Poincaré Invariant Three-Body Scattering at Intermediate Energies
|
|
- Daniella Neal
- 5 years ago
- Views:
Transcription
1 Poincaré Invariant Three-Boy Scattering at Intermeiate nergies Ch. lster T. Lin W. Polyzou, W. Glöcle 5/8/9 Supporte by: U.S. DO, OSC, NRSC
2
3 A Few-Boy Theorist s view of the Nuclear Chart
4 Boun State: H - He Scattering: lastic Inelastic (Breaup) nergy Scale: ev MeV GeV
5 Challenges in N Physics Test of nuclear forces in the simplest nuclear environment (over a large energy range!) Two-boy forces Genuine three-boy forces Reaction mechanisms xamples: euteron breaup, (p,n) charge exchange, exclusive breaup (specific configurations) Higher nergy: Lorentz vs. Galilean Invariance Chec commonly use approximations (e.g. Glauber approach)
6 W.P. Abfalterer et al, PRL 81, 57 (1998)
7 Relativistic ffects at Higher nergies Computational Challenge: N an 4N systems: Solution: stanar treatment base on pw projecte momentum space successful (N scattering up to 5 MeV) but rather teious N: j max 5, N: J max 5/ `channels Computational maximum toay: N: j max 7, N: J max 1/ NO partial wave ecomposition of basis states
8 Roamap for N problem without PW Scalar NN moel Realistic NN Moel NN scattering boun state N boun state N boun state NF N scattering: Full Faeev Calculation lastic scattering Below an above brea-up Brea-up Poincarė Invariant Faeev Calculations NN scattering euteron Potentials AV18 an Bonn-B Brea-up in first orer: (p,n) charge exchange Max. nergy 5 MeV Lorentz inematics xact Faeev Calculation NN interactions High energy limits
9 Three-Boy Scattering - General Transition operator for elastic scattering U PG -1 PT Transition operator for breaup scattering U (1 P)T T tp tg PT Faeev euation (Multiple Scattering Series) U U T tp tg PtP L 1 st Orer in tp t v vg t : NN t-matrix P P 1 P P 1 P Permutation Operator
10 The Faeev uation in momentum space by using Jacobi Variables ( ) ) ( 1 1 p 1 p -Boy Transition Amplitue (NR) PT tg tp T ϕ ϕ ϕ ( ) ( ) ( ) ( ) ε ϕ ε ϕ ϕ i T i t t T m m m s m s " ˆ "," " " ", p, ˆ ", p, ˆ ˆ p s tˆ symmetrize -boy t-matrix 1
11 Variables for D Calculation istinct vectors in the problem: p 5 inepenent variables: p p, x x p pˆ ˆ, ˆ ˆ ( ) ( p) p x system : z system : z Variables invariant uner rotation: freeom to choose coorinate system for numerical calculation
12 Relativistic Faeev Calculations Context: Poincarė Invariant Quantum Mechanics Poincarė invariance is exact symmetry, realize by a unitary representation of the Poincarė group on a fewparticle Hilbert space Instant form Faeev euations same operator form but ifferent ingreients Kinematics Lorentz transformations between frames Dynamics Baamjian-Thomas Scheme: Mass Operator MM V replaces Hamiltonian HH v Connect Galilean two-boy v with Poincarė two-boy v Construct V : M M
13 Lorentz Kinematics: Phase Space Factors ( ) 4 ˆ ) ( ) ( n el U W ϕ ϕ π σ Ω ) ( 4 m p m W NR: (m/) Invariant Mass 4 4 ) ( cm p NR br U m m ϕ φ π σ Ω Ω 4 ) 4( 4 ) ( ) ( ) ( u u p n br U p m p W ϕ φ π σ Ω Ω u 1 p m W m W
14 Kinematics: Poincaré-Jacobi momenta 1 Nonrelativistic (Galilei) p Relativistic (Lorentz)
15 Kinematics: Poincaré-Jacobi Coorinates ( ) ( ) ( ) ( ) p N c.m. frame: 1,, with 1 K Kp ) ( ) ( )] ( ) ( )[ ( Kp ) ( p) ( 1 1 p K Poincarė-Jacobi Coorinates: All expressions relate to permutations much more complicate Depen on vector variables > angle epenent
16 Permutation Operator: PP1PP1P
17 Relativistic inematics: IA (1 st orer) T tp U PG 1 PT Lorentz transformation Lab c.m. frame) (-boy) Phase space factors in cross sections Poincarė-Jacobi momenta Permutations
18 Quantum Mechanics Galilei Invariant: K NR NR NR H h ; h h v1 v1 v M g Poincaré Invariant: H K M ; M M V1 V V 1 V ij M ij M ( m v ), ij ij m, ij Two-boy interaction embee in the -particle Hilbert space m, ij m i p ij m j p ij M m, ij m
19 V ij embee in the -particle Hilbert space ij ij ( m v ) m V M M, ij ij, ij nee matrix elements :
20 Two-Boy Input: T1-operator embee in -boy system T 1 (p', p; ) V (p', p; ) " ( ( V (p', " p ' )) ; ) T 1 (", p; ) ( ( " )) iε Do not solve for V! Obtain fully off-shell matrix elements T 1 (,,) from half shell transition matrix elements by Solving a 1 st resolvent type euation: T 1 () T 1 ( ) T 1 () [g () - g ( )] T 1 ( ) For every single off-shell momentum point Propose in Keister & Polyzou, PRC 7, 145 (6) Carrie out for the first time here [PRC 76, 1141 (7)]
