Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh) Nuclear and Radiation Physics Before we start, let us tackle the following: Why nuclear physics? Why radiation physics? Why in Jordan? Interdisciplinary. Applied. Nuclear Physics at BAU This course

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 2 General subjects to be covered This phenomenological course provides the launch point for other nuclear physics courses that will follow. This is an introductory course that will cover the following general subjects Nuclear properties. Binding energy and nuclear stability. Nuclear models. Spin and moments. Nuclear forces. The structure of the nucleus. Nuclear reactions: energetics and general cross-section behavior. Neutron moderation, fission, controlled fission and fusion. Radioactive decays. Interactions of nuclear radiations (charged particles, gammas, and neutrons) with matter.

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 3 Level Test This is not intended to be a marked exam. The purpose is to collect information about your background. You are NOT required to write your name, but you can do so if you wish.

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 4 Grading Mid-term Exam25% Project, quizzes and HWs25% Final Exam50% Homeworks are due after one week unless otherwise announced. Remarks or questions marked in red without being announced as homeworks should be also seriously considered! Some tasks can (or should) be sent by

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 5 Proposed Projects Experiments to determine nuclear properties. Nuclear power generation. Nuclear safety. Environmental radioactivity. Medical applications. Health physics and radiation protection. Nucleosynthesis. Technological applications (e.g. Material Science). Radioactive ion beams. Neutrino physics. Accelerator driven systems. ….. or (your own selected subject).  Decide on the title of your project within two weeks.  Due date (for written version) : May 11 th.  Presentation: Will be scheduled later.

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 6 Scale and Objectives Dimensional scale: Order of magnitude of 1 x m  1 femtometer  1 fm  1 fermi. Too small for direct investigation. What about time and energy scales? We need to answer ….. 1.What are the building blocks of a nucleus? 2.How do they move relative to each other? 3.What laws governing them? We need to understand: Nuclear forces (Q2, Q3). Nuclear structure (Q2, Q3). We also need High Energy Physics (to answer Q1).

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 7 Constants

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 8 Nomenclature Element vs. Nuclide. >90 natural chemical elements, total > 100. Element  Atomic number (Z)  chemically identical. ~3000 nuclides……? How many are stable? Same Z but different neutron number (N)  Isotopes. Total number of nucleons = Z+N = A  mass number. Radioactive Stable Radioactive Same mass number  Isobars  chemically dissimilar, parallel nuclear features (Radius …).  decay. Same neutron number  Isotones  ?????. Same Z and same A  Isomers  metastable. Stable isotope  (Isotopic) Abundance. Radioactive isotope  Half-life. Chart of Nuclides redundant

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 9 Stable Nuclides HWc 1 Odd AEven A NuclideNZNZ Then plot Z vs. N. Odd AEven A

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 10 PropertiesStructure The energy of the nucleon in the nucleus is in the order of 10 MeV. HW 1 HW 1 Calculate the velocity of a 10 MeV proton and show that it is almost 15% of the speed of light. (Perform both classical and relativistic calculations).  Relativistic effects are not important in considering the motion of nucleons in the nucleus. HW 2 HW 2 Calculate the wavelength of a 10 MeV proton and compare it with the nuclear scale. (Perform both classical and relativistic calculations). Is the nucleus thus a classical or a quantum system?  HW 0  HW 0 Krane, Ch. 2. HW 3 HW 3 Calculate the wavelength for an electron of the same energy to show that it is much too large to be within the nucleus. (Perform both classical and relativistic calculations). Discuss the proton-electron nuclear hypothesis! Basic Nuclear Properties Chadwick, neutron.

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 11 Basic Nuclear Properties Static nuclear properties (Time-independent): Electric charge, radius, mass, binding energy, angular momentum, parity, magnetic dipole moment, electric quadrupole moment, energies of excited states. Dynamic properties (Time-dependent): Self-induced (Radioactive decay). Forced (Nuclear reactions)  cross sections. The key: Interaction between individual nucleons. Excited states: atomic intervals ~ eV. nuclear intervals ~ 10 4 – 10 6 eV. Decays and reactions: Conservation laws and selection rules. HWc 2 HWc 2 Where to find nuclear data???

