Geometrical interpretation of the semimicroscopic algebraic cluster model

Hess, Peter O.; Lévai, G.; Cseh, J.

doi:10.1103/physrevc.54.2345

Cited by 38 publications

(55 citation statements)

References 19 publications

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“…We used the method explained in the last section. For the case of 20 Ne, we found that the phase transition changes dramatically: For y = 1 the phase transition between the SU (3) and SO(4) dynamical symmetries vanishes! This is because the potential at y = 1 has a deformed minimum for all values of x, so no spherical minimum appears!…”

Section: Phase Transitionsmentioning

confidence: 91%

“…The geometric interpretation of the semimicroscopic algebraic cluster model and the role of the Pauli principle H Yépez-Martínez, P O Hess and G Lévai -Phase transitions for excited states in 16 O+ 20 Ne within the SACM G E Morales-Hernández, H Yépez-Martínez and P O Hess -Phenomenological and semimicroscopic cluster models and their phase transitions P R Fraser, H Yépez-Martínez, P O Hess et al …”

Section: Related Contentmentioning

confidence: 99%

“…where the γ parameter has to be set to 1 after the differentiation and the normalization factor N N,n 0 is given in [20]. For convenience here we redefined the total number of relative oscillation quanta by (N + n 0 ).…”

Section: Coherent State and The Mapping To A Semi-classical Potentialmentioning

confidence: 99%

“…A particular application: 20 Ne → 16 O + α In this section we consider a system that has the same model space as 20 Ne→ 16 O+α. In reality we do not consider the physical 20 Ne, because this is given by a fixed value of x and y adjusted to the physical spectrum. Rather, we describe a hypothetical cluster system with the same SU (3) representation as 20 Ne, changing its structure going from x = 1, the SU (3) dynamical symmetry limit, to x = 0, the SO(4) dynamical symmetry limit.…”

Section: Phase Transitionsmentioning

confidence: 99%

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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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Section: Phase Transitionsmentioning

confidence: 91%

Section: Related Contentmentioning

confidence: 99%

Section: Coherent State and The Mapping To A Semi-classical Potentialmentioning

confidence: 99%

Section: Phase Transitionsmentioning

confidence: 99%

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Phase transitions in algebraic cluster models

Yépez-Martínez¹,

Rodríguez²,

Hess³

et al. 2010

J. Phys.: Conf. Ser.

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“…The structure of the Hamiltonian is equivalent to introduce a Lagrange multiplier [13]. The semi-classical potential is obtained by first defining a coherent state [14] …”

Section: The Semimicroscopic Algebraic Cluster Modelmentioning

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

et al. 1997

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Summary. -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.PACS 21.60Fw -Models based on group theory. PACS 21.60.Gx -Cluster models. PACS 01.30.Cc -Conference proceedings. -IntroductionThe Semimicroscopic Algebraic Cluster Model (SACM) was proposed as an approach to the cluster structure of light nuclei [1,2]. Special emphasis was put on the unified description of the clusterization in the neighbourhood of the ground state and in the highly excited region of the molecular resonances. The model turned out to have a simple and transparent relation to other models of light nuclei. Particularly interesting is the fact that the common intersection of the three basic nuclear structure models, i.e., the shell, collective and cluster models, is provided by the U3 dynamic symmetry of the SACM.The interrelation of different cluster configurations can also be handled within this approach in a simple manner. This circumstance provides us with a selection rule applicable for fission channels. Recently an attempt has been initiated in order to extend this method to the territory of heavy nuclei, where various forms of radioactive and fission processes attract much attention these days.

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Geometrical interpretation of the semimicroscopic algebraic cluster model

Cited by 38 publications

References 19 publications

Phase transitions in algebraic cluster models

Phase transitions in algebraic cluster models

Phase transitions for rotational states within an algebraic cluster model

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

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