Phase Transition In Nuclei Research Articles

Proton-Neutron Interactions: New Perspectives on Collective Behaviour, Deformation, and Phase Transitions in Nuclei

Proton-Neutron Interactions: New Perspectives on Collective Behaviour, Deformation, and Phase Transitions in Nuclei

Entanglement entropy as a signature of a quantum phase transition in nuclei in the framework of the interacting boson model and interacting boson-fermion model

Background: One of the fundamental problems of quantum information science is quantum entanglement. Recently, quantum phase transition in nuclear systems is studied in connection with quantum entanglement.Purpose: In this paper, the use of entanglement entropy as a suitable signal for the study of quantum phase transition in the even-even and odd-$A$ nuclei is investigated. The effect of the coupling of a single fermion to a boson core on entanglement entropy is studied.Method: By use of the affine $SU(1,1)$ Lie algebra and through the Schmidt decomposition in the framework of the interacting boson model (IBM) and interacting boson-fermion model (IBFM), entanglement entropy in the even-even and odd-$A$ are obtained. The entanglement entropy is used for tracking and studying the shape phase transition in these nuclei.Results: The entanglement entropy in the IBM and the IBFM is calculated. The entanglement entropy values of the low-lying states of $^{122--134}\mathrm{Xe}, ^{102--110}\mathrm{Pd}$, and $^{123--133}\mathrm{Xe}$ were calculated and analyzed. It is found that entanglement entropy is a suitable order parameter to detect shape phase transition in nuclear systems.Conclusions: The obtained results indicate that the entropy of entanglement is sensitive to the shape-phase transition between spherical and $\ensuremath{\gamma}$-unstable regions in nuclei. The results show that entanglement entropy is a powerful tool for identifying shape phase transitions in nuclei. It is found that the coupling of the single fermion with angular momentum $j$ to the even-even system does not change the geometry imposed by the boson core performing the transition and only the entanglement entropy values have been shifted by the addition of the odd particle with respect to the even case.

Correlation between two quantum concepts within shape phase transitions in nuclei

The present work consists in studying a correlation that we have observed, for the first time, between two well-known quantum concepts, namely: the Minimal Length (ML) and the Deformation-Dependent Mass (DDM) which are widely used in different fields of physics. This correlation was revealed in transitional nuclei near the Critical Point Symmetries (CPS) X(3) and Z(4) through calculations of their energy spectra, moments of inertia and transition probabilities. Based on this correlation which could be considered as a new signature for CPS, we have found eventual new candidate nuclei for these critical points.

Exact solutions of mean-field plus various pairing interactions and shape phase transitions in nuclei

The exact solutions of either spherical or deformed mean-field plus various types of pairing models are briefly reviewed. It is shown that, besides the standard pairing model, there are several special types of pairing interaction that can be solved exactly. In comparison to the standard pairing, the results of several pairing-driven quantities, such as pairing excitation energies, even–odd mass differences, the moment of inertia, etc., show that these types of pairing interaction can indeed be used to describe pairing correlations in nuclei either more accurately or efficiently. Moreover, the shape phase transitional behaviors of nuclei described by the consistent-Q formalism of the interacting boson model are summarized.

Local Part of Two Neutron Separation Energies: Signature of Ground State Phase Transition

In this paper, we have considered the evolution of the local part of two neutron separation energies in the Zr, Gd, Sm, Ba, Xe, Os and Pt isotopic chain. We have used the interacting boson model as the most widely used approach to study the quantum phase transitions in nuclei to determine the global and local parts of two neutron separation energies. The constants of relations are extracted in comparison with the experimental counterparts. Theoretical predictions reproduce the experimental counterparts with high accuracy. Also, the signals of phase transition in some nuclei that show sudden changes in local part of two neutron separation energies are greatly enhanced and show the ability of the interacting boson model calculations to reproduce this picture.

Nuclear Shell Model And Quantum Phase Transitions

The usual nuclear shell model defines nuclear properties through an effective mean-field plus a two-body interaction Hamiltonian in a finite orbital space. In this study we try to understand the correlation between the various parts of the shell model Hamiltonian and the nuclear observables and collectivity in nuclei. By varying specific groups of matrix elements we find signs of a phase transition in nuclei between a non-collective and a collective phase. In all cases studied the collective phase is attained when the single-particle transfer matrix elements are dominant in the shell model Hamiltonian, giving collective characteristics to nuclei.

