Quantum phase transitions in the consistentq hamiltonian of the interacting boson model feng pan1,3, tao wang1,2,yshuo1 and j p draayer3 1 department of physics, liaoning normal university, dalian 116029, peoples republic of china 2 department of physics, tonghua teachers college, tonghua, jilin 4002, peoples republic of china. Interacting boson model 1 ibm1 regularity chaos in ibm1 complete integrability at dynamical symmetries due to cassimir invariants also at o6u5 transition due to underlying o5 symmetry what about the triangle interior. Nuclear structure of the germanium nuclei in the interacting boson model ibm saad naji abood 1, abdul kader saad abdul kader 1 and laith ahmed najim 2 1physics department, college of science, alnahrain university, bagdad, iraq 2physics department, college of science, mosul university, mosul, iraq. Ten isotopes are studied, ranging from the middle of the neutron. The ibm hamiltonian is constructed out of s and d boson operators which define an overall u6 symmetry. This has been achieved using the interacting boson model 2 ibm2 and including configuration mixing ibm2 cm. Nuclear shape phase transition in erybhf isotopes using. Our attention is paid to describe the nuclei shape and to their connecting with shaping coexistence phenomenon. On the relation between e5models and the interacting boson model. In order to present the interacting boson model and its relationship to other nuclear structure theories a short introduction is necessary.
A model of nuclear structure which assumes that the particles making up a complex nucleus are bosons, each of which corresponds to a pair of correlated nucleons explanation of. Ramakrishnan department of physics, indian institute of science bangalore 560012, indk received 6 august 1992. Superfluid and insulating phases in an interacting boson model. An introduction to the interacting boson model of the atomic nucleus pdf. Nuclear shape phase transition in erybhf isotopes using the. Theoretical works of such bands have been presented in framework of cranked random phase approximation rpa 9,10, the collective model 5, the interacting boson model ibm 3,11, the variable moment of inertia vmi model 12 and the alpha particle cluster model 4. Nuclear shape transition using interacting boson model. Shell model basis of the interacting boson model the interacting boson model is related to shell model states constructed from pairs of identical valence nucleons coupled to j 0 and j 2. Abstract interacting boson model ibm 1 has been used to study the energy levels and be2 transition rates in bady n 92 isotones. The interacting boson modeli ibmi is a valuably interactive model developed by iachello and arima.
Lowlying spectra of nuclei away from major closed shells have a relatively simple structure which can be related to the occurrence of collective phenomena. The interacting boson model for exotic nuclei 5 more speci. Dilute limit of a stronglyinteracting model of spinless fermions and hardcore bosons on the square lattice n. Since 1974, the model has been the subject of many investigations and it. All physical observables hamiltonian, transition operators, are expressed in terms of s and d bosons. This work introduces into the interacting boson model, which was created in 1974 by f. In the first version of the interacting boson model ibm1 16,17, no distinction is made between proton and neutron variables while describing triaxiality explicitly. The interacting boson model i ibmi is a valuably interactive model developed by iachello and arima. The first page of the pdf of this article appears above.
After introducing some elementary and basic ideas which illuminate the. Quantum phase transitions in the consistentq hamiltonian of. States with defined total angular momentum are dealt with and the hamilton. The model the single boson states contained in u16 are depicted schematically in fig. Dilute limit of a stronglyinteracting model of spinless. Nuclear shape transition using interacting boson model with the intrinsic coherent state a.
Interacting boson model ibm2 calculations of selected eveneven te nuclei saad n. Volume 3 progress in physics july, 20 nuclear shape transition using interacting boson model with the intrinsic coherent state a. The shell model reveals that the lowlying states of the eveneven nuclei are made up predominantly by nucleon pairs with total spin 0 or 2. The 186198pt isotopes with proton number z78 and neutron numbers n between 108 and 120 in o6 region were investigated. O6 symmetry of even 186198pt isotopes under the framework. Meanfield derivation of the interacting boson model hamiltonian and exotic nuclei kosuke nomura,1 noritaka shimizu,1 and takaharu otsuka1,2,3,4 1department of physics, university of tokyo, hongo, bunkyoku, tokyo, 1033, japan 2center for nuclear study, university of tokyo, hongo, bunkyoku tokyo, 1033, japan 3riken, hirosawa, wakoshi, saitama 3510198. Meanfield derivation of the interacting boson model. Based on the constrained meanfield calculation with the gognyd1m edf, the ibm hamiltonian for an eveneven nucleus and essential ingredients of the interacting bosonfermionfermion model ibffm for describing the neighboring oddodd. Interacting boson model basis and i1amiltonian for tl 4staggering a recent discovery in the spectroscopy of superdeformed so bands is the tl 4 staggering dl4si seen in 149gdand 194hg31.
