DOCSLIB.ORG

Quark Distributions in Nuclei and Nuclear Effects on Nucleon Structure

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Quark Distributions in Nuclei and Nuclear Effects on Nucleon Structure CPC(HEP & NP), 2009, 33(4): 263|268 Chinese Physics C Vol. 33, No. 4, Apr., 2009 Quark distributions in nuclei and nuclear effects on nucleon structure functions * WANG Yan-Zhao(ýð)1 ZHANG Hong-Fei(Üõ)1;1) GAO Yong-Hua(p[u)2 HOU Zhao-Yu(ûð)3;4 DONG Jian-Min(Âï¯)1 DUAN Chun-Gui(ãSB)4 ZUO Wei()1;5 1 (School of Nuclear Science and Technology, Lanzhou University, Lanzhou 730000, China) 2 (Department of Physics, Shijiazhuang College, Shijiazhuang 050801, China) 3 (Department of Mathematics and Physics, Shijiazhuang Railway College, Shijiazhuang 050043, China) 4 (Department of Physics, Hebei Normal University, Shijiazhuang 050016, China) 5 (Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China) Abstract Extended quark distribution functions are presented obtained by fitting a large amount of experi- mental data of the l-A DIS process on the basis of an improved nuclear density model. The experimental data of l-A DIS processes with A> 3 in the region 0:0010 6 x 6 0:9500 are quite satisfactorily described by using the extended formulae. Our knowledge of the influence of nuclear matter on the quark distributions is deepened. Key words improved nuclear density model, quark distributions in nuclei, nuclear effects on nucleon structure functions PACS 12.39.Ba, 13.60.Hb, 25.30.Mr 1 Introduction ting experimental data on deep inelastic scattering. With these formulae, containing now a description of Since the discovery of the EMC effect[1], physi- the nuclear effects in parametric form, the experimen- cists have proposed several models giving a more or tal data of the l-A DIS processes (for A> 12) and the less satisfactory explanation for it[2|7]. Among these nuclear Drell-Yan processes (E772 Collaboration ex- [13, 14] models, the nuclear density model proposed by Frank- perimental data) could be well described . Due furt and Strikman is such a model that explains the to the restriction of the nuclear momentum conserva- EMC effect[8]. It can explain the nuclear effect in tion condition, a gloun distribution formula depend- l-A DIS processes (lepton-nucleus (A) deep inelastic ing on a corresponding parameter was also proposed. scattering) for medium range x values[9]. However, With this also, the nuclear effect on the J/ process [15] the function RA1=A2 (x;Q2) obtained from the nuclear could be explained satisfactorily . density model is used to describe the influence of Although several nuclear effects were explained the nuclear medium on the valence quark distribution satisfactorily by these parametric formulae for the and the sea quark distribution, which does not reflect parton distributions, we think that the original quark their corresponding variations[10|12]. In 2006, Gao et distribution formulae have two shortcomings. First, al. presented an improved nuclear density model and they are obtained by using only a limited set of ex- A 2 A 2 perimental data, therefore some uncertainties exist. obtained formulae for RV (x;Q ), RS (x;Q ) describ- ing the valence quark distribution and the sea quark Second, the original formulae do not include values distribution within the region of 0.00106x6 0:6000 of the phenomenological parameters for the region for a bound nucleon. These functions depending on x> 0:6000, i.e., they cannot describe the distribu- phenomenological parameters were obtained by fit- tions