Physics of Finite and Infinite Nuclear Systems Phys. 477 (542)

Transcription

1 Physics of Finite and Infinite Nuclear Systems Phys. 477 (542) Class: Tu & Th from 11:30 am to 1:00 pm (Compton 241 mostly) Extra hour: Mo 4 pm make-up hour for planned trips to Tokyo, San Francisco, and Trento/Milan, Italy (in Compton 245) Class goals: learn how to apply nonrelativistic quantum mechanics to real systems describe and understand the main physics of nuclei and aspects of infinite nuclear matter (neutron stars) with emphasis on current and future research with radioactive beam experiments Prerequisite: at least one upper-level undergraduate quantum course (471) Requirements: homework (50%), including computer assignments (as group project 20%), participation in Monday session, and a presentation on a related subject of minutes (25%), exit interview (5%); attendance is required; more on schedule and homework can be found at course webpage Helpful to read some material in books on reserve in the library 1

2 Nuclear Physics Broad field with many applications Current funding at NSF for nuclear theory Nuclear Structure (DOE -> FRIB) Hadron Stucture (DOE -> JLAB) Up and Down quark physics (DOE -> RHIC) also considered particle physics by many Publications in Physical Review C Physical Review Letters European counterparts and astrophysics journals At WU: 5.5 senior people; 1 post-doc; 4 grad students 2

3 Energy scales Use Heisenberg uncertainty relation x p 2 for localization of about ( p) 2 m --> 2m N few MeV 3

4 Many manifestations of quantum physics H A = Ultimately linked to a strong interaction Hamiltonian describing nucleons A p 2 A H A = + V (i, j)+... 2m i i=1 i<j=1 A nucleons either p (proton) or n (neutron) Can possibly be approximately treated by A i=1 p 2 2m i + A i<j=1 V (i, j)+... = A { } p 2 + U(i) + H A (residual) 2m i i=1 A { } p 2 + U(i) 2m i i=1 with a single-particle Hamiltonian and the fermion character of nucleons but nucleons are themselves composites... 4

5 Bosons and Fermions Use experimental observations to conclude consequences of identical particles Two possibilities antisymmetric states fermions half-integer spin Pauli from properties of electrons in atoms symmetric states bosons integer spin Considerations related to electromagnetic radiation (photons) Can also consider quantization of field equations e.g. quantize free Maxwell equations (Dirac) Protons and neutrons have intrinsic spin ½ --> fermions 5

6 Global properties of nuclei Different levels of description Identify most relevant degrees of freedom to describe physics of interest Depends on probe --> wavelength of probing radiation and energy scales studied Mostly nucleons at low energy in this course --> quantum manybody problem and one of the most difficult ones 6

7 Chart of nuclides Brookhaven data base Horizontal axis neutron number N Vertical axis proton number Z Notation for a nucleus A ZChemical symbol A Chemical symbol Since A = Z + N and chemical symbol implies Z 7

8 More details Abundance information for stable nuclei Half-life for unstable nuclei Several possible decay modes 8

9 Towards the edges of stability Illustration of current research associated with exotic nuclei 9

10 Binding energy Critical information deciding on decays/stability If every nucleon gets similar binding from every other nucleon --> expect total binding to be proportional to number of bonds = ½ A(A-1) So B/A c(a-1) but experiment says otherwise ---> B/A constant ---> saturation Define BE( A X)=Z M p c 2 + N M n c 2 M ( Z X)c 2 actual mass More easily accessible: atomic binding energy BE( A X atom) = Z M1 Hc 2 + N M n c 2 M( Z X atom)c 2 up to ~ ev the same 10

11 Binding energy per nucleon Often used unit: amu = atomic mass unit = 1/12 mass of 12 C = x kg = MeV/c 2 More later Homework 9 B/A (MeV) A 11

12 Nuclear size / densities In addition to saturation there is charge independence of binding --> each nucleon occupies a roughly fixed volume characterized by a certain radius So nuclear volume V = 4π 3 r3 0A = 4π 3 R3 r 0 leading to a nuclear radius that follows Empirically: charge --> 1.2 fm matter --> 1.4 fm R = r 0 A 1/3 12

13 Experimental determination Example: Phys. Rev. Lett. 58, 195 (1987) 13

14 Central ideas Elastic electron scattering Weakly interacting probe Interaction probe with target precisely known Probe predominantly operates on one target particle at a time --> probe-target interaction dominated by one-body operator experiment possible with sufficient accuracy Elastic electron scattering only for stable nuclei but will be available for some rare isotope beams in the future (collider set-up): Germany and Japan 14

15 Scattering from a fixed Coulomb potential Original experiments generated limited information about the interior charge density distribution and typical results were parametrized by ρ 0 ρ(r) = 1 + exp (r R 0)/a introducing: central density radius at half density diffuseness Analyze Schrödinger equation (nonrelativistic) even though actual experiments range from MeV so much larger than electron rest mass No need for Dirac equation to explain the physics 15

16 Start with { 2 2 S. equation 2m } + V (r) ψ(r) =Eψ(r) Potential due to nuclear charge distibution V (r) = c α d 3 r ρ(r ) r r with fine structure constant so and c α =1.44 MeV fm d 3 r ρ(r) =Z α = e2 4πɛ 0 1 c Visualize scattering process: incoming plane wave + outgoing spherical wave modulated by function of angles 16

17 More scattering Solution S. equation can be written as Energy E = 2 k 2 2m Elastic scattering: ψ(r) =e ik i r + ψ sc (r) k = k i = k f Standard quantum analysis (read Griffiths Ch.11 or more advanced book) generates ψ sc eikr r f(ω) r and cross section (probability to scatter in direction of final momentum - area unit): dσ dω = f(ω) 2 17

18 Analysis Insert assumed solution in S. equation 18