1. One of the most practical nuclear reactions results from the compound nucleus that results from A>230 nuclei absorbing neutrons. Often split into two medium mass nuclear fragments plus additional neutrons. Alpha particle energy Cross Section ,n,n ,2 n ,3 n ,4 n Total NUCLEAR FISSION

2. 1930 Bothe & Becker Studying  -rays bombarding beryllium produced a very penetrating non-ionizing form of radiation  -rays? Irène and Frédéric Joliot-Curie knocked protons free from paraffin targets the proton energy range revealed the uncharged radiation from Be to carry 5.3 MeV 1932 James Chadwick in discussions with Rutherford became convinced could not be  s Assuming Compton Scattering to be the mechanism, E  >52 MeV!

3. Neutron chamber ionization (cloud) chamber Replacing the paraffin with other light substances, even beryllium, the protons were still produced. Nature, February 27, 1932

4. Chadwick developed the theory explaining the phenomena as due to a 5.3 MeV neutral particle with mass identical to the proton undergoing head-on collisions with nucleons in the target. 1935 Nobel Prize in Physics 9 Be has a loosely bound neutron (1.7 MeV binding energy) above a closed shell: 5-6 MeV  from some other decay Q=5.7 MeV Neutrons produced by many nuclear reactions (but can’t be steered, focused or accelerated!)

5. Natural sources of neutrons Mixtures of 226 Ra (  source) and 9 Be  ~constant rate if neutron production also strong  source so often replaced by 210 Po, 230 Pu or 241 Am Spontaneous fission, e.g. 252 Cf (  ½ = 2.65 yr) only 3% of its decays are through fission 97%  -decays Yield is still 2.3  10 12 neutrons/gram  sec !

6. A possible (and observed) spontaneous fission reaction 238 U 119 Pd 8.5 MeV/A 7.5 MeV/A Gains ~1 MeV per nucleon! 2  119 MeV = 238 MeV released by splitting

7. Yet is a rare decay:  ½ = 10 16 yr not as probable as the much more common  -decay  ½ = 4.5  10 9 yr Atomic (chemical) processes ~few eV Fission involves 10 8  as much energy as chemical reactions!

8. From the curve of binding energy per nucleon the most stable form of nuclear matter is as medium mass nuclei.

9. Consider: The Q value (energy release) of this process is The mass differences cancel since the total number of constituents remains unchanged. For simplicity, if we assume the protons and neutrons divide in the same ratio as the total nucleons:

10. The difference in binding energy comes from the surface and coulomb terms so the energy released can then be expressed in terms of the surface energy Es and the coulomb energy Ec of the original nucleus (A,Z). maximum Q is found by setting dQ/dy 1 = 0 Note : maximum occurs when y 1 = y 2 = 1/2.

11. Fission into two equal nuclei (symmetric fission) produces the largest energy output or Q value The process is exothermic (Q > 0) if E c /E s > 0.7. in terms of the fission parameter, x >0.35 Suggesting all nuclei with (Z 2 /A) > 18 (ie heavier than 90 Zr) should spontaneously release energy by undergoing symmetric fission. However

12. Half-life of spontaneous fission as a function of x where and R.Vandenbosch and J.R.Huizenga. Nuclear Fusion, Academic Press, New York, 1973.

13. There is a competition between the nuclear force binding the nucleus together and the coulomb repulsion trying to tear it apart

14. Induced fission as nuclear reaction suggests the absorption of the neutron (and its energy) may induce such distortions/vibrations in the nucleus.

