A method for calculating the Jost function for analytic potentials

Rakityansky, S. A.; Sofianos, S. A.; Amos, K.

doi:10.1007/bf02724658

Cited by 30 publications

(57 citation statements)

References 12 publications

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“…Various technical details of using complex rotation in calculating the Jost functions and Jost matrices can be found in Refs. [30,31,32,33,34,35,36,37,38,39].…”

Section: Complex Rotationmentioning

confidence: 99%

Multi-channel analog of the effective-range expansion

Rakityansky¹,

Elander²

2011

J. Phys. A: Math. Theor.

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Similarly to the standard effective range expansion that is done near the threshold energy, we obtain a generalized power-series expansion of the multi-channel Jostmatrix that can be done near an arbitrary point on the Riemann surface of the energy within the domain of its analyticity. In order to do this, we analytically factorize its momentum dependencies at all the branching points on the Riemann surface. The remaining single-valued matrix functions of the energy are then expanded in the power-series near an arbitrary point in the domain of the complex energy plane where it is analytic. A systematic and accurate procedure has been developed for calculating the expansion coefficients. This means that near an arbitrary point in the domain of physically interesting complex energies it is possible to obtain a semi-analytic expression for the Jost-matrix (and therefore for the Smatrix) and use it, for example, to locate the spectral points (bound and resonant states) as the S-matrix poles.

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“…Various technical details of using complex rotation in calculating the Jost functions and Jost matrices can be found in Refs. [30,31,32,33,34,35,36,37,38,39].…”

Section: Complex Rotationmentioning

confidence: 99%

Multi-channel analog of the effective-range expansion

Rakityansky¹,

Elander²

2011

J. Phys. A: Math. Theor.

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“…In order to obtain the relative motion wave function ϕ k (ρ) the two-body scattering problem is solved using the Jost function method proposed in Ref. [11] with an effective proton-deuteron potential V pd (ρ) which consists of two terms:…”

Section: A Transition Operatormentioning

confidence: 99%

Nonradiative proton-deuteron fusion in stellar plasma

et al. 1997

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The nuclear reaction e + p + d → 3 He + e is considered at thermonuclear energies. The motion of the electron is treated within the adiabatic approximation and the pd scattering state is constructed in the form of an antisymmetrized product of the bound state wave function of the deuteron and of the wave function of the pd relative motion. The latter is calculated using an effective pd potential constructed via the Marchenko inverse scattering method. The bound state wave function of 3 He is obtained using Faddeev-type integrodifferential equations. The reaction rate thus obtained for the solar interior conditions is approximately 10 −4 of the corresponding rate for the radiative capture pd → 3 Heγ.PACS number: 21.45.+v, 97.10.Cv

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“…In our paper we are using direct calculation of the Jost function using the method from Ref. [11]. For the V tn , we employ a potential from Ref.…”

Section: Table1 Energy Eigenvalues E B Ofmentioning

confidence: 99%