Elsevier

Annals of Physics

Volume 150, Issue 2, 15 October 1983, Pages 504-551
Annals of Physics

Three-dimensional nuclear dynamics in the quantized ATDHF approach

https://doi.org/10.1016/0003-4916(83)90025-8Get rights and content

Abstract

The quantized adiabatic time-dependent Hartree-Fock theory is numerically applied to the low energy large amplitude collective dynamics of heavy ion systems ranging from α + α to 16O + 16O. The problem is reduced to three successive steps. First, for the lowest mode the optimal, i.e., maximally decoupled, collective path {∥φq〉} is evaluated by solving a coupled set of nonlinear differential equations for the single-particle wave functions ϕq(a)(r) of ∥φq〉, depending on the collective coordinate q and three spatial coordinates. A density-dependent interaction with a direct finite range Yukawa-term is employed and three-dimensional coordinate- and momentum-grid techniques are used, including fast Fourier methods. In a second step the quantized collective Hamiltonian Hc(q, ddq) is extracted from {∥φq〉} by means of generator coordinate techniques involving, besides q, a conjugate variable p. Starting from {∥φ〉} this procedure includes the numerical evaluation of the classical potential, V(q), of the intertia parameter, M(q), of the quantum corrections with regard to rotation, translation and collective q-motion, L(q), and of the centrifugal potential. The third step consists of actually calculating the subbarrier fusion cross section by means of WKB methods applied to the collective Hamiltonian Hc(q, ddq). The theoretical numbers are compared with results from Hartree-Fock calculations with quadrupole constraint, and with experimental data. The microscopic aspects of the dynamics, the relation to other theories, and the practical and conceptual problems arising from the quantized ATDHF theory are discussed in detail.

References (51)

  • K. Goeke et al.

    Ann. Phys.

    (1978)
  • P.-G. Reinhard et al.

    Nucl. Phys. A

    (1978)
  • K. Goeke et al.

    Ann. Phys.

    (1980)
  • P.-G. Reinhard et al.

    Phys. Lett. B

    (1977)
  • G. Holzwarth et al.

    Nucl. Phys. A

    (1974)
  • J.P. Blaizot et al.

    J. Phys. (Paris)

    (1980)
  • K. Goeke et al.

    Phys. Lett. B

    (1982)
  • K. Goeke et al.

    Nucl. Phys. A

    (1982)
  • P.-G. Reinhard et al.

    Phys. Rev. Lett.

    (1980)
    K. Goeke et al.

    Phys. Lett. B

    (1983)
  • D.J. Thouless et al.

    Nucl. Phys.

    (1962)
  • R.E. Peierls et al.

    Nucl. Phys.

    (1962)
  • D.J. Rowe et al.E.J.V. de Passos
  • D.M. Brink et al.

    Nucl. Phys. A

    (1975)
    D.M. Brink et al.

    Nucl. Phys. A

    (1978)
  • H. Flocard

    Phys. Lett. B

    (1974)
  • P.G. Zint et al.

    Phys. Rev. C

    (1976)
  • H. Flocard et al.

    Nucl. Phys. A

    (1980)
  • J. Cugnon et al.

    Nucl. Phys. A

    (1979)
  • H.J. Mang et al.

    Z. Phys. A

    (1976)
  • K.T.R. Davies et al.

    Nucl. Phys. A

    (1980)
  • P.-G. Reinhard et al.

    Nucl. Phys. A

    (1982)
  • D.J. Rowe
  • J. Stoer et al.
  • P.A.M. Dirac
  • P. Bonche et al.

    Phys. Rev. C

    (1976)
  • H. Flocard et al.

    Phys. Rev. C

    (1978)
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