16. The surface if any arbitrary figure can be expanded as If  lm time-independent: permanent deformation of the nucleus If  lm time-dependent: an oscillation of the nucleus

17. The Spherical Harmonics Y ℓ,m ( ,  ) ℓ = 0 ℓ = 1 ℓ = 2 ℓ = 3

18. ℓ = 0 ℓ = 1 z  Nuclear Charge Density

19. ℓ = 2 Lowest order to be considered: quadrupole deformation For which we write the nuclear radius The l=2, m=0 mode:

20. Z 

21. Example of a vibrational spectrum ( levels denoted by the number of phonons, N ) O.Nathan and S.G.Nilsson, Alpha- Beta- and Gamma-Ray Spectroscopy, Vol.1, (K. Siegbahn, ed.) North Holland, Amsterdam, 1965. Nuclei do show spectra for such vibrational modes

22. We can approximate any small elongation from a spherical shape by The semi-empirical mass formula semi-major axis semi-minor axis From which:

23. With the surface energy (strong nuclear binding force) proportional to area which we can write in the form where Notice  > 0 (so the Coulomb force wins out) for: Same fission parameter introduced when estimating available Q in symmetric fission Coulomb force deforming nucleus surface tension holding spherical shape

24.  r comes from considering small perturbations from a sphere. As long as these disturbances are slight, the Separation, r, of distinct fragments linearly follows for small r separation r V(r) At zero separation the potential just equals the release energy Q For Z 2 /A<49,  is negative.

25.  r for small r separation r V(r) r r While for large r, after the fragments have been scissioned for large r

26. For such quadrupole distortions the figure shows the energy of deformation (as a factor of the original sphere’s surface energy E s ) plotted against  for different values of the fission parameter x. When x > 1 (Z 2 /A>49) the nuclei are completely unstable to such distortions.

27. The potential energy V(r) = constant-B as a function of the separation, r, between fragments. Z 2 /A=36 Z 2 /A=49 such unstable states decay in characteristic nuclear times ~10 -22 sec Tunneling does allow spontaneous fission, but it must compete with other decay mechanisms (  -decay)

29. No stable states with Z 2 /A>49! Tunneling probability drops as Z 2 /A drops (half-life increases).

30. At smaller values of x, fission by barrier penetration can occur, However recall that the transmission factor (e.g., for  -decay) is where m while for  particles (m~4u) this gave reasonable, observable probabilities for tunneling/decay for the masses of the nuclear fragments we’re talking about,  can become huge and X negligible.

31. Neutron absorption by heavy nuclei can create a compound nucleus in an excited state above the activation energy barrier. As we have seen, compound nuclei have many final states into which they can decay: where Z 1 +Z 2 =92, A 1 +A 2 +  =236... in general: Experimentally find the average A 1 /A 2 peaks at  3/2 PROMPT NEUTRONS

32. The incident neutron itself need not be of high energy. Thermal neutrons E< 1 eV Slow neutrons E ~ 1 keV Fast neutronsE ~ 100 keV – 10 MeV Typical of decay Products & nuclear reactions “Thermal neutrons” (slowed by interactions with any material they pass through) have been demonstrated to be particularly effective. This merely reflects the general ~1/v behavior we have noted for all cross sections! Cross section  incident particle velocity, v

33. At such low excitation there may be barely enough available energy to drive the two fragments of the nucleus apart. Thus the individual nucleons settle into the lowest possible energy configurations Division can only proceed if as much binding energy as possible is transformed into the kinetic energy separating them out. involving the most tightly bound final states. (so MOST of the available Q goes into the kinetic energy of the fragments!)

34. There is a strong tendency to produce a heavy fragment of A ~ 140 (with double magic numbers N = 82 and Z = 50).

35. A possible (and observed) spontaneous fission reaction 238 U 119 Pd 8.5 MeV/A 7.5 MeV/A Gains ~1 MeV per nucleon! 2  119 MeV = 238 MeV released by splitting

36. 238 MeV represented an estimate of the maximum available energy for symmetric fission. For the observed distribution of final states the typical average is ~200 MeV per fission. Fragment kinetic energy165 MeV Prompt neutrons5 MeV Prompt gamma rays7 MeV Radioactive decay fragments25 MeV This 200 MeV is distributed approximately as:

