DOCSLIB.ORG

Nuclear Models: Shell Model

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Nuclear Models: Shell Model LectureLecture 33 NuclearNuclear models:models: ShellShell modelmodel WS2012/13 : ‚Introduction to Nuclear and Particle Physics ‘, Part I 1 NuclearNuclear modelsmodels Nuclear models Models with strong interaction between Models of non-interacting the nucleons nucleons Liquid drop model Fermi gas model ααα-particle model Optical model Shell model … … Nucleons interact with the nearest Nucleons move freely inside the nucleus: neighbors and practically don‘t move: mean free path λ ~ R A nuclear radius mean free path λ << R A nuclear radius 2 III.III. ShellShell modelmodel 3 ShellShell modelmodel Magic numbers: Nuclides with certain proton and/or neutron numbers are found to be exceptionally stable. These so-called magic numbers are 2, 8, 20, 28, 50, 82, 126 — The doubly magic nuclei: — Nuclei with magic proton or neutron number have an unusually large number of stable or long lived nuclides . — A nucleus with a magic neutron (proton) number requires a lot of energy to separate a neutron (proton) from it. — A nucleus with one more neutron (proton) than a magic number is very easy to separate. — The first exitation level is very high : a lot of energy is needed to excite such nuclei — The doubly magic nuclei have a spherical form Nucleons are arranged into complete shells within the atomic nucleus 4 ExcitationExcitation energyenergy forfor magicm nuclei 5 NuclearNuclear potentialpotential The energy spectrum is defined by the nuclear potential solution of Schrödinger equation for a realistic potential The nuclear force is very short-ranged => the form of the potential follows the density distribution of the nucleons within the nucleus: for very light nuclei (A < 7), the nucleon distribution has Gaussian form (corresponding to a harmonic oscillator potential ) for heavier nuclei it can be parameterised by a Fermi distribution. The latter corresponds to the Woods-Saxon potential e.g. 3) approximation by the U 1) Woods-Saxon potential: U(r) === −−− 0 rectangular potential well r−−−R with infinite barrier energy : 1+++ e a ∞ 2) a 0: U(r) ∞∞ a=0 approximation by the a>0 rectangular potential well : 0 R r −−−U0 , r <<< R ,0 r <<< R U(r) === U(r) === ,0 r ≥≥≥ R ∞∞∞, r ≥≥≥ R 6 SchrSchr öödingerdinger equationequation ˆ Schrödinger equation: HΨΨΨ === EΨΨΨ (1) Consider U(r) - Single-particle h∇∇∇2 rectangular potential Hˆ === −−− +++U(r) (2) Hamiltonian operator: 2M well with infinite •Eigenstates: ΨΨΨ(r) - wave function barrier energy •Eigenvalues: E - energy ,0 r <<< R U(r) is a nuclear potential – spherically symmetric U(r) === • ∞∞∞, r ≥≥≥ R 1 ∂∂∂ ∂∂∂ 1 ∂∂∂ 1 ∂∂∂ 2 ∇∇∇2 === r 2 +++ ((()(sin θθθ )))+++ r 2 ∂∂∂r ∂∂∂r r 2 sin θθθ ∂∂∂θθθ r 2 sin 2 θθθ ∂∂∂ϕϕϕ 2 1 ∂∂∂ 1 ∂∂∂2 Angular part: λλλˆ === ((()(sin θθθ )))+++ sin θθθ ∂∂∂θθθ sin 2 θθθ ∂∂∂ϕϕϕ 2 2 1 ∂∂∂ ∂∂∂ 1 Lˆ −−− h2λλλˆ === Lˆ2 ∇∇∇2 === r 2 −−− r 2 ∂∂∂r ∂∂∂r r 2 h2 L – operator for the orbital angular momentum ˆ2 h2 L ΥΥΥlm (((θθθ,ϕϕϕ))) === (ll +++ )1 ΥΥΥlm (((θθθ,ϕϕϕ))) (3) Eigenstates: Ylm – spherical harmonics 7 RadialRadial partpart The wave function of the particles in the nuclear potential can be decomposed into two parts: a radial one ΨΨΨ 111(r), which only depends on the radius r, and an angular part Ylm (θ,ϕϕϕ) which only depends on the orientation (this decomposition is possible for all spherically symmetric potentials): (4) ΨΨΨ(((r,θθθ,ϕϕϕ))) === ΨΨΨ1(r)⋅⋅⋅ ΥΥΥlm (((θθθ,ϕϕϕ))) From (4) and (1) => 2 2 h 1 ∂∂∂ ∂∂∂ 1 Lˆ 2 −−− 2 r +++ 2 ΨΨΨ1((()(r)))(ΥΥΥlm ((()θθθ,ϕϕϕ)))(=== E ΨΨΨ1((()r)))(ΥΥΥlm ((()θθθ,ϕϕϕ))) 2M r ∂∂∂r ∂∂∂r r 2M => eq. for the radial part: h2 1 ∂∂∂ ∂∂∂ h2 (ll +++ )1 2 (5) −−− 2 r +++ 2 ΨΨΨ1((()(r)))(=== E ΨΨΨ1((()r))) 2M r ∂∂∂r ∂∂∂r r 2M Substitute in (5): ℜℜℜ )r( ΨΨΨ ((()(r))) === 1 r h2 d 2ℜℜℜ )r( h2 l(l +++ )1 (6) −−− +++ ℜℜℜ )r( === E ℜℜℜ )r( 2M dr 2 r 2 2M 8 ConstraintsConstraints onon EE h2 d 2ℜℜℜ )r( h2 l(l +++ )1 Eq. for the radial part: +++ E −−− ℜℜℜ )r( === 0 (7) 2M dr 2 r 2 2M From (7) 1) Energy eigenvalues for orbital angular momentum l: E: l=0 s l=1 p states l=2 d l=3 f … 2) For each l: -l < m < l => (2 l+1) projections m of angular momentum. The energy is independent of the m quantum number, which can be any integer value between ± l. Since nucleons also have two possible spin directions, this means that the l levels are 2 ·(2 l+1) times degenerate if a spin-orbit interaction is neglected. 3) The parity of the wave function is fixed by the spherical wave function Yml and l reads (−1) : ˆ l P ΨΨΨ(((r,θθθ,ϕϕϕ))) === P ΨΨΨ1(r)⋅⋅⋅ ΥΥΥlm (((θθθ,ϕϕϕ))) === (−−− )1 ΨΨΨ1(r)⋅⋅⋅ ΥΥΥlm (((θθθ,ϕϕϕ))) ⇒ s,d,.. - even states; p,f,… - odd states 9 MainMain quantumquantum numbernumber nn h2 d 2ℜℜℜ )r( h2 l(l +++ )1 Eq. for the radial part : +++ E −−− ℜℜℜ )r( === 0 (7) 2M dr 2 r 2 2M A Solution of differential eq: )r( ′′′′′′ )r( )r( )r( 0 ℜℜℜ )r( === l kr(j ) ℜℜℜ +++ λλλ ℜℜℜ === r Spherical Bessel functions j (x): 2 2ME l k === h2 The wave function: A ΨΨΨ((()(r,θθθ,ϕϕϕ))) === j (kr )⋅⋅⋅ΥΥΥ ((()(θθθ,ϕϕϕ))) r l lm ∞∞∞ U(r) Boundary condition for the surface, i.e. at r =R: Ψ(Ψ(Ψ( R,θ,ϕ) =0 0 R r restrictions on k in Bessel functions: l kR(j ) === 0 ⇒ main quantum number n – corresponds to nodes of the Bessel function : Xnl 2ME ⇒⇒⇒ 2 2 2 ⇒⇒⇒ 2 2 (8) kR === Xnl k R === Xnl 2 R === Xnl h 10 ShellShell modelmodel withwith rectangularrectangular potentialpotential wellwell X 2 h2 Thus, according to Eq. (8) : nl 2 (9) E === Enl === Const ⋅⋅⋅ Xnl nl 2MR 2 Nodes of Bessel function Energy states are quantized structure of energy states Enl l === 0 s −−− states j0 2 state Enl === C ⋅⋅⋅ Xnl degeneracy states with E ≤≤≤ Enl n === 1 X10 === 14.3 2·(2 l+1 ),l=0 s1 E s1 === C ⋅⋅⋅ 86.9 2 2 n === 2 X20 === 28.6 1p E1 p === C ⋅⋅⋅ 20 2. 6 2·(2 l+1 ),l=1 8 n === 3 X30 === 42.9 d1 E1d === C ⋅⋅⋅ 33 2. 10 18 l === 1 p −−− states j1 s2 E2s === C ⋅⋅⋅ 39 5. 2 20 n === 1 X11 === 49.4 1 f E1 f === C ⋅⋅⋅ 48 8. 14 34 n === 2 X21 === 72.7 2 p E2 p === C ⋅⋅⋅59 7. 