Nuclear Theory·nucl-th

Friday·January 11, 2019

6 papers—2 primary·4 cross-listed

01
The pion-nucleon $σ$ term from pionic atoms
E. Friedman🇮🇱 · A. Gal🇮🇱
Earlier work suggested that the in-medium $π N$ threshold isovector amplitude $b_{1} (ρ)$ gets renormalized in pionic atoms by about 30% away from its $ρ = 0$ free-space value, relating such renormalization to the leading low-density decrease of the in-medium quark condensate $< q ˉ q >$ and the pion decay constant $f_{π}$ in terms of the pion-nucleon $σ$ term $σ_{π N}$ . Accepting the validity of this approach, we extracted $σ_{π N}$ from a large-scale fit of pionic-atom level shift and width data across the periodic table. Our fitted value $σ_{π N} = 57 \pm 7$ MeV is robust with respect to variation of $π N$ interaction terms other than the isovector $s$ -wave term with which $σ_{π N}$ was associated. Higher order corrections to the leading order in density involve some cancellations, suggesting thereby only a few percent overall systematic uncertainty. The value of $σ_{π N}$ derived here agrees with values obtained in several recent studies based on near-threshold $π N$ phenomenology, but sharply disagrees with values obtained in recent direct lattice QCD calculations.
nucl-thhep-phnucl-exPLB(2019)·47 citations
02
An essential singularity of the cotangent of the Coulomb-nuclear phase shift, and a finite limit of the nuclear part of the effective-range function derived at zero energy
Yu. V. Orlov🇷🇺
The Coulomb-nuclear phase shift $δ_{l}^{(cs)}$ , $cot δ_{l}^{(cs)}$ and a finite limit of the nuclear part $Δ_{l} (k)$ of the effective-range function (ERF) are derived for an arbitrary orbital momentum $l$ when energy $E \to 0$ . It is proved that $cot δ_{l}^{(cs)}$ has an essential singularity at zero energy, but $Δ_{l} (k)$ does not. The explicit finite limit of $Δ_{l} (0)$ is found. The property of $Δ_{l} (k)$ as a meromorphic function makes possible the analytical continuation of a re-normalized scattering amplitude from the physical energy region to a bound state pole. Then the asymptotic normalization coefficients (ANC) can be deduced from experimental phase-shift data and applied to radiative capture processes which are important in nuclear astrophysics for new elements creation. Our results are in agreement with the results published for $S$ wave scattering.
nucl-th1 citation

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first authorsco-authorsvia INSPIRE

The pion-nucleon σ term from pionic atoms

An essential singularity of the cotangent of the Coulomb-nuclear phase shift, and a finite limit of the nuclear part of the effective-range function derived at zero energy

Affiliations

The pion-nucleon $σ$ term from pionic atoms