Lecture 16: Low-energy nuclear reactions – Part 1 Sotirios Charisopoulos Physics Section, NAPC/NA, IAEA, Vienna Joint ICTP-IAEA Workshop on Electrostatic Accelerator Technologies, Basic Instruments and Analytical Techniques | (smr 3331) ICTP , Trieste, October 28, 2019 http://indico.ictp.it/event/8728/
Nuclear reactions & Nuclear Scattering Nuclear reaction: The process in which two “particles” collide to produce one or more “particles” that are different from the those that began the process (parent “particles”). A nuclear reaction must cause a transformation of at least one particle to another. “Nuclear” ? “Particles” ? Nuclear Scattering: The process in which a “particle” interacts with another “particle” and they then separate without changing their “nature” of any nuclide. “Nuclear” ? “Particles” ? “Nature” ?
Nuclear “reactions” – in general We use nuclear reactions to study nuclear properties (structure and dynamics) Coulomb excitation Transfer and knockout reactions Reactions in the resonance region to study resonances and spins-parities Compound nucleus reactions Heavy ion reactions – fusion evaporation reactions to study structure properties of neutron-deficient nuclei Fission and deep inelastic scattering to study nuclear structure or neutron-rich nuclei Photonuclear reactions and Nuclear Resonance Fluorescence to study the electromagnetic response of the nucleus (Giant Dipole Resonance, Pygmy excitations, etc.) Inelastic scattering to low-lying states to extract spins
Nuclear “reactions” – in general We study nuclear reactions to understand how ions interact with nuclear matter and how nuclear species are produced Surface and bulk analysis of materials Radiation transport in materials Production of radioisotopes for medical applications Nuclear reactor inventories – production of neutrons, fission products, delayed neutrons Fusion plasma erosion of structural material Production of nuclei in the universe: nucleosynthesis (astrophysical reaction rates) etc.
Nuclear reactions & Q-values exit exit reactants channel 1 channel 2 a+A (b+B) + (d+D) + … A(a,b)B target nucleus residual nucleus (undetected part) projectile ejectile (incident beam) (detected particle) Q-value = masses (before) – masses (after) = M a + M A – M B –M b (in energy units)* Q-value > 0 : exothermic (exoergic) Q-value < 0 : endothermic (endoergic) Q-value = 0 : elastic scattering
Binding energy – Nuclear & Atomic mass – Mass Excess The sum of masses of 𝒏 𝒐𝒗𝒅 � 𝑎𝑛 � � 𝑂𝑛 � � Δ𝑛 � 𝑎𝑛 � � 𝑂𝑛 � � �𝜠𝜡/𝑑 � ) nucleons is more than the total nuclear mass Nuclear Binding Energy � 𝑪 𝒂, 𝑶 � � 𝑎𝑛 � � 𝑂𝑛 � � 𝑛 ��� ) 𝑑 � the atomic mass 𝒏 𝒃𝒖𝒑𝒏 𝐵, 𝑎 � 𝒏 𝒐𝒗𝒅 𝐵, 𝑎 � 𝑎𝑛 � � 𝐶 � �𝑎� Nuclear reactions conserve the total charge, i.e. in nuclear reactions: 𝒏 𝒃𝒖𝒑𝒏 𝐵, 𝑎 � 𝒏 𝒐𝒗𝒅 𝐵, 𝑎 atomic mass excess 𝑁. 𝐹. ≡ �𝑛 ���� 𝐵, 𝑎 � 𝐵𝑛 � �𝑑 � Reaction A(a,b)B: � � � �
p + 17 O 14 Ν + α : Q – value = 1191.83 keV
Systems of reference in nuclear collisions: A(a,b)B Laboratory system T arget A in rest Projectile a in move 𝑛 � � 𝑛 � B heavy product b light product 𝑛 � � 𝑛 � Laboratory system Center-of-mass system Projectile energy “Projectile” energy � � �� = � � � � �� �
