A method of deriving the Hamiltonian of the interacting boson model, that is based on the microscopic framework of the nuclear energy density functional, is presented. The constrained self-consistent mean-field calculation with a given energy density functional provides potential energy surface within the relevant collective coordinates, which is subsequently mapped onto the expectation value of the interacting-boson Hamiltonian in the boson condensate state. This procedure completely determines the strength parameters of the IBM, and the diagonalization of the mapped Hamiltonian yields excitation spectra and transition rates for a given nucleus. Two recent applications of the method are discussed, that is, the descriptions of the intruder states in Cadmium isotopes and the octupole correlations in neutron-rich odd-mass Barium isotopes.
We intend to provide a consistent description of the even-even Hg isotopes, 172-200Hg, using the interacting boson model including configuration mixing. We pay special attention to the description of the shape of the nuclei and to its connection with the shape coexistence phenomenon.
We investigate the emergence and evolution of shape coexistence in the neutron-deficient Lead isotopes within the interacting boson model (IBM) plus configuration mixing with microscopic input based on the Gogny energy density functional (EDF). The microscopic potential energy surface obtained from the constrained self-consistent Hartree-Fock-Bogoliubov method employing the Gogny-D1M EDF is mapped onto the coherent-state expectation value of the configuration-mixing IBM Hamiltonian. In this way, the parameters of the IBM Hamiltonian are fixed for each of the three relevant configurations (sphe…
Background: The lead region, Po, Pb, Hg, and Pt, shows up the presence of coexisting structures having different deformation and corresponding to different particle-hole configurations in the Shell Model language. Purpose: We intend to study the importance of configuration mixing in the understanding of the nuclear structure of even-even Po isotopes, where the shape coexistence phenomena are not clear enough. Method: We study in detail a long chain of polonium isotopes, 190-208Po, using the interacting boson model with configuration mixing (IBM-CM). We fix the parameters of the Hamiltonians th…
Background: The Po, Pb, Hg, and Pt region is known for the presence of coexisting structures that correspond to different particle-hole configurations in the Shell Model language or equivalently to nuclear shapes with different deformation. Purpose: We intend to study the configuration mixing phenomenon in the Hg isotopes and to understand how different observables are influenced by it. Method: We study in detail a long chain of mercury isotopes, $^{172-200}$Hg, using the interacting boson model with configuration mixing. The parameters of the Hamiltonians are fixed through a least square fit …
The evolution of the total energy surface and the nuclear shape in the isotopic chain $^{172-194}$Pt are studied in the framework of the interacting boson model, including configuration mixing. The results are compared with a self-consistent Hartree-Fock-Bogoliubov calculation using the Gogny-D1S interaction and a good agreement between both approaches shows up. The evolution of the deformation parameters points towards the presence of two different coexisting configurations in the region 176 $\leq$ A $\leq$ 186.
The properties of the low-lying states, especially the relevant shape coexistence in $^{80}$Ge close to one of most neutron-rich doubly magic nuclei at $N=50$ and $Z=28$ have been investigated within the framework of the proton-neutron interacting model (IBM-2). Based on the fact that the relative energy of the $d$ neutron boson is different from proton bosons', the calculated energy levels of low-lying states, $E2$ transition strengths can reproduce the experimental data very well. Particularly, the first excited state 0$^+_2$ is reproduced quite nicely, which is intimately related with the s…
A schematic model is presented that allows one to study the behavior of interacting pseudo-Fermi matter locked in a thermostatic box. As a function of the box volume and temperature, the matter is seen to show all of the familiar charactersitics of a Van der Waals gas, which include the coexistence of two phases under certain circumstances and the presence of a critical point.
Shape coexistence has been a subject of great interest in nuclear physics for many decades. In the context of the nuclear shell model, intruder excitations may give rise to remarkably low-lying excited $0^+$ states associated with different intrinsic shapes. In heavy open-shell nuclei, the dimension of the shell-model configuration space that includes such intruder excitations becomes exceedingly large, thus requiring a drastic truncation scheme. Such a framework has been provided by the interacting boson model (IBM). In this article we address the phenomenon of shape coexistence and its relev…
A microscopic interpretation of the s and d bosons of the Interacting Boson Model is being suggested: the s, d bosons can be interpreted as symmetric pairs of harmonic oscillator quanta of the valence nuclear shell. Within this interpretation, the SU(3) limit of the Interacting Boson Model results to the Elliott SU(3) symmetry.