of the valence and sea quarks in the large x Received 8 August 2008 * Supported by Natural Science Foundation of China (100775061, 10505016, 10575119), CAS Knowledge Innovation Project (KJCX-SYW-N02), Major State Basic Research Developing Program of China (2007CB815004) and Natural Science Foundation of Hebei Province in China (A2005000535, 103143) 1) E-mail: [email protected] ©2009 Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Sciences and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd 264 Chinese Physics C (HEP & NP) Vol. 33 region. This is true for the l-A DIS processes and The influence of the nuclear medium experienced also for the prediction of other nuclear processes, such by the valence quark and the sea quark momentum as the nuclear Drell-Yan process in the large x re- distributions is not necessarily the same and differ- gion. Therefore we refitted the quark distribution ent descriptions should be used. Explicit forms for A 2 A 2 functions taking into account a larger experimental RV (x;Q ) and RS (x;Q ) (for the valence quark and data for the l-A DIS processes and extended the x the sea quark distributions) for the range 0.00106x6 region. In this paper we obtain the phenomenolog- 0:6000 have been obtained in Ref. [13]. They are given ical valence and sea quark distribution functions for by − 6 6 KV (A)βV (x) 1 the range 0.0010 x 0:9500. The experimental data RA (x;Q2) = 1+ ρ(A); (5) of the l-A DIS processes for A> 3 in this region is V 0:107 then quite satisfactorily explained. The paper is or- K (A)β (x)−1 RA(x;Q2) = 1+ S S ρ(A); (6) ganized as follows. In Sec. 2, the extended parametric S 0:107 quark distribution functions are presented refitting an where βV (x), βS(x) and K V (A), K S(A) are phe- enlarged experimental data set for the l-A DIS pro- nomenological parameters to determine the valence cesses based on an improved nuclear density model. quark distributions and the sea quark distributions The results are shown and discussed in Sec. 3. In the in bound nucleon and have been obtained by fitting a last section some conclusions are drawn. limited set of experimental data of the l-A DIS pro- cess. The number of phenomenological parameters in 2 Improved nuclear density model Eqs. (5,6) has now increased and the expressions are and quark distributions in nuclei more complicated. In order to put Eqs. (5,6) into a more compact form, we write Frankfurt and Strikman suggested the following ∗ RA(x;Q2) = 1+β (x)ρ(A); (7) form for the structure functions: V V A 2 ∗ A N D N − − RS (x;Q ) = 1+βS(x)ρ(A): (8) [F2 =F2 1]=[F2 =F2 1] = ρ(A)/ρ(D); (1) ∗ ∗ N p n The phenomenological parameters β (x), β (x) where F 2 = (F2 +F2 )=2 is the structure function of V S A D in Eqs. (7,8) have been by fitting an extended ex- the free nucleon, F 2 and F 2 are the isoscalar nuclear and deuteron structure functions. They assumed that perimental data set of the l-A DIS process. A value the nuclear effect on the nucleon structure has its ori- of Q2 = 40 GeV2 has been taken for the fitting pro- gin in the differences of the nuclear densities ρ(A) (in cedure. The obtained phenomenological parameter units of nucleon/fm3). Thus Eq. (1) can be written values are listed in Table 1. as follows The nuclear density ρ(A) used in Eqs. (7,8) has been taken from an empirical formula used to describe [F A=F N −1] = β(x)ρ(A) ; (2) 2 2 the average properties of nuclei[17]. where β(x) is for all kinds of nuclei the same, the ρ(A) = 0:011=2 +0:02lnA (9) nuclear effect being described by ρ(A). The function describing