DOCSLIB.ORG

Redalyc.Description of Even–Even 114–134Xe Isotopes in The

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Redalyc.Description of Even–Even 114–134Xe Isotopes in The Brazilian Journal of Physics ISSN: 0103-9733 [email protected] Sociedade Brasileira de Física Brasil Jafarizadeh, M. A.; Fouladi, N.; Sabri, H. Description of Even–Even 114–134Xe Isotopes in the Transitional Region of IBM Brazilian Journal of Physics, vol. 43, núm. 1-2, abril, 2013, pp. 34-40 Sociedade Brasileira de Física Sâo Paulo, Brasil Available in: http://www.redalyc.org/articulo.oa?id=46425766010 How to cite Complete issue Scientific Information System More information about this article Network of Scientific Journals from Latin America, the Caribbean, Spain and Portugal Journal's homepage in redalyc.org Non-profit academic project, developed under the open access initiative Braz J Phys (2013) 43:34–40 DOI 10.1007/s13538-013-0116-3 NUCLEAR PHYSICS Description of Even–Even 114–134Xe Isotopes in the Transitional Region of IBM M. A. Jafarizadeh & N. Fouladi & H. Sabri Received: 1 May 2012 /Published online: 18 January 2013 # Sociedade Brasileira de Física 2013 Abstract Properties of 114–134Xe isotopes are studied in the the anharmonic vibrator, axial rotor and γ-unstable ro- U(5)↔SO(6) transitional region of Interacting Boson Model tor, respectively. More generally, the Hamiltonian can be (IBM-1). The energy levels and B(E2) transition rates are expressed in terms of an invariant operator of that chain calculated via the affine SU(1,1) Lie Algebra. The agree- of symmetries, and a shape phase transition between the ment with the most recent experimental is acceptable. The dynamical symmetry limits results [6–8]. The analytic evaluated Hamiltonian control parameters suggest a spheri- description of the structural change at the critical point cal to γ-soft shape transition and propose the 130Xe nucleus of the phase transition being still an open problem, the as the best candidate for the E(5) symmetry. Hamiltonian must be diagonalized numerically. Pan et al. [9], proposed a new solution based on the affine SU Keywords Interacting Boson Model (IBM) . Infinite (1,1) algebraic technique, which determines the proper- dimensional algebra . Energy levels . B(E2) transition rates ties of nuclei in the U(5)↔SO(6) transitional region of IBM-1 [9, 10]. The xenon isotopes have been previously analyzed both theoretically and experimentally [11–29] with par- 1 Introduction ticular emphasis on describing the experimental data via collective models. The ground state properties of even– General algebraic group techniques, applied to the Inter- even Xe isotopes have been the subject to theoretical acting Boson Model (IBM), have rather successfully [11–20] and experimental studies [22] involving in-beam described the low-lying collective properties of a wide γ-ray spectroscopy. Recently, the nuclear structure of range of nuclei. In the relatively simple Hamiltonian of xenon isotopes have been investigated by Turkan in the the model, the collective states are described by a IBM-1 model [30], while the energy levels, electric system of interacting s-andd-bosons carrying angular quadrupole moments and B(E2) values of even-mass momenta 0 and 2, respectively, which define an overall nuclei such as Ba,Xe were studied within the framework U(6) symmetry [1–5]. The IBM Hamiltonian has exact of the IBM-2 [19, 31–34]. These descriptions suggest solutions in three dynamical symmetry limits [U(5), O these nuclei to be soft with regard to γ deformation with (6), and SU(3)], which are geometrically analogous to a nearly maximum effective trixiality of γ≅30° [11]. As M. A. Jafarizadeh pointed out by Zamfir et al. [11], Xe isotopes in the Department of Theoretical Physics and Astrophysics, mass region A~130 appear to evolve from U(5)-to O(6)- University of Tabriz, Tabriz 51664, Iran like structure in the IBM-1. It is very difficult to apply e-mail: [email protected] conventional mean-field theories to such structures, which M. A. Jafarizadeh are neither vibrational nor rotational. 