21 Obtain embee N t-matrix T 1 (,,z ) halfshell in -boy c.m. frame first : Solution of the relativistic N LS euation with -boy potential
22 Consieration for two-boy t-matrix Relativistic an non-relativistic t-matrix shoul give ientical observables for etermining relativistic effects Or two-boy t-matrices shoul be phase-shift euivalent Four options: Start from relativistic LS euation natural option employe for NN interactions fit to 1 GeV If non-relativistic LS euation is use: Refit of parameters (maybe time consuming in practice) Transformation of Kamaa-Glöcle PRL 8, 547 (1998) Transformation of Coester-Piper-Serue as given in Polyzou PRC 58, 91 (1998)
23 Phase euivalent -boy t-matrices: Coester-Pieper-Serue (CPS) (PRC11, 1 (1975)) A interaction to suare of non-interacting mass operator NO nee to evaluate v irectly, since M, M, h have the same eigenstates Relation between half-shell t-matrices Relativistic an nonrelativistic cross sections are ientical functions of the invariant momentum { }, 4 with 4 v M v u m m u m h mh u M M m t e e m e t NR R ) ( ' ') ( ) ( 4 )) ( ( '
24 Total Cross Section for lastic Scattering: 1 st Orer T t P
25 Unitarity Relation ( ) ( ) φ φ ϑ π φ φ φ φ ϑ π φ φ φ φ φ φ 1 * * ' p ' ' ' U i U U i U U U p ( ) ( ) br el tot n U W σ σ σ ϕ ϕ π,1, Im 16 All calculations use a Malfliet-Tjon type potential
26 Total Cross Section an Unitarity Relation σ tot σ el σ br
27 Faeev uation as multiple scattering series T tp tgpt T tp tg PtP L 1 st Orer or IA
28 Convergence of the Faeev Multiple Scattering Series lab [GeV]
29 Convergence of the Faeev Multiple Scattering Series
30 lastic Scattering: Differential Cross Section
31 Breaup Scattering xclusive: Measure energy & angles of two ejecte particles V.Punjabi et al. PRC 8, 78 (1998) TRIUMF 58 MeV Outgoing protons are measure in the scattering plane
32 xclusive Breaup Scattering lab 58 MeV (symmetric configuration) (V.Punjabi et al. PRC 8, 78 (1998) QFS
33 xclusive Breaup Scattering lab 58 MeV (asymmetric configuration) QFS
34 xclusive Breaup Scattering lab 58 MeV QFS
35 xclusive Breaup Scattering Space-Star lab 58 MeV
36 xclusive Breaup Scattering : Coplanar Star QFS lab 58 MeV [MeV] [MeV]
37 Relevance of Stuy with Moel Interaction
38 Calcula tion: Henry Witala MeV
39 Results for Triton Bining nergy (FB ) 5-Channel Calculation CPS KG
40 Triton Bining nergy with CD-Bonn (arxiv:81.148) NR R Δ 5-ch (s-wave) ch (jm) ch (jm) ch (jm4) ch npnn ch (npnnwigner)
41 Computational uipment IBM Cluster P AMD Opteron ( TFlop) Jacuar: 56 P Opteron Cluster 56 P Itanium Cluster
42 Poincaré Invariant Faeev Calculations Kinematics Phase space factors Lorentz Transformation from Lab to c.m. frame Lorentz Transformation of Jacobi Coorinates Always reuces effects of phase-space factors Kinematics etermines pea positions in brea-up observables Dynamics xact calculation of the two-boy interaction embee in the three-particle Hilbert space The ynamic effects act in general opposite inematic effects
43 Poincaré Invariant Faeev Calculations Carrie out up to GeV for elastic an breaup scattering Solve Faeev euation in vector variables NO partial waves Relativistic effects are important at 5 MeV an higher Relativistic total elastic cross section increases up to 1% compare to the non-relativistic Relativistic inematics etermines QFS pea positions in inclusive an exclusive breaup Breaup: Relativistic effects very large epenent on configuration Above 8 MeV projectile energy: multiple scattering series converges after ~ iterations In breaup QFS conitions 1 st orer calculations sufficient
44 Poincaré Invariant Faeev Calculations Triton calculations: Difference in bining energy between relativistic an nonrelativistic calculation is.1 MeV Provie the CPS realization of a relativistic interaction is use. CPS is in a Hamiltonian context the correct way Future Systematic stuies of selecte cross sections & high energy limits Triton: Question about consistent inclusion of NF Long term: inclue Spin
45
Relativity and Three-Body Systems
Relativity and Three-Body Systems Ch. Elster T. Lin W. Polyzou, W. Glöcle 6/17/008 Supported by: U.S. DOE, OSC, NERSC A Few-Body Theorist s view of the Nuclear Chart Relativistic Three-Body Problem Context:
