J-matrix method for calculations of three-body Coulomb wave functions and cross sections of physical processes

Popov, Yu. V.; Zaytsev, S. A.; Vinitsky, S. I.

doi:10.1134/s1063779611050042

Cited by 6 publications

(6 citation statements)

References 117 publications

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“…He + (1s). This probability is obtained by projecting the two-electron wave packet (after the interaction with the pulse) onto the field-free correlated Jacobi matrix (CJM) wavefunction (see, e.g., [46][47][48][49][50][51][52][53]). The CJM wavefunction describes with high accuracy the correlated single continuum system, e − + He + (n 1), including all processes involving both single ionization without excitation and single ionization with excitation.…”

Section: Theoretical Approachmentioning

confidence: 99%

“…In this work, the field-free, singly ionized continuum states of helium are described by a multichannel scattering wavefunction which can be generated accurately using the so-called Jacobi-or J -matrix method [46][47][48][49][50][51][52][53]. This method, which is a type of Galerkin spectral method, bears a close resemblance to the R-matrix theory (cf [49]).…”

Section: Helium Field-free Correlated Jacobi-matrix Wave Functionsmentioning

confidence: 99%

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Enhanced asymmetry in few-cycle attosecond pulse ionization of He in the vicinity of autoionizing resonances

Djiokap

Jiang

et al. 2012

New J. Phys.

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By solving the two-active-electron, time-dependent Schrödinger equation in its full dimensionality, we investigate the carrier-envelope phase (CEP) dependence of single ionization of He to the He + (1s) state triggered by an intense few-cycle attosecond pulse with carrier frequency ω corresponding to the energyhω = 36 eV. Effects of electron correlations are probed by comparing projections of the final state of the two-electron wave packet onto field-free highly correlated Jacobi matrix wave functions with projections onto uncorrelated Coulomb wave functions. Significant differences are found in the vicinity of autoionizing resonances. Owing to the broad bandwidths of our 115 and 230 as pulses and their high intensities (1-2 PW cm −2 ), asymmetries are found in the differential probability for ionization of electrons parallel and antiparallel to the linear polarization axis of the laser pulse. These asymmetries stem from interference of the one-and two-photon ionization amplitudes for producing electrons with the same momentum along the linear polarization axis. Whereas these asymmetries generally decrease with increasing ionized electron 4 2 kinetic energy, we find a large enhancement of the asymmetry in the vicinity of two-electron doubly excited (autoionizing) states on an energy scale comparable to the widths of the autoionizing states. The CEP dependence of the energyintegrated asymmetry agrees very well with the predictions of time-dependent perturbation theory (Pronin et al 2009 Phys. Rev. A 80 063403).

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Section: Theoretical Approachmentioning

confidence: 99%

Section: Helium Field-free Correlated Jacobi-matrix Wave Functionsmentioning

confidence: 99%

Enhanced asymmetry in few-cycle attosecond pulse ionization of He in the vicinity of autoionizing resonances

Djiokap

Jiang

et al. 2012

New J. Phys.

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“…Both methods give the same converged results. The field-free SIE states of He are described by a multichannel scattering wave function (E,k e ) obtained accurately using the Jacobi-or J-matrix method [23,[31][32][33][34][35][36][37][38]. In each final state channel , the wave function is expanded in a basis of Coulomb-Sturmian functions [23].…”

mentioning

confidence: 99%

Asymmetries in production of He+(n=2)with an intense few-cycle attosecond pulse

Djiokap

Jiang

et al. 2013

Phys. Rev. A

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“…where R N is the turning point for the classical harmonic oscillator discussed above (9). Assuming that an argument of the Bessel function ρR N is large (ρR N 1), we use its asymptotic form…”

Section: Proofmentioning

confidence: 99%

“…Heller and Yamani [1], Yamani and Fishman [2] demonstrated that the oscillator basis yields the tridiagonal or Jacobi form of a reference Hamiltonian for neutral particles, while the Laguerre basis produces the tridiagonal form for the charged particles. The Laguerre basis has been intensively employed for solving three-body problems in nuclear ( [7,8]) and atomic physics ( [9,10]).…”

Section: Introductionmentioning

confidence: 99%

Properties of a potential energy matrix in oscillator basis

2019

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Matrix elements of potential energy are examined in detail. We consider a model problem -a particle in a central potential. The most popular forms of central potential are taken up, namely, square-well potential, Gaussian, Yukawa and exponential potentials. We study eigenvalues and eigenfunctions of the potential energy matrix constructed with oscillator functions. It is demonstrated that eigenvalues coincide with the potential energy in coordinate space at some specific discrete points. We establish approximate values for these points. It is also shown that the eigenfunctions of the potential energy matrix are the expansion coefficients of the spherical Bessel functions in a harmonic oscillator basis. We also demonstrate a close relation between the separable approximation and L 2 basis (J-matrix) method for the quantum theory of scattering.

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J-matrix method for calculations of three-body Coulomb wave functions and cross sections of physical processes

Cited by 6 publications

References 117 publications

Enhanced asymmetry in few-cycle attosecond pulse ionization of He in the vicinity of autoionizing resonances

Enhanced asymmetry in few-cycle attosecond pulse ionization of He in the vicinity of autoionizing resonances

Asymmetries in production of He+(n=2)with an intense few-cycle attosecond pulse

Properties of a potential energy matrix in oscillator basis

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