the effect of nuclear medium on the struc- where " is the mean binding energy in the nucleus ture function of a bound nucleon in a nucleus A is of mass number A. The mean binding energies have then given by been taken from Ref. [18]. A1=A2 2 A1 2 A2 2 For a nucleus A the momentum distribution func- R (x;Q ) = F2 (x;Q )=F2 (x;Q ) = tions of the valence and the sea quarks in a bound [1+β(x)ρ(A1)]=[1+β(x)ρ(A2)]: (3) nucleon are given by A1=A2 2 The ratio R (x;Q ) of Eq. (3) describes the A 2 A 2 N 2 qV f (x;Q ) = RV (x;Q )qV f (x;Q ); (10) result for a parton distribution under the influence of A 2 A 2 N 2 the nuclear medium. However, it does not reflect the qSf (x;Q ) = RS (x;Q )qSf (x;Q ); (11) respective change of the valence and sea quark distri- where q N (x;Q2) and q N (x;Q2) are the correspond- butions in nucleus. If in Eq. (3) A is a deuteron with V f Sf 2 ing momentum distribution functions inside a free a very small density of ρ(D) = 0:0244, we can write nucleon, f denotes the flavor of quarks. From this Eq. (3) in the form we can see that the distributions for quarks in a A1=D 2 t R (x;Q ) 1+β(x)ρ(A1): (4) bound nucleon can be obtained, as described before in ∗ ∗ That Eq. (4) is reasonable can be tested by using ef- Eqs. (7,8), by using parameters βV (x), βS (x) different fective field theory (see Ref. [16]). from those used for the quarks in a free nucleon. No. 4 WANG Yan-Zhao et alµQuark distributions in nuclei and nuclear effects on nucleon structure functions 265 Table 1. Phenomenological parameters as a function of x in the range of 0.00106x6 0:9500 (Q2 = 40 GeV2). ∗ ∗ ∗ ∗ x βV (x) βS(x) x βV (x) βS(x) 0.0010 −0.0098 −2.3198 0.6000 −1.6487 32.4496 0.0100 0.0237 −1.8703 0.6500 −1.8416 49.6185 0.0293 0.0880 −1.0848 0.6800 −1.9000 62.2980 0.0512 0.1485 −0.4628 0.7000 −1.8769 71.8577 0.0805 0.2089 −0.0186 0.7500 −1.6120 100.1080 0.1244 0.2565 −0.0106 0.7800 −1.2012 120.4380 0.1765 0.2481 −0.6628 0.8000 −0.7620 135.6020 0.2451 0.1348 −1.8147 0.8500 1.3384 180.1620 0.3439 −0.2119 −1.8523 0.8800 3.8905 212.5050 0.4390 −0.7081 3.0076 0.9000 6.6845 237.1180 0.5000 −1.0754 10.3060 0.9500 25.2534 315.5230 Fig.
Load more

Recommended publications
  • B2.IV Nuclear and Particle Physics
    B2.IV Nuclear and Particle Physics A.J. Barr February 13, 2014 ii Contents 1 Introduction 1 2 Nuclear 3 2.1 Structure of matter and energy scales . 3 2.2 Binding Energy . 4 2.2.1 Semi-empirical mass formula . 4 2.3 Decays and reactions . 8 2.3.1 Alpha Decays . 10 2.3.2 Beta decays . 13 2.4 Nuclear Scattering . 18 2.4.1 Cross sections . 18 2.4.2 Resonances and the Breit-Wigner formula . 19 2.4.3 Nuclear scattering and form factors . 22 2.5 Key points . 24 Appendices 25 2.A Natural units . 25 2.B Tools . 26 2.B.1 Decays and the Fermi Golden Rule . 26 2.B.2 Density of states . 26 2.B.3 Fermi G.R. example . 27 2.B.4 Lifetimes and decays . 27 2.B.5 The flux factor . 28 2.B.6 Luminosity . 28 2.C Shell Model § ............................. 29 2.D Gamma decays § ............................ 29 3 Hadrons 33 3.1 Introduction . 33 3.1.1 Pions . 33 3.1.2 Baryon number conservation . 34 3.1.3 Delta baryons . 35 3.2 Linear Accelerators . 36 iii CONTENTS CONTENTS 3.3 Symmetries . 36 3.3.1 Baryons . 37 3.3.2 Mesons . 37 3.3.3 Quark flow diagrams . 38 3.3.4 Strangeness . 39 3.3.5 Pseudoscalar octet . 40 3.3.6 Baryon octet . 40 3.4 Colour . 41 3.5 Heavier quarks . 43 3.6 Charmonium . 45 3.7 Hadron decays . 47 Appendices 48 3.A Isospin § ................................ 49 3.B Discovery of the Omega § ......................