More informationPoincaré Invariant Three-Body Scattering
Poincaré Invariant Three-Body Scattering Ch. Elster T. Lin W. Polyzou, W. Glöckle 10/9/008 Supported by: U.S. DOE, OSC, NERSC A Few-Body Theorist s view of the Nuclear Chart Bound State: 3 H - 3 He Scattering:
More informationFirst Order Relativistic Three-Body Scattering. Ch. Elster
First Order Relativistic Three-Body Scattering Ch. Elster T. Lin, W. Polyzou W. Glöcle 4//7 Supported by: U.S. DOE, NERSC,OSC Nucleons: Binding Energy of H NN Model E t [MeV] Nijm I -7.7 Nijm II -7.64
More informationRelativistic Effects in Exclusive pd Breakup Scattering at Intermediate Energies
Relativistic Effects in Exclusive pd Breakup Scattering at Intermediate Energies T. Lin a, Ch. Elster a,b, W. N. Polyzou c, W. Glöckle d, a Institute of Nuclear and Particle Physics, and Department of
More informationLORENTZ BOOSTED NUCLEON-NUCLEON T-MATRIX AND THE TRITON BINDING ENERGY
October 7, 28 22:52 WSPC/INSTRUCTION FILE Modern Physics Letters A c World Scientific Publishing Company LORENTZ BOOSTED NUCLEON-NUCLEON T-MATRIX AND THE TRITON BINDING ENERGY H. KAMADA Department of Physics,
More informationN-d 3-body scattering and NN interactions
N- 3-boy scattering an NN interactions Collaboration o: H. Witała, J. Golak, R. Skibiński, K. Topolnicki, Jagiellonian University, Kraków W. Gloeckle, E. Epelbaum, H. Krebs, Bochum Ul-G. Meibner, A.Nogga,
More informationElastic nucleon-deuteron scattering and breakup with chiral forces
Elastic nucleon-euteron scattering an breakup with chiral orces H.Witała, J.Golak, R.Skibiński, K.Topolnicki JAGIELLONIAN UNIVERSITY LENPIC Collaboration Jagiellonian University, Kraków Ruhr-Universität,
More informationPoincaré Invariant Calculation of the Three-Body Bound State Energy and Wave Function
Poincaré Invariant Calculation of the Three-Body Bound State Energy and Wave Function q [fm ] 8 6 4 M. R. Hadizadeh, Ch. Elster and W. N. Polyzou log Ψ nr 8 7 7 7 3 3 7 7 3 3 4 6 8 log Ψ r p [fm ] 8 4
More informationarxiv: v1 [nucl-th] 3 Sep 2015
Relativistic few-body methods W. N. Polyzou Department of Physics and Astronomy The University of Iowa Iowa City, IA 52242, USA arxiv:1509.00928v1 [nucl-th] 3 Sep 2015 Contribution to the 21-st International
More informationFree rotation of a rigid body 1 D. E. Soper 2 University of Oregon Physics 611, Theoretical Mechanics 5 November 2012
Free rotation of a rigi boy 1 D. E. Soper 2 University of Oregon Physics 611, Theoretical Mechanics 5 November 2012 1 Introuction In this section, we escribe the motion of a rigi boy that is free to rotate
More informationinvolve: 1. Treatment of a decaying particle. 2. Superposition of states with different masses.
Physics 195a Course Notes The K 0 : An Interesting Example of a Two-State System 021029 F. Porter 1 Introuction An example of a two-state system is consiere. involve: 1. Treatment of a ecaying particle.
More informationCalculation of relativistic nucleon-nucleon potentials in three dimensions
Eur. Phys. J. A (7) 53: DOI./epja/i7-9- Regular Article Theoretical Physics THE EUROPEAN PHYSICAL JOURNAL A Calculation of relativistic nucleon-nucleon potentials in three dimensions M.R. Hadizadeh,,a
More informationThe Ehrenfest Theorems
The Ehrenfest Theorems Robert Gilmore Classical Preliminaries A classical system with n egrees of freeom is escribe by n secon orer orinary ifferential equations on the configuration space (n inepenent
More informationarxiv:nucl-th/ v1 10 Nov 2004
March, 8 :7 Proceeings Trim Size: 9in x 6in SP-AgusSalam arxiv:nucl-th/6v ov RESCATTERIG EFFECTS AD TWO-STEP PROCESS I AO PHOTOPRODUCTIO O THE DEUTERO A. SALAM AD. MIAGAWA Simulation Science Center, Okayama
More informationarxiv: v1 [hep-ph] 22 Jun 2012
Electroweak hadron structure in point-form dynamics heavy-light systems arxiv:1206.5150v1 [hep-ph] 22 Jun 2012 and Wolfgang Schweiger Institut für Physik, Universität Graz, A-8010 Graz, Austria E-mail:
More informationFew Body Methods in Nuclear Physics - Lecture I
Few Body Methods in Nuclear Physics - Lecture I Nir Barnea The Hebrew University, Jerusalem, Israel Sept. 2010 Course Outline 1 Introduction - Few-Body Nuclear Physics 2 Gaussian Expansion - The Stochastic
More informationCitation for published version (APA): Martinus, G. H. (1998). Proton-proton bremsstrahlung in a relativistic covariant model s.n.
