The authors review the present status of self-consistent mean-field (SCMF) models for describing nuclear structure and low-energy dynamics. These models are presented as effective energy-density functionals. The three most widely used variants of SCMF's based on a Skyrme energy functional, a Gogny force, and a relativistic mean-field Lagrangian are considered side by side. The crucial role of the treatment of pairing correlations is pointed out in each case. The authors discuss other related nuclear structure models and present several extensions beyond the mean-field model which are currently used. Phenomenological adjustment of the model parameters is discussed in detail. The performance quality of the SCMF model is demonstrated for a broad range of typical applications.

Self-consistent mean-field models for nuclear structure

Thermonuclear reaction rates V

The relativistic mean-field model of the nucleus is reviewed. It describes the nucleus as a system of Dirac nucleons which interact in a relativistic covariant manner via meson fields. The meson fields are treated as mean fields, i.e. as non-quantal c-number fields. The effect of the Dirac sea of the nucleons is neglected. The model is interpreted as a phenomenological ansatz providing a self-consistent relativistic description of nuclei and nuclear dynamics. It is viewed, so to say, as the relativistic generalisation of the Skyrme-Hartree-Fock ansatz. The capability and the limitations of the model to describe nuclear properties are discussed. Recent applications to spherical and deformed nuclei and to nuclear dynamics are presented.

https://iopscience.iop.org/article/10.1088/0034-4885/52/4/002/pdf

The relativistic mean-field description of nuclei and nuclear dynamics

Energy levels of light nuclei A=8,9,10

https://www.cns.s.u-tokyo.ac.jp/~shimoura/research/nuc_data/pdf/11.pdf

Energy levels of light nuclei A = 11-12

The generator coordinate method is reviewed from the point of view that it provides a versatile tool for formal development, in particular for the derivation of a consistent microscopic theory of large-amplitude collective motion. The Gaussian overlap approximation is employed to derive the collective mapping of arbitrary microscopic operators which is the starting point for all further derivation, e.g. of collective dynamics and of the equations determining the optimal collective path. The validity of the Gaussian overlap approximation and possible extensions are discussed. it is furthermore pointed out that one needs for nuclear collective motion dynamic paths where a collective mode is expanded by two conjugate parameters. The complications with dynamic paths can be overcome with the help of an adiabatic expansion in powers of the collective momentum. The final outcome is the quantised adiabatic time-dependent Hartree-Fock theory which is then exemplified in various examples.

https://iopscience.iop.org/article/10.1088/0034-4885/50/1/001/pdf

The generator coordinate method and quantised collective motion in nuclear systems

A consistent microscopic theory of collective motion in the framework of an ATDHF approach

The generator-coordinate-method with conjugate parameters and the unification of microscopic theories for large amplitude collective motion

/pdf/time-dependent-hartree-fock-and-beyond-19guf4831d.pdf

K. Goeke

Papers

The generator coordinate method and quantised collective motion in nuclear systems

A consistent microscopic theory of collective motion in the framework of an ATDHF approach

The generator-coordinate-method with conjugate parameters and the unification of microscopic theories for large amplitude collective motion

Time Dependent Hartree-Fock and Beyond

Three-dimensional nuclear dynamics in the quantized ATDHF approach