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Fission models revisited: reactions and dynamics

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An Introduction to Nuclear Fission

Part of the book series: Graduate Texts in Physics ((GTP))

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Abstract

Chapter 7 is an advanced discussion of models of fission reactions and dynamics. The chapter starts with a general discussion of scattering theory, resonances, and widths to arrive at the formal definition of a cross section and to set the stage for Hauser-Feshbach theory, the framework widely used for the calculation of fission (and other) cross sections. Hauser-Feshbach theory is treated in detail with an extensive discussion of transition state theory and its application to fission. The discussion of the Hauser-Feshbach formalism highlights the importance of two crucial ingredients in the calculations: level densities, already discussed in Chap. 6, and transition strengths introduced in this chapter. Quasifission is discussed along with direct-reaction-induced fission. A brief survey of advanced topics gives a discussion of semi-classical and quantum mechanical methods used in the description of fission dynamics and which represent the state of the art in current research to describe the evolution of the fissioning nucleus to scission and beyond.

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Notes

  1. 1.

    Note that the beam and detected particles do not have to be the same, unless the reaction is elastic.

  2. 2.

    With the caveat that energy, angular momentum, and parity must be conserved throughout the process.

  3. 3.

    We ignore some of the details for the sake of simplicity, namely, parity and the angular momenta of the individual channels α, β, and γ. A more complete version of Eq. (7.23) would include cumbersome summations over those quantum numbers as well [19].

  4. 4.

    In realistic calculations, the situation is usually more complicated with M x and M y themselves functions of x and y and the presence of a cross term in xy with its own inertial mass.

  5. 5.

    For alternate values of the transition state energies and moments of inertia, see, for example, the user’s manual for the TALYS reaction code (available at https://tendl.web.psi.ch/tendl_2019/talys.html).

  6. 6.

    It is worth noting that tritium beams are difficult to come by nowadays, but many \(\left (t,pf\right )\) reaction studies were performed in the 1960s [21].

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Authors and Affiliations

  1. Livermore, CA, USA

    Walid Younes

  2. Department of Chemistry, Oregon State University, Corvallis, OR, USA

    Walter D. Loveland

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Younes, W., Loveland, W.D. (2021). Fission models revisited: reactions and dynamics. In: An Introduction to Nuclear Fission. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-84592-6_7

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