University of Groningen Proton-proton bremsstrahlung in a relativistic covariant model Martinus, Gerard Henk IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you
More informationLagrangian and Hamiltonian Dynamics
Lagrangian an Hamiltonian Dynamics Volker Perlick (Lancaster University) Lecture 1 The Passage from Newtonian to Lagrangian Dynamics (Cockcroft Institute, 22 February 2010) Subjects covere Lecture 2: Discussion
More informationensembles When working with density operators, we can use this connection to define a generalized Bloch vector: v x Tr x, v y Tr y
Ph195a lecture notes, 1/3/01 Density operators for spin- 1 ensembles So far in our iscussion of spin- 1 systems, we have restricte our attention to the case of pure states an Hamiltonian evolution. Toay
More informationSolution of two nucleon systems using vector variables in momentum space - an innovative approach
University of Iowa Iowa Research Online Theses and Dissertations Spring 2011 Solution of two nucleon systems using vector variables in momentum space - an innovative approach Saravanan Veerasamy University
More informationSimplifying the Nuclear Many-Body Problem with Low-Momentum Interactions
Simplifying the Nuclear Many-Body Problem with Low-Momentum Interactions Scott Bogner September 2005 Collaborators: Dick Furnstahl, Achim Schwenk, and Andreas Nogga The Conventional Nuclear Many-Body Problem
More informationRicerca Indiretta di Supersimmetria nei Decadimenti dei Mesoni B
Ricerca Iniretta i Supersimmetria nei Decaimenti ei Mesoni B L. Silvestrini INFN, Roma Introuction to CP Violation in the SM Introuction to CP Violation in the MSSM A moel-inepenent analysis of SUSY effects
More informationLorentz invariant scattering cross section and phase space
Chapter 3 Lorentz invariant scattering cross section and phase space In particle physics, there are basically two observable quantities : Decay rates, Scattering cross-sections. Decay: p p 2 i a f p n
More informationCalculations of three-nucleon reactions
Calculations of three-nucleon reactions H. Witała Jagiellonian University, Kraków in collaboration with: J. Golak, R. Skibiński, K. Topolnicki, Kraków H. Kamada, Kyushu Institute of Technology E. Epelbaum,
More informationNUMERICAL METHODS FOR QUANTUM IMPURITY MODELS
NUMERICAL METHODS FOR QUANTUM IMPURITY MODELS http://www.staff.science.uu.nl/~mitch003/nrg.html March 2015 Anrew Mitchell Utrecht University Quantum impurity problems Part 1: Quantum impurity problems
More informationRelativistic Quantum Mechanics
Relativistic Quantum Mechanics Wayne Polyzou polyzou@uiowa.edu The University of Iowa Relativistic Quantum Mechanics p.1/42 Collaborators F. Coester (ANL), B. Keister (NSF), W. H. Klink (Iowa), G. L. Payne
More informationThree-Body Bound State Calculations by Using Three-Dimensional Low Momentum Interaction V low k
Preprint number: 6.668 Three-Body Bound State Calculations by Using Three-Dimensional Low Momentum Interaction V low k arxiv:6.668v [nucl-th Feb M. R. Hadizadeh, Institute of Nuclear and Particle Physics,
More informationLecture 2 Lagrangian formulation of classical mechanics Mechanics
Lecture Lagrangian formulation of classical mechanics 70.00 Mechanics Principle of stationary action MATH-GA To specify a motion uniquely in classical mechanics, it suffices to give, at some time t 0,
More informationThree- and four-particle scattering
Three- and four-particle scattering A. Deltuva Centro de Física Nuclear da Universidade de Lisboa Few-particle scattering Three-particle scattering equations Three-nucleon system Three-body direct nuclear
More informationNuclear Physics and Astrophysics
Nuclear Physics an Astrophysics PHY-302 Dr. E. Rizvi Lecture 2 - Introuction Notation Nuclies A Nuclie is a particular an is esignate by the following notation: A CN = Atomic Number (no. of Protons) A
More informationG4003 Advanced Mechanics 1. We already saw that if q is a cyclic variable, the associated conjugate momentum is conserved, L = const.