    [Show full text]
  • Particle Production at Small-X in Deep Inelastic Scattering Dajing Wu Iowa State University
    Iowa State University Capstones, Theses and Graduate Theses and Dissertations Dissertations 2014 Particle production at small-x in deep inelastic scattering Dajing Wu Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/etd Part of the Physics Commons Recommended Citation Wu, Dajing, "Particle production at small-x in deep inelastic scattering" (2014). Graduate Theses and Dissertations. 13846. https://lib.dr.iastate.edu/etd/13846 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Particle production at small-x in deep inelastic scattering by Dajing Wu A dissertation submitted to the graduate faculty in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Major: Nuclear Physics Program of Study Committee: Kirill Tuchin, Major Professor James Vary Marzia Rosati Kerry Whisnant Alexander Roitershtein Iowa State University Ames, Iowa 2014 Copyright © Dajing Wu, 2014. All rights reserved. ii DEDICATION I would like to dedicate this thesis to my father, Xianggui Wu, and my mother, Wenfang Tang. Without their encouragement and support, I could not have completed such work. iii TABLE OF CONTENTS LIST OF FIGURES . vi ABSTRACT . x ACKNOWLEGEMENT . xi PART I Theoretical foundations for small-x physics1 CHAPTER 1. QCD as a theory for strong interactions . 2 1.1 QCD Lagrangian . .2 1.2 Perturbative QCD . .2 1.3 Light-cone perturbation theory .
    [Show full text]
  • Physics 301 1-Nov-2004 17-1 Reading Finish K&K Chapter 7 And
    Physics 301 1-Nov-2004 17-1 Reading Finish K&K chapter 7 and start on chapter 8. Also, I’m passing out several Physics Today articles. The first is by Graham P. Collins, August, 1995, vol. 48, no. 8, p. 17, “Gaseous Bose-Einstein Condensate Finally Observed.” This describes the research leading up the first observation of a BE condensate that’s not a superfluid or superconductor. The second is by Barbara Goss Levi, March, 1997, vol. 50, no. 3, p. 17, “Bose Condensates are Coherent Inside and Outside an Atom Trap,” describing the first “atom laser” which was based on a BE condensate. The third is also by Levi, October, 1998, vol. 51, no. 10, p. 17, “At Long Last, a Bose-Einstein Condensate is Formed in Hydrogen,” describing even more progress on BE condensates. In addition, there is a recent Science report on an atomic Fermi Gas, DeMarco, B., and Jin, D. S., September 10, 1999, vol. 285, p. 1703, “Onset of Fermi Degeneracy in a Trapped Atomic Gas.” Bose condensates and Fermi degeneracy are current hot topics in Condensed Matter Research. Searching the preprint server or “Googling” with appropriate keywords is bound to turn up many more articles. More on Fermi Gases So far, we’ve considered the zero temperature Fermi gas and done an approximate treatment of the low temperature heat capacity of Fermi gases. The zero temperature Fermi gas was straightforward. We simply said that all states, starting from the lowest energy state, are filled until we run out of particles. The energy at which this happens is called the Fermi energy and is the same as the chemical potential at 0 temperature, ǫF = µ(τ = 0).