Role of fluctuations in a thermal phase transition in a nucleus probed via the giant dipole resonance

We present an experimental investigation of thermal phase transition in atomic nuclei by measuring the $\ensuremath{\gamma}$ rays from the decay of the giant dipole resonance in $^{169}\mathrm{Tm}$ populated by using the reaction $^{4}\mathrm{He}+^{165}\mathrm{Ho}$. The systematic measurement confirms the prolate shape, similar to the ground-state value, till temperature $T=1.23$ MeV. Moreover, the present data, together with the previous experimental studies, point towards the persistence of prolate shape with deformation similar to that of the ground state till $T=1.5$ MeV. In addition, the emergence and evolution of thermal fluctuations observed directly in the experiment suggest that the sharp phase transition from prolate to near spherical at $T\ensuremath{\approx}1.7$ MeV will not be evident experimentally due to statistical fluctuations owing to the finite size of the nucleus.

Empirical signatures of shape phase transitions in nuclei with odd nucleon numbers

Nuclear level density at low excitation energies is proposed as an indicator of the first order phase transitions in nuclei. The new signature, a maximum value of the level density at the critical point, appears to be sensitive to the detailed way the phase transition takes place in different nuclear regions: it is consistent with phase coexistence in the N=90 region, and with a rapid crossing of the two phases, without their coexistence/mixing at the critical point in the N=60 region, respectively. Candidates for critical point nuclei are proposed for odd-mass and odd-odd nuclei, using correlations between relative excitation energies, and their ratios, for structures (bands) based on unique-parity orbitals.

Two-nucleon transfer reactions as a test of quantum phase transitions in nuclei

A quantal and a semiclassical analysis of two-nucleon transfer intensities is done within the framework of the interacting boson model. The expected features of these quantities for the quantum phase transition (QPT) between spherical, U(5), and axially deformed, SU(3), shapes are discussed. Experimental data for ($p,t$) and $(t,p$) transfer reactions clearly show the occurrence of QPTs in Gd, Sm, and Nd.

Uncovering a Quantum Phase Transition in Nuclei

Uncovering a Quantum Phase Transition in Nuclei

Lie algebra symmetries and quantum phase transitions in nuclei

In this paper, an overview of some aspects of quantum phase transitions (QPT) in nuclei is given and they are: (i) QPT in interacting boson model (sdIBM), (ii) QPT in two-level models, (iii) critical point E(5) and X(5) symmetries, (iv) QPT in a simple solvable model with three-body forces. In addition, some open problems are also given.

Consistent empirical physical formulas for potential energy curves of 38–66Ti isotopes by using neural networks

Nuclear shape transition has been actively studied in the past decade. In particular, the understanding of this phenomenon from a microscopic point of view is of great importance. Because of this reason, many works have been employed to investigate shape phase transition in nuclei within the relativistic and non-relativistic mean field models by examining potential energy curves (PECs). In this paper, by using layered feed-forward neural networks (LFNNs), we have constructed consistent empirical physical formulas (EPFs) for the PECs of 38-66Ti calculated in Hartree-Fock-Bogoliubov (HFB) method with SLy4 Skyrme forces. It has been seen that the PECs obtained by neural network method are compatible with those of HFB calculations.

Pairing and specific heat in hot nuclei

The thermodynamics of pairing phase-transition in nuclei is studied in the canonical ensemble and treating the pairing correlations in a finite-temperature variation after projection BCS approach (FT-VAP). Due to the restoration of particle number conservation, the pairing gap and the specific heat calculated in the FT-VAP approach vary smoothly with the temperature, indicating a gradual transition from the superfluid to the normal phase, as expected in finite systems. We have checked that the predictions of the FT-VAP approach are very accurate when compared to the results obtained by an exact diagonalization of the pairing Hamiltonian. The influence of pairing correlations on specific heat is analysed for the isotopes $^{161,162}$Dy and $^{171,172}$Yb. It is shown that the FT-VAP approach, applied with a level density provided by mean field calculations and supplemented, at high energies, by the level density of the back-shifted Fermi gas model, can approximate reasonably well the main properties of specific heat extracted from experimental data. However, the detailed shape of the calculated specific heat is rather sensitive to the assumption made for the mean field.

EFFECT OF THE STATISTICAL FLUCTUATIONS IN THE PAIRING TRANSITION IN THE CASE OF 166Er

The S-shaped heat capacity, which has recently been claimed to be a fingerprint of the superfluid-to-normal phase transition in nuclei, is studied in the case of 166 Er element. The calculations are performed by means of the modified Bardeen–Cooper–Schrieffer (MBCS) approach that takes into account the thermal fluctuation. The obtained results are compared to the experimental data and to the FT-BCS theoretical predictions. The present study illustrates the effect of the fluctuations of the quasiparticle (QP) number on the heat capacity.

