2016/9/27 Introduction to Nuclear Engineering Kenichi Ishikawa ( ) http://ishiken.free.fr/english/lecture.html ishiken@n.t.u-tokyo.ac.jp 1
References Nuclear Physics basic properties of nuclei nuclear reactions nuclear decays Basdevant, Rich, and Spiro, Fundamentals in Nuclear Physics (Springer, 2005) Krane, Introductory Nuclear Physics (Wiley, 1987) (, 1971) II Course material downloadable from: http://ishiken.free.fr/english/lecture.html 2
Basic properties of nuclei 3
A nucleus is made up of protons and neutrons E = mc 2 + e 0 - e 1.0014 1840 e =1.6022 10 19 C MeV = 10 6 ev nucleon: proton, neutron ev = 1.6022 10 19 J 4
A nucleus is labeled by atomic number and mass number A ZX Z : atomic number = number of protons N : number of neutrons A = Z + N : mass number example 235 92 U or simply 235 U uranium-235 N = 235-92 = 143 5
nuclear binding energy and mass defect mass defect M = Zm p + Nm n m N > 0 proton mass neutron mass nuclear mass binding energy B = Mc 2 =(Zm p + Nm n m N )c 2 max 8.7945 MeV @ 62 Ni binding energy per nucleon B/A (MeV) 8 6 4 ~ 8 MeV 2 0 0 50 100 150 mass number A 6 stable unstable 200 250
Nuclear reactions 7
Nuclear reactions free particle (photon, electron, positron, neutron, proton, ) projectile projectile a + X Y + b target scattering target nuclear reactions X(a,b)Y example α + 14 N 17 O + p (Rutherford, 1919) p + 7 Li 4 He + α (Cockcroft and Walton, 1930) 8
Energetics a + X Y + b m X c 2 + T X + m a c 2 + T a = m Y c 2 + T Y + m b c 2 + T b rest mass kinetic energy reaction Q value Q =(m initial m final )c 2 =(m X + m a m Y m b )c 2 = T Y + T b T X T a excess kinetic energy Q > 0 : exothermic Q < 0 : endothermic 9
Important nuclear reactions for thermal energy generation Fission 235 U+n! X+Y+(2 3) n example 235 U+n! 144 Ba + 89 Kr + 3n + 177 MeV Fusion D+T! 4 He (3.5 MeV) + n (14.1 MeV) D+D! T(1.01 MeV) + p (3.02 MeV)! 3 He (0.82 MeV) + n (2.45 MeV) D+ 3 He! 4 He (3.6 MeV) + p (14.7 MeV) > 10 6 times more efficient than chemical reactions! 10
Nuclei for fission reactors 233 U, 235 U, 239 Pu (fissile materials) fission by thermal neutron capture Fission of 235 U produces ~2.5 neutrons 238 U, 232 Th (fertile materials) change to 239 Pu, 232 Th by neutron capture fast breeder reactor 11
Cross section Probability P proportional to. number density of target particles n target thickness dz dz L dp = ndz Unit of cross section dimension of area m 2, cm 2 size of nucleus ~ a few fm 1 barn (b) = 10-28 m 2 = 10-24 cm 2 12
Differential cross section angular dependence ( ) target detector d Probability that the incident particle is scattered to a solid angle d dp, = d d ndzd for isotropic scattering ( ) d d = 4 differential cross section ( ) total cross section = d d d = 0 2 d 0 d d (, ) sin d 13
Mean free path and reaction rate. flux F df = F ndz L df dz = F n dz F (z) =F (0)e nz = F (0)e z macroscopic cross section ( ) = n [1/length] mean free path if there are different types of target objects (nuclei) reaction rate l =1/ v l =1/ n i in i F(z)/F(0) 1.0 0.8 0.6 0.4 1/e = 0.368 0.2 0.0 1/ n also distribution of free path l = n v 14 z
General characteristics of cross-sections Elastic scattering The internal states of the projectile and target (scatterer) do not change before and after the scattering. Rutherford scattering, (n,n), (p,p), etc. Inelastic scattering (n,γ), (p,γ), (n,α), (n,p), (n,d), (n,t), etc. fission, fusion 15
10 4 10 3 Elastic neutron scattering relevant to (neutron) moderator in nuclear reactors due to the short-range strong interaction JENDL flat region range of the strong interaction el 20 b (2fm) 2 0.1b Cross section (barn) 10 2 10 1 10 0 10-1 1H(n,n) 2H(n,n) 6Li(n,n) 10-5 10-3 10-1 10 1 10 3 10 5 10 7 Energy (ev) resonance p > h/r (p 2 /2m n > 200 MeV) 16