We introduce a class of exactly solvable boson models. We give explicit analytic expressions for energy eigenvalues and eigenvectors for an sd-boson Hamiltonian, which is related to the SO(6) chain of the Interacting Boson Model Hamiltonian.
In this paper, we have studied the shapes coexistence in the 180-190Hg isotopes. The SO(6) representation of eigenstates and a transitional Hamiltonian in the Interacting Boson Model are used to consider the evolution from prolate to oblate shapes for systems with total boson number N = 9-12. Parameter free (up to overall scale factors) predictions for energy spectra and quadrupole transition rates are found to be in good agreement with experimental counterparts. The results for the control parameter of transitional Hamiltonian offer a combination of spherical and deformed shapes in these Hg i…
The exact solution of the boson pairing hamiltonian given by Richardson in the sixties is used to study the phenomena of level crossings and quantum phase transitions in the integrable regions of the sd and sdg interacting boson models.
A symmetry-based approach for describing shape-coexistence, is presented in the framework of the interacting boson model of nuclei. It involves a construction of a number-conserving Hamiltonian which preserves the dynamical symmetry of selected bands associated with each shape, while breaking the symmetries in other states. The resulting structure embodies multiple partial dynamical symmetries. The procedure is applied to prolate-oblate and spherical-prolate-oblate coexistence, at and slightly away from the critical points.
Interacting boson models provide an elegant and powerful method to describe collective excitations of complex systems by introducing a set of effective degrees of freedom. We review the interacting boson model of nuclear structure and discuss a recent extension to the nucleon and its excited states.
In this contribution the symmetry properties of the interacting boson model of Arima and Iachello are reviewed. While the concept of a dynamical symmetry is by now a familiar one, this is not necessarily so for the extended notions of partial dynamical symmetry and quasi dynamical symmetry, which can be beautifully illustrated in the context of the interacting boson model. The main conclusion of the analysis is that dynamical symmetries are scarce while their partial and quasi extensions are ubiquitous.
We study the phase diagram of the proton--neutron interacting boson model (IBM--2) with special emphasis on the phase transitions leading to triaxial phases. The existence of a new critical point between spherical and triaxial shapes is reported.
We introduce an exactly solvable model for interacting bosons that extend up to high spin and interact through a repulsive pairing force. The model exhibits a phase transition to a state with almost complete $sd$ dominance. The repulsive pairing interaction that underlies the model has a natural microscopic origin in the Pauli exclusion principle between contituent nucleons. As such, repulsive pairing between bosons seems to provide a new mechanism for the enhancement of $sd$ dominance, giving further support for the validity of the $sd$ Interacting Boson Model.
The extended interacting boson model with s-, p-, d-, f- and g-bosons being included (spdfg IBM) are investigated. The algebraic structure including the generators, the Casimir operators of the groups at the SU(5) dynamical symmetry and the branching rules of the irreducible representation reductions along the group chain are obtained. The typical energy spectrum of the Symmetry is given.
The relation of the recently proposed E(5) critical point symmetry with the interacting boson model is investigated. The large-N limit of the interacting boson model at the critical point in the transition from U(5) to O(6) is obtained by solving the Richardson equations. It is shown explicitly that this algebraic calculation leads to the same results as the solution of the Bohr differential equation with a $β^4$ potential.
Exact numerical results of the interacting boson model Hamiltonian along the integrable line from U(5) to O(6) are obtained by diagonalization within boson seniority subspaces. The matrix Hamiltonian reduces to a block tridiagonal form which can be diagonalized for large number of bosons. We present results for the low energy spectrum and the transition probabilities for systems up to 10000 bosons, which confirm that at the critical point the system is equally well described by the Bohr Hamiltonian with a $β^4$ potential.