Sharrad1 1department of physics, college of science, university of kerbala, karbala, iraq fadhil. This has been achieved using the interacting boson model2 ibm2 and including configuration mixing ibm2 cm. We show that within this model both the vibrational and the rotational limit can be recovered. Configuration mixing in pt nuclei within interacting boson. Since 1974, the model has been the subject of many investigations and it read more. Since, in a microscopic interpretation, bosons are related to fermion pairs in shell model states 3, the appropriate counting of the boson number n is here more complicated than in the case of u6. We derive a large set of analytic relations for energies. A simplified hamiltonian is used which is written in the creation and annihilation form and for each nucleus, by fitting the selected experimental energy levels and be2 transition rates with the calculated ones to get the best model parameters.
The interacting boson model ibm is a model in nuclear physics in which nucleons protons or. Manybody configurations with s and dboson states are described and creation and annihilationoperators for bosons are introduced. Quantum phase transitions in the consistentq hamiltonian of the interacting boson model feng pan1,3, tao wang1,2,yshuo1 and j p draayer3 1 department of physics, liaoning normal university, dalian 116029, peoples republic of china 2 department of physics, tonghua teachers college, tonghua, jilin 4002. Superfluid and insulating phases in an interactingboson model. Exploring edm enhancements in quadrupoleoctupole interacting. Superfluid and insulating phases in an interacting boson. Quantum phase transitions in the consistentq hamiltonian.
The interacting boson model ibm is a very effective phenomenological model for describing lowlying collective properties of nuclei across an entire major shell. In this study, we have employed the interacting boson model2 ibm2 to determine the most appropriate hamiltonian for the study of tellurium nuclei. We study in detail the vibrational limit and bring attention to the possible existence of an unbroken su5. In this study, we have employed the interacting boson model 2 ibm2 to determine the most appropriate hamiltonian for the study of tellurium nuclei. We consider both vibrational excitations, of which one f boson provides a good. Description of the badyn 92 nuclei in the interacting. Pdf a set of classical variables associated with the interactingboson model is defined. An introduction to the interacting boson model of the atomic. Physics department, faculty of science, alazhar university, egypt. The interacting boson model nuclear collective excitations are described in terms of n s and d bosons.
All physical observables hamiltonian, transition operators, are expressed in terms of the generators of u6. We show that this limit is associated with the group o6 of orthogonal transformations in six dimensions. Algebraic approaches to nuclear structure, interacting boson and fermion models harwood academic publishers, switzerland, 1993. Interacting boson model article about interacting boson. Interacting boson model ibm2 calculations of selected even. The interacting boson model ibm is a model in nuclear physics in which nucleons protons or neutrons pair up, essentially acting as a single particle with boson. Thorn1 institute for fundamental theory department of physics, university of florida, gainesville fl 32611. Interacting boson model ibm2 calculations of selected. Adjusting a small number of parameters, it reproduces the. This article provides to descript a consistent of the eveneven 182200pt isotopes.
Applications ofthe su3 dynamical symmetry of interacting. Interacting boson model wikipedia open wikipedia design nuclear physics. New algebraic solutions for so6 u5 transitional nuclei in. Adjusting a small number of parameters, it reproduces the majority of the lowlying states of such nuclei. It is supposed that, the excitations of the valence protons and neutrons caused the dominance of lowlying collective states in medium and heavy eveneven nucleus away from closed shells i. Their main objective is to reduce the complexities of the full nuclear manybody problem by isolating a few essential degrees of freedom. It has been very successful and widely used to the structure of lowlying states in even even nuclei.