6 40 1g E === C ⋅⋅⋅64 18 58 l === 2 d −−− states j2 1g n === 1 X === 76.5 12 First 3 magic numbers are reproduced, higher – not! l === 3 f −−− states j3 2, 8, 20, 28, 50, 82, 126 n === 1 X13 === 99.6 Note: this result corresponds to for U(r) = rectangular l === 4 g −−− states j 4 potential well with infinite barrier energy 11 n === 1 X14 === 1.8 ShellShell modelmodel withwith WoodsWoods --SaxonSaxon potentialpotential Woods-Saxon potential: U0 U(r) === −−− r−−−R 1+++ e a The first three magic numbers (2, 8 and 20) can then be understood as nucleon numbers for full shells . Thus, this simple model does not work for the higher magic numbers. For them it is necessary to include spin-orbit coupling effects which further split the nl shells. 12 SpinSpin --orbitorbit interactioninteraction Introduce the spin-orbit interaction Vls – a coupling of the spin and the orbital angular momentum: h∇∇∇2 Hˆ === −−− +++U(r)+++Vˆ 2M ls h 2 ∇∇∇ ˆ −−− +++U(r)+++Vls ΨΨΨ(r,θθθ,ϕϕϕ) === E ΨΨΨ(r,θθθ,ϕϕϕ) 2M h∇∇∇2 −−− +++U(r)ΨΨΨ(r,θθθ,ϕϕϕ) === ((()(E −−−Vls ))) ΨΨΨ(r,θθθ,ϕϕϕ) 2M ˆ where Vls ΨΨΨ(r,θθθ,ϕϕϕ) ===Vls ΨΨΨ(r,θθθ,ϕϕϕ) Eigenstates eigenvalues Vˆ C )s,l( - scalar product of l and s •spin-orbit interaction: ls === ls total angular momentum: j === l +++ s 2 2 j ⋅⋅⋅ j === (l +++ s)( l +++ s) === l +++ s +++ 2 sl 1 2 2 2 l ⋅⋅⋅ s === ( j −−− l −−− s ) 2 13 SpinSpin --orbitorbit interactioninteraction 1 2 2 2 C ⋅⋅⋅ ( j −−− l −−− s )ΨΨΨ(r,θθθ,ϕϕϕ) ===V ΨΨΨ(r,θθθ,ϕϕϕ) ls 2 ls h2 Eigenvalues: V === C [[[][ j(j +++ )1 −−− l(l +++ )1 −−− s(s +++ )1 ]]] ls ls 2 Consider: h2 h2 1 1 1 2 1 3 j === l +++ : Vls === Cls (l +++ )( l +++ )−−− l −−− l −−− ⋅⋅⋅ === Cls l 2 2 2 2 2 2 2 h2 h2 1 1 1 2 1 3 j === l −−− : Vls === Cls (l −−− )( l +++ )−−− l −−− l −−− ⋅⋅⋅ === −−−Cls (l +++ )1 2 2 2 2 2 2 2 This leads to an energy splitting ∆Els which linearly increases with the angular momentum as 2l +++1 ∆∆∆E === V ls 2 ls It is found experimentally that Vls is negative , which means that the state with j =l+ 1/2 is always energetically below the j = l − 1/2 level. 14 SpinSpin --orbitorbit interactioninteraction The total angular momentum quantum Single particle energy levels: number j = l±1/2 of the nucleon is denoted by an extra index j: nl j j (2j+1) e.g., the 1f state splits into a 1f 7/2 and a 1f 5/2 state 1f 1f 5/2 1f 7/2 The nlj level is (2 j + 1) times degenerate Spin-orbit interaction leads to a sizeable splitting of the energy states which are indeed (10) (2) (6) comparable with the gaps between the nl (4) shells themselves . (8) (4) Magic numbers appear when the gaps (2) (6) between successive energy shells are (2) particularly large: (4) 2, 8, 20, 28, 50, 82, 126 (2) 15 CollectiveCollective NuclearNuclear ModelsModels 16 CollectiveCollective excitationsexcitations ofof nucleinuclei The single-particle shell model can not properly describe the excited states of nuclei: the excitation spectra of even-even nuclei show characteristic band structures which can be interpreted as vibrations and rotations of the nuclear surface low energy excitations have a collective origin ! The liquid drop model is used for the description of collective excitations of nuclei: the interior structure, i.e., the existence of individual nucleons, is neglected in favor of the picture of a homogeneous fluid-like nuclear matter.
