© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:2406.03378 · Physical Review C

Use of quantality in nuclei and many-body systems

J.-P. Ebran, Louis Heitz, Elias Khan

Published Oct 10, 2024• 2 citations

Abstract

The use of quantality is discussed in the case of nuclei and other many-body systems such as atomic electrons. This dimensionless quantity is known to indicate when a many-body system behaves like a crystal or a quantum liquid. Its role is further analyzed by showing its relation to the scattering length. The emergence of a fundamental length scale, the limit radius, is also shown. It corresponds to the hard-core of the nucleon-nucleon interaction in the case of nucleons, and to a value close to the Bohr radius in the case of atomic electrons. The occurrence of a cluster phase in nuclei is analyzed using the quantality through its relation to the localization parameter, allowing for the identification of both the number of nucleons and the density as control parameters for the occurrence of this phase. The relation of the quantality to the magnitude of the interaction also exhibits a third dimensionless parameter, monitoring the magnitude of the spin-orbit effect in finite systems, through the realization of the pseudospin symmetry. The impact of quantality on the spin-orbit effect is compared in various many-body systems. The role of quantality in the relative effect of the binding energy and the shell one is also analyzed in nuclei. Finally, additional dimensionless quantities are proposed from the generalization of the quantality. Nuclei are found to be exceptional systems because all their dimensionless quantities are close to the order of unity, at variance with other many-body systems.

DOI: 10.1103/physrevc.110.044311

Related papers

Localisation and dimensionless studies in nuclei and many-body systems

J.-P. Ebran, Elias Khan

Dimensionless ratios characterizing many-body systems are a powerful tool to reveal the main universal quantities involved. The recently-introduced localisation parameter allow to study the occurrence of crystal, clusterisation, and quantum liquid states in many-body systems such as nuclei. Its concomitant use with other dimensionless quantities such as the quantality, allows to pinpoint fundamental lengthscales and dimensionless ratios at work in nuclei. Within the present approach, the impact of delocalisation on nuclear saturation is discussed. The transition from a homogeneous to a clusterised state in low density systems is studied. The spin-orbit effect in nuclei and fermionic systems is also reviewed in the light of this analysis. A generalised localisation parameter is derived, showing that the delocalisation properties are not always driven by the quantality. The concepts of quantum fluidity and mobility are finally introduced.

arXiv:1706.00584•Jun 2, 2017•0 citations

Study of nuclear structure by using many-body theory

Nguyễn Quang Hưng

Atomic nucleus consists of nucleons (protons and neutrons) interacting each other with the so-called nucleon-nucleon (NN) forces. The structure of atomic nucleus can be studied via many-body theories. Some of them are the well-known random-phase approximation (RPA) and/or the Bardeen-Cooper-Schrieffer (BCS) theory. These theories produce very well the properties of infinite systems such as superconductors, where the quantal and thermal fluctuations are zero or very small. However, our recent studies have shown that these fluctuations are significant in finite systems such as atomic nuclei. As the result, the physical properties of nuclear systems are changed due to the effects of quantal and thermal fluctuations. Therefore, the conventional many body theories need to be modified to include the effects of these fluctuations when they are applied to atomic nucleus. Recently, we have proposed a self-consistent quasiparticle RPA (SCQRPA) taking into account the effects of quantal and thermal fluctuations. The SCQRPA has been tested and the results obtained are in reasonable agreements with the exact solutions of the model cases as well as those obtained within the quantum Monte-Carlo method for realistic nuclei.

•Jan 1, 2011•0 citations

Modelling an infinite nucleonic system. Static and dynamical properties. Study of density fluctuations

D. Idier, M. Farine, B. Rémaud +1 more

For one decade, several fields in physics as well microscopic as macroscopic benefit from the computational particle-models (astrophysics, electronics, fluids mechanics...). In particular, the nuclear matter offers an interesting challenge as many body problem, owing to the quantal nature of its components and the complexity of the in-medium interaction. Using a model derived from semi-classical Vlasov equation and the projection of the Wigner function on a Gaussian coherent states basis (pseudo-particles), static and dynamical properties of nuclear matter are studied, featuring the growing of bulk instabilities in dilute matter. Using different zero and finite range effective interactions, the effect of the model parameters upon the relation total energy - density - temperature and surface energy of the pseudo-particles fluid is pointed out. The dynamical feature is first based upon a model of the 2-body Uehling-Ulhenbeck collisionnal term. A study of the relaxation of a nucleonic system is performed. At last, the pseudo-particle model is used in order to extract time scale for the growing of density fluctuations. This process is supposed to be a possible way to clusterization during heavy nuclei collisions.