114–134 Research Institute for Fundamental Sciences, Tabriz 51664, Iran Here we examine the even–even Xe isotopes in the U(5)↔SO(6) transition region and calculate the energy lev- : * N. Fouladi H. Sabri ( ) els and B(E2) transition probabilities in the frame work of Department of Nuclear Physics, University of Tabriz, Tabriz 51664, Iran IBM with the affine SU(1,1) algebraic technique. The esti- e-mail: [email protected] mated control parameters indicate a spherical to γ-soft shape Braz J Phys (2013) 43:34–40 35 transition. The same shape transition is revealed by the is generated by the operators Sv, v=0, and ±, which satisfies evolution of two-neutron separation energies S2n [31] de- the following commutation relations: rived from experimental results [19, 32–34]. Also, special Âà 130 Æ Æ þ À values are found for the Xe control parameter and R4/2, S0; S ¼S ; ½¼ÀS ; S 2S0 ð2:1Þ which suggest it as the best candidate for E(5) dynamical symmetry in this isotopic chain. This paper is organized as follows: Section 2 briefly The Casimir operator of SU(1,1) can be written as summarizes the theoretical aspects of transitional Hamilto- ÀÁ nian and the affine SU(1,1) algebraic technique. Section 3 b 0 0 þ À C2 ¼ S S À 1 À S S ; ð2:2Þ presents the numerical results obtained from applying the considered Hamiltonian to different isotopes. Finally, Sec- tion 4 summarizes our findings and the conclusions Representations of SU(1,1) are determined by a single κ extracted from the results in Section 3. number . The representation of the Hilbert space is hence spanned by orthonormal basis |κμ〉, where κ can be any positive number and μ=κ,κ+1,…. Therefore, 2 Theoretical Framework b 0 C2ðÞSUðÞ1; 1 jikμ ¼ kkðÞÀ 1 jikμ ; S jikμ ¼ μjikμ The phenomenological IBM in terms of U(5), O(6) and ð2:3Þ SU(3) dynamical symmetries has been employed to de- scribe the collective properties of several medium- and The bases of U(5)⊃SO(5) and SO(6)⊃SO(5) are simulta- d sd heavy-mass nuclei. These dynamical symmetries are geo- neously the bases of SU (1,1)⊃U(1) and SU (1,1)⊃U(1), metrically analogous to the harmonic vibrator, axial rotor respectively. For U(5)⊃SO(5) case, one has and γ-unstable rotor, respectively [1–5]. While these symmetries have already offered a fairly accurate descrip- jiNndnnΔLM tion of the low-lying nuclear states, attempts to analyti- d 1 5 d 1 5 cally describe the structure at the critical point of the ¼ N; k ¼ n þ ; μ ¼ nd þ ; nΔLM ; phase transition have only been partially successful. 2 2 2 2 Iachello [6, 7] established a new set of dynamical sym- ð2:4Þ metries, i.e. E(5) and X(5), for nuclei located at critical point of transitional regions. The E(5) symmetry, which Where N, n , v, L and M are quantum numbers of U describes a second-order phase transition, corresponds to d (6), U(5), SO(5), SO(3),andSO(2), respectively, while the transitional states in the region from the U(5) to the nΔ is an additional quantum number needed in the O(6) symmetries in the IBM-1. Different analyses of this reduction SO(5)↓SO(3) and κd and μd are quantum transitional region suggested certain nuclei, such