A-2 Induced Fission – 0 Introduction

1. A-2 Induced Fission – 0 Introduction • Generalities • Liquid-drop picture • Chain reactions • Mass distribution • Fission barrier • Double fission barrier • After the scission point • Time scale in fission • Neutron-induced fission • Energy dependence of (n,f) cross sections • Neutron energy spectra • Nuclear reactors • Nuclear energy • A reactor for fundamental research

2. A-2 Induced Fission – 1 Generalities Nuclear fission Decay process in which an unstable nucleus splits into two fragments of comparable mass. 1932: discovery of neutrons 1939: official discovery by Otto Hahn and Fritz Strassmann  fission of 235U  Lise Meitner! (109Mn) 1942: first “chain reacting pile” (E. Fermi) 1945: first nuclear explosion in Alamogordo (New Mexico, USA) 1972: discovery of Oklo (Gabon): unique natural nuclear reactor (1.8 106 y ago)  very abnormal isotopic ratios of 235U/238U in uranium ores

3. A-2 Induced Fission – 2 Liquid-drop picture Fission can be qualitatively understood on the basis of the liquid-drop model electrical repulsion pushes the 2 lobes apart fission fragment n n n n 235U high excitation and strong oscillation formation of a neck fission fragment Note: fission liberates about 200 MeV per atom!

4. A-2 Induced Fission – 3 Chain reactions Chain reactions If at least one neutron from each fission strikes another 235Unucleus and initiates fission, then the chain reaction is sustained. If the reaction will sustain itself, it is said to be "critical", and the mass of 235Urequired to produced the critical condition is said to be a "critical mass". A critical chain reaction can be achieved at low concentrations of 235U if the neutrons from fission are moderatedin water to lower their speed, since the probability for fission with slow neutrons is greater. A fission chain reaction produces intermediate mass fragmentswhich are highly radioactiveand produce further energy by their radioactive decay. Some of them produce neutrons, called delayed neutrons, which contribute to the fission chain reaction.

5. A-2 Induced Fission – 4 Mass distribution When 235U undergoes fission, the average of the fragment mass is about 118, but very few fragments near that average are found. It is much more probable to break up into unequal fragments, and the most probable fragment masses are around mass 95 and 137. Most of these fission fragments are highly unstable, and some of them such as 137Cs and 90Sr are extremely dangerous when released to the environment. 235U + n  236U*  140Xe + 94Sr + 2n T1/2 = 14s  bb  75s 140Cs94Y 64s  bb  19m 140Ba94Zr 13d  b 140La 40h  b 140Ca

6. A-2 Induced Fission – 5 Mass distribution

7. A-2 Induced Fission – 6 Fission barrier Fission barrier Fission occurs if there is an excitation energy greater than UB or an appreciable probability for tunneling through the potential energy barrier. Spontaneous fission occurs via a quantum mechanical tunneling through the fission barrier. Fissibility parameter: x = Z2/A Spontaneous fission is possible only for elements with A  230 and x  45. U barrier UB 1/r electric potential energy r0 r range of the nuclear force Ground states spontaneous fission half-lives for 235U: (9.8  2.8) x 1018 y 238Pu: (4.70 0.08) x 1010 y 256Fm: 2.86 h 238U: (8.2  0.1) x 1015 y 254Cf: 60.7 y 260106Sg: 7.2 ms

8. A-2 Induced Fission – 7 Double fission barrier • 50’s: enhancement in the study of the nuclear deformations for stable nuclei in • between shell closures. •  the spherical shell model is unable to explain the large quadrupolar moments of nuclei at 150 < A < 190 and A > 220 • unified model of A. Bohr and B. Mottelson: macroscopic + individual aspects 1955: S.G. Nilsson develops a deformed shell model  the potential is defined by oscillation frequencies, functions of deformation parameters  if the nucleus is deformed, the degeneracy of the energy levels of the spherical potential is partially lifted  the spreading in energy of these levels increase with the deformation  for small deformations, this spreading leads to an uniform repartition of the levels  for large deformations, on can observe the appearance of shell effects due to the gatherings of Nilsson levels coming from different shells initially The presence of these level gatherings, because they lower the level density, is at the origin of the permanent deformation of some nuclei in their ground state. But, the total energy is overestimated for the high energies…

9. A-2 Induced Fission – 9 A-2 Induced Fission – 8 Double fission barrier The method proposed by Strutinski is the synthesis of the liquid drop model and the deformed shell model in order to describe simultaneously the mean value of the potential energy < Epot > and its local fluctuations as a function of the nucleon number and the nucleus deformation. macroscopic – microscopic model of fission The oscillating aspects of the shell corrections in this model leads to the prediction of a fission barrier with two bumps: the double fission barrier. Epot (MeV) 230Th 240Pu 252Cf 5 Bn 0 deformation with Bn: binding energy of the neutron in the considered nucleus

