Semimicroscopic Algebraic Cluster Model Research Articles

Application of the cranking method to the semimicroscopic algebraic cluster model and nuclear molecules

A particular quantum phase transition (QPT) is studied at excited energies of light nuclei within the Semimicroscopic Algebraic Cluster Model (SACM), using a combination of catastrophe theory and a direct minimization of the potential. A distinct change from a compact nucleus to a nuclear molecule is described as a second order QPT occurring at a certain value of angular momentum. This finding is in accordance with experimental observations when nuclear molecules appear. The method has implication in the fission of heavy nuclei.

Symplectic Symmetry and Clustering in Atomic Nuclei

A new symplectic-based shell-model approach to clustering in atomic nuclei is proposed by considering the simple system $^{20}$Ne. Its relation to the collective excitations of this system is mentioned as well. The construction of the Pauli allowed Hilbert space of the cluster states with maximal permutational symmetry is given for the $^{16}$O+$^{4}$He $\rightarrow$ $^{20}$Ne channel in the case of one-component many-particle nuclear system. The equivalence of the obtained cluster model space to that of the semi-microscopic algebraic cluster model is demonstrated.

A semimicroscopic algebraic cluster model for heavy nuclei

An extension of the Semimicroscopic Algebraic Cluster Model (SACM) is proposed, based on the pseudo-SU(3) model. The Hamiltonian and the spectroscopic factor operator of the model are presented and a procedure of constructing the model space. Because a huge number of SU(3) irreducible representations (irrep) appear, one has to be careful in designing a practical, consistent path to reduce the Hilbert space. The concept of forbiddenness, taking into account excitations of the clusters, is introduced and applied. The applications are to two systems with a low forbiddenness, namely to 236U -> 210Pb + 26Ne and 224Ra -> 210Pb + 14C, and to 236U -> 146Xe + 90Sr, which appears in the fission of 236U, which requires a large forbiddenness. Energies, electromagnetic transitions and spectroscopic factors are calculated.

Results on quantum phase transitions within the semimicroscopic algebraic cluster model and extension to deformed clusters

The properties of quantum phase transitions in the semimicroscopic algebraic cluster model are investigated. The order of the quantum phase transition is shown to depend on the path taken in the parameter space and a novel procedure to obtain the Maxwell set separatrix is discussed. The first steps toward a description of systems of deformed cluster and heavy nuclei are presented.

Quantum Phase Transitions within the Semimicroscopic Algebraic Cluster Model

Quantum Phase Transition (QPT) properties are investigated within the Semimicroscopic Algebraic Cluster Model (SACM), as an example of a model with involved structure. The catastrophe theory is applied to obtain a physical insight and analytic formulas for the process of QPTs. QPTs are obtained up to the third order. We propose a novel procedure which can be used in several models in various sectors of physics.

Analysis of the alpha-transfer reaction in the 12C + 16O system using the semi-microscopic algebraic cluster model

In this work, we revisit the experimental data for elastic, inelastic and $\alpha$-transfer in the 12C + 16O system at 80 and 84 MeV using the coupled reaction channel method to analyze the angular distributions. The spectroscopic amplitudes relevant for the $\alpha$-transfer channel have been calculated from the semi-microscopic algebraic cluster model. The imaginary term of the optical potential was fitted to the experimental elastic scattering data at forward angles. Our calculations describe reasonable well the absolute cross sections for the inelastic scattering and $\alpha$-transfer. We discuss the effect of couplings on the transfer channel.

16O within the Semimicroscopic Algebraic Cluster Model and the importance of the Pauli Exclusion Principle

The Semimicroscopic Algebraic Cluster Model (SACM) is applied to 16O, assumed to consist of a system of four alpha-clusters. For the 4-alpha cluster system a microscopic model space is constructed, which observes the Pauli-Exclusion-Principle (PEP) and is symmetric under permutation of the 4-alpha-particles. A phenomenological Hamiltonian is used, justifying the name Semi in the SACM. The spectrum and transition values are determined. One of the main objectives is to test the importance of the Pauli Exclusion Principle (PEP), comparing the results with the Algebraic Cluster Model (ACM), which does not include the PEP, and claims that the 16O shows evidence of a tetrahedral structure, which can be explained easily by symmetry arguments. We show that PEP is very important and cannot be neglected, otherwise it leads to a wrong interpretation of the band structure and to too many states at low energy.