as numbers of SUd(1,1) and U(1), respectively. On the 134Ba, 108Pd, as examples of that symmetry [9, 14]. other hand, in the IBM-1, the generators of the d-boson Elaborate numerical techniques are required to diag- pairing algebra created by onalize the Hamiltonian in these transitional regions and critical points. To avoid these problems, an algebraic 1 y y 1 solution based on the affine SU(1,1) Lie algebra has SþðdÞ¼ d : d ; SÀðdÞ¼ ed:ed ; been proposed by Pan et al. [9, 10]todescribethe 2 2 X ð2:5Þ properties of nuclei located in the U(5)↔SO(6) transi- 0ð Þ¼1 y þ y S d dn dn dndn tional region. The results of this approach are somewhat 4 n different from those obtained from the IBM, but as pointed out in Refs. [9, 10], there is a clear correspon- s dence with the description of the geometrical model for Similarly, the s-boson pairing forms another SU (1,1) this transitional region. algebra generated by the operators 1 y 1 SþðsÞ¼ s 2 ; SÀðsÞ¼ s2 ; 2.1 The Affine SU(1,1) Approach to the Transitional 2 2 Hamiltonian ð2:6Þ 1 y y S0ðsÞ¼ s s þ ss References [9, 10] describe the SU(1,1) algebra in detail. 4 Here, we briefly outline the basic ansatz and summarize the The infinite dimensional SUð1; 1Þ algebra is then gener- results. The Lie algebra corresponding to the group SU(1,1) ated by the operators [9, 10] 36 Braz J Phys (2013) 43:34–40 ÀÁ ÀÁ Æ þ Æ þ Æ " 2 þ 1 2 þ 5 ¼ 2n 1 ð Þþ 2n 1 ð Þ ; gcs ns 2 gcd n 2 Sn cs S s cd S d ¼ þ ð : Þ À 2 À 2 2 7 xi 1 cs xi 1 cdxi S0 ¼ c2nS0ðsÞþc2nS0ðdÞ n s d X 2 À for i ¼ 1; 2; ...; k ð2:13Þ where Cs and Cd are real parameters and n can be 0,± x À x i6¼j i j 1,±2,…. The generators in Eq. (2.7) satisfy the commutation rela- The eigenvalues E(k) of Hamiltonian (Eq. 2.9)canbe tions expressed in the form [9, 10] Âà Âà S0 ; SÆ ¼SÆ ; Sþ; SÀ ¼2S0 ð2:8Þ ðkÞ ¼ ðkÞ þ ðÞþþ ðÞþþ "Λ0 ; m n mþn m n mþnþ1 E h gn n 3 dLL 1 1 μ μ − … ð2:14Þ It follows that the {Sm , =0,+, ;±1,±2, } generate an Λ0 ¼ 1 2 þ 1 þ 2 þ 5 d 1 cs ns cd n affine Lie algebra SUð1; 1Þ without central extension.
Load more

Recommended publications
  • The Interacting Boson Model
    The interacting boson model P. Van Isacker, GANIL, France Dynamical symmetries of the IBM Neutrons, protons and F-spin (IBM-2) T=0 and T=1 bosons: IBM-3 and IBM-4 Symmetries in N~Z nuclei (III), Valencia, September 2003 The interacting boson model • Nuclear collective excitations are described in terms of N s and d bosons. • Spectrum generating algebra for the nucleus is U(6). All physical observables (hamiltonian, transition operators,…) are expressed in terms of the generators of U(6). • Formally, nuclear structure is reduced to solving the problem of N interacting s and d bosons. Symmetries in N~Z nuclei (III), Valencia, September 2003 Justifications for the IBM • Bosons are associated with fermion pairs which approximately satisfy Bose statistics: (0) ( 2) S + = a a+ ¥ a + Æ s+ , D+ = a a+ ¥ a + Æ d +  j ( j j )0 m  jj '( j j' )m m j jj ' • Microscopic justification: The IBM is a truncation and subsequent bosonization of the shell model in terms of S and D pairs. • Macroscopic justification: In the classical limit (N Æ ∞) the expectation value of the IBM hamiltonian between coherent states reduces to a liquid-drop hamiltonian. Symmetries in N~Z nuclei (III), Valencia, September 2003 Algebraic structure of the IBM • The U(6) algebra consists of the generators U(6) = s +s,s+ d ,d + s,d + d , m,m' = -2, ,+2 { m m m m' } K • The harmonic oscillator in 6 dimensions, +2 + + H = ns + nd = s s +  dm dm = C1[U(6)] ≡ N m = -2 • …has U(6) symmetry since "gi ŒU(6) : [H,gi ]= 0 • Can the U(6) symmetry be lifted while preserving the rotational