Elastic neutron scattering 10 9.6 Cross section (barn) 10 4 10 3 10 2 10 1 10 0 10-1 1H(n,n) 2H(n,n) 6Li(n,n) JENDL resonance 10-5 10-3 10-1 10 1 10 3 10 5 10 7 Energy (ev) Energy (MeV) 9 8 7 6 5 4 3 2 1 0 0 7.253 n + 6 Li 2 4 7.47 6.54 4.63 0.478 0 7 Li The energy levels of 7 Li and two dissociated states n- 6 Li and 3 H- 4 He (t-α) 6 2.466 3 H + 4 He 8 10 n + 6 Li 7 Li * n + 6 Li 17
Nuclear data libraries ENDF (Evaluated Nuclear Data File, USA) JENDL (Japanese Evaluated Nuclear Data Library, Japan) JEFF (Joint Evaluated Fission and Fusion file, Europe) CENDL (Chinese Evaluated Nuclear Data Library, China) ROSFOND (Russia) BROND (Russia) http://www-nds.iaea.org/exfor/endf.htm 18
Inelastic scattering Introduction to Nuclear Engineering (Kenichi ISHIKAWA) for internal use only (Univ. of Tokyo) Neutron capture neutron binding energy = ca. 8 MeV activation exothermic reaction in most cases Highly excited states formed, which subsequently decay. Radiative capture A X(n,γ) A+1 X emits a gamma ray 113 Cd(n,γ) 114 Cd neutron shield Other neutron capture reactions 10 B(n,α) 7 Li, 3 He(n,p) 3 H, 6 Li(n,t) 4 He Applications: neutron detector, shield, neutron capture therapy for cancer 19
Inelastic scattering Introduction to Nuclear Engineering (Kenichi ISHIKAWA) for internal use only (Univ. of Tokyo) neutron radiative capture No threshold exothermic, no Coulomb barrier 10 1 JENDL 10 0 Cross section (barn) 10-1 10-2 10-3 10-4 10-5 1H(n,gamma) 6Li(n,gamma) 2H(n,gamma) JENDL ENDF 10-6 10-5 10-3 10-1 10 1 10 3 10 5 10 7 Energy (ev) E 1/2 1/v discrepancy between JENDL and ENDF 1/v law Energy-independent reaction rate v 20
Neutron capture reactions with large cross section 113 Cd(n,γ) 114 Cd : shield 157 Gd(n,γ) 158 Gd : neutron absorber in nuclear fuel, cancer therapy 10 B(n,α) 7 Li : detector, cancer therapy 3 He(n,p) 3 H : detector 6 Li(n,t) 4 He : shield, filter, detector 21
Inelastic scattering Introduction to Nuclear Engineering (Kenichi ISHIKAWA) for internal use only (Univ. of Tokyo) 10 B(n,α) 7 Li Cross section (barn) 10 5 10 4 10 3 10 2 10 1 10 0 10-1 1/v law 10B(n,alpha)7Li JENDL 10-5 10-3 10-1 10 1 10 3 10 5 10 7 Energy (ev) Applications BF3 proportional counter Boron neutron capture therapy (BNCT) for cancer 3 He(n,p) 3 H Helium-3 proportional counter 22
Photo-nuclear reaction Excitation and break-up (dissociation) through photo-absorption Analog of the photoelectric effect 2.5x10-3 2.0 0.7 2 H 0.6 208 Pb 208Pb(gamma,n)207Pb Cross section (barn) 1.5 1.0 2H(gamma,n)1H Cross section (barn) 0.5 0.4 0.3 0.2 0.5 0.1 0.0 0 5 10 15 20 25 30 Energy (MeV) threshold (2.22 MeV) = binding energy of 2 H 0.0 0 5 10 15 Energy (MeV) giant resonance collective oscillation of protons in the nucleus 20 25 30 23
Energy (MeV) 10 9 8 7 6 5 4 3 2 1 0 0 Cross section (barn) 10 4 10 3 10 2 10 1 10 0 10-1 10-2 10-3 10-4 1/v law (n,n) (n,t) Resonance (n,gamma) 6 Li JENDL resonance (n,p) 10-5 10-3 10-1 10 1 10 3 10 5 10 7 Energy (ev) 7.253 n + 6 Li 2 4 9.6 7.47 6.54 4.63 0.478 0 7 Li 6 2.466 3 H + 4 He 8 10 cross section (barn) 2 10 2 10 10 elastic (x10) (n,γ) (/100) 10 elastic 10 10 1 4 2 1 2 4 (n,fission) (/105) (n,γ) (/10 4 ) Many excited states for heavy nuclei complicated resonance structure 235 U 238 U 2 3 1 10 10 10 Excited states of 239 U E (ev) 24
Resonance line shape (E) Resonance A (E E 0 ) 2 + ( /2) 2 2.0 1.5 1.0 0.5 full width at half maximum (FWHM) long tail Doppler effect 1.0 0.8 0.6 0.4-3 -2-1 1 2 3 Lorentzian Life time = / Decay rate 1 = / = uncertainty principle E : natural width homogeneous width 0.2-3 -2-1 1 2 3 inhomogeneous width (E E 0 ) 2 exp E 2 25
Introduction Fundamentals to Nuclear in Nuclear Engineering Physics (Kenichi ISHIKAWA) for internal use only (Univ. of Tokyo) Nuclear decays 26
