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 = Atomic Mass Number (no. of Nucleons) A = +N (Nucleons = Protons + Neutrons) N = Number of Neutrons (Sometimes Omitte) 14 nucleons 6 protons 8 neutrons Nuclies with ientical but ifferent N are calle ISOTOPES. Nuclies with ientical A are known as ISOBARS. Nuclies with ientical N are known as ISOTONES. Long-live (meta-stable) excite states of nuclei are known as ISOMERIC. There are far too many nuclei to cover in such a course we will only cover a few with informative general properties 2
Units In physics - use SI units: istance: time: mass: energy: metre secon kilogram joule For everyay objects an situations this works well Hanling atomic nuclei is not an everyay occurrance SI units can be use in nuclear physics......but they are cumbersome e.g. proton mass = 1.67 x 10-27 Kg Use a new system of units specifically for this area of physics We are free to choose any system of units provie we are consistent Never mix units 3 Units Distance the fermi (fm) 1 Fermi = 10-15 m = 1 fm Typical Nuclear sizes range from 1 fm to 7 fm for the largest nuclei Time the secon (s) Our familiar unit of time measurement Range of nuclear timescales varies enormously: lifetimes ~10-12 s (1 picosecon) up to millions of years (~1013 s) Energy the electron volt (ev) The energy require to accelerate 1 electron through a 1V potential 1 ev = 1.602 x 10-19 J (conversion rate is electron charge in Coulombs) Typical nuclear energies are in MeV range (106) Typical rest energies are much larger ~ GeV (109) 10-18 10-15 10-12 10-9 10-6 10-3 100 103 106 109 1012 1015 1018 attofemtopiconanomicromilli- none Kilo- MegaGigaTeraPetaExa- 4
Units Mass the atomic mass unit (u) or MeV/c2 Define so one atom of 12C = 12 u Since E=mc2 we can switch between mass & energy as we please One mole of 12C has NA atoms = 6.022 x 1023 atoms 0.012 Kg = NA x 12 u 1 u = 0.012/(NA x 12) Using E=mc2 then, energy equivalent = 1.66 x 10-27 Kg = 1.66 x 10-27 x (2.99 x 108)2 = 1.48 x 10-10 J Convert joules to ev: ivie by electron charge = 931.502 MeV Then 1 u = 931.502 MeV/c2 So, mass can be expresse as u, or in MeV/c2 You shoul never have to multiply any numerical result by 2.99 x108 m/s If you o this, you are probably making an unnecessary step, or a mistake In Krane appenix C a full table of atomic masses is given. 5 Quantum Mechanics As with all phenomena at small istances it is expecte that Quantum Mechanics (QM) will prove an essential tool to help us unerstan an interpret nuclear process It is assume that your have some basic knowlege of QM (1st Year Courses) Detaile solutions of Schröinger Equation beyon this course (see QMA next semester) New topics will be covere qualitatively in the lectures. Nucleons in the are in motion with kinetic energies of orer 10 MeV comparing this with the nucleon rest energy of ~ 1 GeV so it is possible to use non-relativistic QM Schröinger Equation can apply in certain cases: ~2 2 (r) + V (r) (r) = E (r) 2m Nuclear Physics is in general a TOUGH MANY BODY PROBLEM. Will learn how to apply QM to unerstan moels of Nuclear Physics 6
Quantum Mechanics Quantum Mechanical Calculations will be applie to: α ecay β ecay* Shell moel calculations Pauli Exclusion Principle* Quantum Statistics* Angular Momentum calculations* Decay Rate calculations* Introuctory material on QM for nuclear physics in chapter 2 of Krane. Rea this chapter to get an overview We will not be concerne with mathematical solutions to Schröinger eqn. *These topics will require an unerstaning of QM beyon 1st Year The techniques use for these will be covere in QMA course next semester Not neee irectly for this course 7 Properties The list of instructions require to characterise all the interactions of a 50 nucleon woul be of orer 1064 We o not have the time For now we consier some of the more basic properties The Nuclear Raius Like the raius of an atom, the raius of a is not precisely efine size of the epens on what is use to probe it. If one fires electrons fire at the one etermines the nuclear charge istribution α particles measure the electromagnetic an strong interaction: istribution of nuclear matter Builing on the work of Rutherfor who set a limit on the Nuclear raius The original Nobel Prize winning work was one by Hofstater Nobel prize 1961 8