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 12 Nuclear Mass (Introduction) Unified atomic mass unit u based on 12 C. Replaced both physical and chemical amu based on 16 O and natural oxygen, respectively (Find conversion factors). 1 u = M( 12 C)/12 = ……… kg = …………… MeV/c 2. Rest masses uMeV/c 2 kg electron ………… …………… ……… proton ………… …………… ……… neutron ………… …………… ……… 12 C12 …………… ……… Avogadro’s number.. !! What is the number of atoms in 1 kg of pure 238 U? Mass  Stability. E = mc 2. Tendency towards lower energy  Radioactivity. Neutron heavier than proton  “Free” neutron decays (T ½ = ???):

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 13 Nuclear Mass (Introduction) Nuclear masses measured to high accuracy: mass spectrograph. energy measurement in nuclear reactions. Mass decrement = difference between actual mass and mass number: Δ = m – A Δ of parent(s) > Δ of product(s)  radioactivity. Binding Energy? Stability? Fission? Fusion? More later ……..  Usually atomic masses are tabulated.  Mass of the atom < Zm H + Nm n.

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 14 The Valley of Stability

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 15 Nuclear Size Different experiments give different results  Radius not well defined. Depends on probe and relevant physics. Probes should be close to the order of the size of the nucleus ~ m. Visible light? much larger. 1 MeV  ? = ?? x m. Interacts with orbital electrons. Suitable probes: p, n, , e....Charge distribution. Mass distribution. All experiments agree qualitatively and somehow quantitatively. Project ….  R  A ⅓ R = r 0 A ⅓ with r 0 dependent on the method. Matter distribution  charge distribution. [Recently some halo nuclei, e.g. 11 Li, found]. What is that?

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 16 Nuclear Size  0 = nucleon density near the center. t = “skin” thickness. a = thickness parameter. R = Half-density radius. HW 4 Experiments show that t = (2.4 ± 0.3) fm for all nuclei  t / R  A -1/3 Is surface effect the same for all nuclei? HWc 3 Compare for A = 4, 40, 120 and 235.

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 17 Nuclear Size High-energy e scattering Light nuclei? R  A ⅓ From some experiments….! Charge distribution: r 0 = 1.07 fm. a = 0.55 fm. Matter distribution: r 0 = 1.25 fm. a = 0.65 fm.  0 decreases with A? YesNo Why?

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 18 Nuclear Size HW 5 Nucleus Z/ACharge density 40 Ca ….. ….. 59 Co ….. … In ….. … Au ….. ….. Charge radius ~ nuclear radius, even though heavy nuclei have more neutrons than protons. Explain… Density of ordinary atomic matter ~ 10 3 kg/m 3. Density of nuclear matter ~ kg/m 3. Neutron stars, 3 solar masses, only 10 km across ….. !!! Surface effect?

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 19 Nuclear Size Three conclusions can be drawn: Inside the nucleus the density is fairly uniform. The transitional surface layer is thin. The central density has a similar value for different nuclei. Saturation? Get an estimate for nuclear density and thus inter- nucleon distance.

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 20 Nuclear Size Neutron Detector 1 Ci Pu-Be Neutron Source Absorber Beam From Optical Model Preferably low Different targets How can we get r 0 from the graph? HW 6 Dimensions

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 21 Nuclear Size Alpha particle (+2e) Gold nucleus (+79e) d Quite old!!! Not exactly for Au!!!

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 22 Nuclear Size Closest approach “d”. E  = E Coulomb  d = 2kZe 2 /E  What about the recoil nucleus? HW 7 HW 7 Show that where m N : mass of the nucleus m  : mass of alpha What are the values of d for 10, 20, 30 and 40 MeV  on Au? How does this explain … ?

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 23 Nuclear Shape Crude Nucleons in the nucleus are confined to an approximately spherically symmetric structure  Nuclear radius. Deformations…! Consequences….!! Is there a sharp spherical wall…???!!! HW 8 if it is assumed that the charge is uniformly spherically distributed in a nucleus, show that the electric potential energy of a proton is given by:

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 24 Nuclear Binding Energy B tot (A,Z) = [ Zm H + Nm n - m(A,Z) ] c 2 B  m  HW 9 B ave (A,Z) = B tot (A,Z) / A HW 9 Krane 3.9 HW 10 Atomic masses from: HW 10 Krane Separation Energy Neutron separation energy: (BE of last neutron) S n = [ m(A-1,Z) + m n – m(A,Z) ] c 2 HW 11 = B tot (A,Z) - B tot (A-1,Z)  HW 11 Show that HW 12 HW 12 Similarly, find S p and S . HW 13HW 14 HW 13 Krane 3.13HW 14 Krane 3.14 Magic numbers