Decay rate, natural width probability to decay in an interval dt dp = dt = number of unstable nuclei dt decay rate mean life time N(t) =N(t = 0)e t/ half life t 1/2 = (ln 2) =0.693 7 Li (7.459 MeV) n 6 Li, 3 H 4 He τ = 6 10 21 sec 76 Ge 76 Se 2e 2 e t 1/2 =1.78 10 21 yr > 10 11 (age of universe)! An unstable particle has an energy uncertainty or natural width = = = 6.58 10 22 MeV sec 27
Decay diagram half life branching ratio 28
alpha decay = 4 2He A ZX! A 4 Z 2 Y+ example 238 U! 234 Th + (4.2 MeV) half life = 4.468 10 9 years 29
beta decay decay + decay A ZN A ZN A Z+1N +e A Z + e 1N +e + + e half life = 5730 years dating 30
Emitted electron (positron) energy has a broad distribution 64 Cu _ 64 + β Cu β 0.2 0.6 1.0 1.4 1.8 0.2 0.6 1.0 1.4 1.8 p (MeV/c) p (MeV/c) β β β 31
beta decay decay + decay A ZN A ZN A Z+1N +e A Z + e 1N +e + + e half life = 5730 years dating The existence of the neutrino was predicted by Wolfgang Pauli in 1930 to explain how beta decay could conserve energy, momentum, and angular momentum. Pauli 32
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Electron capture (EC) a) b) (A,Z) k l m c) (A,Z 1) (A,Z 1) l m νe 40 Ar 18 γ followed by characteristic x-ray emission Auger effect 40 K 19 10.72%1.5049 MeV EC γ 0+ 1.277 10 9 a radiation from the human body 4-89.28%1.31109 MeV β 40 20Ca 0+ A ZN + e A Z 1N + e fundamental process: pe n e neutrino energy: E = M(A, Z)c 2 M(A, Z 1)c 2 atomic mass (not nuclear mass) 34
Gamma-ray emission (gamma decay) gamma decay A A+ gamma ray spontaneous emission unstable high-energy state (stable) low-energy state m A >m A m A m A m A momentum conservation p = E c energy conservation E + p2 2m A =(m A m A ) c 2 recoil energy (energy loss) E R = E2 2m A c 2 m A c 2 A 931.5 MeV E R E E (m A m A ) c 2 but E R > in general Emitted gamma rays are not resonantly re-absorbed by other nuclei in gases 35
4 3 2 1 Internal conversion An excited nucleus can interact with an electron in one of the lower atomic orbitals, causing the electron to be emitted (ejected) from the atom. s-electrons have finite probability density at the nuclear position. s for a hydrogen atom 1s The electron may couple to the excited state of the nucleus and take the energy of the nuclear transition directly, without an intermediate gamma ray. probability density 0 0 0.5 0.4 0.3 0.2 0.1 0.0 0 0.020 0.015 0.010 0.005 0.000 0 0.12 1 1 1 2 2 2 3 3 3 4 4 4 2s 2p 3s 5 5 5 interaction Energy of the conversion electron followed by characteristic x-ray emission Auger effect 0.08 0.04 E ce (m A m A ) c 2 E b E E b 0.00 0 1 2 r (atomic unit) 3 4 5 binding energy of the electron 36
Mössbauer effect recoil energy (energy loss) Emitted gamma rays are not resonantly re-absorbed by other nuclei in gases. but... E R = Inverse transition (resonant re-absorption) possible when nuclear recoil is suppressed in a crystal ( very very large ma ) Mössbauer effect (discovered in 1957) the excited nucleus decays in flight with the Doppler effect compensating the nuclear recoil E2 2m A c 2 37
Mössbauer spectroscopy 191 Os 0.0417 191 Ir 191 Os source γ 191 Ir γ absorber detector γ 0.129 v v v(cm/sec) 4 0 4 8 12 0.2 % absorption 0.4 0.6 0.8 1.0 20 0 20 40 E (µ ev) 191 38
Mössbauer effect + Doppler shift Test of Albert Einstein's theory of general relativity Gravitational red shift of light Clocks run differently at different places in a gravitational field Gravitational shift h(f r f e )=mgh hf e = mc 2 f r =1+ gh f e c 2 Doppler shift s f r 1 v/c = f e 1+v/c 1 v = gh c v c =7.36 10 7 m/s gamma ray (14.4 kev) 57 Fe f e f r blue shift by falling H = 22.5 m 57 Fe v by Pound and Rebka, 1959 Jefferson laboratory (Harvard University) 39