1 v. L18.pdf Spring 2010, P627, YK February 22, 2012

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L18.pdf Spring 2010, P627, YK February 22, 2012 18 T2 Nuclear Information Service at LANL: http://t2.lanl.

1 L18.pdf Spring 2010, P627, YK February 22, T2 Nuclear Information Service at LANL: ENDF/B VI Neutron Data : bin/nuclides/endind Thermal neutron x sections: lengths/list.html Q: what is energy of thermal neutrons? Hydrogen 1 v

2 Hydrogen

3 Hydrogen

4 Classification of neutrons by their energy: Neutrons called E kinetic T, K velocity Wavelength, UCN ~250 nev ~ m/s ~ 600 Å Cold <3 mev <35 ~ 760 m/s ~ 5 Å = cm Thermal ~25.9 mev 300 ~ 2,224 m/s ~ 1.8 Å Resonance ~1 ev ~10 4 ~ m/s ~ 0.3 Å Slow ~100 ev ~10 6 ~ m/s ~ 0.03 Å Intermed. energy ~10 kev ~10 8 ~ m/s ~ Å Fast ~ 1 MeV ~10 10 ~ c ~ Å High energy ~ 100 MeV ~10 12 ~ 0.43 c ~ 3 fm= cm Relativistic >1 GeV >10 13 > c < 0.9 fm

6 1 v Neutron total cross sections in the energy interval from 0.01 ev to 10 7 ev for 1 H, 2 D, H 2 O, and D 2 O. At low energies 1/v contribution of absorption is clearly visible.

7 Note 1 v dependence of neutron absorption x-sections

8 Total cross sections in barns vs energy in ev for Be, B, C, and O

9 Total cross sections in barns vs energy in ev for Na, Mg, Al, and K

10 ENDF/B VI Neutron Data : bin/nuclides/endind

12 Fission of heavy elements: 235U (92p + 143n) + n X + Y + 2.5n + Q X, Y nuclei with atomic mass ~ 95 and 140 u ~2.5n produced per fission: 1n used to maintain the fission reaction and 1.5n can be utilized as a n source 99% of neutrons are prompt (<10 14 sec), but delayed neutrons (in seconds and minute range) are most essential for maintaining controlled chain reaction Q ~ 210 MeV per fission released: ~ 175 MeV kinetic energy of fission fragment; ~ 7 MeV prompt gamma rays ~ 5 MeV kinetic energy of fission n s ~ 7 MeV betas from fission products ~ 6 MeV gammas from fission products ~ 10 MeV neutrinos (invisible) dn/de (a.u.) for U 235 (red line) and Pu 239 (blue line).

13 235 U and 238 U fission cross section 235: neutrons should be slowed down for efficient fission 238 : no fission with slow neutrons

15 Detection of neutrons Examples of processes used for neutron detection: n p n p - elastic scattering (good for MeV neutrons) n p d (2.2 MeV) radiative capture (e.g. in KamLAND) n 10 7 B Li 6 3 n Li t 3 3 n He t p n 235 U fission

16 How moderation works? Mechanism of moderation of fast and slow neutrons is n - A elastic scattering. Maximum energy E (max) transferred to recoil A 4mM nucleus is E (max) = E, where A ( m+ M) m and E are mass and energy of the neutron n and M - mass of the nucleus. For isotropic n - A scattering, energy E is A distributed uniformely from 0 to E (max) and A therefore average transferred energy per collision 1 is E. Remaining average energy of the neutron 2 A æ ö 2mM 1 per collision is (E - E ) = E 1 n 2 A n - 2 ç ( m+ M) çè ø After k collisions neutron energy becomes: k æ ö 2mM E = E 1 k 0-2 ç ( m+ M) çè ø Probability of neutron anbsorption per collision is ratio of sabs ( E) stotal ( E ). In thermal energy region s µ 1. abs v n 2 n For thermal total and absorption cross sections see: lengths/list.html Most efficient moderators should have low A (atomic mass) and small abs. Commonly used moderators: LH 2, LD 2, H 2 O, D 2 O, Be, C Thermalization by elastic collisions: æ1 ö eg.. for hydrogen: Ek = E0 ç çè2 ø k - number of el. collisions k

17 Thermalization of neutrons Moderation of neutrons in thick moderators leads to thermalization of neutrons: neutrons share their energy with nuclei in the media by elastic collisions until they reach thermal equilibrium with nuclei of the media (when statistically downscattering = upscattering). The spectrum of velocities for thermalized neutrons is described by Maxwellian distribution with temperature T: Normalized Maxwellian distribution of velocities: n( v ) 4 m 2kT 3 2 v 2 2 mv exp 2kT Thermal beam flux (relative units) T=300K k J K 1 = ev K 1 Some properties of neutron Maxwellian distribution: 2kT Most probable velocity: v m. p T m/sec m 8kT Average velocity: v vm. p T m/sec m 2 mvm. p. 5 Energy corresponding to v m. p. : kt T [ev] 2 Energy distribution can be obtained from: dv n ( v )dv n( v( E )) de o 0 de Non-normalized Maxwellian distribution for neutron energy: E n ( E ) A E exp kt kt mv 2 3 Most probable energy: E m. p. ; Average energy: kt Neutron energy, ev Maxwellian energy distribution of the thermal neutron beam flux Flux ~ n v Energy that maximize the flux density, i.e. max {n(e) v(e)}: E max_flux = kt

html Total bound n scattering cross section for thermal neutrons: 82.

20 CM effect in scattering See NIST thermal neutron X-sections in Elements: Total bound n scattering cross section for thermal neutrons: barns. Compare with particle particle x section at E n =0.025 ev (below): Condensed matter effect

22 UCN Properties of selected materials

Slowing down the neutrons

Slowing down the neutrons Clearly, an obvious way to make a reactor work, and to make use of this characteristic of the 3 U(n,f) cross-section, is to slow down the fast, fission neutrons. This can be accomplished,