    [Show full text]
  • Superfast Quarks, Short Range Correlations and QCD at High Density John Arrington Argonne National Laboratory
    Superfast Quarks, Short Range Correlations and QCD at High Density John Arrington Argonne National Laboratory A(e,e’) at PDFs at x>1 High Energy Superfast quarks PN12, The Physics of Nuclei with 12 GeV Electrons Workshop, Nov. 1, 2004 Superfast Quarks, Short Range Correlations and QCD at High Density John Arrington Argonne National Laboratory Nuclear structure SRCs Nuclear PDFs A(e,e’) at PDFs at x>1 EMC effect High Energy Superfast quarks QCD Phase Transition Cold, dense nuclear matter PN12, The Physics of Nuclei with 12 GeV Electrons Workshop, Nov. 1, 2004 Short Range Correlations (SRCs) Mean field contributions: k < kF Well understood High momentum tails: k > kF Calculable for few-body nuclei, nuclear matter. Dominated by two-nucleon short range correlations. Calculation of proton momentum distribution in 4He Wiringa, PRC 43 k > 250 MeV/c 1585 (1991) 15% of nucleons 60% of the K.E. k < 250 MeV/c 85% of nucleons 40% of the K.E. Isolate short range interaction (and SRCs) by probing at high Pm (x>1) V(r) N-N potential Poorly understood part of nuclear structure Significant fraction of nucleons have k > kF 0 Uncertainty in short-range interaction leads to uncertainty at large momenta (>400-600 MeV/c), even for the Deuteron r [fm] ~1 fm A(e,e’): Short range correlations 56Fe(e,e/ )X We want to be able to isolate and probe -1 10 /A 2 Fe two-nucleon and multi-nucleon SRCs F -2 F2 /A 10 x=1 x = 1 -3 10 -4 Dotted =mean field approx.
    [Show full text]
  • Phenomenological Review on Quark–Gluon Plasma: Concepts Vs
    Review Phenomenological Review on Quark–Gluon Plasma: Concepts vs. Observations Roman Pasechnik 1,* and Michal Šumbera 2 1 Department of Astronomy and Theoretical Physics, Lund University, SE-223 62 Lund, Sweden 2 Nuclear Physics Institute ASCR 250 68 Rez/Prague,ˇ Czech Republic; [email protected] * Correspondence: [email protected] Abstract: In this review, we present an up-to-date phenomenological summary of research developments in the physics of the Quark–Gluon Plasma (QGP). A short historical perspective and theoretical motivation for this rapidly developing field of contemporary particle physics is provided. In addition, we introduce and discuss the role of the quantum chromodynamics (QCD) ground state, non-perturbative and lattice QCD results on the QGP properties, as well as the transport models used to make a connection between theory and experiment. The experimental part presents the selected results on bulk observables, hard and penetrating probes obtained in the ultra-relativistic heavy-ion experiments carried out at the Brookhaven National Laboratory Relativistic Heavy Ion Collider (BNL RHIC) and CERN Super Proton Synchrotron (SPS) and Large Hadron Collider (LHC) accelerators. We also give a brief overview of new developments related to the ongoing searches of the QCD critical point and to the collectivity in small (p + p and p + A) systems. Keywords: extreme states of matter; heavy ion collisions; QCD critical point; quark–gluon plasma; saturation phenomena; QCD vacuum PACS: 25.75.-q, 12.38.Mh, 25.75.Nq, 21.65.Qr 1. Introduction Quark–gluon plasma (QGP) is a new state of nuclear matter existing at extremely high temperatures and densities when composite states called hadrons (protons, neutrons, pions, etc.) lose their identity and dissolve into a soup of their constituents—quarks and gluons.
    [Show full text]
  • Deep-Inelastic Scattering on the Tri-Nucleons
    Three-body dynamics in hadron structure & hadronic systems: A symposium in celebration of Iraj Afnan’s 70th birthday Jefferson Lab, July 24, 2009 Deep-inelastic scattering on the tri-nucleons Wally Melnitchouk Outline Motivation: neutron structure at large x d/u ratio, duality in the neutron Status of large-x quark distributions nuclear corrections new global analysis of inclusive DIS data (CTEQx) DIS from A=3 nuclei model-independent extraction of neutron F2 plans for helium-3/tritium experiments Quark distributions at large x Parton distributions functions (PDFs) provide basic information on structure of hadronic systems needed to understand backgrounds in searches for new physics beyond the Standard Model in high-energy colliders, neutrino oscillation experiments, ... DGLAP evolution feeds low x, high Q2 from high x, low Q 2 1 dq(x, t) αs(t) dy x x = Pqq q(y, t)+Pqg g(y, t) dt 2π x y y y ! " # $ # $ % 2 2 t = log Q /ΛQCD Ratio of d to u quark distributions at large x particularly sensitiveHigher to twistsquark dynamics in nucleon SU(6) spin-flavor symmetry (a) (b) (c) proton wave function ↑ 1 ↑ √2 ↓ p = d (uu)1 d (uu)1 −3 − 3 Higher twists √2 ↑ 1 ↓ 1 ↑ + u (ud)1 u (ud)1 + u (ud)0 τ = 2 6 τ >− 23 √2 (τ = 2) (a) (b) (c) diquark spin single quark interactingqq and qg corquarkrelationsspectator scattering diquark τ = 2 τ > 2 single quark qq and qg scattering correlations Ratio of d to u quark distributions at large x particularly sensitive to quark dynamics in nucleon SU(6) spin-flavor symmetry proton wave function ↑ 1 ↑ √2 ↓ p = d (uu)1 d (uu)1 −3 − 3 √2 ↑ 1 ↓ 1 ↑ + u (ud)1 u (ud)1 + u (ud)0 6 − 3 √2 u(x)=2d(x) for all x n F2 2 p = F2 3 scalar diquark dominance M∆ >MN =⇒ (qq)1 has larger energy than (qq)0 .