12C within the Semimicroscopic Algebraic Cluster Model

The Semimicroscopic Algebraic Cluster Model (SACM) is applied to 12C as a system of three alpha- clusters. The microscopic model space, which observes the Pauli-Exclusion-Principle (PEP), is constructed. It is shown that the 12C nucleus can effectively be treated as a two-cluster system 8Be+alpha. The experimental spectrum is well reproduced. The geometrical mapping is discussed and it is shown that the ground state must correspond to a triangular structure, which is in agreement with other microscopic calculations. The non-zero B(E2; 0_2+ --> 2_1+) transition requires a mixing of SU(3) irreducible representations (irreps) whose consequences are discussed. The Hoyle state turns out to contain large shell excitations. The results are compared to another phenomenological model, which assumes a triangular structure and, using simple symmetry arguments, can reproduce the states observed at low energy. This model does not observe the PEP and one objective of our contribution is to verify the extend of importance of the PEP.

Phase transitions for rotational states within an algebraic cluster model

The ground state and excited, rotational phase transitions are investigated within the Semimicroscopic Algebraic Cluster Model (SACM). The catastrophe theory is used to describe these phase transitions. Short introductions to the SACM and the catastrophe theory are given. We apply the formalism to the case of 16O+α→20Ne.

Semimicroscopic algebraic description ofαclustering in22Ne

The alpha-cluster states of $^{22}$Ne are studied within the framework of the semimicroscopic algebraic cluster model (SACM). The band structure, energy spectrum as well as E2 and E1 transitions are calculated and are compared with the experimental data. The results are also compared with those obtained from two microscopic models: the deformed-basis antisymmetrized molecular dynamics (DAMD) approach and the generator-coordinate method (GCM). It is found that the prominent bands obtained in the latter frameworks all have equivalents in the SACM and the agreement between the calculated spectroscopic properties is rather good, especially for positive-parity states.

The geometric interpretation of the semimicroscopic algebraic cluster model and the role of the Pauli principle

We study the properties of the Semimicroscopic Algebraic Cluster Model (SACM) under phase transitions. We show that the SACM can undergo first and second order phase transitions and a critical line appears. When the Pauli principle is not observed, the critical line appears, but other non-physical properties arise. At the end the meaning of the SO(4) dynamical limit is discussed.

Comparing the group theoretical approaches to the description of dipole and quadrupole collectivity in nuclei

The comparison of the two types of collectivity in nuclear dynamics is based on the equal realizations of their basic symmetries, represented by the algebra-chain u(3) ⊃ su(3) ⊃ so(3). We illustrate this on the example of two phenomenological algebraic models: the semimicroscopic algebraic cluster model (SACM) with one of the clusters considered as a scalar and the interacting two vector boson model (IVBM). In both of them the root group structure that leads to the above chain is based on the coupling of two different U(3) representations, with different physical interpretations. These similarities allow for the use of the same mathematical tools in building the theory, but there are important differences that come from the different higher symmetries in which this equal substructures are embedded.

Phase transitions for excited states in 16O+α → 20Ne within the SACM

We present the cranking of the Semimicroscopic Algebraic Cluster Model (SACM) for two spherical clusters. A geometrical mapping is applied and a discussion on phase transition as a function of the cranking parameter is given. This parameter can be related to the average angular momentum of the nucleus. The particular cluster system considered is 16O+α → 20Ne. We also investigate the phase transition property when the Pauli exclusion principle is not observed. We show that phase transitions may occur within the same dynamical symmetry limit.

