1. 5. Compound nucleus reactions Prof. Dr. A.J. (Arjan) Koning 1,2 1 International Atomic Energy Agency, Vienna 2 Division of Applied Nuclear Physics, Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden Email: A.koning@iaea.org EXTEND European School on Experiment, Theory and Evaluation of Nuclear Data, Uppsala University, Sweden, August 29 - September 2, 2016

2. THE COMPOUND NUCLEUS MODEL Elastic Fission (n,n’), (n,  ), (n,  ), etc… Inelastic OPTICALMODEL T lj  Reaction Shape elastic Direct components  NC PRE-EQUILIBRIUM COMPOUND NUCLEUS NUCLEUS

3. THE COMPOUND NUCLEUS MODEL (basic formalism) Compound nucleus hypothesis - Continuum of excited levels - Independence between incoming channel a and outgoing channel b abababab=  (CN) P b aaaa  (CN) = T a aaaa p kakakaka 2 Pb=Pb=Pb=Pb= TbTbTbTb S TcS TcS TcS Tc c  Hauser- Feshbach formula = abababab p kakakaka 2 Ta TbTa TbTa TbTa Tb S TcS TcS TcS Tc c

4. THE COMPOUND NUCLEUS MODEL (qualitative feature) Compound angular distribution & direct angular distributions 45° 90° 135°

5. THE COMPOUND NUCLEUS MODEL (complete channel definition) Channel Definition a + A  (CN )*  b+B Incident channel a = (l a, j a =l a +s a, J A,p A, E A, E a )      Conservation equations Total energy : E a + E A = E CN = E b + E B Total momentum : p a + p A = p CN = p b + p B Total angular momentum : l a + s a + J A = J CN = l b + s b + J B Total parity : p A (-1) = p CN = p B (-1)             lala lblb

6. THE COMPOUND NUCLEUS MODEL (loops over all quantum numbers) In realistic calculations, all possible quantum number combinations have to be considered s ab = (2J+1) (2I A +1) (2s a +1) S p kaka 2 J=| I A – s a | I A + s a + l a max p =  S l a = | j a – s a |j a = | J – I A | S S ja + sa ja + sa J + IAJ + IA l b = | j b – s b |j b = | J – I B | S S j b + s b J + IBJ + IB T JpT Jp a, l a, j a, b, l b, j b W T JpT Jp c, l c, j c T c S d p (a) d p (b) T JpT Jp a, l a, j a T T JpT Jp b, l b, j b T Width fluctuation correction factor to account for deviations from independence hypothesis Given by OMP Parity selection rules

7. THE COMPOUND NUCLEUS MODEL (the GOE triple integral)

8. THE COMPOUND NUCLEUS MODEL (flux redistribution illustration)

9. THE COMPOUND NUCLEUS MODEL (multiple emission) E N N c -1NcNc N c -2 Z ZcZc Z c -1 SnSn SpSp SaSa SnSn SpSp SaSa n’ n (2) fission SnSn SaSa SnSn SpSp SaSa p JpJp SnSn SpSp SaSa a SnSn SpSp SaSa d g g g n n TargetCompound Nucleus + Loop over CN spins and parities

10. REACTION MODELS & REACTION CHANNELS Optical model + Statistical model + Pre-equilibrium model s R = s d + s PE + s CN n + 238 U Neutron energy (MeV) Cross section (barn) = s nn’ + s nf + s n g +...

11. THE COMPOUND NUCLEUS MODEL (compact expression) and T b ( b ) = transmission coefficient for outgoing channel b associated with the outgoing particle b J = l a + s a + I A = j a + I A and  =  -1   A with lala =  ab where b = g, n, p, d, t, …, fission  b  ab =  k a 2  J,   2J+1   2s+1  2I+1   d T lj  a  JJ  a,ba,b WabWab T b  b  JJ T d  d  JJ  NC

12. THE COMPOUND NUCLEUS MODEL (various decay channels) Possible decays Emission to a discrete level with energy E d Emission in the level continuum Emission of photons, fission T b ( b ) = given by the O.M.P. JpJp T lj ( b ) T b ( b ) = E  JpJp T lj ( b ) r (E,J, p ) dE E + D E r(E,J,p) density of residual nucleus’ levels (J,p) with excitation energy E Specific treatment

13. Exercise Neutrons + Cu-65 Two incident energies: 1.6 and 5.5 MeV Plot elastic scattering angular distributions for both of them: the direct, compound and total component Exp data: 1.6 MeV: Cu-0, 5.5 MeV: Cu-65 Use TALYS sample case 3 for inspiration 13