PIONIC HYDROGEN

2005 ◽  
Vol 20 (02n03) ◽  
pp. 349-357 ◽  
Author(s):  
◽  
DETLEV GOTTA
Keyword(s):  
Coupling Constant ◽  
S Wave ◽  
Pionic Hydrogen ◽  
Pion Nucleon ◽  
Scattering Lengths ◽  
Set Up ◽  
Paul Scherrer ◽  
S States ◽  
Precision Test ◽  
Pertubation Theory

The measurement of the pion–nucleon scattering lengths constitutes a high–precision test of the methods of Chiral Pertubation Theory (χPT), which is the low–energy approach of QCD. The πN s–wave scattering lengths and the pion–nucleon coupling constant are related to the strong–interaction shift ∊1s and width Γ1s of the s–states in the pionic hydrogen atom. ∊1s and Γ1s are determined from the measured energies and line widths of X–ray transitions to the 1s ground state when compared to the calculated electromagnetic values. A new experiment, set up at the Paul–Scherrer–Institut (PSI), has completed a first series of measurements.

PRECISION CALCULATION OF THE π-d SCATTERING LENGTH

2011 ◽  
Vol 26 (03n04) ◽  
pp. 589-591
Author(s):  
M. HOFERICHTER ◽  
V. BARU ◽  
C. HANHART ◽  
B. KUBIS ◽  
A. NOGGA ◽  
...  
Keyword(s):  
Virtual Photon ◽  
Charged Pion ◽  
Scattering Length ◽  
Coupling Constant ◽  
Hydrogen Atoms ◽  
Sum Rule ◽  
Pionic Hydrogen ◽  
Pion Nucleon ◽  
Using Data ◽  
Scattering Lengths

We present a calculation of the π-d scattering length in the framework of chiral perturbation theory (ChPT) with focus on virtual-photon effects. Using data on pionic deuterium and pionic hydrogen atoms, we extract the isoscalar and isovector pion–nucleon scattering lengths [Formula: see text] and [Formula: see text], as well as—via the Goldberger–Miyazawa–Oehme sum rule—the charged-pion–nucleon coupling constant [Formula: see text]

scholarly journals Redetermination of the strong-interaction width in pionic hydrogen

2021 ◽  
Vol 57 (2) ◽  
Author(s):  
A. Hirtl ◽  
D. F. Anagnostopoulos ◽  
D. S. Covita ◽  
H. Fuhrmann ◽  
H. Gorke ◽  
...  
Keyword(s):  
Nucleon Nucleon ◽  
Low Energy ◽  
Nucleon Scattering ◽  
Pionic Hydrogen ◽  
Pionic Atom ◽  
Pion Nucleon ◽  
Consistent Picture ◽  
Scattering Lengths ◽  
Paul Scherrer ◽  
Bent Crystals

AbstractThe hadronic width of the ground state of pionic hydrogen has been redetermined by X-ray spectroscopy to be $$\varGamma ^{\pi \mathrm {H}}_{1s}=(856\,\pm \,16_\mathrm{stat}\,\pm \,22_\mathrm{sys})$$ Γ 1 s π H = ( 856 ± 16 stat ± 22 sys )  meV. The experiment was performed at the high-intensity low-energy pion beam of the Paul Scherrer Institute by using the cyclotron trap and a high-resolution Bragg spectrometer with spherically bent crystals. Coulomb de-excitation was studied in detail by comparing its influence on the line shape by measuring the three different transitions K$$\alpha $$ α , K$$\beta $$ β , and K$$\gamma $$ γ at various hydrogen densities. The pion-nucleon scattering lengths and other physical quantities extracted from pionic-atom data are in good agreement with the results obtained from pion-nucleon and nucleon-nucleon scattering experiments and confirm that a consistent picture is achieved for the low-energy pion-nucleon sector with respect to the expectations of chiral perturbation theory.

scholarly journals Determination of the pion-nucleon coupling constant and scattering lengths

2002 ◽  
Vol 66 (1) ◽  
Author(s):  
T. E. O. Ericson ◽  
B. Loiseau ◽  
A. W. Thomas
Keyword(s):  
Coupling Constant ◽  
Pion Nucleon ◽  
Scattering Lengths

scholarly journals A PHENOMENOLOGICAL DETERMINATION OF THE PION-NUCLEON SCATTERING LENGTHS FROM PIONIC HYDROGEN

2005 ◽  
Vol 20 (08n09) ◽  
pp. 1650-1655 ◽  
Author(s):  
T. E. O. ERICSON ◽  
B. LOISEAU ◽  
S. WYCECH
Keyword(s):  
Short Range ◽  
Scattering Length ◽  
Hadronic Interaction ◽  
Pionic Hydrogen ◽  
Relativistic Approach ◽  
Pion Nucleon ◽  
Extended Charge ◽  
Model Independent ◽  
Scattering Lengths

A model independent expression for the electromagnetic corrections to a phenomenological hadronic pion-nucleon (πN) scattering length ah, extracted from pionic hydrogen, is obtained. In a non-relativistic approach and using an extended charge distribution, these corrections are derived up to terms of order α2 log α in the limit of a short-range hadronic interaction. We infer [Formula: see text] which gives for the πNN coupling through the GMO relation [Formula: see text].

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