Low Energy Nuclear Theory, Exercises of Nuclear Physics

Download Low Energy Nuclear Theory and more Exercises Nuclear Physics in PDF only on Docsity! Low Energy Nuclear Theory National Nuclear Physics Summer School 2019 Low Energy Nuclear Theory KD Launey LA Light Source Louisiana State University Low Energy Nuclear Theory National Nuclear Physics Summer School 2019 Low Energy Nuclear Theory KD Launey LA Light Source Louisiana State University LA Light Source @ LSU Fantastic 4 Low Energy Nuclear Theory National Nuclear Physics Summer School 2019 Lecture 1 … nuclei… elements… stars… q uar ks & g luons U N I V E R S E Condensed Matter Nuclear p ro tons neu trons 1. How did visible matter come into being and how does it evolve? 2. How does subatomic matter organize itself and what phenomena emerge? 3. Are the fundamental interactions that are basic to the structure of matter fully understood? 4. What are the origins of heavy elements? The Big Science Questions Low Energy Nuclear Theory National Nuclear Physics Summer School 2019 Lecture 1 … nuclei… elements… stars… q uar ks & g luons U N I V E R S E Condensed Matter Nuclear p ro tons neu trons FRIB (Facility for Rare Isotope Beams) Astrophysics: the origin of the elements NIF (National Ignition Facility) at Lawrence Livermore National Lab T2K; DUNE Advanced LIGO Neutrino physics; fundamental symmetries Nuclei: fuel of the Cosmos and ideal labs! Applied energy From Sherrill (2012) From Nunes (2017) Neutrino Detectors 12C, 16O, 40Ar Neutrinoless ββ decay Low Energy Nuclear Theory National Nuclear Physics Summer School 2019 Lecture 1 … nuclei… elements… stars… q uar ks & g luons U N I V E R S E Condensed Matter Nuclear p ro tons neu trons FRIB (Facility for Rare Isotope Beams) Density Functional Theory Ab initio Theory Astrophysics: the origin of the elements NIF (National Ignition Facility) at Lawrence Livermore National Lab T2K; DUNE Advanced LIGO Neutrino physics; fundamental symmetries Nuclei: fuel of the Cosmos and ideal labs! Applied energy Neutrino Detectors 12C, 16O, 40Ar Neutrinoless ββ decay Low Energy Nuclear Theory National Nuclear Physics Summer School 2019 Lecture 1 Nucleus – relevant scales baryon chemical potential = measure of net baryon density baryon = made of 3 quarks (protons, neutrons, …) mesons = made of quark-antiquark (pions, …) hadrons Low Energy Nuclear Theory National Nuclear Physics Summer School 2019 Lecture 1 Nucleus – relevant scales Mass of nucleon (proton or neutron) ~1 GeV = 103MeV Separation energy per particle 6-8 MeV Low Energy Nuclear Theory National Nuclear Physics Summer School 2019 Lecture 1 Nucleus – relevant scales Mass of nucleon (proton or neutron) ~1 GeV = 103MeV Separation energy per particle 6-8 MeV Nuclear forces are induced through exchange by mediating quanta: (virtual) mesons (similar to electromagnetic interaction: generated by the exchange of photons) do f= n uc le on s + m es on s Mass of pion ~140 MeV low-energy nuclear physics (note: these are excitation energies of nucleus, not binding energy, nor beam energy) Low Energy Nuclear Theory National Nuclear Physics Summer School 2019 Lecture 1 Modeling Nuclei and Nuclear Reactions Low Energy Nuclear Theory National Nuclear Physics Summer School 2019 Lecture 1 Modeling the nucleus … The challenges Interaction between particles States NN, 3N, ... E.g., 6 particles in 200 states: 8x1010 ways !!! E.g., 2 particles in 4 states |1100> |0011> |1010> |0101> |1001> |0110> Model space available to nucleus All possible ways: 20 particles in 80 states HUGE! Low Energy Nuclear Theory National Nuclear Physics Summer School 2019 Lecture 1 Reproduces NN scattering (these are free nucleons, not in nuclear medium; I will refer to this force as “bare”) In addition, there might be 3N, 4N, … Modeling the nucleus … The ingredients Specified by basis, model space (size & resolution) Many-body Approach Nuclear properties: structure & reactions Nuclear force Leff 1/Λeff “size” “resolution” Resolving high- momentum physics Important for wave function tail, large shapes/clusters, asymptotics, etc. Low Energy Nuclear Theory National Nuclear Physics Summer School 2019 Lecture 1 Chiral Potentials Quark/gluon dynamics (Quantum chromodynamics, QCD) Degrees of freedom Symmetry High energy What is most important for a theory? The symmetries and not the degrees of freedom The usual (Lorentz covariance, parity, etc.)