scholarly journals A Note on Inverse Scattering Calculations of Energy-Independent Potentials

1973 ◽  
Vol 26 (4) ◽  
pp. 561
Author(s):  
JL Cook
Keyword(s):  
Phase Shift ◽  
Inverse Scattering ◽  
Single Channel ◽  
Resonance Parameters ◽  
Channel Potential ◽  
Scattering Phase

It is shown that a method proposed for determining one single-channel potential from a real scattering phase shift using resonance parameters allows the determination of an energy-independent potential.

scholarly journals ππ P-wave resonant scattering from lattice QCD

2018 ◽  
Vol 175 ◽  
pp. 05022
Author(s):  
Srijit Paul ◽  
Constantia Alexandrou ◽  
Luka Leskovec ◽  
Stefan Meinel ◽  
John W. Negele ◽  
...  
Keyword(s):  
Phase Shift ◽  
Lattice Qcd ◽  
Pion Mass ◽  
Resonant Scattering ◽  
P Wave ◽  
Statistics Analysis ◽  
Resonance Parameters ◽  
Lattice Size ◽  
Scattering Phase

We present a high-statistics analysis of the ρ resonance in ππ scattering, using 2 + 1 flavors of clover fermions at a pion mass of approximately 320 MeV and a lattice size of approximately 3:6 fm. The computation of the two-point functions are carried out using combinations of forward, sequential, and stochastic propagators. For the extraction of the ρ-resonance parameters, we compare different fit methods and demonstrate their consistency. For the ππ scattering phase shift, we consider different Breit-Wigner parametrizations and also investigate possible nonresonant contributions. We find that the minimal Breit-Wigner model is suffcient to describe our data, and obtain amρ = 0:4609(16)stat(14)sys and gρππ = 5:69(13)stat(16)sys. In our comparison with other lattice QCD results, we consider the dimensionless ratios amρ/amN and amπ/amN to avoid scale setting ambiguities.

GENERAL FORMULA FOR THE SECOND VIRIAL COEFFICIENT

1961 ◽  
Vol 39 (11) ◽  
pp. 1563-1572 ◽  
Author(s):  
J. Van Kranendonk
Keyword(s):  
Phase Shift ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Resolvent Operators ◽  
Simple Derivation ◽  
Scattering Phase ◽  
Scattering Phase Shifts ◽  
Quantization Volume ◽  
Mechanical Expression ◽  
The Waves

A simple derivation is given of the quantum mechanical expression for the second virial coefficient in terms of the scattering phase shifts. The derivation does not require the introduction of a quantization volume and is based on the identity R(z)−R0(z) = R0(z)H1R(z), where R0(z) and R(z) are the resolvent operators corresponding to the unperturbed and total Hamiltonians H0 and H0 + H1 respectively. The derivation is valid in particular for a gas of excitons in a crystal for which the shape of the waves describing the relative motion of two excitons is not spherical, and, in general, varies with varying energy. The validity of the phase shift formula is demonstrated explicitly for this case by considering a quantization volume with a boundary the shape of which varies with the energy in such a way that for each energy the boundary is a surface of constant phase. The density of states prescribed by the phase shift formula is shown to result if the enclosed volume is required to be the same for all energies.

K+p interactions in the range 0.9–1.5 GeV/c and elastic scattering phase shift analysis

1970 ◽  
Vol 20 (2) ◽  
pp. 301-319 ◽  
Author(s):  
G. Giacomelli ◽  
P. Lugaresi-Serra ◽  
G. Mandrioli ◽  
A.M. Rossi ◽  
F. Griffiths ◽  
...  
Keyword(s):  
Elastic Scattering ◽  
Phase Shift ◽  
Phase Shift Analysis ◽  
Shift Analysis ◽  
Scattering Phase

Complete determination of polarization state in the hard X-ray region

1991 ◽  
Vol 24 (6) ◽  
pp. 982-986 ◽  
Author(s):  
T. Ishikawa ◽  
K. Hirano ◽  
S. Kikuta
Keyword(s):  
Phase Shift ◽  
Linear Polarization ◽  
Amplitude Ratio ◽  
Polarization State ◽  
Perfect Crystal ◽  
Electric Vector ◽  
X Ray ◽  
Complete Determination ◽  
Unpolarized Radiation

A new method for complete determination of polarization state in the hard X-ray region is described. The system consists of a perfect-crystal phase retarder and a linear polarization analyzer. This method gives not only the amplitude ratio of mutually perpendicular electric vector components and the phase shift between them but also the proportion of unpolarized radiation.

scholarly journals Hermitizing the HAL QCD potential in the derivative expansion

2020 ◽  
Vol 2020 (2) ◽  
Author(s):  
Sinya Aoki ◽  
Takumi Iritani ◽  
Koichi Yazaki
Keyword(s):  
Phase Shift ◽  
Wave Functions ◽  
Leading Order ◽  
Many Body ◽  
Derivative Expansion ◽  
Local Part ◽  
Scattering Phase ◽  
Many Body Systems ◽  
Local Term ◽  
Better Than

Abstract A formalism is given to hermitize the HAL QCD potential, which needs to be non-Hermitian except for the leading-order (LO) local term in the derivative expansion as the Nambu– Bethe– Salpeter (NBS) wave functions for different energies are not orthogonal to each other. It is shown that the non-Hermitian potential can be hermitized order by order to all orders in the derivative expansion. In particular, the next-to-leading order (NLO) potential can be exactly hermitized without approximation. The formalism is then applied to a simple case of $\Xi \Xi (^{1}S_{0}) $ scattering, for which the HAL QCD calculation is available to the NLO. The NLO term gives relatively small corrections to the scattering phase shift and the LO analysis seems justified in this case. We also observe that the local part of the hermitized NLO potential works better than that of the non-Hermitian NLO potential. The Hermitian version of the HAL QCD potential is desirable for comparing it with phenomenological interactions and also for using it as a two-body interaction in many-body systems.

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