Load more

Recommended publications
  • Probing Pulse Structure at the Spallation Neutron Source Via Polarimetry Measurements
    University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange Masters Theses Graduate School 5-2017 Probing Pulse Structure at the Spallation Neutron Source via Polarimetry Measurements Connor Miller Gautam University of Tennessee, Knoxville, [email protected] Follow this and additional works at: https://trace.tennessee.edu/utk_gradthes Part of the Nuclear Commons Recommended Citation Gautam, Connor Miller, "Probing Pulse Structure at the Spallation Neutron Source via Polarimetry Measurements. " Master's Thesis, University of Tennessee, 2017. https://trace.tennessee.edu/utk_gradthes/4741 This Thesis is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Masters Theses by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council: I am submitting herewith a thesis written by Connor Miller Gautam entitled "Probing Pulse Structure at the Spallation Neutron Source via Polarimetry Measurements." I have examined the final electronic copy of this thesis for form and content and recommend that it be accepted in partial fulfillment of the equirr ements for the degree of Master of Science, with a major in Physics. Geoffrey Greene, Major Professor We have read this thesis and recommend its acceptance: Marianne Breinig, Nadia Fomin Accepted for the Council: Dixie L. Thompson Vice Provost and Dean of the Graduate School (Original signatures are on file with official studentecor r ds.) Probing Pulse Structure at the Spallation Neutron Source via Polarimetry Measurements A Thesis Presented for the Master of Science Degree The University of Tennessee, Knoxville Connor Miller Gautam May 2017 c by Connor Miller Gautam, 2017 All Rights Reserved.
    [Show full text]
  • A Suggestion Complementing the Magic Numbers Interpretation of the Nuclear Fission Phenomena
    World Journal of Nuclear Science and Technology, 2018, 8, 11-22 http://www.scirp.org/journal/wjnst ISSN Online: 2161-6809 ISSN Print: 2161-6795 A Suggestion Complementing the Magic Numbers Interpretation of the Nuclear Fission Phenomena Faustino Menegus F. Menegus V. Europa, Bussero, Italy How to cite this paper: Menegus, F. Abstract (2018) A Suggestion Complementing the Magic Numbers Interpretation of the Nu- Ideas, solely related on the nuclear shell model, fail to give an interpretation of clear Fission Phenomena. World Journal of the experimental central role of 54Xe in the asymmetric fission of actinides. Nuclear Science and Technology, 8, 11-22. The same is true for the β-delayed fission of 180Tl to 80Kr and 100Ru. The repre- https://doi.org/10.4236/wjnst.2018.81002 sentation of the natural isotopes, in the Z-Neutron Excess plane, suggests the Received: November 21, 2017 importance of the of the Neutron Excess evolution mode in the fragments of Accepted: January 23, 2018 the asymmetric actinide fission and in the fragments of the β-delayed fission Published: January 26, 2018 of 180Tl. The evolution mode of the Neutron Excess, hinged at Kr and Xe, is Copyright © 2018 by author and directed by the 50 and 82 neutron magic numbers. The present isotope repre- Scientific Research Publishing Inc. sentation offers a frame for the interpretation of the post fission evaporation This work is licensed under the Creative of neutrons, higher for the AL compared to the AH fragments, a tenet in nuc- Commons Attribution International License (CC BY 4.0). lear fission.
