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Fission models revisited: structure

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An Introduction to Nuclear Fission

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

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Abstract

This chapter deals with the nuclear structure aspects of fission at an advanced level. The discussion starts with the isotropic harmonic oscillator potential and describes in detail the Strutinsky shell correction method and its application. Pairing, which plays an important role in fission and more generally in many nuclear physics phenomena, is discussed in detail. Next, we consider the concept of level densities which are used in both nuclear structure and nuclear reaction models and are a critical component of fission cross-section calculations. Therefore, the chapter includes a detailed discussion of the calculation of level densities in nuclei. In the advanced topics section of the chapter, we build up to the Hartree-Fock approximation, the foundation of modern (so-called microscopic) theories of fission. Starting with solutions of the Schrödinger equation for many particles moving in a common potential, we arrive at the concept of a “mean field,” where the particles themselves generate that common potential in a self-consistent way.

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Notes

  1. 1.

    In more technical terms, this is a thermodynamic approach in the grand-canonical ensemble to the state density problem.

  2. 2.

    A more natural derivation of the Hartree-Fock equation, with antisymmetrization built in from the get-go, requires the use of second quantization, which is beyond the scope of this textbook (but see, e.g., [20, 41]).

  3. 3.

    Most effective interactions used at present also typically include a term that depends nonlinearly on the nucleon density \(\rho \left (\mathbf {r}\right )\). These terms modify somewhat the form of Eq. (6.91), and we will not discuss them here (see [20, 41] for more details).

  4. 4.

    Some authors use a definition that is 1∕2 the one in Eq. (6.95).

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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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  1. Walid Younes
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  2. Walter D. Loveland
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Younes, W., Loveland, W.D. (2021). Fission models revisited: structure. In: An Introduction to Nuclear Fission. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-84592-6_6

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