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 25 Nuclear Binding Energy Magic numbers

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 26 Nuclear Binding Energy In general X  Y + a S a (X) = (m a + m Y –m X ) c 2 = B X –B Y –B a The energy needed to remove a nucleon from a nucleus ~ 8 MeV  average binding energy per nucleon (Exceptions???). Mass spectroscopy  B. Nuclear reactions  S. Nuclear reactions  Q-value

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 27 Nuclear Binding Energy ~200 MeV  Fission Fusion  Coulomb effectSurface effect HWc 4 Think of a computer program to reproduce this graph.

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 28 Nuclear Binding Energy HW 15 A typical research reactor has power on the order of 10 MW. a) Estimate the number of 235 U fission events that occur in the reactor per second. b) Estimate the fuel-burning rate in g/s.

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 29 Nuclear Binding Energy Is the nucleon bounded equally to every other nucleon? C ≡ this presumed binding energy. B tot = C(A-1)  A  ½ B ave = ½ C(A-1) Linear ??!!! Directly proportional ??!!! Clearly wrong … !  wrong assumption  finite range of strong force, and force saturation.

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 30 Nuclear Binding Energy Lead isotopes Z = 82 For constant Z S n (even N) > S n (odd N) For constant N S p (even Z) > S p (odd Z) Remember HW 14 (Krane 3.14). 208 Pb (doubly magic)  can then easily remove the “extra” neutron in 209 Pb. Neutron Number N Neutron Separation Energy S n (MeV) 208 Pb

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 31 Nuclear Binding Energy Extra Binding between pairs of “identical” nucleons in the same state (Pauli … !)  Stability (e.g.  -particle, N=2, Z=2). S n (A, Z, even N) – S n (A-1, Z, N-1) This is the neutron pairing energy. even-even more stable than even-odd or odd-even and these are more tightly bound than odd-odd nuclei.

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 32 Abundance Systematics Odd NEven NTotal Odd Z Even Z Total Compare: even Z to odd Z. even N to odd N. even A to odd A. even-even to even-odd to odd-even to odd-odd. HWc 1 \

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 33 Neutron Excess Odd A Even A Z = N Asymmetry Remember HWc 1.

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 34 Neutron Excess Remember HWc 1. Asymmetry

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 35 Abundance Systematics

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 36 Abundance Systematics NEUTRON NUMBER MASS NUMBER ABUNDANCE NEUTRON CAPTURE CROSS SECTION r s Formation process  Abundance

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 37

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 38 The Semi-empirical Mass Formula von Weizsäcker in Liquid drop. Shell structure. Main assumptions: 1.Incompressible matter of the nucleus  R  A ⅓. 2.Nuclear force saturates. Binding energy is the sum of terms: 1.Volume term.4. Asymmetry term. 2.Surface term.5. Pairing term. 3.Coulomb term.6. Closed shell term. …..

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 39 The Semi-empirical Mass Formula Volume Term B v = + a v A B v  volume  R 3  A  B v / A is a constant i.e. number of neighbors of each nucleon is independent of the overall size of the nucleus. The other terms are “corrections” to this term. constant

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 40 The Semi-empirical Mass Formula Surface Term B s = - a s A ⅔ Binding energy of inner nucleons is higher than that at the surface. Light nuclei contain larger number (per total) at the surface. At the surface there are: Nucleons. Remember t / R  A -1/3

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 41 The Semi-empirical Mass Formula Coulomb Term B C = - a C Z(Z-1) / A ⅓ Charge density   Z / R 3. W   2 R 5. Why ??? W  Z 2 / R. Actually: W  Z(Z-1) / R. B C / A = - a C Z(Z-1) / A 4/3 Remember HW 8 … ?!

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 42 The Semi-empirical Mass Formula

Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 43 The Semi-empirical Mass Formula Quiz 1 so far From our information so far we can write: For A = 125, what value of Z makes M(A,Z) a minimum? Is this reasonable…??? So …..!!!!