Extraction of spin-orbit potentials from scattering data via inversion

“…It can also be proved that Eq. ( 10) is uniquely solvable for continuous expansion functions, therefore the ansatz for the transformation kernel (9) does not restrict the solution of the GL-type integral equation.…”

Section: Cox-thompson Methodsmentioning

confidence: 99%

“…From that, as mentioned before, the CT inverse potential q(x) can easily be obtained by employing Eqs. (10), (9), and (6).…”

Section: Cox-thompson Methodsmentioning

confidence: 99%

“…Because of the spin-orbit coupling, each partial wave provides two phase shifts, δ + l and δ − l . In case of a weak spin-orbit coupling the combined phase shifts δ l = [(l + 1)δ + l + lδ − l ]/(2l + 1) are characteristic of the underlying central potential [9]. Our input data will be the set of phase shifts at energy E lab n = 12 MeV.…”

Section: Applicationsmentioning

confidence: 99%

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Semi-Analytic Equations to the Cox–thompson Inverse Scattering Method at Fixed Energy for Special Cases

2008

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Solution of the Cox-Thompson inverse scattering problem at fixed energy [1,2,3] is reformulated resulting in semi-analytic equations. The new set of equations for the normalization constants and the nonphysical (shifted) angular momenta are free of matrix inversion operations. This simplification is a result of treating only the input phase shifts of partial waves of a given parity. Therefore, the proposed method can be applied for identical particle scattering of the bosonic type (or for certain cases of identical fermionic scattering). The new formulae are expected to be numerically more efficient than the previous ones. Based on the semi-analytic equations an approximate method is proposed for the generic inverse scattering problem, when partial waves of arbitrary parity are considered.

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“…which are valid in the case of odd l's. These equations determine the unknown sets T e or T o of shifted angular momenta L and, thus, replace either of the corresponding generic solutions (9). Notice the simplified structure of the nonlinear equations ( 17) and ( 18), compared to equations (9).…”

Section: Even (Odd) Angular Momentum Treatmentmentioning

confidence: 99%

Simplified solutions of the Cox–Thompson inverse scattering method at fixed energy

Palmai¹,

Horváth²,

Apagyi³

2008

J. Phys. A: Math. Theor.

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Extraction of spin-orbit potentials from scattering data via inversion

Cited by 16 publications

References 26 publications

Solution of a Coupled Channel Inverse Scattering Problem at Fixed Energy by a Modified Newton-Sabatier Method

Solution of a Coupled Channel Inverse Scattering Problem at Fixed Energy by a Modified Newton-Sabatier Method

Semi-Analytic Equations to the Cox–thompson Inverse Scattering Method at Fixed Energy for Special Cases

Simplified solutions of the Cox–Thompson inverse scattering method at fixed energy

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