Annales de Physique•Jan 1, 1994•22 citations

Effective interactions and the nuclear shell-model

D. J. Dean, T. Engel, Morten Hjorth-Jensen +2 more

This review aims at a critical discussion of the interplay between effective interactions derived from various many-body approaches and spectroscopic data extracted from large scale shell-model studies. To achieve this, our many-body scheme starts with the free nucleon-nucleon (NN) interaction, typically modelled on various meson exchanges. The NN interaction is in turn renormalized in order to derive an effective medium dependent interaction. The latter is in turn used in shell-model calculations of selected nuclei. We also describe how to sum up the parquet class of diagrams and present initial uses of the effective interactions in coupled cluster many-body theory.

•Jan 1, 2004•44 citations

Computer Modeling of Quantum Liquids and Crystals

Malvin H. Kalos, Paula A. Whitlock, David M. Ceperley

There are a number of many-body systems which exhibit quantum effects on a macroscopic scale. These include liquid and crystal states of both He-3 and He-4, the electron gas, and neutron matter which probably constitutes the interior of pulsors. In addition, "nuclear matter" - a hypothetical extensive system of nucleons has been studied for the insight one may gain into the nature of finite nuclei. The theoretical studies of these systems have by now a long history, but are by no means concluded. In the last few years, significant advances have been made. This has come in part from the maturity of and gradual unification of many-body theory, in part from the development and application of powerful new expansion procedures, especially varieties of hypernetted-chain equations ( 1 ) and finally to the growing power of computer simulation methods for quantum systems. This article is intended as a review of some recent

ACS symposium series•Jun 1, 1978•1 citation

The Coupled Cluster Method

R. F. Bishop, Hermann G. Kümmel

Liquids and solids, atoms and molecules, nuclei—all these clearly are interacting many-body systems. Even a nucleon may be regarded as a manyparticle system, not just because it is now known to consist of three quarks interacting via gluons, but because of the possibility in quantum field theory of virtual excitation of many particles from the vacuum. in the table page 56 we list some of the many-particle systems we encounter in the physical world at length scales that range from a few centimeters to a few fermis. Many of these systems exhibit phenomena—superconductivity in solids and fission in nuclei, for example—whose understanding does not follow immediately from knowledge of the constituents of the system and the interactions among the constituents, but requires new concepts and ideas. Many-body physics is the branch of theoretical physics that studies the new phenomena or “emergent properties” that arise from interactions among “elementary” constituents of a many-particle system and provides means and methods for carrying out precise calculations of such characteristic properties of these systems as may be compared with experimental results to verify hypotheses about the nature of the constituents and their interactions.

Physics Today•Mar 1, 1987•194 citations

The use of quantality is discussed in the case of nuclei and other many-body systems such as atomic electrons. This dimensionless quantity is known to indicate when a many-body system behaves like a crystal or a quantum liquid. Its role is further analyzed by showing its relation to the scattering length. The emergence of a fundamental length scale, the limit radius, is also shown. It corresponds to the hard-core of the nucleon-nucleon interaction in the case of nucleons, and to a value close to the Bohr radius in the case of atomic electrons. The occurrence of a cluster phase in nuclei is analyzed using the quantality through its relation to the localization parameter, allowing for the identification of both the number of nucleons and the density as control parameters for the occurrence of this phase. The relation of the quantality to the magnitude of the interaction also exhibits a third dimensionless parameter, monitoring the magnitude of the spin-orbit effect in finite systems, through the realization of the pseudospin symmetry. The impact of quantality on the spin-orbit effect is compared in various many-body systems. The role of quantality in the relative effect of the binding energy and the shell one is also analyzed in nuclei. Finally, additional dimensionless quantities are proposed from the generalization of the quantality. Nuclei are found to be exceptional systems because all their dimensionless quantities are close to the order of unity, at variance with other many-body systems.

Dimensionless ratios characterizing many-body systems are a powerful tool to reveal the main universal quantities involved. The recently-introduced localisation parameter allow to study the occurrence of crystal, clusterisation, and quantum liquid states in many-body systems such as nuclei. Its concomitant use with other dimensionless quantities such as the quantality, allows to pinpoint fundamental lengthscales and dimensionless ratios at work in nuclei. Within the present approach, the impact of delocalisation on nuclear saturation is discussed. The transition from a homogeneous to a clusterised state in low density systems is studied. The spin-orbit effect in nuclei and fermionic systems is also reviewed in the light of this analysis. A generalised localisation parameter is derived, showing that the delocalisation properties are not always driven by the quantality. The concepts of quantum fluidity and mobility are finally introduced.