Phenomenological and microscopic cluster models. I. The geometric mapping

The geometrical mapping of algebraic nuclear cluster models is investigated within the coherent state formalism. Two models are considered: the Semimicroscopic Algebraic Cluster Model (SACM) and the Phenomenological Algebraic Cluster Model (PACM), which is a special limit of the SACM. The SACM strictly observes the Pauli exclusion principle while the PACM does not. The discussion of the SACM is adapted to the coherent state formalism by introducing the new SO(3) dynamical symmetry limit and third-order interaction terms in the Hamiltonian. The potential energy surface is constructed in both models and it is found that the effects of the Pauli principle can be simulated by higher-order interaction terms in the PACM. The present study is also meant to serve as a starting point for investigating phase transitions in the two algebraic cluster models.

Phenomenological and microscopic cluster models. II. Phase transitions

Based on the results of a previous paper (Paper I), by performing the geometrical mapping via coherent states, phase transitions are investigated and compared within two algebraic cluster models. The difference between the semimicroscopic algebraic cluster model (SACM) and the phenomenological algebraic cluster model (PACM) is that the former strictly observes the Pauli exclusion principle between the nucleons of the individual clusters, while the latter ignores it. From the technical point of view the SACM is more involved mathematically, while the formalism of the PACM is closer to that of other algebraic models with different physical content. First- and second-order phase transitions are identified in both models, while in the SACM a critical line also appears. Analytical results are complemented with numerical studies on $\ensuremath{\alpha}$-cluster states of the ${}^{20}$Ne and ${}^{24}$Mg nuclei.

Phenomenological and semimicroscopic cluster models and their phase transitions

Two algebraic cluster models of nuclear structure which use the same Hamiltonian are explored: a Phenomenological Algebraic Cluster Model (PACM), and a Semi-microscopic Algebraic Cluster Model (SACM). The PACM does not incorporate the Pauli exclusion principle, while the SACM does. The Hamiltonian considered is an admixture of three dynamical symmetries; the SU(3), SO(4), and SO(3), with weighting of each determined by parameters. The classical potential is constructed using coherent states, and the model Hilbert space of the SACM is constructed in such a way as to include all shell model states which correspond to the cluster structure of interest. Phase transitions and their orders are investigated for each model, and parameter phase diagrams are presented, wherein it is found that consideration of the Pauli principle has significant consequences. Also shown are fits of Hamiltonian parameters for a nucleus of 2 spherical clusters, when moving between the symmetry limits.

α-clusterstructure in Be isotopes

The Be chain of isotopes is investigated within the semimicroscopicalgebraic cluster model (SACM). For that the SACM is applied to odd-massp-shell nuclei. We show that the main features of the Be isotopes can bewell explained. Though for the neutron halo nucleus 11Be someproblems remain, the shell model still can roughly describe the structuresof halo nuclei. In 11Be a shell inversion takes place as a result of thehigh deformation of the system. The quadrupole-quadrupole interaction isfound to play a dominant role in the structure of p-shell nuclei.

From Common Many-Body Problems to Uncommon Two-Body Problems: An Algebraic Approach to Clusterization

The basic concepts and the geometric content of the semimicroscopic algebraic cluster model are presented. The model is applied for a unified description of the 56Ni nucleus, including both the low-lying states and the molecular 28Si +28Si resonances.

The Semimicroscopic Algebraic Cluster Model: I. — Basic concepts and relations to other models

The basic concepts of the Semimicroscopic Algebraic Cluster Model, and its relation to other approaches are reviewed. Possible extensions to heavy nuclei and the connection to cold fission are also discussed.

The Semimicroscopic Algebraic Cluster Model: II. — Detailed analysis

We present examples for recent applications of the Semimicroscopic Algebraic Cluster Model and also discuss its prospective extensions in various directions. The examples considered here include core+α-particle-type cluster configurations and more complex cluster systems. The former ones are relatively simple in technical terms, so the basics of the model can be demonstrated by them in a transparent way, while the latter ones, though technically more involved, illustrate the ability of the model to handle in a unified way clustering phenomena that are usually treated in terms of essentially different approaches.