We introduce the basic concepts of catastrophe theory needed to derive analytically the phase diagram of the proton-neutron interacting boson model (IBM-2). Previous studies [1,2,3] were based on numerical solutions. We here explain the whole IBM-2 phase diagram including the precise order of the phase transitions in terms of the cusp catastrophe.
We discuss the symmetry of the parameter space of the interacting boson model (IBM). It is shown that for any set of the IBM Hamiltonian parameters (with the only exception of the U(5) dynamical symmetry limit) one can always find another set that generates the equivalent spectrum. We discuss the origin of the symmetry and its relevance for physical applications.
We describe a class of exactly-solvable models of interacting bosons based on the algebra SO(3,2). Each copy of the algebra represents a system of neutron and proton bosons in a given bosonic level interacting via a pairing interaction. The model that includes s and d bosons is a specific realization of the IBM2, restricted to the transition regime between vibrational and gamma-soft nuclei. By including additional copies of the algebra, we can generate proton-neutron boson models involving other boson degrees of freedom, while still maintaining exact solvability. In each of these models, we ca…
The interacting boson model (IBM) of Arima and Iachello is applied to calculate nuclear charge radii and electric monopole transitions of even-even nuclei in the rare-earth region. Consistent operators are used for the two observables. A relation between summed M1 strength and $ρ({\rm E0})$ values is pointed out.
Double-$γ$ vibrations in deformed nuclei are studied in the context of the interacting boson model with special reference to their anharmonic character. It is shown that large anharmonicities can be obtained with interactions that are (at least) of three-body nature between the bosons. As an example the $γ$ vibrations of the nucleus $^{166}_{\phantom{0}68}$Er$^{\phantom{00}}_{98}$ are studied in detail.
The interacting boson model is extended to describe the spectroscopy of superdeformed bands. Microscopic structure of the model in the second minimum is discussed and superdeformed bosons are introduced as the new building blocks. Solutions of a quadrupole Hamiltonian are implemented through the $1/N$ expansion method. Effects of the quadrupole parameters on dynamic moment of inertia and electric quadrupole transition rates are discussed and the results are used in a description of superdeformed bands in the Hg-Pb and Gd-Dy regions.
The boson-conserving one-nucleon transfer operator in the interacting boson model (IBA) is reanalyzed. Extra terms are added to the usual form used for that operator. These new terms change generalized seniority by one unit, as the ones considered up to now. The results obtained using the new form for the transfer operator are compared with those obtained with the traditional form in a simple case involving the pseudo-spin Bose-Fermi symmetry $U^{B}(6) \otimes U^F(12)$ in its $U^{BF}(5) \otimes U^F(2)$ limit. Sizeable differences are found. These results are of relevance in the study of transf…
The self-consistent cranking method is tested by comparing the cranking calculations in the interacting boson model with the exact results obtained from the SU(3) and O(6) dynamical symmetries and from numerical diagonalization. The method is used to study the spin dependence of shape variables in the $sd$ and $sdg$ boson models. When realistic sets of parameters are used, both models lead to similar results: axial shape is retained with increasing cranking frequency while fluctuations in the shape variable $γ$ are slightly reduced.
The signature splitting of the $γ$-vibrational band of several Ru, Pd, Xe, Ba, Os and Pt isotopes is analyzed in the framework of the interacting boson model (IBM). The nuclei studied are close to the $γ$-unstable SO(6) limit of the IBM and have well-known $γ$ bands. It is shown that in most nuclei the signature splitting is better reproduced by the inclusion of a three-body interaction between the $d$ bosons. In none of the nuclei evidence for a stable, triaxial ground-state shape is found.
The case of U(5)--$\hat{Q}(χ)\cdot\hat{Q}(χ)$ mixing in the configuration-mixed Interacting Boson Model is studied in its mean-field approximation. Phase diagrams with analytical and numerical solutions are constructed and discussed. Indications for first-order and second-order shape phase transitions can be obtained from binding energies and from critical exponents, respectively.