    [Show full text]
  • Keynote Address: One Hundred Years of Nuclear Physics – Progress and Prospects
    PRAMANA c Indian Academy of Sciences Vol. 82, No. 4 — journal of April 2014 physics pp. 619–624 Keynote address: One hundred years of nuclear physics – Progress and prospects S KAILAS1,2 1Bhabha Atomic Research Centre, Mumbai 400 085, India 2UM–DAE Centre for Excellence in Basic Sciences, Mumbai 400 098, India E-mail: [email protected] DOI: 10.1007/s12043-014-0710-0; ePublication: 5 April 2014 Abstract. Nuclear physics research is growing on several fronts, along energy and intensity fron- tiers, with exotic projectiles and targets. The nuclear physics facilities under construction and those being planned for the future make the prospects for research in this field very bright. Keywords. Nuclear structure and reactions; nuclear properties; superheavy nuclei. PACS Nos 21.10.–k; 25.70.Jj; 25.70.–z 1. Introduction Nuclear physics research is nearly one hundred years old. Currently, this field of research is progressing [1] broadly in three directions (figure 1): Investigation of nuclei and nuclear matter at high energies and densities; observation of behaviour of nuclei under extreme conditions of temperature, angular momentum and deformation; and production and study of nuclei away from the line of stability. Nuclear physics research began with the investiga- tion of about 300 nuclei. Today, this number has grown many folds, nearly by a factor of ten. In the area of high-energy nuclear physics, some recent phenomena observed have provided interesting connections to other disciplines in physics, e.g. in the heavy-ion collisions at relativistic energies, it has been observed [2] that the hot dense matter formed in the collision behaved like an ideal fluid with the ratio of shear viscosity to entropy being close to 1/4π.
    [Show full text]
  • Interaction of Neutrons with Matter
    Interaction of Neutrons With Matter § Neutrons interactions depends on energies: from > 100 MeV to < 1 eV § Neutrons are uncharged particles: Þ No interaction with atomic electrons of material Þ interaction with the nuclei of these atoms § The nuclear force, leading to these interactions, is very short ranged Þ neutrons have to pass close to a nucleus to be able to interact ≈ 10-13 cm (nucleus radius) § Because of small size of the nucleus in relation to the atom, neutrons have low probability of interaction Þ long travelling distances in matter See Krane, Segre’, … While bound neutrons in stable nuclei are stable, FREE neutrons are unstable; they undergo beta decay with a lifetime of just under 15 minutes n ® p + e- +n tn = 885.7 ± 0.8 s ≈ 14.76 min Long life times Þ before decaying possibility to interact Þ n physics … x Free neutrons are produced in nuclear fission and fusion x Dedicated neutron sources like research reactors and spallation sources produce free neutrons for the use in irradiation neutron scattering exp. 33 N.B. Vita media del protone: tp > 1.6*10 anni età dell’universo: (13.72 ± 0,12) × 109 anni. beta decay can only occur with bound protons The neutron lifetime puzzle From 2016 Istitut Laue-Langevin (ILL, Grenoble) Annual Report A. Serebrov et al., Phys. Lett. B 605 (2005) 72 A.T. Yue et al., Phys. Rev. Lett. 111 (2013) 222501 Z. Berezhiani and L. Bento, Phys. Rev. Lett. 96 (2006) 081801 G.L. Greene and P. Geltenbort, Sci. Am. 314 (2016) 36 A discrepancy of more than 8 seconds !!!! https://www.scientificamerican.com/article/neutro
    [Show full text]
  • 14. Structure of Nuclei Particle and Nuclear Physics
    14. Structure of Nuclei Particle and Nuclear Physics Dr. Tina Potter Dr. Tina Potter 14. Structure of Nuclei 1 In this section... Magic Numbers The Nuclear Shell Model Excited States Dr. Tina Potter 14. Structure of Nuclei 2 Magic Numbers Magic Numbers = 2; 8; 20; 28; 50; 82; 126... Nuclei with a magic number of Z and/or N are particularly stable, e.g. Binding energy per nucleon is large for magic numbers Doubly magic nuclei are especially stable. Dr. Tina Potter 14. Structure of Nuclei 3 Magic Numbers Other notable behaviour includes Greater abundance of isotopes and isotones for magic numbers e.g. Z = 20 has6 stable isotopes (average=2) Z = 50 has 10 stable isotopes (average=4) Odd A nuclei have small quadrupole moments when magic First excited states for magic nuclei higher than neighbours Large energy release in α, β decay when the daughter nucleus is magic Spontaneous neutron emitters have N = magic + 1 Nuclear radius shows only small change with Z, N at magic numbers. etc... etc... Dr. Tina Potter 14. Structure of Nuclei 4 Magic Numbers Analogy with atomic behaviour as electron shells fill. Atomic case - reminder Electrons move independently in central potential V (r) ∼ 1=r (Coulomb field of nucleus). Shells filled progressively according to Pauli exclusion principle. Chemical properties of an atom defined by valence (unpaired) electrons. Energy levels can be obtained (to first order) by solving Schr¨odinger equation for central potential. 1 E = n = principle quantum number n n2 Shell closure gives noble gas atoms. Are magic nuclei analogous to the noble gas atoms? Dr.