Atomic nucleus consists of nucleons (protons and neutrons) interacting each other with the so-called nucleon-nucleon (NN) forces. The structure of atomic nucleus can be studied via many-body theories. Some of them are the well-known random-phase approximation (RPA) and/or the Bardeen-Cooper-Schrieffer (BCS) theory. These theories produce very well the properties of infinite systems such as superconductors, where the quantal and thermal fluctuations are zero or very small. However, our recent studies have shown that these fluctuations are significant in finite systems such as atomic nuclei. As the result, the physical properties of nuclear systems are changed due to the effects of quantal and thermal fluctuations. Therefore, the conventional many body theories need to be modified to include the effects of these fluctuations when they are applied to atomic nucleus. Recently, we have proposed a self-consistent quasiparticle RPA (SCQRPA) taking into account the effects of quantal and thermal fluctuations. The SCQRPA has been tested and the results obtained are in reasonable agreements with the exact solutions of the model cases as well as those obtained within the quantum Monte-Carlo method for realistic nuclei.

For one decade, several fields in physics as well microscopic as macroscopic benefit from the computational particle-models (astrophysics, electronics, fluids mechanics...). In particular, the nuclear matter offers an interesting challenge as many body problem, owing to the quantal nature of its components and the complexity of the in-medium interaction. Using a model derived from semi-classical Vlasov equation and the projection of the Wigner function on a Gaussian coherent states basis (pseudo-particles), static and dynamical properties of nuclear matter are studied, featuring the growing of bulk instabilities in dilute matter. Using different zero and finite range effective interactions, the effect of the model parameters upon the relation total energy - density - temperature and surface energy of the pseudo-particles fluid is pointed out. The dynamical feature is first based upon a model of the 2-body Uehling-Ulhenbeck collisionnal term. A study of the relaxation of a nucleonic system is performed. At last, the pseudo-particle model is used in order to extract time scale for the growing of density fluctuations. This process is supposed to be a possible way to clusterization during heavy nuclei collisions.

This review aims at a critical discussion of the interplay between effective interactions derived from various many-body approaches and spectroscopic data extracted from large scale shell-model studies. To achieve this, our many-body scheme starts with the free nucleon-nucleon (NN) interaction, typically modelled on various meson exchanges. The NN interaction is in turn renormalized in order to derive an effective medium dependent interaction. The latter is in turn used in shell-model calculations of selected nuclei. We also describe how to sum up the parquet class of diagrams and present initial uses of the effective interactions in coupled cluster many-body theory.

There are a number of many-body systems which exhibit quantum effects on a macroscopic scale. These include liquid and crystal states of both He-3 and He-4, the electron gas, and neutron matter which probably constitutes the interior of pulsors. In addition, "nuclear matter" - a hypothetical extensive system of nucleons has been studied for the insight one may gain into the nature of finite nuclei. The theoretical studies of these systems have by now a long history, but are by no means concluded. In the last few years, significant advances have been made. This has come in part from the maturity of and gradual unification of many-body theory, in part from the development and application of powerful new expansion procedures, especially varieties of hypernetted-chain equations ( 1 ) and finally to the growing power of computer simulation methods for quantum systems. This article is intended as a review of some recent

Liquids and solids, atoms and molecules, nuclei—all these clearly are interacting many-body systems. Even a nucleon may be regarded as a manyparticle system, not just because it is now known to consist of three quarks interacting via gluons, but because of the possibility in quantum field theory of virtual excitation of many particles from the vacuum. in the table page 56 we list some of the many-particle systems we encounter in the physical world at length scales that range from a few centimeters to a few fermis. Many of these systems exhibit phenomena—superconductivity in solids and fission in nuclei, for example—whose understanding does not follow immediately from knowledge of the constituents of the system and the interactions among the constituents, but requires new concepts and ideas. Many-body physics is the branch of theoretical physics that studies the new phenomena or “emergent properties” that arise from interactions among “elementary” constituents of a many-particle system and provides means and methods for carrying out precise calculations of such characteristic properties of these systems as may be compared with experimental results to verify hypotheses about the nature of the constituents and their interactions.