G4003 Avance Mechanics 1 The Noether theorem We alreay saw that if q is a cyclic variable, the associate conjugate momentum is conserve, q = 0 p q = const. (1) This is the simplest incarnation of Noether
More informationConservation Laws. Chapter Conservation of Energy
20 Chapter 3 Conservation Laws In orer to check the physical consistency of the above set of equations governing Maxwell-Lorentz electroynamics [(2.10) an (2.12) or (1.65) an (1.68)], we examine the action
More informationLecture 6:Feynman diagrams and QED
Lecture 6:Feynman diagrams and QED 0 Introduction to current particle physics 1 The Yukawa potential and transition amplitudes 2 Scattering processes and phase space 3 Feynman diagrams and QED 4 The weak
More informationFour-nucleon scattering
Four-nucleon scattering A. Deltuva Centro de Física Nuclear da Universidade de Lisboa Hamiltonian H + i> j 4N scattering v i j 1 v 12 4 3 2 Wave function: Schrödinger equation (HH + Kohn VP) [M. Viviani,
More informationCharge Form Factor and Cluster Structure of 6 Li Nucleus
Charge Form Factor an Cluster Structure of Nucleus G. Z. Krumova 1, E. Tomasi-Gustafsson 2, an A. N. Antonov 3 1 University of Rousse, 7017 Rousse, Bulgaria 2 DAPNIA/SPhN, CEA/Saclay, F-91191 Gif-sur-Yvette
More informationNucleon Nucleon Forces and Mesons
Canada s ational Laboratory for Particle and uclear Physics Laboratoire national canadien pour la recherche en physique nucléaire et en physique des particules ucleon ucleon Forces and Mesons Sonia Bacca
More information1 The pion bump in the gamma reay flux
1 The pion bump in the gamma reay flux Calculation of the gamma ray spectrum generated by an hadronic mechanism (that is by π decay). A pion of energy E π generated a flat spectrum between kinematical
More informationWeak interactions. Chapter 7
Chapter 7 Weak interactions As already discussed, weak interactions are responsible for many processes which involve the transformation of particles from one type to another. Weak interactions cause nuclear
More informationParticles and Deep Inelastic Scattering
Particles and Deep Inelastic Scattering Heidi Schellman University HUGS - JLab - June 2010 June 2010 HUGS 1 Course Outline 1. Really basic stuff 2. How we detect particles 3. Basics of 2 2 scattering 4.
More informationIntroduction to the Vlasov-Poisson system
Introuction to the Vlasov-Poisson system Simone Calogero 1 The Vlasov equation Consier a particle with mass m > 0. Let x(t) R 3 enote the position of the particle at time t R an v(t) = ẋ(t) = x(t)/t its
More informationThree- and Four-Nucleon Dynamics at Intermediate Energies
Three- and Four-Nucleon Dynamics at Intermediate Energies By: Ghanshyam Khatri 05 June, 2013 G. Khatri, MPD Symposium, Kraków 1 \ 20 Outline Motivation 3N dynamics Experiment with BINA: present work -
More informationMini Review of Poincaré Invariant Quantum Theory
Mini Review of Poincaré Invariant Quantum Theory Few-Body Systems ISSN 0177-7963 Volume 49 Combined 1-4 Few-Body Syst (2010) 49:129-147 DOI 10.1007/s00601-010-0149- x 1 23 Your article is protected by
More information1. Kinematics, cross-sections etc
1. Kinematics, cross-sections etc A study of kinematics is of great importance to any experiment on particle scattering. It is necessary to interpret your measurements, but at an earlier stage to determine
More informationParticle Physics Lecture 1 : Introduction Fall 2015 Seon-Hee Seo
Particle Physics Lecture 1 : Introduction Fall 2015 Seon-Hee Seo Particle Physics Fall 2015 1 Course Overview Lecture 1: Introduction, Decay Rates and Cross Sections Lecture 2: The Dirac Equation and Spin
More informationMany-Body Theory of the Electroweak Nuclear Response
Many-Body Theory of the Electroweak Nuclear Response Omar Benhar INFN and Department of Physics Università La Sapienza, I-00185 Roma Collaborators N. Farina, D. Meloni, H. Nakamura, M. Sakuda, R. Seki
More informationCoupled-cluster theory for medium-mass nuclei
Coupled-cluster theory for medium-mass nuclei Thomas Papenbrock and G. Hagen (ORNL) D. J. Dean (ORNL) M. Hjorth-Jensen (Oslo) A. Nogga (Juelich) A. Schwenk (TRIUMF) P. Piecuch (MSU) M. Wloch (MSU) Seattle,
More informationQFT. Unit 11: Cross Sections and Decay Rates
QFT Unit 11: Cross Sections and Decay Rates Decays and Collisions n When it comes to elementary particles, there are only two things that ever really happen: One particle decays into stuff Two particles
More informationLecture Models for heavy-ion collisions (Part III): transport models. SS2016: Dynamical models for relativistic heavy-ion collisions
Lecture Models for heavy-ion collisions (Part III: transport models SS06: Dynamical models for relativistic heavy-ion collisions Quantum mechanical description of the many-body system Dynamics of heavy-ion
More informationRelativistic Formulation of Reaction Theory
Relativistic Formulation of Reaction Theory W. N. Polyzou Department of Physics and Astronomy, The University of Iowa, Iowa City, IA 52242, USA Ch. Elster Institute of Nuclear and Particle Physics, and
More informationarxiv:nucl-th/ v1 18 Jan 1999
Modern NN Force Predictions for the Total ND Cross Section up to 3 MeV H. Wita la, H. Kamada, A. Nogga, W. Glöckle Institute for Theoretical Physics II, Ruhr-University Bochum, D-4478 Bochum, Germany.
