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Modified effective range theory is applied as a tool to determine bound and virtual state energies in low-energy positron elastic scattering by atoms and molecules. This is achieved by the S-matrix continuation into the complex momentum plane, allowing to identify poles related to shallow energy states. The influence of the long-range polarization potential (∼ r ^−4 ) on the bound and virtual-state pole positions is analyzed for noble gases and nonpolar molecules such as H _2 , N _2 , and CH _4 . The quantitative relations between the S-matrix poles and the s -wave scattering length accounting for dipole polarization are introduced.

More than one hundred years of experimental and theoretical investigations of electron scattering in gases delivered cross-sections in a wide energy range, from few meV to keV. An analogy in optics, characterizing different materials, comes under the name of the dispersion relation, i.e., of the dependence of the refraction index on the light wavelength. The dispersion relation for electron (and positron) scattering was hypothesized in the 1970s, but without clear results. Here, we review experimental, theoretical, and semi-empirical cross-sections for N2, CO2, CH4, and CF4 in search of any hint for such a relation—unfortunately, without satisfactory conclusions.

On constant movement of frontiers between Science and Theology. Part 2: MetaphysicsIn the first part (Karwasz, Scientia et Fides, 3(1) 2015) entitled “Physics” we showed how discoveries of modern sciences do not contradict Bible: neither in the subject of the beginning of the word nor in the subjects of the homogeneity of Homo Sapiens and the common origin of Euroasiatic languages. In this part we show that numerous “explanations” of natural phenomena like Pauli’s exclusion principle governing the chemistry, like space-time of Einstein, like apparent paradoxes of quantum mechanics, in reality move the border of our knowledge towards metaphysics: writings of philosophers from Aristotle, S. Augustine, S. Thomas to Kant are not in contrast with ontological conclusions of modern physics. In this way, the explanations based on philosophical principles find their place in natural sciences.

On constant movement of frontiers between Theology and Science: PhysicsPope Benedict XVI wrote in 1979 in “Four sermons on the Creation of world” that scientific discoveries cause a kind of retreat of the faith on “defensive” positions, giving an impression that in few centuries there would be no single dogma of faith valid. Discussing progresses of physics in last century (inflation of Universe, non-locality of quantum mechanics), of linguistics (the origin of Indo-European languages) and of genetics (mitochondrial DNA of Homo sapiens) we show that scientific discoveries make the faith retreat only apparently. In fact, the progress of science does not change the principles of Faith, but only illustrates and validates them: remain valid thesis of St. Thomas and St. Augustine. Every science discovery creates new questions, making clear that man has to depend both on reason and Faith. The aim of the article is not to “explain” the Bible according the newest discoveries but to show that these discoveries do not corrode the principles of Faith. In this way the border between natural sciences and theology remains in a constant movement: theology leaves to science obvious facts, entering deeper to the mystery of Revelation.