    [Show full text]
  • EVE Xe ISOTOPES by the FRAMEWORK of IBA Đsmail Maraş , Ramazan Gümüş and Nurettin Türkan Celal
    Mathematical and Computational Applications , Vol. 15, No. 1, pp. 79-88, 2010. © Association for Scientific Research THE IVESTIGATIO OF EVE-EVE 114-120 Xe ISOTOPES BY THE FRAMEWORK OF IBA Đsmail Maraş 1*, Ramazan Gümüş 2 and Nurettin Türkan 3,4 1Celal Bayar University, Faculty of Arts and Science, Manisa, Turkey [email protected] 2Celal Bayar University, Institute of Science, Manisa, Turkey [email protected] 3University of Wisconsin, Department of Physics, 53715 Madison, WI, USA 4Bozok University, Faculty of Arts and Science, 66200 Yozgat, Turkey [email protected] Abstract- In this work, the ground state, quasi beta and quasi gamma band energies of 114,116,118,120 Xe isotopes have been investigated by using the both (IBM-1 and IBM-2) versions of interacting boson model (IBM). In calculations, the theoretical energy levels have been obtained by using PHINT and NP-BOS program codes. The presented results are compared with the experimental data in respective tables and figures. At the end, it was seen that the obtained theoretical results are in good agreement with the experimental data. Key Words- Interacting Boson Model, Even-Even Xe, Band Energies (Ground State, Quasi Beta and Quasi Gamma Band). 1. ITRODUCTIO One of the most remarkable simplicities of atomic nuclei is that the thousands of 2-body nucleonic interactions in a nucleus can be reduced to and simulated by a 1-body potential [1]. This is done with the interacting boson model (IBA) [2], which is a useful model to formalize description of symmetry in nuclei. This model (IBA) has a U(6) group structure leading to sub-groups chains denoted by U(5), SU(3) and O(6), which describe vibrational, axially symmetric rotational and γ-soft rotational nuclei.
    [Show full text]
  • Generalized Interacting Boson Model and the Collective Behaviour in Nuclei
    PramS.a, Vol. 17, No. 5, November 1981, pp. 381-387. © Printed in India Generalized interacting boson model and the collective behaviour in nuclei M SUGUNA, R D RATNA RAJU and V K B KOTA* Theoretical Group, Department of Physics, Andhra University, Waltair 530 003, India *Department of Physics and Astronomy, University of Rochester, Rochester, New York, USA *Permanent Address: Physical Research Laboratory, Ahmedabad 380 009, India MS received 9 May 1981 ; revised 3 October 1981 Abstract. The effect of including the high spin bosons on the manifestation of collec- tive behaviour in nuclei is examined by plotting the B(E2; 2+ ~ 0+) rates as a function of neutron number for various values of )/, where ~ is the highest angular momentum of the bosons included in the calculation. B(E2; 2+ ~ 0 +) values of a large number of nuclei in various regions of the nuclear periodic table are calculated with a single value for the effective charge in the generalized scheme. Irreducible representations of SU(3) contained in the symmetric partition [N] of U(15) are worked out for integers N upto N = 15, to enable the explicit inclusion of the g boson into calculations. The experimentally observed odd-K bands in 284U and 184W are described as a direct conse- quence of the g boson. Keywords. Generalized interacting boson model; irreducible representations; sym- metric partitions; g boson. 1. Introduction The interacting boson model 0~M) of Arima and Iachello (1976, 1978) describes the collective properties of nuclei by considering pairs of protons and neutrons coupled to S = 0 and J -----L = 0, and 2.
