Nuclear Data Sheets for A = 89

Nuclear Data Sheets for A = 191

The Hamiltonian obtained from the linearization of the free collective Schr?dinger equation can be understood as a supercharge. The inclusion of a scalar potential shows that the linearization procedure is equivalent to the factorization method applied in supersymmetric quantum mechanics. Finally a supersymmetric Hamiltonian is constructed which includes the collective Schr?dinger equation as well as the linearized collective Schr?dinger equation.

https://iopscience.iop.org/article/10.1088/0954-3899/25/5/103/pdf

Linearized collective Schrödinger equation and supersymmetry.

The linearisation of the Schrodinger equation leads to a description of odd-even nuclei with spin 3/2 in the ground state. In order to generalise this description to nuclei with arbitrary spins in their ground states, we construct the Bargmann-Wigner equations (BWEs) for the [1, 1]SO(5)-representation, which can be applied to odd-odd nuclei with spins 1 and 3, and for the [3/2, 3/2]SO(5)-representation which can describe odd-even nuclei having ground-state spins of 3/2, 5/2 and 9/2. We also present the nonrelativistic limit of the BWE for [1, 1]SO(5)-representation in the case of a particle moving in an electromagnetic field with minimal coupling.

Bargmann-Wigner equations in five-dimensional space

Nuclear Data Sheets for A = 193

The linearized collective Schroedinger equation for nuclear quadrupole vibrations describes nuclei with spin 3/2 in the ground state. Another model, which has been developed for nuclei with spin 3/2, is the [ital j]=3/2 interacting boson fermion model. We use a special property of the Clifford algebra, which appears in the linearized collective Schroedinger equation, to establish a connection between both models. We also compare the predictions of both approaches for various spin-3/2 nuclei.

Spin-dependent generalized collective model in relation to the j=3/2 interacting boson fermion model

The Spin-dependent Generalized Collective Model, derived from a linearized collective Schrodinger equation in quadrupole coordinates, describes nuclei with spin 3/2 in the ground state. In this paper, we extend this model to arbitrary half-integer spins and apply it to even-odd nuclei with spins 1/2 and 5/2.

Extension of the spin-dependent generalized collective model to even-odd nuclei with spin 1/2 and 5/2

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Spin-dependent generalized collective model in relation to the j=3/2 interacting boson fermion model

Extension of the spin-dependent generalized collective model to even-odd nuclei with spin 1/2 and 5/2