    [Show full text]
  • 1663-29-Othernuclearreaction.Pdf
    it’s not fission or fusion. It’s not alpha, beta, or gamma dosimeter around his neck to track his exposure to radiation decay, nor any other nuclear reaction normally discussed in in the lab. And when he’s not in the lab, he can keep tabs on his an introductory physics textbook. Yet it is responsible for various experiments simultaneously from his office computer the existence of more than two thirds of the elements on the with not one or two but five widescreen monitors—displaying periodic table and is virtually ubiquitous anywhere nuclear graphs and computer codes without a single pixel of unused reactions are taking place—in nuclear reactors, nuclear bombs, space. Data printouts pinned to the wall on the left side of the stellar cores, and supernova explosions. office and techno-scribble densely covering the whiteboard It’s neutron capture, in which a neutron merges with an on the right side testify to a man on a mission: developing, or atomic nucleus. And at first blush, it may even sound deserving at least contributing to, a detailed understanding of complex of its relative obscurity, since neutrons are electrically neutral. atomic nuclei. For that, he’ll need to collect and tabulate a lot For example, add a neutron to carbon’s most common isotope, of cold, hard data. carbon-12, and you just get carbon-13. It’s slightly heavier than Mosby’s primary experimental apparatus for doing this carbon-12, but in terms of how it looks and behaves, the two is the Detector for Advanced Neutron Capture Experiments are essentially identical.
    [Show full text]
  • Nuclear Physics: the ISOLDE Facility
    Nuclear physics: the ISOLDE facility Lecture 1: Nuclear physics Magdalena Kowalska CERN, EP-Dept. [email protected] on behalf of the CERN ISOLDE team www.cern.ch/isolde Outline Aimed at both physics and non-physics students This lecture: Introduction to nuclear physics Key dates and terms Forces inside atomic nuclei Nuclear landscape Nuclear decay General properties of nuclei Nuclear models Open questions in nuclear physics Lecture 2: CERN-ISOLDE facility Elements of a Radioactive Ion Beam Facility Lecture 3: Physics of ISOLDE Examples of experimental setups and results 2 Small quiz 1 What is Hulk’s connection to the topic of these lectures? Replies should be sent to [email protected] Prize: part of ISOLDE facility 3 Nuclear scale Matter Crystal Atom Atomic nucleus Macroscopic Nucleon Quark Angstrom Nuclear physics: femtometer studies the properties of nuclei and the interactions inside and between them 4 and with a matching theoretical effort theoretical a matching with and facilities experimental dedicated many with better and better it know to getting are we but Today Becquerel, discovery of radioactivity Skłodowska-Curie and Curie, isolation of radium : the exact form of the nuclear interaction is still not known, known, not still is interaction of nuclearthe form exact the : Known nuclides Known Chadwick, neutron discovered History 5 Goeppert-Meyer, Jensen, Haxel, Suess, nuclear shell model first studies on short-lived nuclei Discovery of 1-proton decay Discovery of halo nuclei Discovery of 2-proton decay Calculations with