    [Show full text]
  • Density and Moisture Content Measurements by Nuclear Methods Interim Report
    NATIONAL COOPERATIVE HIGHWAY RESEARCH PROGRAM REPORT 14. DENSITY AND MOISTURE CONTENT MEASUREMENTS BY NUCLEAR METHODS INTERIM REPORT HIGHWAY RESEARCH BOARD NATIONAL ACADEMY OF SCIENCES - NATIONAL RESEARCH COUNCIL HIGHWAY RESEARCH BOARD 1965 Officers DONALD S. BERRY, Chairman J. B. McMORRAN, First Vice Chairman EDWARD G. WETZEL, Second Vice Chairman GRANT MICKLE, Executive Director W. N. CAREY, JR., Deputy Executive Director Executive Committee REX M. WHrrrON, Federal Highway Administrator, Bureau of Public Roads (ex officio) A. E. JOHNSON, Executive Secretary, American Association of State Highway Officials (ex officio) LOUIS JORDAN, Executive Secretary, Division of Engineering and Industrial Research, National Research Council (ex officio) C. D. CURTISS, Special Assistant to the Executive Vice President, American Road Builders' Association (ex officio, Past Chairman 1963) WILBUR S. SMITH, Wilbur Smith and Associates (ex officio, Past Chairman 1964) W. BAUMAN, Managing Director, National Slag Association DONALD S. BERRY, Chairman, Department of Civil Engineering, Northwestern University MASON A. BUTCHER, County Manager, Montgomery County, Md. J. DOUGLAS CARROLL, JR., Executive Director, Tn-State Transportation Committee, New York City HARMER E. DAVIS, Director, Institute of Transportation and Traffic Engineering, University of California DUKE W. DUNBAR, Attorney General of Colorado JOHN T. HOWARD, Head, Department of City and Regional Planning, Massachusetts Institute of Technology PYKE JOHNSON, Retired LOUIS C. LUNDSTROM, Director, General Motors Proving Grounds BURTON W. MARSH, Executive Director, Foundation for Traffic Safety, American Automobile Association OSCAR T. MARZKE, Vice President, Fundamental Research, U. S. Steel Corporation J. B. McMORRAN, Superintendent of Public Works, New York State Department of Public Works CLIFFORD F. RASSWEILER, Retired M. L. SHADBUTRN, State Highway Engineer, Georgia State Highway Department T.