This work introduces into the Interacting Boson Model, which was created in 1974 by F. Iachello and A. Arima and then extended by numerous papers. Many-body configurations with s- and d-boson states are described and creation- and annihilation-operators for bosons are introduced. States with defined total angular momentum are dealt with and the Hamilton operator of the IBM1-model is expressed in terms of Casimir operators. Level energies and electromagnetic transition probabilities are compared with measured data. A short introduction to Lie algebras and their application to the IBM1-model are…
Analysis of the recently obtained experimental data for collective states of ^{160}Dy is presented. The Interacting Vector Boson Model (IVBM) was applied for the classification of low lying states with positive parity 0^{+},2^{+},4^{+},6^{+}and for description of rotational ground, S, γ and two octupole bands. The energies of the bands are reproduced with high accuracy using only one set of the model parameters for all bands.
An intrinsic-state formalism for IBM-4 is presented. A basis of deformed bosons is introduced which allows the construction of a general trial wave function which has Wigner's spin-isospin SU(4) symmetry as a particular limit. Intrinsic-state calculations are compared with exact ones showing good agreement.
We introduce a method for isospin restoration in the calculation of nuclear matrix elements (NME) for $0νββ$ and $2νββ$ decay within the framework of interacting boson model (IBM-2). With this method, we calculate NME for all processes of interest in $0νβ^-β^-$, $2νβ^-β^-$, and in $0νβ^+β^+$, $0νβ^+ EC^+$, $R0νECEC$, $2νβ^+β^+$, $2νβ^+EC$, and $2νECEC$. With this method, the Fermi (F) matrix elements for $2νββ$ vanish, and those for $0νββ$ are considerably reduced.
The Interacting Boson Model with broken-pairs has been extended to include mixed proton-neutron configurations in the fermion model space. The extended version of the model has been used to describe high-spin bands in the transitional nucleus $^{136}$Nd. Model calculations reproduce ten bands of positive and negative parity states, including the two dipole high-spin structures based on the $(πh_{11/2})^2$ $(νh_{11/2})^2$ configuration.
It is shown that the proton-neutron interacting boson model (pnIBM) admits new symmetry limits with O(12) algebra which break F-spin but preserves the quantum number M_F. The generators of O(12) are derived and the quantum number `v' of O(12) for a given boson number N is determined by identifying the corresponding quasi-spin algebra. The O(12) algebra generates two symmetry schemes and for both of them, complete classification of the basis states and typical spectra are given. With the O(12) algebra identified, complete classification of pnIBM symmetry limits with good M_F is established.
In terms of the Interacting Boson Model, shape invariants for the ground state, formed by quadrupole moments up to sixth order, are studied in the dynamical symmetry limits and, for the first time, over the whole structural range of the IBM-1. The results are related to the effective deformation parameters and their fluctuations in the geometrical model. New signatures that can distinguish vibrator and gamma-soft rotor structures, and one that is related to shape coexistence, are identified.
We present a symmetry-based approach for prolate-oblate and spherical-prolate-oblate shape coexistence, in the framework of the interacting boson model of nuclei. The proposed Hamiltonian conserves the SU(3) and $\overline{\rm SU(3)}$ symmetry for the prolate and oblate ground bands and the U(5) symmetry for selected spherical states. Analytic expressions for quadrupole moments and $E2$ rates involving these states are derived and isomeric states are identified by means of selection rules.
Bosonic degrees of freedom and their emergence as a part of complex quantum many-body dynamics, symmetries, collective behavior, clustering and phase transitions play an important role in modern studies of quantum systems. In this work we present a systematic study of many-boson systems governed by random interactions. Our findings show that ground states of randomly interacting bosons are not random, being dominated by a few collective configurations containing condensates of clusters.
