev. A 78, 062711 (2008)] on supercritical Dirac resonance parameters from extrapolated analytic continuation, obtained with a Fourier grid method, is generalized by numerically solving the coupled Dirac radial equations to a high precision. The equations, which contain the multipole decomposition of the two-center potential, are augmented by a complex absorbing potential and truncated at various orders in the partial wave expansion to demonstrate convergence of the resonance parameters in the limit of vanishing absorber. The convergence of the partial-wave spinor and of the multipole potential expansions is demonstrated in the supercritical regime. The comparison of critical distances with literature values shows that the work provides benchmark results for future two-center calculations without multipole expansion.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Calculation of supercritical Dirac resonance parameters for heavy-ion systems from a coupled-differential-equation approach

Marsman

Horbatsch

2011

Phys. Rev. A

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“…For very closely spaced extended nuclei the monopole approximation turns out to be enough for calculation the critical distances R cr with an accuracy of about 5% [38,39]. Moreover, the monopole approximation can be used by computing the parameters of the resonances, arising by diving of discrete electronic levels into the lower continuum [40,41]. However, when the internuclear distance increases, the monopole approximation becomes too rough, and so the higher multipoles of expansion of the two-center Coulomb potential are required.…”

Section: Methods For Dealing With Two-center Dementioning

confidence: 99%

Estimating the radiative part of QED effects in superheavy nuclear quasimolecules

Roenko

Sveshnikov

2018

Phys. Rev. A

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A method for calculating the electronic levels in the compact superheavy nuclear quasi-molecules, based on solving the two-center Dirac equation using the multipole expansion of two-center potential, is developed. For the internuclear distances up to d ∼ 100 fm such technique reveals a quite fast convergence and allows for computing the electronic levels in such systems with accuracy ∼ 10 −6 . The critical distances Rcr between the nuclei for 1σg and 1σu electronic levels in the region Z ≃ 87 − 100 are calculated. By means of the same technique the shifts of electronic levels due to the effective interaction ∆UAMM of the electron's magnetic anomaly with the Coulomb field of the closely spaced heavy nuclei are evaluated as a function of the internuclear distance and the charge of the nuclei, non-perturbatively both in Zα and (partially) in α/π. It is shown, that the levels shifts near the lower continuum decrease with the enlarging size of the system of Coulomb sources both in the absolute units and in units of Z 4 α 5 /πn 3 . The last result is generalized to the whole self-energy contribution to the level shifts and so to the possible behavior of radiative part of QED-effects with virtual photon exchange near the lower continuum in the overcritical region.

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“…(7) is restricted to the zeroth term, l = 0, the electron-nuclear interaction is governed by the spherically symmetric potential V T C (r, R) = V 0 (r, R). The solution of the Dirac equation within such a monopole approximation is well-elaborated and has been discussed in a number of works [13][14][15][16][17]. In particular, the eigenfunctions of the monopole Hamilto-nianĤ…”

Section: A Stationary Two-center Dirac Problemmentioning

confidence: 99%

Solution of the two-center time-dependent Dirac equation in spherical coordinates: Application of the multipole expansion of the electron-nuclei interaction

et al. 2012

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A non-perturbative approach to the solution of the time-dependent, two-center Dirac equation is presented with a special emphasis on the proper treatment of the potential of the nuclei. In order to account for the full multipole expansion of this potential, we express eigenfunctions of the two-center Hamiltonian in terms of well-known solutions of the "monopole" problem that employs solely the spherically-symmetric part of the interaction. When combined with the coupled-channel method, such a wavefunction-expansion technique allows for an accurate description of the electron dynamics in the field of moving ions for a wide range of internuclear distances. To illustrate the applicability of the proposed approach, the probabilities of the K-as well as L-shell ionization of hydrogen-like ions in the course of nuclear α-decay and slow ion-ion collisions have been calculated.center system at a fixed internuclear distance R. The performance of the coupled-channel methods depends, therefore, on the efficiency of the spectrum generation of the time-independent Hamiltonian at each required R.

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Numerical calculation of supercritical Dirac resonance parameters by analytic continuation methods

Cited by 29 publications

References 31 publications

Calculation of supercritical Dirac resonance parameters for heavy-ion systems from a coupled-differential-equation approach

Calculation of supercritical Dirac resonance parameters for heavy-ion systems from a coupled-differential-equation approach

Estimating the radiative part of QED effects in superheavy nuclear quasimolecules

Solution of the two-center time-dependent Dirac equation in spherical coordinates: Application of the multipole expansion of the electron-nuclei interaction

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