More informationElectromagentic Reactions and Structure of Light Nuclei
Electromagentic Reactions and Structure of Light Nuclei Sonia Bacca CANADA'S NATIONAL LABORATORY FOR PARTICLE AND NUCLEAR PHYSICS Owned and operated as a joint venture by a consortium of Canadian universities
More informationInelastic scattering
Inelastic scattering When the scattering is not elastic (new particles are produced) the energy and direction of the scattered electron are independent variables, unlike the elastic scattering situation.
More informationPHY-494: Applied Relativity Lecture 5 Relativistic Particle Kinematics
PHY-494: Applied Relativity ecture 5 Relativistic Particle Kinematics Richard J. Jacob February, 003. Relativistic Two-body Decay.. π 0 Decay ets return to the decay of an object into two daughter objects.
More informationTopic 7: Convergence of Random Variables
Topic 7: Convergence of Ranom Variables Course 003, 2016 Page 0 The Inference Problem So far, our starting point has been a given probability space (S, F, P). We now look at how to generate information
More informationJacopo Ferretti Sapienza Università di Roma
Jacopo Ferretti Sapienza Università di Roma NUCLEAR RESONANCES: FROM PHOTOPRODUCTION TO HIGH PHOTON VIRTUALITIES ECT*, TRENTO (ITALY), -6 OCTOBER 05 Three quark QM vs qd Model A relativistic Interacting
More informationMICROSCOPIC OPTICAL POTENTIAL FROM NN CHIRAL POTENTIALS. Carlotta Giusti Università and INFN, Pavia. Matteo Vorabbi (TRIUMF) Paolo Finelli (Bologna)
MICROSCOPIC OPTICAL POTENTIAL FROM NN CHIRAL POTENTIALS Carlotta Giusti Università and INFN, Pavia Matteo Vorabbi (TRIUMF) Paolo Finelli (Bologna) Nuclear ab initio Theories and Neutrino Physics: INT Seattle
More informationarxiv: v2 [hep-ph] 10 May 2018
Extraction of V cb from two-boy haronic B ecays arxiv:180.05417v [hep-ph] 10 May 018 Noriaki Kitazawa 1, Kyo-suke Masukawa an Yuki Sakai 3 Department of Physics, Tokyo Metropolitan University, Hachioji,
More informationQuantum mechanical approaches to the virial
Quantum mechanical approaches to the virial S.LeBohec Department of Physics an Astronomy, University of Utah, Salt Lae City, UT 84112, USA Date: June 30 th 2015 In this note, we approach the virial from
More informationNuclear structure I: Introduction and nuclear interactions
Nuclear structure I: Introduction and nuclear interactions Stefano Gandolfi Los Alamos National Laboratory (LANL) National Nuclear Physics Summer School Massachusetts Institute of Technology (MIT) July
More informationNucleon-nucleon interaction in covariant chiral effective field theory
Guilin, China The Seventh Asia-Pacific Conference on Few-Body Problems in Physics Nucleon-nucleon interaction in covariant chiral effective field theory Xiu-Lei Ren School of Physics, Peking University
More informationKern- und Teilchenphysik I Lecture 2: Fermi s golden rule
Kern- und Teilchenphysik I Lecture 2: Fermi s golden rule (adapted from the Handout of Prof. Mark Thomson) Prof. Nico Serra Dr. Patrick Owen, Mr. Davide Lancierini http://www.physik.uzh.ch/de/lehre/phy211/hs2017.html
More informationParticle Physics. Michaelmas Term 2011 Prof Mark Thomson. Handout 5 : Electron-Proton Elastic Scattering. Electron-Proton Scattering
Particle Physics Michaelmas Term 2011 Prof Mark Thomson Handout 5 : Electron-Proton Elastic Scattering Prof. M.A. Thomson Michaelmas 2011 149 i.e. the QED part of ( q q) Electron-Proton Scattering In this
More informationQuantum mechanics of many-fermion systems
Quantum mechanics of many-fermion systems Kouichi Hagino Tohoku University, Sendai, Japan 1. Identical particles: Fermions and Bosons 2. Simple examples: systems with two identical particles 3. Pauli principle
More informationParticle Physics, Fall 2012 Solutions to Final Exam December 11, 2012
Particle Physics, Fall Solutions to Final Exam December, Part I: Short Answer [ points] For each of the following, give a short answer (- sentences, or a formula). [5 points each]. [This one might be har
More informationQUANTUMMECHANICAL BEHAVIOUR IN A DETERMINISTIC MODEL. G. t Hooft
QUANTUMMECHANICAL BEHAVIOUR IN A DETERMINISTIC MODEL G. t Hooft Institute for Theoretical Physics University of Utrecht, P.O.Box 80 006 3508 TA Utrecht, the Netherlans e-mail: g.thooft@fys.ruu.nl THU-96/39
More informationChapter 2 Lagrangian Modeling
Chapter 2 Lagrangian Moeling The basic laws of physics are use to moel every system whether it is electrical, mechanical, hyraulic, or any other energy omain. In mechanics, Newton s laws of motion provie
More informationFINAL-STATE INTERACTIONS IN QUASIELASTIC ELECTRON AND NEUTRINO-NUCLEUS SCATTERING: THE RELATIVISTIC GREEN S FUNCTION MODEL
FINAL-STATE INTERACTIONS IN QUASIELASTIC ELECTRON AND NEUTRINO-NUCLEUS SCATTERING: THE RELATIVISTIC GREEN S FUNCTION MODEL Carlotta Giusti and Andrea Meucci Università and INFN, Pavia Neutrino-Nucleus
More informationScattering amplitudes and the Feynman rules
Scattering amplitudes and the Feynman rules based on S-10 We have found Z( J ) for the phi-cubed theory and now we can calculate vacuum expectation values of the time ordered products of any number of
More informationComputing Exact Confidence Coefficients of Simultaneous Confidence Intervals for Multinomial Proportions and their Functions
Working Paper 2013:5 Department of Statistics Computing Exact Confience Coefficients of Simultaneous Confience Intervals for Multinomial Proportions an their Functions Shaobo Jin Working Paper 2013:5
More informationQuantitative understanding nuclear structure and scattering processes, based on underlying NN interactions.