Lifetime measurements in neutron-rich odd-A yttrium isotopes ($^{93-99}$Y): Investigation of shape coexistence and the intertwined quantum phase transition
Universität zu Köln（科隆大学）；Nuclear Research Center-Negev（内盖夫核科学研究中心）；Tel Aviv University（特拉维夫大学）；Institut Laue-Langevin（朗之万研究所）；Institute of Nuclear Physics, PAN（波兰科学院核物理研究所）；Institut of Physique des 2 Infinis de Lyon（里昂两无限物理研究所）；INFN Sezione di Milano（意大利国家核物理研究所米兰分部）
The evolution and coexistence of the nuclear shapes as well as the corresponding low-lying collective states and electromagnetic transition rates are investigated along the Krypton isotopic chain within the framework of the interacting boson model (IBM). The IBM Hamiltonian is determined through mean-field calculations based on the several parametrizations of the Gogny energy density functional and the relativistic mean-field Lagrangian. The mean-field energy surfaces, as functions of the axial $β$ and triaxial $γ$ quadrupole deformations, are mapped onto the expectation value of the interacti…
The phase diagram of two-level boson Hamiltonians, including the Interacting Boson Model (IBM), is studied beyond the standard mean field approximation using the Holstein-Primakoff mapping. The limitations of the usual intrinsic state (mean field) formalism concerning finite-size effects are pointed out. The analytic results are compared to numerics obtained from exact diagonalizations. Excitation energies and occupation numbers are studied in different model space regions (Casten triangle for IBM) and especially at the critical points.
The role of configuration mixing in the Pt region is investigated. For this chain of isotopes, the nature of the ground state changes smoothly, being spherical around mass $A\sim 174$ and $A\sim 192$ and deformed around the mid-shell N=104 region. This has a dramatic effect on the systematics of the energy spectra as compared to the systematics in the Pb and Hg nuclei. Interacting Boson Model with configuration mixing calculations are presented for gyromagnetic factors, $α$-decay hindrance factors, and isotope shifts. The necessity of incorporating intruder configurations to obtain an accurate…
Random interactions are used to investigate to what extent the low-lying behavior of even-even nuclei depend on particular nucleon-nucleon interactions. The surprising results that were obtained for the interacting boson model, i.e. the dominance of ground states with L=0 and the occurrence of both vibrational and rotational structure, are interpreted and explained in terms of a mean-field analysis.
A $γγ$ angular correlation experiment has been performed to investigate the low-energy states of the nucleus $^{98}$Mo. The new data, including spin assignments, multipole mixing ratios and lifetimes reveal evidence for shape coexistence and mixing in $^{98}$Mo, arising from a proton intruder configuration. This result is reproduced by a theoretical calculation within the proton-neutron interacting boson model with configuration mixing, based on microscopic energy density functional theory. The microscopic calculation indicates the importance of the proton particle-hole excitation across the Z…
We investigate the origin of the regular features observed in numerical studies of the interacting boson model with random interactions, in particular the dominance of L=0 ground states and the occurrence of vibrational and rotational band structures. It is shown that all of these properties can be interpreted and explained in terms of a Hartree-Bose mean-field analysis, in which different regions of the parameter space are associated with geometric shapes. The same conclusions hold for the vibron model.
We investigate the finite-size scaling exponents for the critical point at the shape phase transition from U(5) (spherical) to O(6) (deformed $γ$-unstable) dynamical symmetries of the Interacting Boson Model, making use of the Holstein-Primakoff boson expansion and the continuous unitary transformation technique. We compute exactly the leading order correction to the ground state energy, the gap, the expectation value of the $d$-boson number in the ground state and the $E2$ transition probability from the ground state to the first excited state, and determine the corresponding finite-size scal…
We study the quantum phase transition mechanisms that arise in the Interacting Boson Model. We show that the second-order nature of the phase transition from U(5) to O(6) may be attributed to quantum integrability, whereas all the first-order phase transitions of the model are due to level repulsion with one singular point of level crossing. We propose a model Hamiltonian with a true first-order phase transition for finite systems due to level crossings.
A general time-dependent projection technique is applied to the study of the dynamics of quantum correlations in a system consisting of interacting fermionic and bosonic subsystems, described by the Jaynes-Cummings Hamiltonian. The amplitude modulation of the Rabi oscillations which occur for a strong, coherent initial bosonic field is obtained from the spin intrinsic depolarization resulting from collisional corrections to the mean-field approximation.
