Classical and quantal aspects of rotating atomic nuclei

The use of quantality is discussed in the case of nuclei and other many-body systems such as atomic electrons. This dimensionless quantity is known to indicate when a many-body system behaves like a crystal or a quantum liquid. Its role is further analyzed by showing its relation to the scattering length. The emergence of a fundamental length scale, the limit radius, is also shown. It corresponds to the hard-core of the nucleon-nucleon interaction in the case of nucleons, and to a value close to the Bohr radius in the case of atomic electrons. The occurrence of a cluster phase in nuclei is analyzed using the quantality through its relation to the localization parameter, allowing for the identification of both the number of nucleons and the density as control parameters for the occurrence of this phase. The relation of the quantality to the magnitude of the interaction also exhibits a third dimensionless parameter, monitoring the magnitude of the spin-orbit effect in finite systems, through the realization of the pseudospin symmetry. The impact of quantality on the spin-orbit effect is compared in various many-body systems. The role of quantality in the relative effect of the binding energy and the shell one is also analyzed in nuclei. Finally, additional dimensionless quantities are proposed from the generalization of the quantality. Nuclei are found to be exceptional systems because all their dimensionless quantities are close to the order of unity, at variance with other many-body systems.The use of quantality is discussed in the case of nuclei and other many-body systems such as atomic electrons. This dimensionless quantity is known to indicate when a many-body system behaves like a crystal or a quantum liquid. Its role is further analyzed by showing its relation to the scattering length. The emergence of a fundamental length scale, the limit radius, is also shown. It corresponds to the hard-core of the nucleon-nucleon interaction in the case of nucleons, and to a value close to the Bohr radius in the case of atomic electrons. The occurrence of a cluster phase in nuclei is analyzed using the quantality through its relation to the localization parameter, allowing for the identification of both the number of nucleons and the density as control parameters for the occurrence of this phase. The relation of the quantality to the magnitude of the interaction also exhibits a third dimensionless parameter, monitoring the magnitude of the spin-orbit effect in finite systems, through the realization of the pseudospin symmetry. The impact of quantality on the spin-orbit effect is compared in various many-body systems. The role of quantality in the relative effect of the binding energy and the shell one is also analyzed in nuclei. Finally, additional dimensionless quantities are proposed from the generalization of the quantality. Nuclei are found to be exceptional systems because all their dimensionless quantities are close to the order of unity, at variance with other many-body systems.

arXiv:2406.03378Physical Review COct 10, 20242 citations

A Quantum Mechanical Approach to Nuclear Rotations

Nouredine Zettili

Bulletin of the American Physical SocietyOct 8, 20140 citations

Quantal and classical radiative cascade in Rydberg plasmas

M. Raymond Flannery, D. Vrinceanu

Atoms in high- $(n,\mathcal{l})$ states formed in cold Rydberg plasmas decay to the ground state in a succession of radiative transitions populating intermediate excited states. A classical treatment presents radiative cascade in a physically transparent way and reveals the ``trajectory'' in $n\mathcal{l}$ space obeyed by the cascade, scaling rules, and other aspects hidden within the quantal approach. Quantal-classical correspondence in radiative decay is directly demonstrated. Classical transition probabilities are also presented and are in excellent agreement with quantal transition probabilities, even for moderate quantum numbers.Atoms in high-$(n,\mathcal{l})$ states formed in cold Rydberg plasmas decay to the ground state in a succession of radiative transitions populating intermediate excited states. A classical treatment presents radiative cascade in a physically transparent way and reveals the ``trajectory'' in $n\mathcal{l}$ space obeyed by the cascade, scaling rules, and other aspects hidden within the quantal approach. Quantal-classical correspondence in radiative decay is directly demonstrated. Classical transition probabilities are also presented and are in excellent agreement with quantal transition probabilities, even for moderate quantum numbers.

Physical Review ASep 11, 200338 citations

Nuclear collective rotations and coherent state dynamics

J. Broeckhove, E. Kesteloot, Piet Van Leuven

The European Physical Journal ASep 1, 19881 citation

Coherent rotational states in nuclear and molecular systems

Norma Mankoč Borštnik

Jan 1, 19850 citations

Atoms in high-

(n,\mathcal{l})

states formed in cold Rydberg plasmas decay to the ground state in a succession of radiative transitions populating intermediate excited states. A classical treatment presents radiative cascade in a physically transparent way and reveals the ``trajectory'' in

n\mathcal{l}

space obeyed by the cascade, scaling rules, and other aspects hidden within the quantal approach. Quantal-classical correspondence in radiative decay is directly demonstrated. Classical transition probabilities are also presented and are in excellent agreement with quantal transition probabilities, even for moderate quantum numbers.