    [Show full text]
  • Arxiv:1112.0335V1 [Astro-Ph.HE] 1 Dec 2011 Ini Nitnesuc Fnurnso L Aos It flavors
    Proto-Neutron Star Cooling with Convection: The Effect of the Symmetry Energy L.F. Roberts,1 G. Shen,2 V. Cirigliano,2 J.A. Pons,3 S. Reddy,2, 4 and S.E. Woosley1 1Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064 USA 2Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87544 3Departament de F´ısica Aplicada, Universitat d’Alacant, Ap. Correus 99, 03080 Alacant, Spain 4Institute for Nuclear Theory, University of Washington, Seattle, Washington 98195 We model neutrino emission from a newly born neutron star subsequent to a supernova explosion to study its sensitivity to the equation of state, neutrino opacities, and convective instabilities at high baryon density. We find the time period and spatial extent over which convection operates is sensitive to the behavior of the nuclear symmetry energy at and above nuclear density. When convection ends within the proto-neutron star, there is a break in the predicted neutrino emission that may be clearly observable. PACS numbers: 26.50.+x, 26.60.-c, 21.65.Mn, 95.85.Ry The hot and dense proto-neutron star (PNS) born sub- formation. It has long been recognized that the outer sequent to core-collapse in a type II supernova explo- PNS mantle is unstable to convection soon after the pas- sion is an intense source of neutrinos of all flavors. It sage of the supernova shock, due to negative entropy gra- emits the 3 − 5 × 1053 ergs of gravitational binding en- dients [10]. This early period of instability beneath the ergy gained during collapse as neutrino radiation on a neutrino spheres has been studied extensively in both one time scale of tens of seconds as it contracts, becomes and two dimensions, with the hope that it could increase increasingly neutron-rich and cools.
    [Show full text]
  • Nuclear Physics and Astrophysics SPA5302, 2019 Chris Clarkson, School of Physics & Astronomy [email protected]
    Nuclear Physics and Astrophysics SPA5302, 2019 Chris Clarkson, School of Physics & Astronomy [email protected] These notes are evolving, so please let me know of any typos, factual errors etc. They will be updated weekly on QM+ (and may include updates to early parts we have already covered). Note that material in purple ‘Digression’ boxes is not examinable. Updated 16:29, on 05/12/2019. Contents 1 Basic Nuclear Properties4 1.1 Length Scales, Units and Dimensions............................7 2 Nuclear Properties and Models8 2.1 Nuclear Radius and Distribution of Nucleons.......................8 2.1.1 Scattering Cross Section............................... 12 2.1.2 Matter Distribution................................. 18 2.2 Nuclear Binding Energy................................... 20 2.3 The Nuclear Force....................................... 24 2.4 The Liquid Drop Model and the Semi-Empirical Mass Formula............ 26 2.5 The Shell Model........................................ 33 2.5.1 Nuclei Configurations................................ 44 3 Radioactive Decay and Nuclear Instability 48 3.1 Radioactive Decay...................................... 49 CONTENTS CONTENTS 3.2 a Decay............................................. 56 3.2.1 Decay Mechanism and a calculation of t1/2(Q) .................. 58 3.3 b-Decay............................................. 62 3.3.1 The Valley of Stability................................ 64 3.3.2 Neutrinos, Leptons and Weak Force........................ 68 3.4 g-Decay...........................................
    [Show full text]
  • Chapter 10 Nuclear Properties
    Chapter 10 Nuclear Properties Note to students and other readers: This Chapter is intended to supplement Chapter 3 of Krane’s excellent book, ”Introductory Nuclear Physics”. Kindly read the relevant sections in Krane’s book first. This reading is supplementary to that, and the subsection ordering will mirror that of Krane’s, at least until further notice. A nucleus, discovered by Ernest Rutherford in 1911, is made up of nucleons, a collective name encompassing both neutrons (n) and protons (p). Name symbol mass (MeV/c2 charge lifetime magnetic moment neutron n 939.565378(21) 0 e 881.5(15) s -1.91304272(45) µN proton p 938.272046(21) 1 e stable 2.792847356(23) µN The neutron was theorized by Rutherford in 1920, and discovered by James Chadwick in 1932, while the proton was theorized by William Prout in 1815, and was discovered by Rutherford between 1917 and 1919m and named by him, in 1920. Neutrons and protons are subject to all the four forces in nature, (strong, electromagnetic, weak, and gravity), but the strong force that binds nucleons is an intermediate-range force that extends for a range of about the nucleon diameter (about 1 fm) and then dies off very quickly, in the form of a decaying exponential. The force that keeps the nucleons in a nucleus from collapsing, is a short-range repulsive force that begins to get very large and repulsive 1 for separations less than a nucleon radius, about 2 fm. See Fig. 10.1 (yet to be created). 1 2 CHAPTER 10. NUCLEAR PROPERTIES The total nucleon−nucleon force 10 5 (r) (arbitrary units) 0 nn,att −5 (r) + V −10 nn,rep V 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 r (fm) Figure 10.1: A sketch of the nucleon-nucleon potential.