37. 235 U

38. Isobars off the valley of stability (dark squares on preceding slide)  -decay to a more stable state.

39.  and  decays can leave a daughter in an excited nuclear state 187 W 1/2  5/2  187 Re 0.13425 0.20625 0.61890 0.68610  198 Au 22 00 198 Hg 0.412 MeV 1.088 MeV 

40. With the fission fragments radioactive, a decay sequence to stable nuclei must follow

41. 0.03% 25 sec  18 min  4 hr  33 d  65 sec  13 d  40 h  1.40% 6 sec  7 min  10 hr  10 6 yr  5 sec  3 hr  4 h  sometimesor

42. For 235 U fission, average number of prompt neutrons ~ 2.5 with a small number of additional delayed neutrons.

43. with every neutron freed comes the possibility of additional fission events This avalanche is the chain reaction.

44. 235 U will fission (n,f) at all energies of the absorbed neutron. It is a FISSILE material. However such a reaction cannot occur in natural uranium (0.7% 235 U, 99.3% 238 U)

45. Total (  t ) and fission (  f ) cross sections of 235 U. 1 b = 10 -24 cm 2

47. 238 U has a threshold for fission (n,f) at a neutron energy of 1MeV. The difference between these two isotopes of uranium is explained by the presence of the pairing term in the semi-empirical mass formula. Notice: for Z even, N even for Z odd, N odd for A odd Like nucleons couple pairwise into especially stable configurations.

48. Note the strong resonant capture of neutrons (n,  ) in the energy range 10-100 eV (particularly for 238 U where the cross-section reaches high values)

49. The fission neutron energy spectrum peaks at around 1 MeV

50. At 1 MeV the inelastic cross-section (n,n') in 238 U exceeds the fission cross-section. This effectively prevents fission from occurring in 238 U.

51. Natural uranium (0.7% 235 U, 99.3% 238 U) undergoes thermal fission only the Fission produces mostly fast neutrons Mev but is most efficiently induced by slow neutrons E (eV)

52. Consider fission neutrons created deep enough in a lump of natural uranium that we’ll just (for now) ignore that some neutrons may simply escaping from the sample.

53. 1000 100 10 1 1000 100 10 1 10000 0.1 Cross-section (barns) The processes competing with neutron-induced fusion have approximate cross-sections (read from the graphs at right) of 238 U (n,n) elastic scattering ~ 5 barn (n,n’) inelastic scattering ~ 2 barn (n,  ) ~0.2 barn (n,f) fission ~0.6 barn 235 U (n,n) elastic scattering ~ 5 barn (n,n’) inelastic scattering ~ 3 barn (n,  ) ~0.2 barn (n,f) fission ~ 2 barn

54. 238 U (n,n) elastic scattering 8.3 (n,n’) inelastic scattering 3.3 (n,  ) 0.3 (n,f) fission 1 235 U (n,n) elastic scattering 6.7 (n,n’) inelastic scattering 1.7 (n,  ) 0.3 (n,f) fission 3.3 Giving a relative probability to each of:  0.7/99.3

55. With 2-3 neutrons generated by each fission, only ~20 neutrons in the second generation - this is insufficient to sustain a chain reaction. Of the first 100 fission neutrons we start with 238 U (n,n) elastic scattering 63 (n,n’) inelastic scattering 25 (n,  ) 2 (n,f) fission 8 235 U (n,n) elastic scattering 1 (n,n’) inelastic scattering0 (n,  ) 0 (n,f) fission 0 ~98 are captured in the dominant 238 U only 8 of these captures result in fission

56. mixing natural uranium with a material to slow (but not absorb) neutrons to lower energies where the fission cross-section for 235 U is large. Most fissions are then induced by neutrons with thermal energies (~0.025 eV). FAST REACTOR a 50-50 mix of the two isotopes will sustain a chain reaction (most fission events occurring now in 235 U by neutron energies in the range 0.3 - 2.0 keV. Enriching the 235 U content THERMAL REACTOR moderating the neutrons to thermal speeds

57. Granulated powders can be mixed for this purpose. Powdered uranium Or blocks of uranium fuel can be alternately stacked with graphite to form a nuclear pile.

