Semianalytical method for treatment of the N-body problem with complex total energy within the hyperharmonics approach

Pupyshev, V. V.; Rakityansky, S. A.

doi:10.1007/bf01291921

Cited by 14 publications

(20 citation statements)

References 5 publications

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“…In the present study, we describe a mathematically rigorous and numerically accurate and stable method for solving the two‐channel (generally, N ‐channel) quantum mechanical problem. For the last 10 years, various aspects of this method were developed 46–58. In this work, we suggest an approach to analyzing the contribution of resonance S ‐matrix poles to the scattering picture.…”

Section: Introductionmentioning

confidence: 99%

Analyzing the contribution of individual resonance poles of the S‐matrix to two‐channel scattering

Rakityansky

Elander

2005

Int J of Quantum Chemistry

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ABSTRACT:A two-channel problem is considered within a method based on firstorder differential equations that are equivalent to the corresponding Schrödinger equation but more convenient for dealing with resonant phenomena. Using these equations, it is possible to calculate directly the Jost matrix for practically any complex value of the energy. The spectral points (bound and resonant states) can therefore be located in a rigorous way, namely, as zeros of the Jost matrix determinant. When calculating the Jost matrix, the differential equations are solved and thus, at the same time, the wave function is obtained with the correct asymptotic behavior analytically embedded in the solution. The method offers a very accurate way of calculating not only total widths of resonances but their partial widths as well. For each pole of the S-matrix, its residue can be calculated rather accurately, which makes it possible to obtain the Mittag-Leffler-type expansion of the Smatrix as a sum of the singular terms (representing the resonances) and the background term (contour integral). As an example, the two-channel model by Noro and Taylor is considered. It is demonstrated how the contributions of individual resonance poles to the scattering cross section can be analyzed using the Mittag-Leffler expansion and the Argand plot technique. This example shows that even poles situated far away from the physical real axis may make significant contributions to the cross section.

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Section: Introductionmentioning

confidence: 99%

Analyzing the contribution of individual resonance poles of the S‐matrix to two‐channel scattering

Rakityansky

Elander

2005

Int J of Quantum Chemistry

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“…The present work is a continuation of a series of papers [4,6,7] in which a practical method for quantum mechanical calculations is developed. The method is based on direct calculations of the Jost function and Jost solutions and is a combination of the variableconstant method with the complex coordinate rotation.…”

Section: Discussionmentioning

confidence: 99%

“…We integrated Eqs. (33) by the Runge-Kutta method from r min = 10 −4 fm to r int = 1 fm with the boundary conditions A (4) (k, r min ) and B (4) (k, r min ) . Then from r int = 1 fm we integrated Eqs.…”

Section: Examplesmentioning

confidence: 99%

“…In this work, we show that the Jost function can be calculated directly by simply solving certain first order coupled differential equations. These equations are based on the variablephase approach [3] and their solution at any fixed value of the radial variable r, provides the Jost function and its complex conjugate counterpart, which correspond to the potential truncated at the point r. Such equations were proposed in the past for bound and scattering state calculations, that is for calculations in the upper half of the complex momentum plane [4].…”

Section: Introductionmentioning

confidence: 99%

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Jost function for coupled partial waves

Rakityansky

Sofianos

1998

J. Phys. A: Math. Gen.

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An exact method for direct calculation of the Jost functions and Jost solutions for non-central potentials which couple partial waves of different angular momenta is presented. A combination of the variable-constant method with the complex coordinate rotation is used to replace the matrix Schrödinger equation by an equivalent system of linear first-order differential equations. Solving these equations numerically, the Jost functions can be obtained to any desired accuracy for all complex momenta of physical interest, including the spectral points corresponding to bound and resonant states. The effectiveness of the method is demonstrated using the Reid soft-core and Moscow nucleon-nucleon potentials which involve tensor forces.

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“…It has been shown in [10] that a radial truncation of such couplings gives rise to unphysical poles of the S-matrix, which were referred to in that article as artificial poles. In that work, integrations were carried out to large radii and so these unphysical poles were located very close to the origin of the complex energy plane.…”

Section: Introductionmentioning

confidence: 99%

Long-range interactions and artificial poles

Stott¹,

Thompson²,

Tostevin³

1999

J. Phys. G: Nucl. Part. Phys.

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The structure of the three-body continuum of the 6 He nucleus within the hyperspherical harmonic calculation scheme has been the subject of extensive study. An approximate treatment of the long-range couplings inherent in such models gives rise to unphysical poles in the deduced Smatrix at complex energies. We consider here a simple two-channel example, which includes long-range interactions, and demonstrates the existence of these artificial S-matrix poles. This is also illustrated in a physical context by considering the extreme adiabatic approximation of the hyperspherical harmonics technique for 6 He. A correct treatment of the long-range (1/ρ λ ) behaviour of the channel potentials is shown to remove the artificial poles from the physically significant region of the complex energy plane.

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Semianalytical method for treatment of the N-body problem with complex total energy within the hyperharmonics approach

Cited by 14 publications

References 5 publications

Analyzing the contribution of individual resonance poles of the S‐matrix to two‐channel scattering

Analyzing the contribution of individual resonance poles of the S‐matrix to two‐channel scattering

Jost function for coupled partial waves

Long-range interactions and artificial poles

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