Rutherfor Scattering Rutherfors' famous scattering experiment foune nuclear physics Scatter energetic α particles off gol foil Measure angular eflection of α particles At that time (1906) JJ Thompsons' moel of atom was soli ball of electrons & protons Deflections shoul be ue to multiple interactions - many ranom collisions Rutherfor notice that some collisions lea to very large eflections - rare Incompatible with the multiple scattering single har scatter Rutherfor propose moel of ense atomic an erive scattering formula Foun experiment escribe his moel expectation r Think of this as reaction rate as function of eflection angle. Will efine this in lecture 6 alpha particle θ = ze2 16 0 T 1 sin4 ( /2) See Krane 400-401 for experimental evience of Rutherfor Scattering 9 Hofstater Experiment Rutherfor was lucky classical solution = quantum solution But, looking insie, nee probe wavelength smaller than nuclear raius i.e. Quantum mechanics istribution of electrons scattere from etermines charge ensity = M ott Mott Scattering Rutherfor scattering formula for point-like electron - electron scattering F (q) 2 Form Factor Contains all info on charge ensity of 10
Nuclear Raius From Hofstater Experiment ' eiki r for particle of momentum pi = ~ki initial electron wave function is Q i Transition amplitue from initial state to final state (ki kf) is: r - r F (ki, kf ) = f V (r) F (q) = eiq r V (r) v r electron r i v where q = ki kf the integration V(r) epens on the nuclear charge ensity potential ue to charge element Q is V ρe(r') = istribution of nuclear charge v' = volume element integrating over v' gives total interaction potential Form factor F(q) is a fourier transform of charge ensity F (q) = eiq r 0 e (r therefore measure F(q) an use equation to etermine ρe(r') )v 11 F (q) = Q eiq r 0 e (r )v where q = ki kf where ρe(r') is istribution of nuclear charge r - r r electron r We cannot easily measure the coorinate space insie a but we can measure momentum transfer of our projectile Fourier transforms switch one variable into another e.g. spatial co-orinates into momentum co-orinates Thats what the form factor is: fourier transform of the charge istn in terms of momentum transfer inverse transform gives us ρe(r') back again 12
570 1 9 6 1 R.HOFSTADTER http://www.nobelprize.org/nobel_prizes/physics/laureates/1961/hofstater.html Nuclear Charge Distribution Results shown for several nuclei Nucleons are not crushe in the centre of Density is approximately constant out to some surface Hyrogen an helium behave ifferently to the others... 4 3 A ' constant R3 R = R0 A1/3 R0 1.2 fm Dr Eram Rizvigives a summary of the approximate charge Nuclearensity Physics an Astrophysics - Lecture 2 Fig. 8. This figure istributions foun for various nuclei stuie by electron-scattering methos. The central ensities are the least well etermine positions of the curves. Note, however, the large isparity between thenuclear average central ensities of the proton an all other nuclei. The alpha parproperties ticle (4He) is also a unique case an exhibits a much larger central ensity than all heavier nuclei. 13 Nuclear Mass Determination lustrate in Fig. 8, where a summary of the charge istributions foun by the electron-scattering metho is presente for various nuclei. Except for the extremely light nuclei of hyrogen an helium the constancy of the central Mass Spectrometer: nuclear ensity is clearly represente in the figure. ionise atoms/molecules subjecte to E an B fiels The results obtaine with heavier nuclei inicate that the electron-scat E fiel exerts upwar force qe Mass Determination: tering metho coul also be applie to the very light nuclei an even to the B fiel exerts ownwar force qvb Spectrometer measures relative proton itself. Accoringly, in early 1954 experiments were initiate on hy- abunances by etecting isotope current at en en of path Select E/B such that ions of particular v are selecte i.e. ions uneflecte when qe=qvb Nuclie Abunance: Spectrometer measures relative abunances by etecting isotope current at en en of path Finally uniform B fiel bens ions in circle with raius r = mv/qb Isotope Separation: Continuous running of spectrometer tune to one mass accumulates large quantity of one isotope 14