58. Moderator (Graphite) Moderator (Graphite) FUEL 1. Starting with neutrons/fission 2. Avg of  neutrons after fast fission 238 U 3.  p survive thermalization 4.  pf number captured in 235 U 235 U 5. k =  pf  (  f /  total ) number producing fission

59. One fission event produces k =  pf  (  f /  total ) secondary fission events. k is the reproduction factor. A chain reaction requires k  1. If k=1 the core is “critical” and self-sustaining. Typical values for natural uranium/graphite piles are k=1.07

60. Uranium is not dumped into the core like coal shoveled into a furnace. Instead it is processed and formed into fuel pellets (~pencil eraser size). The fuel pellets are stacked inside hollow metal tubes to form fuel rods 11 to 25 feet in length. Before it is used in the reactor, the uranium fuel is not very radioactive.

61. The fuel rods are arranged in a regular lattice inside the moderator. The rods are typically 2-3 cm in diameter and spaced about 25 cm apart. The rods metal sheath or cladding – most commonly stainless steel or alloys of zirconium. This cladding supports the fuel mechanically, prevents release of radioactive fission products into the coolant stream and provides extended surface contact with the coolant in order to promote effective heat transfer.

62. A single fuel rod cannot generate enough heat to make the amount of electricity needed from a power plant. Fuel rods are carefully bound together in assemblies, each of which can contain over 200 fuel rods. The assemblies hold the fuel rods apart so that when they are submerged in the reactor core, water can flow between them. In nuclear power plants, the moderator is often water (though some types do still use graphite). (though some types do still use graphite).

63. Fuel cell channels in face of reactor core.

65. Control rods slide in or out between the fuel rods to regulate the chain reaction. contain cadmium or boron (high cross section for neutron absorption, without fission). e.g., natural Boron is 20% 10 B Control rods act like sponges to absorb excess neutrons. with a cross section for thermal neutrons of 3840 b for the process

66. When the core temperature drops too low, the control rods are slowly pulled out of the core, and fewer neutrons are absorbed. When the temperature in the core rises, the rods are slowly inserted. To maintain a controlled nuclear chain reaction, the control rods are manipulated until each fission results in just one neutron on average, all other neutrons effectively absorbed by the control rods. Temperature changes in the core are generally very gradual. However should monitors detect a sudden change in temperature, the reactor immediately shuts down automatically by dropping all the control rods into the core. A shutdown takes only seconds and halts the nuclear chain reaction.

67. This very common type makes use of the excellent properties of water as both coolant and moderator (ordinary water does absorb neutrons – converting hydrogen into deuterium). The Boiling Water Reactor (BWR) allows the water to boil in the reactor core and uses the steam to drive the turbines.

68. The highest temperature possible for liquid water (critical temperature 374°C) is a limitation for devices that use water to convey heat. In this ideal case the heat is received isothermally (the working fluid at T 1 ) but rejected isothermally (at T 2 ) with all processes reversible. No real power plant operates on an ideal Carnot cycle, but the expression shows the higher T 1, the higher the efficiency (T 2 cannot be lower than the outside temperature). Furthermore recall: the Carnot engine efficiency  is The core must be contained within a pressure vessel of welded steel (typically withstanding pressures of about 1.55 x107 Pa or 153 bar. 1st land based pressurized water reactor: Shippingport USA (1957).

69. Pressure vessels are enormous with 9 inch thick walls, often weighing more than 300 tons. The pressure vessel surrounds and protects the reactor core, providing a safety barrier and holding the fuel assemblies, control rods, and coolant. Pressure vessels are made of carbon steel and lined with a layer of stainless steel to prevent rust. The pressure vessel is located inside the containment building, a thick concrete structure reinforced with steel bars.