IBAR: Interacting boson model calculations for large system sizes

Scaling the system size of the interacting boson model-1 (IBM-1) into the realm of hundreds of bosons has many interesting applications in the field of nuclear structure, most notably quantum phase transitions in nuclei. We introduce IBAR, a new software package for calculating the eigenvalues and eigenvectors of the IBM-1 Hamiltonian, for large numbers of bosons. Energies and wavefunctions of the nuclear states, as well as transition strengths between them, are calculated using these values. Numerical errors in the recursive calculation of reduced matrix elements of the d-boson creation operator are reduced by using an arbitrary precision mathematical library. This software has been tested for up to 1000 bosons using comparisons to analytic expressions. Comparisons have also been made to the code PHINT for smaller system sizes. Program summaryProgram title: IBARCatalogue identifier: AELI_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELI_v1_0.htmlProgram obtainable from: CPC Program Library, Queenʼs University, Belfast, N. IrelandLicensing provisions: GNU General Public License version 3No. of lines in distributed program, including test data, etc.: 28 734No. of bytes in distributed program, including test data, etc.: 4 104 467Distribution format: tar.gzProgramming language: C++Computer: Any computer system with a C++ compilerOperating system: Tested under LinuxRAM: 150 MB for 1000 boson calculations with angular momenta of up to L=4Classification: 17.18, 17.20External routines: ARPACK (http://www.caam.rice.edu/software/ARPACK/)Nature of problem: Construction and diagonalization of large Hamiltonian matrices, using reduced matrix elements of the d-boson creation operator.Solution method: Reduced matrix elements of the d-boson creation operator have been stored in data files at machine precision, after being recursively calculated with higher than machine precision. The Hamiltonian matrix is calculated and diagonalized, and the requested transition strengths are calculated using the eigenvectors.Restrictions: The 1000 boson coefficients for L=0 and L=20 have been included in the IBAR distribution and the 7.3 GB of data that make up the remaining coefficients for L=21 to L=2000 are available upon request.Running time: If the provided example is changed to include 100 bosons, the calculation requires about 1 second of run time. For 1000 bosons, the calculation requires about 9 minutes of run time.

Covariant density functional theory with spectroscopic properties and a microscopic theory of quantum phase transitions in nuclei

Covariant Density functional theory is used as a basis for a microscopic description of spectroscopic properties of quantum phase transitions in nuclei. Since it is well known that the mean field approximation breaks down in transitional nuclei, where configuration mixing and fluctuations connected with broken symmetries play an important role, a theory is developed which uses the Relativistic Generator Coordinate Method to perform configuration mixing calculations of angular momentum and particle number projected wave functions. As applications with show 3D-calculations of the spectrum of low-lying collective states in the nucleus 24Mg. This method can also be used to study the behavior of characteristic physical quantities as a function of the physical control parameter, the number of nucleons, in the region of quantum phase transitions.

Remarks on shape phase transitions in nuclei

Various aspects of shape phase transitions in even as well as odd systems are reviewed. Firstly, the case of an odd j = 3/2 particle coupled to an even-even boson core that undergoes a transition from spherical limit (U(5)) to the γ-unstable limit (0(6)) is illustrated. Energy spectrum and electromagnetic transitions, in correspondence of the critical point, display behaviors qualitatively similar to those of the even core and they agree qualitatively with the model based on the E(5/4) boson-fermion symmetry. Secondly, we describe a study on two-particle transfer reactions: the evolution of the transfer spectroscopic intensities within the interacting boson model is analyzed as a possible signature of shape phase transitions In correspondence to the critical points characterizing the phase transitions, the two-particl transfer matrix elements to both ground and excited 0+ states display a rapid dicontinuit that might help validating the experimental search for the critical point

Spin dependence of critical point behavior for first and second order phase transitions in nuclei

A study of first and second order nuclear shape phase transitional behavior in yrast states of even-even nuclei in the context of the Interacting Boson Model-1 is presented. Finite boson number effects are identified using calculations with up to 150 bosons, and the role of the rotational degree of freedom of observables in first and second order quantum phase transitional nuclei is discussed. We aim to provide a first investigation of the angular momentum dependence of experimentally accessible phase transitional signatures in finite-sized quantum nuclear systems.

Nuclear, chemical and mechanical instability and the liquid-gas phase transition in nuclei

The thermodynamic properties of nuclei are studied in a mean-field model by using a Skryme interaction. Properties of two-component systems are investigated over the complete range of proton fraction from a system of pure neutrons to a system of only protons. Besides volume, symmetry, and Coulomb effects we also include momentum- or velocity-dependent forces. Applications of the results developed are then given and include nuclear mechanical and chemical instability and an associated liquid-gas phase transition in two-component systems. The velocity dependence leads to further changes in the coexistence curve and nuclear mechanical and chemical instability curves.

Bimodalities: A survey of experimental data and models

Bimodal distributions of some chosen variables measured in nuclear collisions were recently proposed as a non ambiguous signature of a first order phase transition in nuclei. This section presents a compilation of both theoretical and experimental studies on bimodalities performed so far, in relation with the liquid-gas phase transition in nuclear matter.