Reaction thresholds & reaction kinematics (1/2) Energy and linear momentum conservation allows to calculate the energy of the ejectiles 𝑛 � 𝑛 � 𝐹 � cos 𝜄 𝑛 � 𝑛 � 𝐹 � 𝑑𝑝𝑡 � 𝜄 � �𝑛 � �𝑛 � ��𝑛 � 𝑅 � 𝑛 � � 𝑛 � 𝐹 � � {..} C 𝐹 � � � 𝑛 � � 𝑛 � 𝑛 � � 𝑛 � Non-relativistic kinematic formula for a two-body nuclear reaction Eq. 1 Similarly for E B by permuting symbols b and B and replacing θ with φ Q-value < 0 : endothermic Threshold energy E th Eq. 1: Two possible solutions for E b , acceptable only if: 𝑛 � � 𝑛 � 𝑛 � 𝑅 � 𝑛 � � 𝑛 � 𝐹 � � 0 ⇒ 𝐹 � � �𝑛 � 𝑅 𝐹 �� � �𝑅 : � 𝐹 ��� 𝑛 � � 𝑛 � � 𝑛 � 𝑛 � � 𝑛 � When E th � E α � Ε max two groups of part. b are observed if E α � E th no reaction and the emission angle θ is between 0 O � θ � θ max � 90 O • at E th part. b emerge at θ� 0 Ο • with increasing E α , part . b C {..}=0 are emitted in a cone that 𝑑𝑝𝑡 � 𝜄 ��� � � 𝑛 � � 𝑛 � 𝑛 � 𝑅 � 𝑛 � � 𝑛 � 𝐹 � becomes wider until its angle is maximized: 2 θ max �180 O 𝑛 � 𝑛 � 𝐹 �
Reaction thresholds & reaction kinematics (2/2) Q�0 exothermic: E b is single-valued function of θ ; decreasing with increasing θ , if m α � m B 𝑅 � 0 𝑛 � � 𝑛 � 𝒑𝒔 𝑅 � 0 𝐹 � � 𝐹 ��� 𝑅 � 0 𝑛 � � 𝑛 � 𝒑𝒔 𝑅 � 0 𝑛 � � 𝑛 � 𝐹 �� � 𝐹 � � 𝐹 ��� emitted particles b emitted particles b projectiles α projectiles α 𝐹 � 𝐹 � A 𝜄 A 𝜄 𝑛𝑏𝑦 �target� �target� • Particles b are emitted in all directions; • Particles b are emitted at forward angles • 𝐹 � increases at forward angles and only 𝜄 � 𝜄 ��� reaches maximum at 𝜄 � 0 � ; • At each emission angle 𝜄, two particle • 𝐹 � decreases at backward angles and energy groups are detected. reaches minimum at 𝜄 � 180 �
Exercise 1: the 7 Li(p,n) 7 Be reaction Which is the Q-value of the 7 Li(p,n) 7 Be reaction? • Has the reaction a threshold? If yes what is the threshold energy? • Which is the E max of the reaction, if applicable? • If the proton-beam energy is 1.9 MeV, which direction(s) will the emitted • neutron(s) take? What energies can the emitted neutron have? • Which energy has the proton beam to have so that the 7 Li(p,2n) reaction occurs? • Exercise 2: elastic scattering of α-particles Calculate the final energy of a 2-MeV α-particle scattered at 90 o by 40 Ca. • In case 40 Ca is replaced by 197 Au, the energy of the scattered α-particle will decrease? • Which will be the final energy of the α-particle if subsequently scattered at 60 o ? •
Reaction cross section 𝛣 𝛯 � � 𝜍 𝑀 � 𝐵 𝑂 � 1 b = 10 -24 cm 2 𝜏 � 𝑂 � 𝑂 𝑂 � 𝑂 � 𝜊 measure for probability that a certain reaction takes place at a given “projectile” energy Ε Reaction rate ….the link to nuclear astrophysics Τ ρ reactions / sec / cm 3 Μ Y i
Types of measured cross sections � � �
Reaction thresholds – Q values – Cross sections https://doi.org/10.1016/S0969-8043(00)00388-2
Classification of nuclear reactions Ӿ) Always possible; can be due to simple Coulomb repulsion or 𝒃 � 𝑩 → 𝑩 � 𝒃 by more complicated nuclear interactions. When Coulomb • Elastic Scattering forces dominant, then Coulomb or Rutherford scattering. 𝑅 � 0 Plays key role in surface layer analysis. 𝒃 � 𝑩 → 𝑩 ∗ � 𝒃 � � 𝑹 Both A and α can be in excited state; if so • Inelastic Scattering then excited state of A* decays via γ-ray 𝑅 � 0 𝐹 �� ≅ �𝑅 𝑛 � � 𝑛 � emission �for analysis purposes, γ-rays are 𝑛 � preferred to be detected, instead of α’ �� �� 𝑒 � 𝑂 → 𝐷 � 𝛽 � 13.575 MeV • Rearrangement or 𝒃 � 𝑩 → 𝑪 𝜿 � 𝒄 � 𝑹 𝒋 𝐷 ∗ � 𝛽 � 9.142 MeV �� �� Collisions 𝑒 � 𝑂 → �� 𝐷 ∗ 𝑏𝑢 𝐹 � � 4.433 MeV ��� ��� 𝛽 � 𝐵𝑣 → 𝑈𝑚 � 𝑜 � 𝑜 � 𝑜 � 25.4 𝑁𝑓𝑊 • Many body 𝒃 � 𝑩 → 𝑪 � 𝒄 𝟐 � 𝒄 𝟑 � ⋯ � 𝑹 or reactions ��� ��� 𝐵𝑣�𝛽, 3𝑜� 𝑈𝑚 �� �� 𝜹 � 𝑩 → 𝑪 � 𝒄 � 𝑹 𝛿 � 𝐷 → 𝐷 � 𝑜 � 18.72 𝑁𝑓𝑊 • Photonuclear reactions 𝑅 � 0 Carbon trace detection of 12 C; highly sensitive analytical method 𝒃 � 𝑩 → 𝑫 ∗ → 𝑫 � 𝜹 Energy calibration of electrostatic • Radiative Capture �� �� accelerators 𝐵𝑚�𝑞, 𝛿� 𝑇𝑗 Ӿ) before 1990 𝑅 � 0 �Resonances�
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