70. A Fast Reactor has no moderator and consequently a much smaller core.

71. The very high power involved means that liquid metals have to be used as coolants! Liquid sodium is the most common but has the disadvantage of becoming radioactive itself through 23 Na(n,  ) 24 Na. As well as generating power fast reactors are used for breeding fissile material.

72. Breeder Reactors If uranium fission reactors used as sole source of electrical power needs all high-grade ores used up within a few decades! Fermi, Zinn (1944) Can fissile nuclei be grown? (the result of any nuclear reaction) Can we create fissile material as a by product of any reaction? The parent nuclei that spawns the fissile material is described as being a fertile nuclide.

73. Example: build a reactor core that runs on 239 Pu (the fuel) packed within a bed of 238 U (the fertile nuclide) =2.91 fast neutrons/ 239 PU fission Only one of these on average producing an additional fission is sufficient for sustainability. If the rest are incident on 238 U there’s a chance of inducing  1/2 = 25 min    1/2 = 2.3 days   A well designed breeder reactor can double the amount of fissile material in 7 – 10 years.

74. While neither natural Uranium cannot maintain a chain reaction even small lumps of pure 235U or 239Pu cannot explode simply because of the number of neutrons that escape before inducing fission. Recall we need k =  pf  (  f /  total ) > 1

75. A large enough (critical) mass of 235 U or 239 Pu can chain react and the reaction set off by any accidental initial neutron (even from a rare spontaneous fission event). If N neutrons (initially even 1 or 2) are present at time t their number will increase during the next moment dt by where  is related to k and obviously depends on the fissile material and its geometry. For critical samples of 235 U  ~10 8 Hz. As long as we can treat  as a constant where   =1/  is the “generation time.”

76. Five grades of uranium are commonly recognized: 1. Depleted uranium: containing < 0.71% 235 U. 2. Natural uranium: containing 0.71% 235 U. 3. Low-enriched uranium (LEU), between 0.71 – 20% 235 U. commercial power reactors use 2-6 % 235 U fuels. cannot be used to make nuclear explosives 4. Highly enriched uranium (HEU): containing > 20% 235 U. Research and naval reactors use either LEU or HEU fuel. 5. Weapon-grade uranium: HEU containing > 90% 235 U. Uranium- 233: fissile, weapon-useable isotope, derived from irradiating 232 Th with neutrons,  ½ =160,000 years; 10-20 kg required for a nuclear device; less common than U-235 for making nuclear explosives. Uranium-235: best suited for fission bomb (or fast reactor) when enriched to > 90% purity; 6-25 kg required for a nuclear bomb; “significant quantities” standards (for UN inspections) is as little as 3 kg; a recent international study estimates 1,750 tons of highly enriched 235 U have been produced worldwide.

77. Plutonium-239: Highly carcinogenic  ray emitter. Unlike uranium, all (but trace quantities) of Pu are manufactured. 239 Pu is produced in nuclear reactors when 238 U is irradiated with neutrons.  ½ = 24,000 years, and it is a fissile material. Subsequent neutron captures lead to accumulations of 240 Pu, 241 Pu and 242 Pu. 241 Pu is fissile, but 240 Pu and 242 Pu are not. However, all are fissionable by fast neutrons, and can be used either in combination or alone in nuclear explosives ; best fission explosive nuclear material. 3-8 kg required for nuclear explosive; "significant quantities standard" 1 kg. Plutonium is ~10 times more toxic than nerve gas. When inhaled, the smallest particles cause cancer: inhaling 12,000 micrograms (millionths of a gram) causes death within 60 days. The dispersal of 3.5 ounces of plutonium could kill every-one in a large office building. For weapon production, plutonium has to be at least 93% enriched. Plutonium technology for bomb construction is judged to be more difficult than 235 U techniques. The bomb dropped on Nagasaki contained 6.1 kg. There are about 1,200 metric tons of Plutonium on our planet of which some 230 tons have been produced for military purposes.