+ Chiral symmetryL = − 1 4 Gµν a Ga µν + qLiγµDµqL + qRiγµDµqR − qM q Nucleon/pion dynamics (Effective field theory) Low energy Low Energy Nuclear Theory National Nuclear Physics Summer School 2019 Lecture 1 Chiral Potentials Quark/gluon dynamics (Quantum chromodynamics, QCD) Nucleon/pion dynamics (Effective field theory) Degrees of freedom Symmetry High energy Low energy L = − 1 4 Gµν a Ga µν + qLiγµDµqL + qRiγµDµqR − qM q Leff = Lππ (2) +LπN (1) +LπN (2) +LNN (0) +LNN (2) +... Approximate chiral symmetry Consistent with explicit and spontaneous chiral symmetry breaking left- and right-handed quarks transform independently Low Energy Nuclear Theory National Nuclear Physics Summer School 2019 Lecture 1 Chiral Potentials Chiral effective field theory Low-energy theory of nucleon/pion Low energy Symmetry + Separation of scale Sy st em at ic e xp an sio n Leff = Lππ (2) +LπN (1) +LπN (2) +LNN (0) +LNN (2) +... Low Energy Nuclear Theory National Nuclear Physics Summer School 2019 Lecture 1 Chiral potentials … the challenges Chiral effective field theory Low-energy theory of nucleon/pion Sy st em at ic e xp an sio n Fit to NN scattering (future: lattice QCD) Consistent in 2N and 3N forces Fit to 3H binding energy and lifetime Challenges: local/non-local regulator, UV cutoff; 4N; Weinberg power counting There are 3N, 4N, … at higher order Coupling constants: Low Energy Nuclear Theory National Nuclear Physics Summer School 2019 Lecture 1 ISBN 978-981-3146-04-4 This book is a unique collection of reviews that share a common topic, emergent phenomena in atomic nuclei, while revealing the multifaceted nature of the subject, from quarks to heavy nuclei. It tells an amazing story of a decades-long journey of trials and successes, up to present days, with the aim to understand the vast array of experimental data and the fundamentals of strongly interacting fermions. The emphasis is on discovering emergent orderly patterns amidst the overarching complexity of many-particle quantum-mechanical systems. Recent findings are discussed within an interesting framework: a combination of nuclear theory and experiment, of group theory and computational science, and of pivotal models of astonishing simplicity and state-of-the-art models empowered by supercomputers. A special theme resonates throughout the book: the important role of symmetries, exact and approximate, in exposing emergent fea- tures and guiding large-scale nuclear modeling. World-renowned experts offer their unique perspective on symmetries in the world of quarks and gluons, and that of protons and neurons — from chi- ral symmetry, through spin-isospin and quasi-spin symmetries, to symplectic symmetry, — as well as on the emergent nature of nu- clear collectivity, clustering, and pairing, viewed from spectrosco- py, microscopic considerations, and first principles. The book pro- vides an excellent foundation that allows researchers and graduate students in physics and applied mathematics to review the current status of the subject, and to further explore the research literature through exhaustive sets of references that also point to studies underpinned by similar techniques in condensed matter and atom- ic physics along with quantum information. World Scientific www.worldscientific.com 10180 hc World Scientific Emergent Phenomena in Atomic Nuclei from Large-Scale Modeling A Symmetry-Guided Perspective Kristina D Launey Em ergent Phenom ena in Atom ic Nuclei from Large-Scale M odeling Launey Emergent Phenomena in Atomic Nuclei from Large-Scale Modeling Nuclear Collectivity – Experimental perspective (John L Wood) Configuration-interaction models (Calvin W Johnson) Symplectic rotor model (David J Rowe) Electron Scattering in the Symplectic Shell Model (Jutta E Escher) Lattice QCD (Thomas Luu and Andrea Shindler) Ab Initio Lattice Effective Field Theory (Dean Lee) Correlated Gaussian Approach and Clustering (Yasuyuki Suzuki and Wataru Horiuchi) Symmetry-Adapted No-Core Shell Model (Jerry P Draayer, Tomas Dytrych and KD Launey) Auxiliary-Field Quantum Monte Carlo Methods (Yoram Alhassid) Lie Density Functional Theory (George Rosensteel) Exactly Solvable Pairing (Feng Pan, Xin Guan & Jerry P Draayer)