    [Show full text]
  • Investigation of Shape Coexistence in Te Isotopes
    Investigation of shape coexistence in 118-128Te isotopes H. Sabria1, Z. Jahangirib, M. A. Mohammadia a Department of Physics, University of Tabriz, Tabriz 51664, Iran. b Physics Department, Payame Noor University, Tehran 19395-4697, Iran. 1 Corresponding Author E-mail: [email protected] 1 Abstract In this paper, we have considered the interplay between phase transitions and configuration mixing of intruder excitations in the 118-128Te isotopes. A transitional interacting boson model Hamiltonian in both IBM-1 and IBM-2 versions which are based on affine SU (1,1) Lie Algebra are employed to describe the evolution from spherical to deformed gamma unstable shapes along the chain of Te isotopes. The excitation energies, B(E0) and B(E2) transition rates are rather well reproduced in comparison with experimental counterparts when the weight of SO(6) limit is increased in Hamiltonian. Also our results show obvious relations between the configuration mixing ratio and quadrupole, hexadecapole and hexacontatetrapole deformation values in this isotopic chain. Keywords: intruder states; Interacting Boson Model (IBM); infinite dimensional algebra; energy levels; B(E0) and B(E2) transition probabilities. PACS: 21.60.Fw; 21.10.Re; 27.60.+j 1. Introduction Shape coexistence has been observed in many mass regions throughout the nuclear chart and has become a very useful paradigm to explain the competition between the monopole part of the nuclear effective force that tends to stabilize the nucleus into a spherical shape, in and near to shell closures, and the strong correlations (pairing, quadrupole in particular) that favors the nucleus into a deformed shapes in around mid-shell regions [1-15].
    [Show full text]
  • Evolution of Intrinsic Nuclear Structure in Medium Mass Even-Even Xenon Isotopes from a Microscopic Perspective*
    Chinese Physics C Vol. 44, No. 7 (2020) 074108 Evolution of intrinsic nuclear structure in medium mass even-even Xenon isotopes from a microscopic perspective* Surbhi Gupta1 Ridham Bakshi1 Suram Singh2 Arun Bharti1;1) G. H. Bhat3 J. A. Sheikh4 1Department of Physics, University of Jammu, Jammu- 180006, India 2Department of Physics and Astronomical Sciences, Central University of Jammu, Samba- 181143, India 3Department of Physics, SP College, Cluster University Srinagar- 190001, India 4Cluster University Srinagar - Jammu and Kashmir 190001, India Abstract: In this study, the multi-quasiparticle triaxial projected shell model (TPSM) is applied to investigate γ-vi- brational bands in transitional nuclei of 118−128Xe. We report that each triaxial intrinsic state has a γ-band built on it. The TPSM approach is evaluated by the comparison of TPSM results with available experimental data, which shows a satisfactory agreement. The energy ratios, B(E2) transition rates, and signature splitting of the γ-vibrational band are calculated. Keywords: triaxial projected shell model, triaxiality, yrast spectra, band diagram, back-bending, staggering, reduced transition probabilities DOI: 10.1088/1674-1137/44/7/074108 1 Introduction In the past few decades, the use of improved and sophisticated experimental techniques has made it pos- sible to provide sufficient data to describe the structure of The static and dynamic properties of a nucleus pre- nuclei in various mass regions of the nuclear chart. In dominantly dictate its shape or structure, and these prop- particular, the transitional nuclei around mass A ∼ 130 erties depend on the interactions among its constituents, have numerous interesting features, such as odd-even i.e, protons and neutrons.
