Complex local potential by Marchenko inversion of partly real and partly complex phase shift

Papastylianos, A.; Sofianos, S. A.; Fiedeldey, H.; Alt, E. O.

doi:10.1103/physrevc.42.142

Cited by 11 publications

(15 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the approximation carried out in this paper, twenty poles (M=20) were used for˜( ) S k 0 . This number of poles has been shown to accurately constrain scattering phases with a momentum dependence similar to those in this paper, for example in [43,52]. The distribution of the computed poles of˜( ) S k 0 in the complex momentum plane are shown in figures 2 and 3.…”

Section: Distribution Of the Poles Of The Scattering Matrix Approximasupporting

confidence: 60%

“…Using˜( ) S k 0 , the integral in equation (4) for the input kernel was computed through the Cauchy Residue theorem as shown in [45,53]. The GLM equation was solved as outlined in [43,45,52,53]. The potentials obtained for the Λp interaction are shown in figures 4(a) and (b), while those for the Λn interaction are shown in figures 5(a) and (b).…”

Section: Spin-dependent Potentialsmentioning

confidence: 99%

“…The complex constants a 0 m are estimated by rewriting the rational function in Equation ( 8) as a Padé approximation of order [M/M ] [35,41,42]. By selecting M data points (k j , S 0 (k j )) from the original scattering matrix data S 0 (k) and substituting into the Padé approximation, a linear system is obtained, as shown in [43]. In the Padé approximation of order [P/Q], the requirement P = Q ensures that S0 (k) → 1 as k → ∞, a condition that is satisfied by short-range potentials.…”

Section: Separability Of the Kernelsmentioning

confidence: 99%

See 2 more Smart Citations

Effective lambda-proton and lambda-neutron potentials from subthreshold inverse scattering

Meoto

Lekala

2019

J. Phys. Commun.

View full text Add to dashboard Cite

Potentials are constructed for the lambda-nucleon interaction in the S 1 0 and S 3 1 channels. These potentials are recovered from scattering phases below the inelastic threshold through Gel'fand-Levitan-Marchenko theory. Experimental data with good statistics is not available for lambda-nucleon scattering. This leaves theoretical scattering phases as the only option through which the rigorous theory of quantum inverse scattering can be used in probing the lambda-nucleon force. Using rational-function interpolations on the theoretical scattering data, the kernels of the Gel'fand-Levitan-Marchenko integral equation become degenerate, resulting in a closed-form solution. The new potentials restored, which are shown to be unique through the Levinson theorem, bear the expected features of short-range repulsion and intermediate-range attraction. Charge symmetry breaking, which is perceptible in the scattering phases, is preserved in the new potentials. The lambdanucleon force in the S 1 0 channel is observed to be stronger than in the S 3 1 channel, as expected. In addition, the potentials bear certain distinctive features whose effects on hypernuclear systems can be explored through Schrödinger calculations.

show abstract

Section: Distribution Of the Poles Of The Scattering Matrix Approximasupporting

confidence: 60%

Section: Spin-dependent Potentialsmentioning

confidence: 99%

Section: Separability Of the Kernelsmentioning

confidence: 99%

See 1 more Smart Citation

Effective lambda-proton and lambda-neutron potentials from subthreshold inverse scattering

Meoto

Lekala

2019

J. Phys. Commun.

View full text Add to dashboard Cite

show abstract

“…The method has been successfully applied to construct nucleon-nucleon potential by von Geramb and collaborators (see Refs. [29,30] and references therein), as well as neutron-deuteron potentials [31,32]. The Marchenko integral equation, fully equivalent to the Schrödinger equation, reads…”

Section: B Inverse Scattering Methodsmentioning

confidence: 99%

In-medium nucleon-nucleon potentials in configuration space

Beyer¹,

Sofianos

2001

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

View full text Add to dashboard Cite

Based on the thermodynamic Green function approach two-nucleon correlations in nuclear matter at finite temperatures are revisited. To this end, we derive phase equivalent effective r-space potentials that include the effect of the Pauli blocking at a given temperature and density. These potentials enter into a Schrödinger equation that is the r-space representation of the Galitskii-Feynman equation for two nucleons. We explore the analytical structure of the equation in the complex k-plane by means of Jost functions. We find that despite the Mott effect the correlation with deuteron quantum numbers are manifested as antibound states, i.e., as zeros of the Jost function on the negative imaginary axis of the complex momentum space. The analysis presented here is also suited for Coulombic systems.

show abstract

“…The used diagonal Padé approximants of the corresponding S-matrix allow an analytical solution of the Marchenko integral equation [2,4]. For single partial wave the general solution was presented in [5,9]. We present a solution for coupled partial waves.…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of the optical potential from scattering data

Khokhlov

Knyr

2006

Phys. Rev. C

View full text Add to dashboard Cite

We propose a method for reconstruction of the optical potential from scattering data. The algorithm is a two-step procedure. In the first step the real part of the potential is determined analytically via solution of the Marchenko equation. At this point we use a diagonal Pad\'{e} approximant of the corresponding unitary $S$-matrix. In the second step the imaginary part of the potential is determined via the phase equation of the variable phase approach. We assume that the real and the imaginary parts of the optical potential are proportional. We use the phase equation to calculate the proportionality coefficient. A numerical algorithm is developed for a single and for coupled partial waves. The developed procedure is applied to analysis of $^{1}S_{0}$ $NN$, $^{3}SD_{1}$ $NN$, $P31$ $\pi^{-} N$ and $S01$ $K^{+}N$ data.Comment: 26 pages, 8 figures, results of nucl-th/0410092 are refined, some new results are presente

show abstract

Complex local potential by Marchenko inversion of partly real and partly complex phase shift

Cited by 11 publications

References 14 publications

Effective lambda-proton and lambda-neutron potentials from subthreshold inverse scattering

Effective lambda-proton and lambda-neutron potentials from subthreshold inverse scattering

In-medium nucleon-nucleon potentials in configuration space

Reconstruction of the optical potential from scattering data

Contact Info

Product

Resources

About