10. A-2 Induced Fission – 9 Double fission barrier Experimental consequences • hierarchy of the states of the fissioning nucleus as a function of deformation: • compound states of class I: normally deformed and very dense (level density D = 0.1-1 eV)  compound states of class II: superdeformed with a reduced excitation energy E* ~ 2-3 MeV with a smaller level density (D = 0.05-10 KeV) These states have comparable properties: their presence and coupling with tunnel effect through the intermediate barrier have allowed a coherent interpretation of numerous experimental results in disagreement with the predictions of the liquid drop model. E excited states spectroscopy g class II states fission isomers class I states spontaneous fission deformation

11. A-2 Induced Fission – 10 Double fission barrier Fission isomers • lowest class II states • de-excitation through: - fission (tunneling through the 2nd barrier) - g emission after tunneling to the 1st well through the 1st barrier • these “form isomers” have a greater deformation than the ground state in the 1st well • 1st discovery in 1962 (Polikanov), ~ 30 isomers have been observed in the U-Bk region • E* = Eg.s. + 2-3 MeV few tens of ps < T1/2 < 14ms • one measures the variation with the incident energy of the ratio between the number of delayed fissions (coming from the isomer) and the number of prompt fissions A statistical model allows generally to extract the height of the second well and the shape of the second barrier.

12. A-2 Induced Fission – 11 After the scission point Beyond the barriers, the system evolves irreversibly towards the scission. This transition is very fast (few 10-22 s). During the scission, the system gets a large amount of energy (~20-30 MeV) that is used as deformation energy of the fragments. Just after the scission, the fragments convert their Coulomb energy in translation kinetic energy. They reach then 90% of their final kinetic energy in 1.3 10-20 s. As soon as the distance between the two fragments is larger than the nuclear force range (~ 2.5 10-13 cm), they get a deformation energy that they convert rapidly in internal excitation energy (this conversion is done with a damping of the collective vibrations in ~ 10-21 s). The prompt neutron emission is performed in 10-14 s (the distance between fragments is then 2. 10-8 cm). The g’s are emitted in a larger time length which can reach few ms. The formed fragments are unstable because too rich in neutrons. The delayed neutrons represent only 1% of the total neutron emission but they are of great importance for the reactivity of reactors.

13. A-2 Induced Fission – 12 Time scale in fission

14. A-2 Induced Fission – 13 Energies in 235U thermal fission The total kinetic energy of the fragments increases with the mass and the charge of the fissioning nucleus as Z2/A1/3. In the contrary, it is independent of the excitation energy of the fissioning system due to the effect of the Coulomb repulsion of the fragments formed at the scission.

15. A-2 Induced Fission – 14 Neutron-induced fission In the history of fission research, neutron-induced fission has always played the most important role (Hahn & Strassmann). The neutrons do not feel the Coulomb repulsion, only the nuclear attraction. Therefore nuclear reactions can be induced by neutrons of arbitrarily low energies. The asymmetric fission is largely favoured. The light mass peak goes towards heavier fragments when the mass of the fissioning nucleus increases. MeV En < 0.1 eV L.E. Glendenin et al., Phys. Rev. C (1981) 2600

16. A-2 Induced Fission – 15 Energy dependence of (n,f) cross sections Case of 235U and 237Nb thermal neutrons 235U: neutron binding energy > maximum fission barrier  large cross section 237Nb: neutron binding energy < maximum fission barrier  small cross section  when excitation energy E* > maximum fission barrier  sharp rise of sf

17. A-2 Induced Fission – 16 Neutron energy spectra The most prominent neutron emission source is the evaporation from the fully accelerated fragments. The integral neutron spectrum can be fitted with a Maxwellian distribution: With TM the only parameter characterizing the distribution. The average neutron energy is given by <En> = 3/2 TM. 235U(n,f) TM = 1.352 MeV <En> = 2.028 MeV B.E. Watt, Phys. Rev. 2 (1952) 1037

18. A-2 Induced Fission – 17 Nuclear reactors It takes 1011 fissions per second to produce one watt of electrical power. As a result, about one gram of fuel is consumed per day per megawatt of electrical energy produced. This means that one gram of waste products is produced per megawatt per day, which includes 0.5 grams of 239Pu. Pressurized Water Reactor Boiling Water Reactor BWR: the most common in case of a leak the water can become radioactive PWR: the moderating and turbine waters are separated more expensive LMFBR: liquid sodium is used as moderator and heat transfer medium Liquid-Metal Fast-Breeder Reactor

19. A-2 Induced Fission – 18 Nuclear energy Electricity production in 2001 %

20. A-2 Induced Fission – 19 A reactor for fundamental research Institute Laue-Langevin (Grenoble): a french-german-english lab