    [Show full text]
  • Interacting Boson Model of Collective Octupole States (I)
    Nuclear Physics A472 (1987) 61-84 North-Holland, Amsterdam INTERACTING BOSON MODEL OF COLLECTIVE OCTUPOLE STATES (I). The rotational limit J. ENGEL’ and F. IACHELLO A. W. Wright Nuclear Structure Laboratory, Yale University, New Haven, Connecticut 06.511, USA Received 5 March 1987 Abstract: We discuss the problem of describing low-lying collective negative-parity states within the framework of the interacting boson model. We suggest that a simultaneous description of quadrupole and octupole states in nuclei be done in terms of the group U(16), which includes f- and p-bosons in addition to the usual d- and s-bosons. We analyze the dynamical symmetries associated with the rotational limit of this model and discuss their classical (large-N) analogs. We conclude with a preliminary application of the model to the radium isotopes. 1. Introduction Low-lying collective nuclear states are dominated by the occurrence of quadrupole vibrations and deformations. Their properties can be described in terms of shape variables, aZcL (CL= 0, kl, *2), ref ‘) or alternatively in terms of interacting s- and d-bosons with Jp = O+ and Jp = 2+ respectively ‘). The role played by d-bosons is easily understood since they can be thought of as a quantization of the variables (yzcI. The introduction of s-bosons is less obviously necessary and arose from a study of the underlying microscopic structure which led to an interpretation of bosons in terms of nucleon pairs ‘). It reflects the existence in nuclei of a pairing interaction in addition to the quadrupole interaction. An important consequence of the introduc- tion of s-bosons is that it facilitates phenomenological descriptions of spectra.
    [Show full text]
  • Quest for Superheavy Nuclei Began in the 1940S with the Syn­ Time It Takes for Half of the Sample to Decay
    FEATURES Quest for superheavy nuclei 2 P.H. Heenen l and W Nazarewicz -4 IService de Physique Nucleaire Theorique, U.L.B.-C.P.229, B-1050 Brussels, Belgium 2Department ofPhysics, University ofTennessee, Knoxville, Tennessee 37996 3Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 4Institute ofTheoretical Physics, University ofWarsaw, ul. Ho\.za 69, PL-OO-681 Warsaw, Poland he discovery of new superheavy nuclei has brought much The superheavy elements mark the limit of nuclear mass and T excitement to the atomic and nuclear physics communities. charge; they inhabit the upper right corner of the nuclear land­ Hopes of finding regions of long-lived superheavy nuclei, pre­ scape, but the borderlines of their territory are unknown. The dicted in the early 1960s, have reemerged. Why is this search so stability ofthe superheavy elements has been a longstanding fun­ important and what newknowledge can it bring? damental question in nuclear science. How can they survive the Not every combination ofneutrons and protons makes a sta­ huge electrostatic repulsion? What are their properties? How ble nucleus. Our Earth is home to 81 stable elements, including large is the region of superheavy elements? We do not know yet slightly fewer than 300 stable nuclei. Other nuclei found in all the answers to these questions. This short article presents the nature, although bound to the emission ofprotons and neutrons, current status ofresearch in this field. are radioactive. That is, they eventually capture or emit electrons and positrons, alpha particles, or undergo spontaneous fission. Historical Background Each unstable isotope is characterized by its half-life (T1/2) - the The quest for superheavy nuclei began in the 1940s with the syn­ time it takes for half of the sample to decay.
    [Show full text]
  • 22.05 Reactor Physics – Part One Course Introduction
    22.05 Reactor Physics – Part One Course Introduction 1. Instructor: John A. Bernard 2. Organization: Homework (20%) Four Exams (20% each; lowest grade is dropped) Final Exam (3.0 hours) (20%) 3. Text: The text book for this course is: Introduction to Nuclear Engineering, 3rd Edition, by John Lamarsh. This covers basic reactor physics as part of a complete survey of nuclear engineering. Readings may also be assigned from certain of the books listed below: Nuclear Reactor Analysis by A. F. Henry Introduction to Nuclear Power by G. Hewitt and J. Collier Fundamentals of Nuclear Science and Engineering by J. Shultis and R. Faw Atoms, Radiation, and Radiation Protection by J. Turner Nuclear Criticality Safety by R. Kneif Radiation Detection and Measurement by G. Knoll 4. Course Objective: To quote the late Professor Allan Henry: “The central problem of reactor physics can be stated quite simply. It is to compute, for any time t, the characteristics of the free-neutron population throughout an extended region of space containing an arbitrary, but known, mixture of materials. Specifically we wish to know the number of neutrons in any infinitesimal volume dV that have kinetic energies between E and E + ∆E and are traveling in directions within an infinitesimal angle of a fixed direction specified by the unit vector Ω. If this number is known, we can use the basic data obtained experimentally and theoretically from low-energy neutron physics to predict the rates at which all possible nuclear reactions, including fission, will take place throughout the region. Thus we can 1 predict how much nuclear power will be generated at any given time at any location in the region.” There are several reasons for needing this information: Physical understanding of reactor safety so that both design and operation is done intelligently.
