Hyperspherical close-coupling method extended to the two-electron continuum region: test on the s-wave model for e-H scattering

Watanabe, Shinichi; Hosoda, Yasuo; Kato, Daiji

doi:10.1088/0953-4075/26/16/002

Cited by 26 publications

(12 citation statements)

References 20 publications

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“…For this precise reason, we employed the hyperspherical close-coupling (HSCC) method in our preliminary work for ionization [17], using the Poet-Temkin (PT) s-wave model [18] in which the angular momenta of both electrons are limited to 0, namely the s2 configuration. The hyperspherical coordinates make the two-electron atomic SchrOdinger equation locally quasiseparable,…”

Section: Two-electron Correlations In E+ H E+e+ P Near Thresholdmentioning

confidence: 99%

“…Thus, in Ref. [17],we extracted the ionization amplitude by projecting the internal HSCC solutions onto the asymptotic solutions represented in the independent particle coordi-where fkl pertain to the outgoing and incoming spherical waves. We note that on account of the obvious symmetry of the problem, we limit our subsequent considerations to the domain r~~r2.…”

Section: Two-electron Correlations In E+ H E+e+ P Near Thresholdmentioning

confidence: 99%

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Two-Electron Correlations ine+H→e+e+pNear Threshold

1995

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We present an ab initio calculation of the ionization cross section of atomic hydrogen near threshold with precision that compares excellently with the Shah-Elliot-Gilbody experiment [J. Phys. B 20, 3501 (1987)]. This fills the gap between theory and experiment down to 0.1 a.u. above threshold, complementing the recent spectacular work of Bray and Stelbovics [Phys. Rev. Lett. 70, 746 (1993)].The angular momentum distributions of the secondary electron display an evolution in correlation patterns toward the threshold. PACS numbers: 34.50.Fa, 34.80.Dp Electron-impact ionization of hydrogen is one of the most fundamental processes involving one heavy and two light particles in disintegration without charge transfer. Its particular simplicity allows one to estimate the order of magnitude of the total cross section readily [1].Nonetheless, theory has been considered largely incomplete because theoretical methods [2,3] could evaluate cross sections with a far less precision than can the experiment [4]. A terse historical account of this can be found in the recent Letter by Bray and Stelbovics that has succeeded in bridging this long-standing gap from intermediate to high energies by means of the convergent close-coupling (CCC) method [5]. However, they left a gap on the low-energy side unresolved. The current techniques are well suited to the study of threshold ionization whereas the CCC method is not, though an enlargement of the basis set might as well improve the convergence of the CCC method even at low energies. The present work investigates the low-energy region rather close to threshold within the framework of the time-independent scattering theory. Throughout this Letter, we use atomic units, i.e. , 1 a.u. of length = 5.29 X 10 " m (Bohr radius ao) and 1 a.u. of energy = 27.2 eV.For clarifying the spirit, let us employ an index K = 1/$2~E~, an analog of the single-electron wavelength, for both below and above threshold. Here and throughout, E is measured from the threshold so that K represents the distance in energy from the threshold and serves as a rough measure of the spatial range where the two-electron correlation [6] is important; the characteristic distance associated with the correlation is of the order of K according to Wannier [7]. The energy range may be divided into three regions. The high-energy region (~ (( 1) is where the perturbative treatment yields moderately reliable results. As a matter of fact, the controversial ratio of the single-to-double ionization of He by photon impact at K « 1 appears to be reasonably well represented by perturbation theory [8]. Here, the electron-electron correlations occur at rather short mutual distances during a short time interval, thus the two electrons may be consid-ered largely independent. The low-energy region (~~1) is, on the contrary, where the correlations become particularly important because the incident electron has ample time to see the detailed level structure of the target atom;the target in turn has ample time to respond to the electric field ...

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Section: Two-electron Correlations In E+ H E+e+ P Near Thresholdmentioning

confidence: 99%

Section: Two-electron Correlations In E+ H E+e+ P Near Thresholdmentioning

confidence: 99%

Two-Electron Correlations ine+H→e+e+pNear Threshold

1995

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“…This method has been used for bound states in atomic [23][24][25][26][27][28][29][30][31][32][33][34][35], nuclear [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53] and particle physics [54][55][56]. Attempts have been made to use it in scattering problems as well [57]. In this method, the wave function is expanded in a complete set of hyperspherical harmonics (HH), which are the six-dimensional analogue of the angular part of eigenfunctions of the 3-dimensional Laplacian operator.…”

Section: Introductionmentioning

confidence: 99%

Investigation of halo structure of 6He by hyperspherical three-body method

Khan

Das

2001

Pramana - J Phys

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Hyperspherical harmonics expansion method is applied to a three-body model of two neutron halo nuclei. Convergence of the expansion has been ensured. A repulsive part is introduced in the interaction between the core and the extra-core neutron, to simulate Pauli principle. Two neutron separation energy, r.m.s. radii, correlation factor and probability density distributions have been calculated for 6 He. It is found that the convergence of the two neutron separation energy is relatively slow, while other quantities reach convergence quickly.

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“…This method has been used for bound states in atomic [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34], nuclear [35][36][37][38][39][40][41][42][43][44][45][46] and particle physics [47][48][49]. Attempts have been made to use it in scattering problems as well [50]. In this method, the wave function is expanded in a complete set of hyperspherical harmonics (HH), which are, for a three body system, the six-dimensional analogue of ordinary spherical harmonics, which are the angular part of eigenfunctions of 3-dimensional Laplacian operator.…”

Section: Introductionmentioning

confidence: 99%

Study of ΛΛ dynamics and ground state structure of low and medium mass double Λ hypernuclei

Khan

Das

2001

Pramana - J Phys

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We critically review the ££ dynamics by examining £ £ and £-nucleon phenomenological potentials in the study of the bound state properties of double-£ hypernuclei ££ He, ½¼ ££ Be, ½ in the frame work of (core·£·£) three body model. An effective £AE potential is obtained by folding the phenomenological £AE potential into the density distribution of the core nuclei. The former two cases (i.e. ££ He and ½¼ ££ Be) are revisited to justify the correctness of the present potential model. Assuming the same potential model we predicted some of the structural properties of heavier doubly £-hypernuclei. The hyperspherical harmonics expansion method, which is an essentially exact method has been employed for the three body system. A convergence in binding energy up to 0.15% for ÃÑ Ü ¾ ¼ has been achieved. In our calculation we have made no approximation in restricting the allowed Ð-values of the interacting pairs.

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Hyperspherical close-coupling method extended to the two-electron continuum region: test on the s-wave model for e-H scattering

Cited by 26 publications

References 20 publications

Two-Electron Correlations ine+H→e+e+pNear Threshold

Two-Electron Correlations ine+H→e+e+pNear Threshold

Investigation of halo structure of 6He by hyperspherical three-body method

Study of ΛΛ dynamics and ground state structure of low and medium mass double Λ hypernuclei

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