Pdf application of interacting boson model1 for even n6878. Meanfield derivation of the interacting boson model hamiltonian and exotic nuclei kosuke nomura,1 noritaka shimizu,1 and takaharu otsuka1,2,3,4 1department of physics, university of tokyo, hongo, bunkyoku, tokyo, 1033, japan. We discuss a third limit of the interacting boson model. In this model, collective excitations in even even nuclei are described in terms of a system of fixed number n of bosons of two types. The interacting boson model ibm is a model in nuclear physics in which nucleons protons or neutrons pair up, essentially acting as a single particle with boson properties, with integral spin of 0, 2 or 4. In the interacting boson modell, one assumes that lowlying collective quadrupole states can be generated as states of a system of n bosons able to occupy two. The interacting boson model spectrum generating algebra for the nucleus is u6. New algebraic solutions for so6 u5 transitional nuclei. Pdf the low lying nuclear structure of even 120122124126128te isotopes has been studied under the frame work of interacting boson.
Ibm assumed that the even even nucleus is a collection of. Based on the constrained meanfield calculation with the gognyd1m edf, the ibm hamiltonian for an eveneven nucleus and essential ingredients of the interacting boson fermionfermion model ibffm for describing the neighboring oddodd nucleus are determined in a microscopic way. Arima, the interacting boson model cambridge university press, 1987. Quantum field theory of the standard model charles b. We propose a unified description of collective nuclear states in terms of a system of interacting bosons. Find out information about interacting boson model. University of groningen the interacting boson approximation model. Dawson physics department, brookhaven national laboratory, upton, ny 11973 abstract a basic introduction to the physics of the standard model higgs boson is given. However, there is growing evidence that octupole deformation may also occur in nuclei. Explains that the model was originally introduced with only one kind of collective boson variable with angular momentum jo and j2 the interacting boson model1, and subsequently, a. Explains that the model was originally introduced with only one kind of collective boson variable with angular momentum jo and j2 the interacting boson model 1, and subsequently, a more. Pdf classical limit of the interactingboson model researchgate.
The interacting boson model the interacting boson model arima, a. The dl4s corresponds to asystematic displacement oflevels di. Nuclear shape transition using interacting boson model with. The extended interacting boson model with s, p, d, f and gbosons being included spdfg ibm are investigated. Interacting boson model of collective nuclear states iv. We derive, within the framework of this symmetry, several closed expressions for energies and electromagnetic transition rates. Since, in a microscopic interpretation, bosons are related to fermion pairs in shellmodel states 3, the appropriate counting of the boson number n is here more complicated than in the case of u6. This book gives an account of the properties of the interacting boson model. You are advised to consult the publishers version publishers pdf if you. Study of the nuclear structure of 4 58 ce 76 isotope within. The interacting boson model the interacting boson model dieperink, a e l. Study of the nuclear structure of 4 58 ce 76 isotope. Since 1974, the model has been the subject of many investigations and it has been extended to cover most aspects of nuclear structure.
As the results are most conveniently discussed in a secondquantization formalism. Nucleus nucleons p, n nuclear matter nuclear force nuclear structure nuclear reaction. An introduction to the interacting boson model of the. January, 20 progress in physics volume 1 a theoretical description of u5su3 nuclear shape transitions in the interacting boson model a.
Octupole degrees of freedom in the interacting boson mode jonathan fngel abstract we discuss the problem of describing collective states with negative parity by adding f bosons to the interacting boson model. Finitesize scaling exponents in the interacting boson model. The original version of interacting boson model sd ibm1 provides an elegant and powerful tool for description of collective nuclei 1. The interacting boson model was introduced in 1974 as an attempt to describe collective properties of nuclei in a unified way. The interacting boson approximation model and applications. This can be done by introducing the cubic terms in the boson operators 18,19. The interacting boson model ibm is suitable for describing intermediate and heavy atomic nuclei. The interacting boson model sometimes named interacting boson approximation iba reduces the number of states heavily. The algebraic structure including the generators, the casimir operators of the groups at the su5 dynamical symmetry and the branching.
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