    [Show full text]
  • Systematics of Nucleon Density Distributions and Neutron Skin of Nuclei
    Systematics of nucleon density distributions and neutron skin of nuclei W. M. Seif and Hesham Mansour Physics Department, Faculty of Science, Cairo University, Egypt Abstract Proton and neutron density profiles of 760 nuclei in the mass region of are analyzed using the Skyrme energy density for the parameter set SLy4. Simple formulae are obtained to fit the resulting radii and diffuseness data. These formulae are useful to estimate the values of the unmeasured radii, and especially in extrapolating charge radii values for nuclei which are far from the valley of stability or to perform analytic calculations for bound and/or scattering problems. The obtained neutron and proton root-mean-square radii and the neutron skin thicknesses are in agreement with the available experimental data and previous Hartree-Fock calculations. I. Introduction To get accurate information on the density distributions of finite nuclei is of high priority in nuclear physics. Basically, to describe perfectly finite nuclei we have to start with full information regarding the root-mean-square (rms) radii of their proton and neutron density distributions, their surface diffuseness, and their neutron skin thickness. Unlike the available experimental data on the charged proton distributions, the available data for the neutral neutron distributions and their rms radii inside nuclei, as well as the neutron skin thickness are not enough yet. Previous extensive studies are aimed to investigate the correlation between the differences in the proton and neutron radii in finite nuclear systems and the nuclear symmetry energy [1, 2, 3, and 4] and neutron skin thickness. Most works are restricted to spherical nuclei.
    [Show full text]
  • Formation of Hot Heavy Nuclei in Supernova Explosions
    Physics Letters B 584 (2004) 233–240 www.elsevier.com/locate/physletb Formation of hot heavy nuclei in supernova explosions A.S. Botvina a,b, I.N. Mishustin c,d,e a Cyclotron Institute, Texas A&M University, College Station, TX 77843, USA b Institute for Nuclear Research, 117312 Moscow, Russia c Institut für Theoretische Physik, Goethe Universität, D-60054 Frankfurt am Main, Germany d Niels Bohr Institute, DK-2100 Copenhagen, Denmark e Kurchatov Institute, RRC, 123182 Moscow, Russia Received 30 December 2003; accepted 23 January 2004 Editor: P.V. Landshoff Abstract We point out that during the supernova II type explosion the thermodynamical conditions of stellar matter between the protoneutron star and the shock front correspond to the nuclear liquid–gas coexistence region, which can be investigated in nuclear multifragmentation reactions. We have demonstrated, that neutron-rich hot heavy nuclei can be produced in this region. The production of these nuclei may influence dynamics of the explosion and contribute to the synthesis of heavy elements. 2004 Elsevier B.V. All rights reserved. PACS: 25.70.Pq; 26.50.+x; 26.30.+k; 21.65.+f In recent years significant progress has been made nucleons and lightest clusters (vaporisation). These by nuclear community in understanding properties of different intermediate states can be understood as a highly excited nuclear systems. Such systems are rou- manifestation of the liquid–gas type phase transition tinely produced now in nuclear reactions induced by in finite nuclear systems [1]. A very good description hadrons and heavy ions of various energies. Under cer- of such systems is obtained within the framework of tain conditions, which are well studied experimentally, statistical multifragmentation model (SMM) [2].
    [Show full text]