Different but the same: A unified explanation of zero-energy resonant and transparent collisions

R. O. BARRACHINA; MACRI, P. A.

Aarhus

Conferencia; 11th European Conference on Atoms, Molecules and Photons; 2013

In the late 1930s it was discovered that the scattering of low neutrons by ortho-hydrogen could be several times larger than in the case para-hydrogen [1]. This zero-energy resonance was in the antipodes of the Ramsauer-Townsend effect, where certain gases become transparent to electron swarms at given low energies. It was immediately assumed that the dissimilarity between both effects was not only in the magnitude of their cross sections, which were much larger or smaller than any reasonable estimate, but also on how they were explained. While the zero-energy resonance was described in terms of the poles of Scattering operator [2], the standard explanation of the transparency effect relied on a partial wave decomposition of the scattering amplitude [3].In spite of this long standing tradition of explaining both effects on such dissimilar grounds, we demonstrate that they have a similar origin and that a unified description in terms of Jost functions [4] is possible. The joint explanation of both effects relies on the distribution of the zeros of the Jost functions. This is akin to the standard description of the zero-energy resonance, where a single zero of the s-wave Jost function located near the origin is held responsible for the increase of the cross section. However, it can be shown that this single zero does not guarantee the effect, and that the contributions of other zeros of the Jost function can play a relevant role and even preclude the resonance. Similarly, the zero-energy transparency is shown to be a collective effect where the contributions of all zeros cancel exactly.Our explanation provides a very general ground to these effects, making them independent of the particularities of the collision itself. For instance, it can be demonstrated that in the zero-energy resonance and transparency effects the standard threshold dependence of the ℓ−wave partial cross section is changed into that of an ℓ−1 or ℓ+1 partial wave for ℓ>0, respectively [5]. Furthermore, our explanation can be extended to inelastic collisions, where the cross section at the opening of a channel with ℓ symmetry can show important deviations from the celebrated Wigner threshold law. In particular, at a zero-energy resonance it is shown to change into that of a ℓ−2 partial wave for ℓ>0 [6].References:[1] J. Halpern, I. Estermann, O. C. Simpson, O. Stern, Phys. Rev. 52, 142 (1937).[2] R. G. Newton, Phys. Rev. 100, 412 (1966).[3] D. Bohm, Quantum Theory (Prentice-Hall, Englewood Cliffs, 1951) p 568.[4] R. Jost, A. Pais, Phys. Rev. 82, 840 (1951).[5] P. A. Macri, R. O. Barrachina, J. Phys. B 46, 065202 (2013).[6] R. O. Barrachina and P. A. Macri, Few-Body Systems 34, 175 (2004