    [Show full text]
  • Three Related Topics on the Periodic Tables of Elements
    Three related topics on the periodic tables of elements Yoshiteru Maeno*, Kouichi Hagino, and Takehiko Ishiguro Department oｆ physics, Kyoto University, Kyoto 606-8502, Japan * [email protected] (The Foundations of Chemistry: received 30 May 2020; accepted 31 July 2020) Abstaract: A large variety of periodic tables of the chemical elements have been proposed. It was Mendeleev who proposed a periodic table based on the extensive periodic law and predicted a number of unknown elements at that time. The periodic table currently used worldwide is of a long form pioneered by Werner in 1905. As the first topic, we describe the work of Pfeiffer (1920), who refined Werner’s work and rearranged the rare-earth elements in a separate table below the main table for convenience. Today’s widely used periodic table essentially inherits Pfeiffer’s arrangements. Although long-form tables more precisely represent electron orbitals around a nucleus, they lose some of the features of Mendeleev’s short-form table to express similarities of chemical properties of elements when forming compounds. As the second topic, we compare various three-dimensional helical periodic tables that resolve some of the shortcomings of the long-form periodic tables in this respect. In particular, we explain how the 3D periodic table “Elementouch” (Maeno 2001), which combines the s- and p-blocks into one tube, can recover features of Mendeleev’s periodic law. Finally we introduce a topic on the recently proposed nuclear periodic table based on the proton magic numbers (Hagino and Maeno 2020). Here, the nuclear shell structure leads to a new arrangement of the elements with the proton magic-number nuclei treated like noble-gas atoms.
    [Show full text]
  • Low-Energy Nuclear Physics Part 2: Low-Energy Nuclear Physics
    BNL-113453-2017-JA White paper on nuclear astrophysics and low-energy nuclear physics Part 2: Low-energy nuclear physics Mark A. Riley, Charlotte Elster, Joe Carlson, Michael P. Carpenter, Richard Casten, Paul Fallon, Alexandra Gade, Carl Gross, Gaute Hagen, Anna C. Hayes, Douglas W. Higinbotham, Calvin R. Howell, Charles J. Horowitz, Kate L. Jones, Filip G. Kondev, Suzanne Lapi, Augusto Macchiavelli, Elizabeth A. McCutchen, Joe Natowitz, Witold Nazarewicz, Thomas Papenbrock, Sanjay Reddy, Martin J. Savage, Guy Savard, Bradley M. Sherrill, Lee G. Sobotka, Mark A. Stoyer, M. Betty Tsang, Kai Vetter, Ingo Wiedenhoever, Alan H. Wuosmaa, Sherry Yennello Submitted to Progress in Particle and Nuclear Physics January 13, 2017 National Nuclear Data Center Brookhaven National Laboratory U.S. Department of Energy USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26) Notice: This manuscript has been authored by employees of Brookhaven Science Associates, LLC under Contract No.DE-SC0012704 with the U.S. Department of Energy. The publisher by accepting the manuscript for publication acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or any third party’s use or the results of such use of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights.