78. Weapons can be made out of plutonium with low concentrations of 239 Pu and high concentrations of 240 Pu, 241 Pu, or 242 Pu. The plutonium used in nuclear weapons typically contains mostly 239 Pu and relatively small fractions of other plutonium isotopes. Plutonium discharged in power reactor fuel typically contains significantly less 239 Pu and more of other plutonium isotopes. The following grades of plutonium are widely used: 1. Weapon-grade plutonium: containing < 7% 240 Pu. 2. Fuel-grade plutonium: 7 - 18 % 240 Pu. 3. Reactor-grade plutonium, containing over 18 percent 240 Pu. The term "super-grade plutonium" is sometimes used to describe plutonium containing less than 3 percent plutonium 240. The term "weapon-usable plutonium" is often used to describe plutonium in separated form and, thus able to be quickly turned into weapons components

79. Before triggering, fissile material is kept in subcritical quantities to prevent accidental explosions. An electrical trigger sets off chemical explosives that drive the subcritical parts together. Gun Trigger Assembly Propellant Tamper Active Material each 2/3 critical

81. Hiroshima Enola Gay Little Boy Size: length - 3 meters, diameter - 0.7 meters. Weight: 4 tons. Nuclear material: Uranium 235. Energy released: equivalent to 12.5 kilotons of TNT. Code name:"Little Boy"

82. Once triggered the chain reaction builds exponentially. Note logarithmic scale! After ~50 generations (0.50  sec) the energy released is increasing so rapidly it heats the material to the point it expands explosively. This scatters the remaining fissile material in subcritical quantities, and the chain reaction ends.

83. Dropping the first atomic bomb At 2:45am local time (August 6, 1945), the Enola Gay, a B-29 bomber took off from the US air base on Tinian Island in the western Pacific. 6½ hours later, at 8:15 A.M. Japan time, its atomic bomb was dropped and exploded a minute later at an estimated altitude of 580  20 meters over central Hiroshima. Initial explosive conditions Maximum temperature at burst point: several million degrees C. A 15m radius fireball formed in 0.1 millisecond, with a temperature of 300,000 o C, and expanded to its huge maximum size in one second. The top of the atomic cloud reached an altitude of 17,000 meters. Black rain Radioactive debris fell in a “black rain” for > hour over a wide area.

84. Damaging effects of the atomic bomb Thermal heat Intense thermal heat emitted by the fireball caused severe burns and loss of eyesight. Thermal burns of bare skin occurred as far as 3.5 kilometers from ground zero (directly below the burst point). Most people exposed to thermal rays within 1-kilometer radius of ground zero died. Tile and glass melted; all combustible materials were consumed. Blast An atomic explosion causes an enormous shock wave followed instantaneously by a rapid expansion of air (the blast); these carry ~half the explosion's released energy. Maximum wind pressure of the blast: 35 tons per square meter. Maximum wind velocity: 440 meters per second. Wooden houses within 2.3 km of ground zero collapsed. Concrete buildings near ground zero (blast from above) had ceilings crushed, windows and doors blown off. Radiation Exposure within 500 meters of ground zero was fatal. People exposed at distances of 3-5 kilometers later showed symptoms of aftereffects, including radiation-induced cancers. Deaths With an uncertain population figure, the death toll could only be estimated. According to data submitted to the United Nations by Hiroshima City in 1976, the death count reached 140,000 (plus or minus 10,000) by the end of December, 1945.

85. Active Material ( 235 U or 239 Pu) each 1/3 critical electrical trigger chemical explosive Active Material ( 235 U or 239 Pu) subcritical density chemical explosive Implosion Assembly Designs

86. Nagasaki Fat Man The atomic bomb dropped on Nagasaki exploded at 11:02 A.M. on August 9. Using 6.1 kg of 239 Pu it delivered the explosive power of 20 kilotons of TNT-equivalent, And left an estimated 70,000 dead by the end of 1945.