    [Show full text]
  • Phase Diagram of the Proton-Neutron Interacting Boson Model
    PHYSICAL REVIEW LETTERS week ending VOLUME 93, NUMBER 21 19 NOVEMBER 2004 Phase Diagram of the Proton-Neutron Interacting Boson Model J. M. Arias,1 J. E. Garcı´a-Ramos,2 and J. Dukelsky3 1Departamento de Fı´sica Ato´mica, Molecular y Nuclear, Facultad de Fı´sica, Universidad de Sevilla, Apartado 1065, 41080 Sevilla, Spain 2Departamento de Fı´sica Aplicada, Universidad de Huelva, 21071 Huelva, Spain 3Instituto de Estructura de la Materia, CSIC, Serrano 123, 28006 Madrid, Spain (Received 2 June 2004; revised manuscript received 3 September 2004; published 15 November 2004) We study the phase diagram of the proton-neutron interacting boson model 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. DOI: 10.1103/PhysRevLett.93.212501 PACS numbers: 21.60.Fw, 05.70.Fh, 21.10.Re, 64.60.Fr Quantum phase transitions (QPT) have become a sub- IBM-1 there are three dynamical symmetries: SU(5), ject of great interest in the study of several quantum O(6), and SU(3). These correspond to well-defined nu- many-body systems in condensed matter, quantum optics, clear shapes: spherical, deformed -unstable, and prolate ultracold quantum gases, and nuclear physics. QPT are axial deformed, respectively. The structure of the IBM-1 structural changes taking place at zero temperature as a Hamiltonian allows to study systematically the transition function of a control parameter (for a recent review, see from one shape to another. There were some pioneering [1]). Examples of control parameters are the magnetic works along these lines in the 1980s [10–12], but it has field in spin systems, quantum Hall systems, and ultra- been the recent introduction of the concept of critical cold gases close to a Feshbach resonance, or the hole- point symmetry that has recalled the attention of the doping in cuprate superconductors.
    [Show full text]
  • Lesson 1 : Structure of Animal and Plant Cells
    Lesson 1 : Structure of Animal and Plant Cells It is important that you know the structure of animal and plant cells and are able to label the different parts. It is a favourite with examiners to have diagrams of cells requiring labelling in exams. Task 1: from memory label the cells below and write in the function Check your answers: There are many similarities and differences between animal and plant cells. Make sure you know these. Similarities Differences 1. Have a nucleus 1. Plant cells have a cellulose cell wall 2. Have a cytoplasm 2. Plant cells have a vacuole containing cell sap 3. Have a cell 3. Plant cells have chloroplast membrane 4. Contain 4. Many plant cells have a box-like shape whilst animal cell shape varies mitochondria 5. Plant cells have the nucleus to the side of the cell, animal cells have a nucleus in 5. Contain ribosomes the middle Task 2: Complete the sentences by filling in the gaps. Both plant and animal cells contain a nucleus. This holds genetic information. Both animal and plant cells have a cell membrane. This controls what enters and leaves the cell. Only a plant cell contains chloroplasts. This is where photosynthesis happens. Both cells contain mitochondria. This is where respiration occurs. Check your answers: Both plant and animal cells contain a nucleus. This holds genetic information. Both animal and plant cells have a cell membrane. This controls what enters and leaves the cell. Only a plant cell contains chloroplasts. This is where photosynthesis happens. Both cells contain mitochondria. This is where respiration occurs.
