Model for independent particle motion

Abstract

Independent particle model in nuclear physics assumes that the nucleon in the nucleus moves in the average (mean field) potential generated by all other nucleons. This chapter gives a short overview of basic features of the independent particle motion in atomic nuclei and its theoretical realization in the framework of shell models for spherical, deformed and rotating nuclei as well as in more sophisticated approaches such as microscopic+macroscopic model and density functional theories. Independent particle motion of nucleons leads to global and single-particle consequences. The global ones manifest themselves in the shell structure and its consequences for global structure of nuclear landscape, the existence of superheavy nuclei and the superdeformation at high spin are briefly reviewed. The latter shows itself in the single-particle properties such as energies, alignments and densities; their manifestations are illustrated on specific examples.

arXiv comment38 pages, 14 figures, Contribution to the "Handbook of Nuclear Physics", Springer Nature, 2022, Eds. I. Tanihata, H. Toki and T. Kajino, revised version

References in corpus (45)

• Nuclear ground-state masses and deformations: FRDM(2012)
• Relativistic Continuum Hartree Bogoliubov Theory for Ground State Properties of Exotic Nuclei
• Nuclear magic numbers: new features far from stability
• Relativistic Nuclear Energy Density Functionals: Mean-Field and Beyond
• Shell structure of superheavy nuclei in self-consistent mean-field models
• Structure of even-even nuclei using a mapped collective Hamiltonian and the D1S Gogny interaction
• DIRHB -- a relativistic self-consistent mean-field framework for atomic nuclei
• Global performance of covariant energy density functionals: ground state observables of even-even nuclei and the estimate of theoretical uncertainties
• Progress on tilted axis cranking covariant density functional theory for nuclear magnetic and antimagnetic rotation
• Time-odd components in the mean field of rotating superdeformed nuclei
• One-quasiparticle States in the Nuclear Energy Density Functional Theory
• Cranked Relativistic Hartree-Bogoliubov Theory: Formalism and Application to the Superdeformed Bands in the $A\sim 190$ region
• Rod-shaped Nuclei at Extreme Spin and Isospin
• A proton density bubble in the doubly magic ${}^{34}$Si nucleus
• The neutron drip line: single-particle degrees of freedom and pairing properties as sources of theoretical uncertainties
• Covariant density functional theory: Reexamining the structure of superheavy nuclei
• Linear chain structure of four-$\alpha$ clusters in ${}^{16}$O
• Rotational properties of ${}^{252,253,254}$No. Influence of pairing correlations
• Pairing and rotational properties of actinides and superheavy nuclei in covariant density functional theory
• Properties of nuclei in the nobelium region studied within the covariant, Skyrme, and Gogny energy density functionals
• Time-odd mean fields in covariant density functional theory I. Non-rotating systems
• Central depression in nuclear density and its consequences for the shell structure of superheavy nuclei
• Description of rotating $N=Z$ nuclei in terms of isovector pairing
• Additivity of Quadrupole Moments in Superdeformed Bands: Single-Particle Motion at Extreme Conditions
• Central depression in nucleonic densities: Trend analysis in nuclear density-functional-theory approach
• Beyond the Unified Model
• Extension of nuclear landscape to hyperheavy nuclei
• Time-odd mean fields in the rotating frame: microscopic nature of nuclear magnetism
• Properties of single-particle states in a fully self-consistent particle-vibration coupling approach
• Shape evolution in Yttrium and Niobium neutron-rich isotopes
• Relativistic Mean Field Theory in Rotating Frame: Single-particle Properties at Superdeformation
• Deformed one-quasiparticle states in covariant density functional theory
• Superdeformed bands in 32S and neighboring nuclei predicted within the Hartree-Fock method
• Superheavy nuclei in microscopic collective Hamiltonian approach: the impact of beyond mean field correlations on the ground state and fission properties
• Searching for 4$\alpha$ linear-chain structure in excited states of ${}^{16}$O with a covariant density functional theory
• Polarization Effects in Superdeformed Nuclei
• Additivity of effective quadrupole moments and angular momentum alignments in the A~130 nuclei
• Rotational excitations in rare-earth nuclei: a comparative study within three cranking models with different mean fields and the treatments of pairing correlations
• Spin-orbit splittings of neutron states in $N=20$ isotones from covariant density functionals and their extensions
• Single-particle spatial dispersion and clusters in nuclei
• From cluster structures to nuclear molecules: the role of nodal structure of the single-particle wave functions
• Many-body approach to superfluid nuclei in axial geometry
• Hyperheavy spherical and toroidal nuclei: the role of shell structure
• Superdeformations in Relativistic and Non-Relativistic Mean Field Theories
• Cluster structures, ellipsoidal shapes and nuclear molecules in light A=12-50 nuclei