Periodic Reporting for period 1 - GENESE 17 (Geometries of Exotic NuclEar StructurE 17)
Berichtszeitraum: 2018-12-01 bis 2020-11-30
Symmetry originates from the word “Συμμετρία” and means “with rule”. This meaning is close to the concept of rhythm in the sense of a well-defined pattern. In modern science, the concept of symmetry plays a profound role in understanding the structure of matter and the fundamental interactions, among others. For example, in nuclear structure, the rhythms (symmetries) that nucleons collectively “dance” within an atomic nucleus reflect the geometrical shapes presented on the surface of that nucleus.
GENESE 17 originated from investigating the relation between nuclear shapes and the symmetries of fundamental interactions in conjunction with exploring the structure of short-lived nuclei. These are the exotic nuclei that die in a very short time after their genesis inside the stars. On earth, exotic nuclei are produced artificially in laboratories such as GANIL in France using Radioactive Beams (RIBs). GENESE 17 is a project in basic research and as such, its importance for society is of long term.
The objectives of this project are classified into two parts: The first part includes the theoretical description and analysis of phenomena investigated mainly in exotic nuclei such as shape coexistence, pear-shaped nuclei, and proton emitters. The second part introduces a novel theoretical understanding of nuclear structure using conformal symmetry. In addition, it proposes new phenomena to be examined in nuclear physics experiments with RIBs.
GENESE 17 originated from investigating the relation between nuclear shapes and the symmetries of fundamental interactions in conjunction with exploring the structure of short-lived nuclei. These are the exotic nuclei that die in a very short time after their genesis inside the stars. On earth, exotic nuclei are produced artificially in laboratories such as GANIL in France using Radioactive Beams (RIBs). GENESE 17 is a project in basic research and as such, its importance for society is of long term.
The objectives of this project are classified into two parts: The first part includes the theoretical description and analysis of phenomena investigated mainly in exotic nuclei such as shape coexistence, pear-shaped nuclei, and proton emitters. The second part introduces a novel theoretical understanding of nuclear structure using conformal symmetry. In addition, it proposes new phenomena to be examined in nuclear physics experiments with RIBs.
The work started with the comparison with the experimental data of the shape coexistence scenarios that had been developed during the first postdoc of the Fellow at the Racah Institute of Physics, Hebrew University, Israel and constitute the first study of shape coexistence in the Geometric Collective Model using a computationally tractable version of the latter the so called Algebraic Collective Model. After elaborating on the initial scenarios, the elements in the Ar-Si-S series and especially 44-46Ar were identified as candidate nuclei of spherical-gamma-unstable coexistence. However, more experimental data are needed for a detailed comparison especially in the population of higher excited states. The initial scenarios were also extended to the investigation of coexistence between spherical and axially symmetric shapes through two internship theses from graduate students that were supervised by the Fellow. We report the first case where the ACM does not manifest convergence in an axially symmetric shape that coexists with a spherical shape.
In pear-shaped nuclei the work started by the theoretical investigation of the empirical rules for the correlations between the energies of the 2+ and the 3- states in neutron deficient xenons around 100Sn. Our results do not reproduce an unusual, enhanced B(E3) transition in 114-112Xe and follow the empirical rules which however do not conform to a symmetry pattern for those isotopes. The training through research was realized in microscopic calculations in the Shell Model using realistic interactions for the reproduction of monopole, quadrupole and the octupole degrees of freedom through boson mappings. The results finally led to the formulation of a semi-empirical binding energy formula for proton emitters around 100Sn with specific predictions of proton separation energies and their half-lives.
The transition to the second part is guided by the conformal invariance implied by the symmetry of quantum critical points in Shape/Phase transitions. To that aspect, the interdisciplinary aspects of the project were focused on the physics of trapped cold atoms that manifest the unitary limit – which supports a quantum critical point - in the vicinity of Feshbach resonances. The application of these methods in the Interacting Boson Model of nuclear structure led to the major achievement of the project. This is the regularity pattern of fluctuations of cross sections in A+2n (two neutrons) compound nuclei that represents conformal symmetry in nuclear structure. The energies and the widths of such fluctuations are calculated, and a new type of a two-neutron transfer reaction is proposed for the examination of the unitary limit in A+2n compound and exotic nuclei. These fluctuations tune the scattering length that reaches the unitary limit when the incident two neutrons are captured as an intermediate boson in the A+2n compound nucleus. As a result, a novel theoretical understanding emerges for the A+2n compound nucleus as a cold and dilute gas of nucleons (in formal analogy with a cold and dilute atomic gas) where paired nucleons form IBM bosons (in formal analogy with the formation of diatomic molecules in Feshbach resonances between cold atoms) at low temperatures.
The first theoretical implication of the unitary limit is the manifestation of the BCS-BEC crossover in nuclear physics. The second is the underlying quantum critical point that appears through the maximization of the fluctuations of cross sections. Finally, we discuss the relation of symmetries of collective nuclear states with the large N limit of the SU(N) gauge group through the introduction of elements of algebras with an infinite number of generators that classify the reaction channels of A+2n compound nuclei.
