Q for 235 U + n 236 U is 6.54478 MeV. Table 13.11 in Krane: Activation energy E A for 236 U 6.2 MeV (Liquid drop + shell) 235 U can be fissioned with zero-energy neutrons. Q for 238 U + n 239 U is 4.??? MeV. E A for 239 U 6.6 MeV MeV neutrons are needed. Pairing term: δ =??? (Fig. 13.1111 in Krane). What about 232 Pa and 231 Pa? (odd Z). Odd-N nuclei have in general much larger thermal fission cross sections than even-n nuclei (Table 13.1 in Krane). 1
Why not use it? σ f,th 584 2.7x10-6 700 0.019 b 2
Thermal neutron fission of 235 U forms compound nucleus that splits up in more than 40 different ways, yielding over 80 primary fission fragments (products). 235 92 U + 1 0n 90 37Rb + 144 55Cs + 2 1 0n 235 92 U + 1 0n 87 35Br + 146 57La + 3 1 0n 235 92 U + 1 0n 72 30Zn + 160 62Sm + 4 1 0n The fission yield is defined as the proportion (percentage) of the total nuclear fissions that form products of a given mass number. Nuclear Reactors, Theory, BAU, 1 st JU, Semester, First Semester, 2007-2008 2010-2011 (Saed Dababneh). 3
Remember neutron excess. (A,Z) (A,Z+1) or(a1 (A-1,Z). Only left side of the mass parabola. 4
235 U + n 93 Rb + 141 Cs + 2n Q =???? What if other fragments? Different number of neutrons. Take 200 MeV as a representative value. 165 MeV average kinetic energy carried by fission fragments per fission. 66 MeV 98 MeV Heavy fragments Light fragments miscalibrated 5
ν neutrons emitted per fission. ν depends on fissioning nuclide and on neutron energy inducing i fission. India? 6
Mean neutron energy 2 MeV. 2.5 neutrons per fission (average) 5 MeV average kinetic energy carried by prompt neutrons per fission. Nuclear Fission Show that the average momentum carried by a neutron is only 1.5 % that carried by a fragment. Thus neglecting neutron momenta, show that the ratio between kinetic energies of the two fragments is the inverse of the ratio of their masses. E1 m2 95 E 66 E m 98 140 2 1 7
HW 7 1.036E χ( E ) = 0.453 e sinh 2. 29 E The experimental spectrum of prompt neutrons is fitted by the above equation. Calculate the mean and the most probable neutron energies. 8
The fission gamma radiation Prompt with average energy of 0.9 MeV. β delayed gammas. HW 8 Investigate how prompt gammas interact with water, uranium and lead. Nuclear Reactors, Theory, BAU, 1 st JU, Semester, First Semester, 2007-2008 2010-2011 (Saed Dababneh). 9
Fission Products β and γ emissions from radioactive fission products carry part of the fission energy, even after shut down. On approaching end of the chain, the decay energy decreases and half-life increases. Long-lived isotopes constitute the main hazard. Can interfere with fission process in the fuel. Example? Important for research. β-decay favors high energy ~20 MeV compared to ~6 MeV for γ. Only ~ 8 MeV from β-decay appears as heat. Why? p Example? (poisoning). 10
Segrè Distribution of fission energy Lost! a b c How much is recoverable? What about capture gammas? (produced by Note again that c < (a+b a+b). (produced by ν-1 neutrons) Nuclear Reactors, Theory, BAU, 1 st JU, Semester, First Semester, 2007-2008 2010-2011 (Saed Dababneh). 11
Enge Distribution of fission energy Krane sums them up as β Lost! decays. 12
Fission Products f β - A-1, Z j (n,γ) (n,γ) A, Z i β - A, Z-1 k A+1, Z A, Z+1 dn i /dt = Formation Rate - Destruction rate - Decay Rate dn dt i = γ in σ φ f f + N σ φ j j + λk Nk N σ φ λ i i i Ni N i saturates and is higher with higher neutron flux, larger fission yield and longer half-live. Nuclear Reactors, Theory, BAU, 1JU, st Semester, First Semester, 2007-2008 2010-2011 13 (Saed
Fission Products HW 9 Investigate the activity, decay and gamma energies of fission i products as a function of time. Comment on consequences (e.g. rod cooling). Shutdown HW 10 dn dt i = λ N λ N k k i i λ N > N λ N < λ Ni Investigate both λ k k i i and k k i giving full description for the buildup and decay of fission fragment i. Nuclear Reactors, Theory, BAU, 1 st JU, Semester, First Semester, 2007-2008 2010-2011 (Saed Dababneh). 14
P ( t ) Fission Products 11 0.2 0.2 = 4.1x10 [ t ( t + T ) ] MeV / s per watt of original operating power. T = time of operation. Fission product activity after reactor shutdown? Nuclear Reactors, Theory, BAU, 1 st JU, Semester, First Semester, 2007-2008 2010-2011 (Saed 15
It is necessary to evaluate the potential hazards associated with an accidental release of fission products into the environment. It is required to determine a proper cooling time of the spent fuel (before it becomes ready for reprocessing) that depends on the decay times of fission products. It is necessary to estimate the rate at which the heat is released as a result of radioactive decay of the fission products after the shut down of a reactor. The poisoning is needed to be calculated (the parasitic capture of neutrons by fission products that accumulate during the reactor operation). Nuclear Reactors, Theory, BAU, 1JU, st Semester, First Semester, 2007-2008 2010-2011 (Saed 16
Recoverable energy release 200 MeV per 235 U fission. Fission rate = 2.7x10 21 P fissions per day. P in MW. 3.12x10 16 fissions per second per MW, or 1.2x10-5 gram of 235 U per second per MW (thermal). Burnup rate: 1.05 P g/day. P in MW. The fissioning of 1.05 g of 235 U yields 1 MWd of energy. Specific Burnup = 1 MWd / 1.05 g 950000 MWd/t (pure 235 U!!!!!!!!!). Fractional Burnup =??? Actually much less (all heavy material). Thermal reactor loaded with 98 metric tons of UO 2, 3% enriched, operates at 3300 MWt for 750 days. 86.4 t U. Specific burnup 28650 MWd/t. Fast fission of 238 U. 238 U converted to plutonium more fission. Not all fissions from 235 U. U 17
Capture-to-fission t i ratio: α( E) = σ γ σ f σ (E) ( E) Consumption rate: 1.05(1+α) P g/day. Read all relevant material in Lamarsh Ch. 4. We will come back to this later. Two neutrinos are expected immediately from the decay of the two fission products, what is the minimum flux of neutrinos expected at 1 km from the reactor. 4.8x10 12 m -2 s -1 18
3.1x10 10 fissions per second per W. In thermal reactor, majority of fissions i occur in thermal energy region, φ and Σ are maximum. Ttlfi Total fission i rate in a thermal reactor of volume V V Σ f φ Thermal reactor power (quick calculation) P th = V Σ f φ f 3.1x10 10 Nuclear Reactors, Theory, BAU, JU, 1 st Semester, First Semester, 2007-2008 2010-2011 (Saed 19