- Email: [email protected]
Statistical scrutiny of the phenomenological redshift-distance square law
ABSTRACTS
OF PAPERS
TO
APPEAR
IN
FUTURE
ISSUES
505
electrical resistivity. The relationship of these modes with the m = 1 ideal MHD internal kink mode is studied and the effects of toroidal geometry are briefly discussed. Statistical Scrutiny of the Phenomenologieal Redshif-Distance Square Law. J. F. NICOLL AND I. E. SEGAL, Massachusetts lnstitute of Technology, Cambridge, Massachusetts 02139. The phenomenological redshift-distance square law for low-redshift galaxies is scrutinized from the standpomt of further statistical refinements, possible untreated selection effects, and new data. In particular the question of approximate normality of the bright end of the luminosity function is studied, and answered affirmatively for the square-law absolute magnitudes. The problem of a possible effect due to redshift incompleteness is addressed through the analysis of samples limited in surface brightness and/or luminosity. An analysis is given which is based on the Uppsala General Catalogue, rather than the Reference Guide to Bright Galaxies earlier used as data source. As earlier, maximum-h kelihood estimates for the redshift-distance exponent p in the empirical redshift-distance relation z cc rp are p N 2 + E with Q < 0.2 in all substantial redshift ranges. OfiShell E@cts in s- Wace Pion Absorption. * FR. HACHENBERG AND H. J. PraNsa+, Institut fur Theoretische Physik der Universitlt, D-6900 Heidelberg, Germany. The effect of s-wave pion absorption on the pion-nucleus optical potential is calculated. We assume absorption by two uncorrelated nucleons with off-shell pion rescattering. For the pion-nucleon interaction we develop a field theoretic model which can be used on- and off-mass shell. A fully relativistic calculation of the pion polarization operator then gives UOrt = -4~ B”p2(2~))r, with B. = (0.094 + i0.036)p-4, as contribution from s-wave absorption to the optical potential. The imaginary part agrees well with the experimentally determined value, while pion dispersion (real part of B,) does not explain the observed repulsion in the s-wave pion nucleus interaction. We demonstrate the relevance of off-shell dynamics in pion-nucleon scattering. The ratio R, of Yabsorption rates by neutron-proton and proton-proton pairs is much smaller than predicted by on-shell models. For equal numbers of neutrons and protons we get R, = 3.0. We also apply the formalism to s-wave pion production in nucleon-nucleon collisions and obtain qualitative agreement with the data. In particular the longstanding puzzle of the small imaginary pion deuteron scattering length compared to Im B,, is explained. Our calculation gives Im arm = 3.7 x 10-3jl-'.
OF PAPERS
TO
APPEAR
IN
FUTURE
ISSUES
505
electrical resistivity. The relationship of these modes with the m = 1 ideal MHD internal kink mode is studied and the effects of toroidal geometry are briefly discussed. Statistical Scrutiny of the Phenomenologieal Redshif-Distance Square Law. J. F. NICOLL AND I. E. SEGAL, Massachusetts lnstitute of Technology, Cambridge, Massachusetts 02139. The phenomenological redshift-distance square law for low-redshift galaxies is scrutinized from the standpomt of further statistical refinements, possible untreated selection effects, and new data. In particular the question of approximate normality of the bright end of the luminosity function is studied, and answered affirmatively for the square-law absolute magnitudes. The problem of a possible effect due to redshift incompleteness is addressed through the analysis of samples limited in surface brightness and/or luminosity. An analysis is given which is based on the Uppsala General Catalogue, rather than the Reference Guide to Bright Galaxies earlier used as data source. As earlier, maximum-h kelihood estimates for the redshift-distance exponent p in the empirical redshift-distance relation z cc rp are p N 2 + E with Q < 0.2 in all substantial redshift ranges. OfiShell E@cts in s- Wace Pion Absorption. * FR. HACHENBERG AND H. J. PraNsa+, Institut fur Theoretische Physik der Universitlt, D-6900 Heidelberg, Germany. The effect of s-wave pion absorption on the pion-nucleus optical potential is calculated. We assume absorption by two uncorrelated nucleons with off-shell pion rescattering. For the pion-nucleon interaction we develop a field theoretic model which can be used on- and off-mass shell. A fully relativistic calculation of the pion polarization operator then gives UOrt = -4~ B”p2(2~))r, with B. = (0.094 + i0.036)p-4, as contribution from s-wave absorption to the optical potential. The imaginary part agrees well with the experimentally determined value, while pion dispersion (real part of B,) does not explain the observed repulsion in the s-wave pion nucleus interaction. We demonstrate the relevance of off-shell dynamics in pion-nucleon scattering. The ratio R, of Yabsorption rates by neutron-proton and proton-proton pairs is much smaller than predicted by on-shell models. For equal numbers of neutrons and protons we get R, = 3.0. We also apply the formalism to s-wave pion production in nucleon-nucleon collisions and obtain qualitative agreement with the data. In particular the longstanding puzzle of the small imaginary pion deuteron scattering length compared to Im B,, is explained. Our calculation gives Im arm = 3.7 x 10-3jl-'.