In pear-shaped nuclei the work started by the theoretical investigation of the empirical rules for the correlations between the energies of the 2+ and the 3- states in neutron deficient xenons around 100Sn. Our results do not reproduce an unusual, enhanced B(E3) transition in 114-112Xe and follow the empirical rules which however do not conform to a symmetry pattern for those isotopes. The training through research was realized in microscopic calculations in the Shell Model using realistic interactions for the reproduction of monopole, quadrupole and the octupole degrees of freedom through boson mappings. The results finally led to the formulation of a semi-empirical binding energy formula for proton emitters around 100Sn with specific predictions of proton separation energies and their half-lives.
The transition to the second part is guided by the conformal invariance implied by the symmetry of quantum critical points in Shape/Phase transitions. To that aspect, the interdisciplinary aspects of the project were focused on the physics of trapped cold atoms that manifest the unitary limit – which supports a quantum critical point - in the vicinity of Feshbach resonances. The application of these methods in the Interacting Boson Model of nuclear structure led to the major achievement of the project. This is the regularity pattern of fluctuations of cross sections in A+2n (two neutrons) compound nuclei that represents conformal symmetry in nuclear structure. The energies and the widths of such fluctuations are calculated, and a new type of a two-neutron transfer reaction is proposed for the examination of the unitary limit in A+2n compound and exotic nuclei. These fluctuations tune the scattering length that reaches the unitary limit when the incident two neutrons are captured as an intermediate boson in the A+2n compound nucleus. As a result, a novel theoretical understanding emerges for the A+2n compound nucleus as a cold and dilute gas of nucleons (in formal analogy with a cold and dilute atomic gas) where paired nucleons form IBM bosons (in formal analogy with the formation of diatomic molecules in Feshbach resonances between cold atoms) at low temperatures.
The first theoretical implication of the unitary limit is the manifestation of the BCS-BEC crossover in nuclear physics. The second is the underlying quantum critical point that appears through the maximization of the fluctuations of cross sections. Finally, we discuss the relation of symmetries of collective nuclear states with the large N limit of the SU(N) gauge group through the introduction of elements of algebras with an infinite number of generators that classify the reaction channels of A+2n compound nuclei.
The progress beyond the state of the art in nuclear collective models is reflected in the observation of the limitation of the ACM in the solvability of spherical-axially symmetric coexistence. In proton-emitting nuclei such progress is reflected in the formulation of the semi-empirical binding energy formula that applies locally to elements around 100Sn
In the second part, the results contribute beyond the state of the art in nuclear physics. It is known since the 60s with the prominent work of Mack and Salam that conformal symmetry is not represented in elementary particles because a particle is identified as such by their invariant mass and conformal symmetry does not conserve mass. However, an example for the representation of conformal symmetry was provided by strings that led into what is known today as string theory. Our results indicate that conformal symmetry is associated with the experimental observable of a compound nucleus: The fluctuations of the cross section which in addition tune the scattering length in nuclear physics. This is an important observation that answers to the how and by what means the scattering length is tuned in nuclear physics. Of equal importance is the proposal of the regularity pattern of the fluctuations of the cross section which contrasts with their usual random appearance. This regularity pattern proposes a new observable fact (phenomenon) that emerges out of the representations of conformal symmetry in the structure of A+2n compound nuclei.
This project does not connect conformal symmetry with shape coexistence or pear-shaped nuclei. On the other hand, our results indicate connections with gravity and cosmology because the conformal group is interpreted either as an Anti de Sitter space or as a Conformal Field Theory. GENESE 17 introduces the question of the analysis of the collective “dances” of nucleons within an atomic nucleus in terms of the rhythms (symmetries) of the classical limit of the strong interactions. For that question, conformal symmetry serves to introduce a common algebraic framework of the symmetries of collective nuclear motions together with the algebras that appear at the classical limit of the strong interactions.
In the second part, the results contribute beyond the state of the art in nuclear physics. It is known since the 60s with the prominent work of Mack and Salam that conformal symmetry is not represented in elementary particles because a particle is identified as such by their invariant mass and conformal symmetry does not conserve mass. However, an example for the representation of conformal symmetry was provided by strings that led into what is known today as string theory. Our results indicate that conformal symmetry is associated with the experimental observable of a compound nucleus: The fluctuations of the cross section which in addition tune the scattering length in nuclear physics. This is an important observation that answers to the how and by what means the scattering length is tuned in nuclear physics. Of equal importance is the proposal of the regularity pattern of the fluctuations of the cross section which contrasts with their usual random appearance. This regularity pattern proposes a new observable fact (phenomenon) that emerges out of the representations of conformal symmetry in the structure of A+2n compound nuclei.
This project does not connect conformal symmetry with shape coexistence or pear-shaped nuclei. On the other hand, our results indicate connections with gravity and cosmology because the conformal group is interpreted either as an Anti de Sitter space or as a Conformal Field Theory. GENESE 17 introduces the question of the analysis of the collective “dances” of nucleons within an atomic nucleus in terms of the rhythms (symmetries) of the classical limit of the strong interactions. For that question, conformal symmetry serves to introduce a common algebraic framework of the symmetries of collective nuclear motions together with the algebras that appear at the classical limit of the strong interactions.