Semimicroscopic Algebraic Cluster Model of Light Nuclei. I. Two-Cluster-Systems with Spin-Isospin-Free Interactions

Cseh, J.; Lévai, G.

doi:10.1006/aphy.1994.1024

Cited by 108 publications

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“…The products of all types of boson creation with boson annihilation operators form a U R (4) group. For a detailed description of the SACM, please consult [1,2].…”

Section: The Semimicroscopic Algebraic Cluster Modelmentioning

confidence: 99%

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Phase transitions for rotational states within an algebraic cluster model

López‐Moreno¹,

Hernández

Hess

et al. 2016

J. Phys.: Conf. Ser.

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Tests of Predictions of the IntroductionThe Semimicroscopic Algebraic Cluster Model (SACM) [1, 2] is a successful cluster model for nuclei. It takes into account the Pauli exclusion principle for any cluster model. It was successfully applied to nuclei in the sd shell, where one of the last applications is published in [3]. Cluster systems of astrophysical interest were considered and also spectroscopic factors [4] calculated. A detailed study of quantum phase transitions of the ground state where published in [5,6]. However, this study was done in a pedestrian way, not using the latest technology available, which is the catastrophe theory [7]. Excited, rotational states were considered in [8], but also here the treatment was simple. The objective of this contribution is to apply the catastrophe theory to nuclear cluster system, in order to study in a very effective and detailed manner the structure of phase transitions in nuclear cluster systems, in the ground state and for excited states. The catastrophe theory was applied with great success, also in nuclear systems [9,10]. Of special interest, because of its relation to the case presented here, is [11].

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“…The products of all types of boson creation with boson annihilation operators form a U R (4) group. For a detailed description of the SACM, please consult [1,2].…”

Section: The Semimicroscopic Algebraic Cluster Modelmentioning

confidence: 99%

“…The Semimicroscopic Algebraic Cluster Model (SACM) [1,2] is a successful cluster model for nuclei. It takes into account the Pauli exclusion principle for any cluster model.…”

Section: Introductionmentioning

confidence: 99%

Phase transitions for rotational states within an algebraic cluster model

López‐Moreno¹,

Hernández

Hess

et al. 2016

J. Phys.: Conf. Ser.

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“…The calculation is restricted to only a few SU (3) irreps as band-heads of symplectic excitations, which start from SU (3) bad heads in the valence shell and adds 2 ω excitations. This model has a lot in common with the Semimicroscopic Alegbraic Cluster Model (SACM) [6,7], which also starts from SU (3) irreps in the 0 ω shell and includes intershell excitations by adding relative oscillation quanta. Due to its starting point of a cluster picture, it is able to describe complicated cluster configurations.…”

Section: Introductionmentioning

confidence: 99%

The concept of nuclear cluster forbiddenness

Yépez-Martínez

Hess

2015

J. Phys. G: Nucl. Part. Phys.

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In nuclear cluster systems, a rigorous structural forbiddenness of virtual nuclear division into unexcited fragments is obtained. We reanalyze the concept of forbiddenness, introduced in [1] for the understanding of structural effects in nuclear cluster physics. We show that the concept is more involved than the one presented previously, where some errors were committed. Due to its importance, it is reanalyzed here. In the present contribution a simple way for the determination of forbiddenness is given, which may easily be extended to any number of clusters, though in this contribution we discuss only twocluster systems, for illustrative reasons. A simple rule is obtained for the minimization of the forbiddenness, namely to start from a cluster system with a large SU (3) irrep (λ c , µ c ), but minimizing (λ c − µ c ), i.e. the system has to be oblate. The rule can be easily implemented in structural studies, done up to now with an oversimplified definition of forbiddenness. The new method is applied to various systems of light clusters and to some decay channels of 236 U and 252 Cf.

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“…One is the Phenomenological Algebraic Cluster Model (PACM), while the other is the Semimicroscopic Algebraic Cluster Model (SACM) [14,15]. The first set does not obey the Pauli exclusion…”

Section: Introductionmentioning

confidence: 99%

Phase transitions in algebraic cluster models

Yépez-Martínez¹,

Rodríguez²,

Hess³

et al. 2010

J. Phys.: Conf. Ser.

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Abstract. Two algebraic cluster models are studied from the point of view of phase transitions: one in which the Pauli exclusion principle is taken into account and one in which it isn't. A third-order interaction is introduced to avoid instabilities in the model spectra, which is generally not taken into account. It is shown that both first-and second-order phase transitions occur. The 20 Ne→ 16 O+α system is considered as an example. Without taking into account the Pauli exclusion principle the transition from the SU (3) to the SO(4) dynamical symmetry is of first or second order, depending on the strength of the quadrupole-quadrupole interaction. It is shown that the inclusion of the Pauli-principle can be simulated by higher-order interactions when the model space is not truncated. IntroductionThe study of phase transitions enjoys a substantial interest in algebraic models of nuclear structure. The first examples [1,2] were related to the Interaction Boson Approximation (IBA) [3] and the vibron model [4,5]. In these approaches a coherent state is constructed in terms of collective variables and a semi-classical potential is defined as the expectation value of the Hamiltonian with respect to the coherent state. Phase changes are identified with discontinuities in the derivatives of the potential with respect to specific parameters taken at the potential minima. An important conjucture was that phases are determined by quasi-dynamical symmetries. This approximate symmetry is also denoted as an effective symmetry and its mathematically sound definition, called embedded symmetry [6] has been applied to the shell model of the nucleus in [7]. The role of the quasi-dynamical symmetry in relation with the phase-transition was discussed in [8,9,10].Here we discuss phase transitions within algebraic cluster models, in which the relative motion is described by the vibron model. It was found that the corresponding phase transition is of second order [11]. In [12] phase transitions in U (n) algebraic models were discussed using interaction terms up to second order and the existence of a second-order phase transition was confirmed. In [13] a numerical study was performed within a realistic cluster system and it was argued (without proof) that the transition might be of first order.Here we revisit phase transitions within a particular set of cluster models. One is the Phenomenological Algebraic Cluster Model (PACM), while the other is the Semimicroscopic Algebraic Cluster Model (SACM) [14,15]. The first set does not obey the Pauli exclusion

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Semimicroscopic Algebraic Cluster Model of Light Nuclei. I. Two-Cluster-Systems with Spin-Isospin-Free Interactions

Cited by 108 publications

References 0 publications

Phase transitions for rotational states within an algebraic cluster model

Phase transitions for rotational states within an algebraic cluster model

The concept of nuclear cluster forbiddenness

Phase transitions in algebraic cluster models

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