Microscopic descriptions of nuclear scattering and reaction processes on the basis of chiral EFT M. Kohno Research Center for Nuclear Physics, Osaka, Japan Quantitative understanding nuclear structure
More informationPhysics 5153 Classical Mechanics. The Virial Theorem and The Poisson Bracket-1
Physics 5153 Classical Mechanics The Virial Theorem an The Poisson Bracket 1 Introuction In this lecture we will consier two applications of the Hamiltonian. The first, the Virial Theorem, applies to systems
More informationCalculating Binding Energy for Odd Isotopes of Beryllium (7 A 13)
Journal of Physical Science Application 5 (2015) 66-70 oi: 10.17265/2159-5348/2015.01.010 D DAVID PUBLISHING Calculating Bining Energy for O Isotopes of Beryllium (7 A 13) Fahime Mohammazae, Ali Akbar
More informationQuantum Monte Carlo calculations of neutron and nuclear matter
Quantum Monte Carlo calculations of neutron and nuclear matter Stefano Gandolfi Los Alamos National Laboratory (LANL) Advances and perspectives in computational nuclear physics, Hilton Waikoloa Village,
More informationDecays and Scattering. Decay Rates Cross Sections Calculating Decays Scattering Lifetime of Particles
Decays and Scattering Decay Rates Cross Sections Calculating Decays Scattering Lifetime of Particles 1 Decay Rates There are THREE experimental probes of Elementary Particle Interactions - bound states
More informationCluster Models for Light Nuclei
Cluster Models for Light Nuclei N. Itagaki, T. Otsuka, University of Tokyo S. Aoyama, Niigata University K. Ikeda, RIKEN S. Okabe, Hokkaido University Purpose of the present study Cluster model explore
More informationParticles and Deep Inelastic Scattering
Particles and Deep Inelastic Scattering University HUGS - JLab - June 2010 June 2010 HUGS 1 k q k P P A generic scatter of a lepton off of some target. k µ and k µ are the 4-momenta of the lepton and P
More informationTheoretical Optical Potential Derived From Chiral Potentials
NUCLEAR THERY, Vol. 35 (206) eds. M. Gaidarov, N. Minkov, Heron Press, Sofia Theoretical ptical Potential Derived From Chiral Potentials M. Vorabbi,2, P. Finelli 3, C. Giusti 2 TRIUMF, 4004 Wesbrook Mall,
More informationPolarization: an essential tool for the study of the nucleon structure
Polarization: an essential tool for the study of the nucleon structure Egle Tomasi-Gustafsson IRFU/SPhN, Saclay and IN2P3/IPN Orsay Wolfgang Pauli Niels Bohr (années 30) GDR, 7-VII-2009 1 PLAN Part I Generalities,definitions
More informationNuclear structure Anatoli Afanasjev Mississippi State University
Nuclear structure Anatoli Afanasjev Mississippi State University 1. Nuclear theory selection of starting point 2. What can be done exactly (ab-initio calculations) and why we cannot do that systematically?