    [Show full text]
  • Description of Transitional Nuclei in the Sdg Boson Model
    UM-P-91/102 . Description of transitional nuclei in the sdg boson model V.-S. Lac and S. Kuyucak School of Physics, University of Melbottrne, Parkville, Victoria 3052, Australia Abstract We study the transitional nuclei in the framework of the sdg boson model. This extension is necessitated by recent measurements of E2 and E4 transitions in the Pt and Os isotopes which can not be explained in the sd boson models. We show how 7-unstable and triaxial shapes arise from special choices of sdg model Hamiltonians and discuss ways of limiting the number of free parameters through consistency and coherence conditions. A satisfactory description of E2 and E4 properties is obtained for the Pt and Os nuclei, which also predicts dynamic shape transitions in these nuclei. \V ' i 1. Introduction Description of transitional nuclei has been one of the most challenging tasks for collective models of nuclei. A complicating feature of these nuclei is the triaxial nature of their energy surface which is neither 7-rigid as in the Davydov-Filippov model *) nor 7-unstable as in the Wilets-Jean model 2), but rather 7-soft which necessitates introduction of more elaborate geometric models such as the Generalized Collective Model3). More recently, the interacting boson model (IBM)4) has provided a very simple description for the transitional nuclei based on the 0(6) limit and its perturbations 5-6). The 0(6) limit had been especially successful in explaining the E2 transitions among the low-lying levels of the Pt isotopes 5_6). Its main shortcomings are (i) the energy surface is 7-unstable which leads to too much staggering in the quasi-7 band 7), (ii) the quadrupole moments vanish 8), (iii) the B(E2) values fall off too rapidly due to boson cut-off 9), (iv) it fails to describe the E4 properties 10-18).
    [Show full text]
  • Physics of Superheavy Elements Kouichi Hagino
    Frontiers in Science II 2013.11.6 Physics of superheavy elements Kouichi Hagino Nuclear Theory Group, Department of Physics, Tohoku University What is nuclear physics? What are superheavy elements? How to create superheavy elements? What are chemical properties of superheavy elements? Introduction: atoms and atomic nuclei What would you see if you magnified the dog? ~ 50 cm Introduction: atoms and atomic nuclei cells ~ 50 cm ~ m = 10-6 m Introduction: atoms and atomic nuclei DNA cells -8 ~ 50 cm ~ m = 10-6 m ~ 10 m atom All things are made of atoms. ~ 10-10 m All things are made of atoms. • Thales, Democritus (ancient Greek) • Dalton (chemist, 19th century) • Boltzmann(19th century) • Einstein (1905) ~ 10-10 m STM image (surface physics group, Tohoku university) Introduction: atoms and atomic nuclei DNA cells -8 ~ 50 cm ~ 10 m atom atomic nucleus ~ 10-15 m ~ 10-10 m proton (+e) neutron (no charge) electron cloud (-e) Neutral atoms: # of protons = # of electrons Chemical properties of atoms # of electrons Mp ~ Mn ~ 2000 Me the mass of atom ~ the mass of nucleus Periodic table of chemical elements tabular arrangement of chemical elements based on the atomic numbers (= # of electrons = # of protons) What are we made of ? oxygen 43 kg cerium 40 mg gallium 0.7 mg carbon 16 kg barium 22 mg tellurium 0.7 mg hydrogen 7 kg iodine 20 mg yttrium 0.6 mg nitrogen 1.8 kg tin 20 mg bismuth 0.5 mg calcium 1.0 kg titanium 20 mg thallium 0.5 mg phosphorus 780 g boron 18 mg indium 0.4 mg potassium 140 g nickel 15 mg gold 0.2 mg sulphur 140 g selenium
    [Show full text]