    [Show full text]
  • Range of Usefulness of Bethe's Semiempirical Nuclear Mass Formula
    RANGE OF ..USEFULNESS OF BETHE' S SEMIEMPIRIC~L NUCLEAR MASS FORMULA by SEKYU OBH A THESIS submitted to OREGON STATE COLLEGE in partial fulfillment or the requirements tor the degree of MASTER OF SCIENCE June 1956 TTPBOTTDI Redacted for Privacy lrrt rtllrt ?rsfirror of finrrtor Ia Ohrr;r ef lrJer Redacted for Privacy Redacted for Privacy 0hrtrurn of tohoot Om0qat OEt ttm Redacted for Privacy Dru of 0rrdnrtr Sohdbl Drta thrrlr tr prrrEtrl %.ifh , 1,,r, ," r*(,-. ttpo{ by Brtty Drvlr ACKNOWLEDGMENT The author wishes to express his sincere appreciation to Dr. G. L. Trigg for his assistance and encouragement, without which this study would not have been concluded. The author also wishes to thank Dr. E. A. Yunker for making facilities available for these calculations• • TABLE OF CONTENTS Page INTRODUCTION 1 NUCLEAR BINDING ENERGIES AND 5 SEMIEMPIRICAL MASS FORMULA RESEARCH PROCEDURE 11 RESULTS 17 CONCLUSION 21 DATA 29 f BIBLIOGRAPHY 37 RANGE OF USEFULNESS OF BETHE'S SEMIEMPIRICAL NUCLEAR MASS FORMULA INTRODUCTION The complicated experimental results on atomic nuclei haYe been defying definite interpretation of the structure of atomic nuclei for a long tfme. Even though Yarious theoretical methods have been suggested, based upon the particular aspects of experimental results, it has been impossible to find a successful theory which suffices to explain the whole observed properties of atomic nuclei. In 1936, Bohr (J, P• 344) proposed the liquid drop model of atomic nuclei to explain the resonance capture process or nuclear reactions. The experimental evidences which support the liquid drop model are as follows: 1. Substantially constant density of nuclei with radius R - R Al/3 - 0 (1) where A is the mass number of the nucleus and R is the constant of proportionality 0 with the value of (1.5! 0.1) x 10-lJcm~ 2.
    [Show full text]
  • Upper Limit in Mendeleev's Periodic Table Element No.155
    AMERICAN RESEARCH PRESS Upper Limit in Mendeleev’s Periodic Table Element No.155 by Albert Khazan Third Edition — 2012 American Research Press Albert Khazan Upper Limit in Mendeleev’s Periodic Table — Element No. 155 Third Edition with some recent amendments contained in new chapters Edited and prefaced by Dmitri Rabounski Editor-in-Chief of Progress in Physics and The Abraham Zelmanov Journal Rehoboth, New Mexico, USA — 2012 — This book can be ordered in a paper bound reprint from: Books on Demand, ProQuest Information and Learning (University of Microfilm International) 300 N. Zeeb Road, P. O. Box 1346, Ann Arbor, MI 48106-1346, USA Tel.: 1-800-521-0600 (Customer Service) http://wwwlib.umi.com/bod/ This book can be ordered on-line from: Publishing Online, Co. (Seattle, Washington State) http://PublishingOnline.com Copyright c Albert Khazan, 2009, 2010, 2012 All rights reserved. Electronic copying, print copying and distribution of this book for non-commercial, academic or individual use can be made by any user without permission or charge. Any part of this book being cited or used howsoever in other publications must acknowledge this publication. No part of this book may be re- produced in any form whatsoever (including storage in any media) for commercial use without the prior permission of the copyright holder. Requests for permission to reproduce any part of this book for commercial use must be addressed to the Author. The Author retains his rights to use this book as a whole or any part of it in any other publications and in any way he sees fit.
    [Show full text]
  • Nuclear Physics
    Massachusetts Institute of Technology 22.02 INTRODUCTION to APPLIED NUCLEAR PHYSICS Spring 2012 Prof. Paola Cappellaro Nuclear Science and Engineering Department [This page intentionally blank.] 2 Contents 1 Introduction to Nuclear Physics 5 1.1 Basic Concepts ..................................................... 5 1.1.1 Terminology .................................................. 5 1.1.2 Units, dimensions and physical constants .................................. 6 1.1.3 Nuclear Radius ................................................ 6 1.2 Binding energy and Semi-empirical mass formula .................................. 6 1.2.1 Binding energy ................................................. 6 1.2.2 Semi-empirical mass formula ......................................... 7 1.2.3 Line of Stability in the Chart of nuclides ................................... 9 1.3 Radioactive decay ................................................... 11 1.3.1 Alpha decay ................................................... 11 1.3.2 Beta decay ................................................... 13 1.3.3 Gamma decay ................................................. 15 1.3.4 Spontaneous fission ............................................... 15 1.3.5 Branching Ratios ................................................ 15 2 Introduction to Quantum Mechanics 17 2.1 Laws of Quantum Mechanics ............................................. 17 2.2 States, observables and eigenvalues ......................................... 18 2.2.1 Properties of eigenfunctions .........................................
    [Show full text]