More informationLight Front (LF) Nuclear Structure Gerald A Miller, U. of Washington
Light Front (LF) Nuclear Structure Gerald A Miller, U. of Washington formulate the NN interaction on the light front solve the Weinberg equation for the deuteron prescription from FS 81 review constructs
More informationLectures - Week 10 Introduction to Ordinary Differential Equations (ODES) First Order Linear ODEs
Lectures - Week 10 Introuction to Orinary Differential Equations (ODES) First Orer Linear ODEs When stuying ODEs we are consiering functions of one inepenent variable, e.g., f(x), where x is the inepenent
More informationFour-, Five-, and. Double Strangeness
Four-, Five-, and Six-Body Calculations of Double Strangeness s-shell Hypernuclei H. Nemura Institute of Particle and Nuclear Studies, KEK This talk is based on the work S= 2 world nucl-th/0407033 in collaboration
More informationDr Victoria Martin, Spring Semester 2013
Particle Physics Dr Victoria Martin, Spring Semester 2013 Lecture 3: Feynman Diagrams, Decays and Scattering Feynman Diagrams continued Decays, Scattering and Fermi s Golden Rule Anti-matter? 1 Notation
More informationThe 7th Asia-Pacific Conference on Few-Body Problems in Physics. Dp breakup reaction investigation using polarized and unpolarized deuteron beam
The 7th Asia-Pacific Conference on Few-Body Problems in Physics Dp breakup reaction investigation using polarized and unpolarized deuteron beam M. Janek on behalf of DSS collaboration (Russia-Japan-JINR-Romania-Bulgaria-Slovakia)
More informationDynamical coupled channel calculation of pion and omega meson production
Dynamical coupled channel calculation of pion and omega meson production INT-JLab Workshop on Hadron Spectroscopy 2009/11/11 Mark Paris Center for Nuclear Studies Data Analysis Center George Washington
More informationAb Initio Nuclear Structure Theory
Ab Initio Nuclear Structure Theory Lecture 1: Hamiltonian Robert Roth Overview Lecture 1: Hamiltonian Prelude Many-Body Quantum Mechanics Nuclear Hamiltonian Matrix Elements Lecture 2: Correlations Two-Body
More informationNew Frontiers in Nuclear Structure Theory
New Frontiers in Nuclear Structure Theory From Realistic Interactions to the Nuclear Chart Robert Roth Institut für Kernphysik Technical University Darmstadt Overview Motivation Nucleon-Nucleon Interactions
More informationUltrarelativistic Heavy-Ions
Kinematics November 11, 2010 / GSI Outline Introduction 1 Introduction 2 3 3 Notation Introduction A parallel to z-axis (beam): A A = A A transverse to z-axis: A = A A A = A Transverse mass: m = m 2 +
More informationConservation of Linear Momentum : If a force F is acting on particle of mass m, then according to Newton s second law of motion, we have F = dp /dt =
Conservation of Linear Momentum : If a force F is acting on particle of mass m, then according to Newton s second law of motion, we have F = dp /dt = d (mv) /dt where p =mv is linear momentum of particle
More informationCoupling of Angular Momenta Isospin Nucleon-Nucleon Interaction
Lecture 5 Coupling of Angular Momenta Isospin Nucleon-Nucleon Interaction WS0/3: Introduction to Nuclear and Particle Physics,, Part I I. Angular Momentum Operator Rotation R(θ): in polar coordinates the
More informationNew Forms of Deuteron Equations and Wave Function Representations. Abstract
New Forms of Deuteron Equations an Wave Function Representations I. Fachruin, Ch. Elster,W.Glöckle Institut für Theoretische Physik II, Ruhr-Universität Bochum, D-780 Bochum, Germany. Institut für Kernphysik,
More informationRG & EFT for nuclear forces
RG & EFT for nuclear forces Andreas Nogga, Forschungszentrum Jülich ECT* school, Feb/March 2006 Low momentum interactions: Using the RG to simplify the nuclear force for many-body calculations. Application
More informationNonlinear Adaptive Ship Course Tracking Control Based on Backstepping and Nussbaum Gain
Nonlinear Aaptive Ship Course Tracking Control Base on Backstepping an Nussbaum Gain Jialu Du, Chen Guo Abstract A nonlinear aaptive controller combining aaptive Backstepping algorithm with Nussbaum gain
More informationSpace-time Linear Dispersion Using Coordinate Interleaving
Space-time Linear Dispersion Using Coorinate Interleaving Jinsong Wu an Steven D Blostein Department of Electrical an Computer Engineering Queen s University, Kingston, Ontario, Canaa, K7L3N6 Email: wujs@ieeeorg
More informationProperties of the S-matrix
Properties of the S-matrix In this chapter we specify the kinematics, define the normalisation of amplitudes and cross sections and establish the basic formalism used throughout. All mathematical functions
More informationInelastic scattering on the lattice
Inelastic scattering on the lattice Akaki Rusetsky, University of Bonn In coll with D. Agadjanov, M. Döring, M. Mai and U.-G. Meißner arxiv:1603.07205 Nuclear Physics from Lattice QCD, INT Seattle, March
More informationA Poincaré Covariant Nucleon Spectral Function for A=3 nuclei within the Light-front Hamiltonian Dynamics
A Poincaré Covariant Nucleon Spectral Function for A=3 nuclei within the Light-front Hamiltonian Dynamics Giovanni Salmè INFN - Rome In collaboration with: Emanuele Pace ( Tor Vergata Rome U.& INFN) Sergio
More informationDe Broglie s Pilot Waves
De Broglie s Pilot Waves Bohr s Moel of the Hyrogen tom: One way to arrive at Bohr s hypothesis is to think of the electron not as a particle but as a staning wave at raius r aroun the proton. Thus, nλ
More informationExperimental Investigation of Few-Nucleon Dynamics at Medium Energies
Experimental Investigation of Few-Nucleon Dynamics at Medium Energies by Ghanshyam Khatri 1 \ 22 Outline Introduction Three-body (3N) force Experimental tools BINA Detector and it s status at CCB (Krakow)
More informationMass and Isospin Dependence of Short-Range Correlations
Mass and Isospin Dependence of Short-Range Correlations Maarten Vanhalst, Wim Cosyn, Jan Ryckebusch Department of Physics and Astronomy, Ghent University Nuclear Structure and Dynamics at Short Distances
More information