Abstract
Bremsstrahlung emission in collisions between charged nuclei is equivalent to nuclear gamma decay between continuum states. The way the continuum spectrum can be treated is not unique, and efficiency and accuracy of cross section calculations depend on the chosen method. In this work we describe, relate, and compare three different methods in practical calculations of inelastic cross sections, that is, by (i) treating the initial and final states as pure continuum states on the real energy axis, (ii) discretizing the continuum states on the real energy axis with a box boundary condition, and (iii) complex rotation of the hamiltonian (complex scaling method). The electric quadrupole transitions, 2+ → 0+ and 4+ → 2+, in α + α scattering are taken as an illustration.
Similar content being viewed by others
References
Alder K., Bohr A., Huus T., Mottelson B., Winther A.: Study of Nuclear Structure by Electromagnetic Excitation with Accelerated Ions. Rev. Mod. Phys. 28, 432 (1956)
Langanke K., Rolfs C.: Resonant E2 capture into the 8Be ground state. Phys. Rev. C 33, 790–792 (1986)
Bertulani C.A., de Paula D.T., Zelevinsky V.G.: Bremsstrahlung radiation by a tunneling particle: A time-dependent description. Phys. Rev. C 60, R031602 (1999)
Myo T., Ohnioshi A., Kato K.: Resonance and continuum components of the strength function. Prog. Theor. Phys. 99, 801–817 (1998)
Ho Y.K.: The method of complex coordinate rotation and its applications to atomic collision processes. Phys. Rep. 99, 1–68 (1983)
Garrido E., Jensen A.S., Fedorov D.V.: Inelastic cross sections and continuum transitions illustrated by 8Be results. Phys. Rev. C 86, 064608 (2013)
Garrido, E., Jensen, A.S., Fedorov, D.V.: Rotational bands in the continuum illustrated by 8Be results. Phys. Rev. C 88, 024001 (2013)
Tanimura O., Mosel U.: Bremsstrahlung in heavy-ion molecular resonances. Nucl. Phys. A 440, 173–188 (1985)
Zel’dovich Ya.B.: On the theory of unstable states. Zh. Exp. Theor. Fiz. 39, 776–780 (1960)
Langanke K.: Potential model study of α + α bremsstrahlung. Phys. Lett. B 174, 27–31 (1986)
Buck B., Friedrich H., Wheatley C.: Local potential models for the scattering of complex nuclei. Nucl. Phys. A 275, 246–268 (1977)
Ali S., Bodmer A.R.: Phenomenological α − α potentials. Nucl. Phys. A 80, 99–122 (1966)
Krolle D., Assenbaum H.J., Funk C., Langanke K.: Possible experiments to distinguish between different methods of treating the Pauli principle in nuclear potential models. Phys. Rev. C 35, 1631–1636 (1987)
Tilley D.R., Kelley J.H., Godwin J.L., Millener D.J., Purcell J., Sheu C.G., Weller H.R.: Energy levels of light nuclei A = 8,9,10. Nucl. Phys. A 745, 155–362 (2004)
Langanke K., Rolfs C.: Resonant and intrastate transitions to the 2+ state in 8Be. Z. Phys. A 324, 307–310 (1986)
Greiner W.: Quantum Mechanics: Special chapters. pp. 121, pp. 121. Springer, Berlin (2001)
Bertulani C.A.: 7Be(p, γ) 8B cross section from indirect breakup experiments. 356, 293– (1996)
Nunes F.M., Thompson I.J.: Multistep effects in sub-Coulomb breakup. Phys. Rev. C 59, 2652–2659 (1999)
Forssén C., Shulgina N.B., Zhukov M.V.: Radiative capture and electromagnetic dissociation involving loosely bound nuclei: The 8B example. Phys. Rev. C 67, 045801 (2003)
Moiseyev N.: Quantum theory of resonances: calculating energies, widths and cross-sections by complex scaling. Phys. Rep. 302, 212–293 (1998)
Alon O.E., Moiseyev N.: Balslev-Combes theorem within the framework of the finite-matrix approximation. Phys. Rev. A 46, 3807–3811 (1992)
Kato K.: Resonances and continuum states in the complex scaling method. J. Phys.: Conf. Ser. 49, 73–78 (2006)
Giraud B., Kato K.: Complex-scaled spectrum completeness for pedestrians. Ann. Phys. 308, 115–142 (2003)
Economou, E.N.: Green’s functions in quantum physics, Chapter 1. Springer Series in Solid-State Sciences 7, Springer, Berlin, (2006)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Garrido, E., Jensen, A.S. & Fedorov, D.V. Techniques to Treat the Continuum Applied to Electromagnetic Transitions in 8Be. Few-Body Syst 55, 101–119 (2014). https://doi.org/10.1007/s00601-013-0791-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00601-013-0791-1