Connecting the proxy-SU(3) symmetry to the shell model

Proxy-SU(3) symmetry is an approximation scheme extending the Elliott SU(3) algebra of the sd shell to heavier shells. When introduced in 2017, the approximation had been justified by calculations carried out within the Nilsson model. Recently our group managed to map the cartesian basis of the Elliott SU(3) model onto the spherical shell model basis, proving that the proxy-SU(3) approximation corresponds to the replacement of the intruder orbitals by their de Shalit-Goldhaber partners, paving the way for using the proxy-SU(3) approximation in shell model calculations. The connection between the proxy-SU(3) scheme and the spherical shell model has also been worked out in the original framework of the Nilsson model, with identical results.

Ratios of negative-to-positive parity level densities in Mo isotopes

The ratios of negative-to-positive parity level densities in ^94,96,98Mo isotopes are calculated using a microscopic formalism based on the BCS model. In this calculation, the single-particle energies are obtained with the Nilsson model. Mass number, shell and deformation effects on the parity equilibration phenomena in these isotopes are discussed in this work.

Nonlinear extension of the u(3) algebra as the symmetry algebra of the three-dimensional anisotropic quantum harmonic oscillator with rational ratios of frequencies and the Nilsson model

The symmetry algebra of the N-dimensional anisotropic quantum har- monic oscillator with rational ratios of frequencies is constructed by a method of general applicability to quantum superintegrable systems. The special case of the 3-dim oscillator is studied in more detail, because of its relevance in the description of superdeformed nuclei and nuclear and atomic clusters. In this case the symmetry algebra turns out to be a nonlinear extension of the u(3) algebra. A generalized angular momentum operator useful for labeling the degenerate states is constructed, clarifying the connection of the present formalism to the Nilsson model.

Magic numbers for shape coexistence

The increasing deformation in atomic nuclei leads to the change of the classical magic numbers (2,8,20,28,50,82…) which dictate the arrangement of nucleons in complete shells. The magic numbers of the three-dimensional harmonic oscillator (2,8,20,40,70,…) emerge at deformations around ε=0.6. At lower deformations the two sets of magic numbers antagonize, leading to shape coexistence. A quantitative investigation is performed using the usual Nilsson model wave functions and the recently introduced proxy–SU(3) scheme.

Lawson method for obtaining wave functions and g factors of Ar isotopes

Lawson has shown that one can obtain sensible wave functions even in the weak deformation limit of the Nilsson model as long as one projects out states of good total angular momentum. We apply this method to obtain wave functions and magnetic [Formula: see text] factors of excited states of select even–even Ar isotopes with emphasis on the comparison of [Formula: see text]Ar and [Formula: see text]Ar. These [Formula: see text] factors are compared with the values that are obtained by matrix diagonalization in the same space using the WBT residual interaction.

Kaji Ulang Model Nilsson untuk Proton atau Neutron dengan Z, N <= 50

Telah dilakukan kaji ulang mengenai model inti Nilsson. Model ini dikembangkan dari model kulit dengan penambahan asumsi bahwa tidak ada interaksi antar nukleon (proton dan neutron). Jenis potensial yang digunakan adalah potensial osilator harmonik dengan menambahkan suku koreksi spin orbit dan koreksi bagian dasar potensial. Dengan metode ini didapatkan wakilan aras-aras energi pada diagram Nilsson yang gayut terhadap bilangan kuantum utama, bilangan kuantum radial pada sumbu simetri, bilangan kuantum radial pada sumbu tegak lurus, dan bilangan kuantum orbital yang diproyeksikan pada sumbu simetri. Wakilan aras-aras energi yang dihitung dalam kajian ini dibatasi pada cacah proton (Z) atau neutron (N) yang kurang dari atau sama dengan 50.kata kunci: model Nilsson; model kulit; diagram Nilsson

Nuclear Physics

The chapter gives an overview of nuclear physics from the discovery of the neutron to ongoing research topics. General properties of atomic nuclei are considered: the valley of stability, the nuclear potential, the pairing of nucleons and the strong force. The semi-empirical liquid drop model is presented as a description of relatively large atomic nuclei. The nuclear shell model is described, along with its relationship to magic numbers and beta decay, and is then refined to produce the Nilsson model. Gamow tunnelling is used to explain alpha decay and the Geiger–Nuttall law. It is then applied to nuclear fission and used to calculate rates for thermonuclear fusion in stars. ITER and controlled nuclear fusion are also discussed. Production of superheavy nuclei is detailed and the existence of exotic nuclei, such as halo nuclei, is considered. The Yukawa theory of the strong force is discussed, including its relationship to QCD.

The Deformation Structure of the Nuclei 32S and 36Ar

We applied two different approaches to investigate the deformation structures of the two nuclei S32 and Ar36 . In the first approach, we considered these nuclei as being deformed and have axes of symmetry. Accordingly, we calculated their moments of inertia by using the concept of the single-particle Schrödinger fluid as functions of the deformation parameter β. In this case we calculated also the electric quadrupole moments of the two nuclei by applying Nilsson model as functions of β. In the second approach, we used a strongly deformed nonaxial single-particle potential, depending on β and the nonaxiality parameter γ , to obtain the single-particle energies and wave functions. Accordingly, we calculated the quadrupole moments of S32 and Ar36 by filling the single-particle states corresponding to the ground- and the first excited states of these nuclei. The moments of inertia of S32 and Ar36 are then calculated by applying the nuclear superfluidity model. The obtained results are in good agreement with the corresponding experimental data.