W14 - Neutron Interactions I/II

Question 1

What is the definition of BE?

Answer 1

Mass defect is positive for all nuclei

If the nucleus could be pulled apart and separated into its constituent protons and neutrons, there would be an increase in mass equal to the mass defect

The equivalent amount of energy, the BE, would need to be expended to carry out this disassembly.

Question 2

Define fissionable materials. Provide examples

Answer 2

Isotopes that are capable of undergoing nuclear fission after capturing either fast (~MeV) or thermal (~0.025eV) neutrons

E.g. U238, Pu240, U235, U233, Pu239, Pu241

Question 3

Define fissile materials, provide examples

Answer 3

Isotopes that are capable of undergoing nuclear fission only after capturing a thermal neutron

E.g. U235, U233, Pu239, Pu241

Question 4

Define Fertile Materials and provide examples

Answer 4

Isotopes that are not fissionable by thermal neutrons but can be converted into fissile isotopes (after neutron absorption and subsequent decay)

E.g. U238, Th232

Question 5

What happens to the fission fragments post fission

Answer 5

Fission fragments (Daughter nuclei):
• highly charged
• High speeds they emerge from fission cause electrons to be ripped from their shells as they encounter surround atoms
• interaction with surround atoms creates ion pairs, which reduces the KE of fragments causing deceleration
• +ve ions and free electrons subsequently reunite, liberating energy in the form of heat
• range is a few microns

Question 6

What happens the non-fission fragments post fission event

Answer 6

Alpha beta particles have much greater ranges than fission fragments

Neutrons, gamma rays, and neutrinos travel in straight lines until making a collision, at which point they’re scattered or absorbed
• straight lines due to zero charge

Neutrons are only scattered from nuclei whereas gamma rays are scattered by nuclei and electrons

(More than 80% of the energy released in fission appears as KE from fission fragments)

Question 7

What is the K and L factors in neutron multiplication?

Answer 7

K (chain reaction multiplier)
“the ration of fission neutrons born in one generation to those born in the prior generation”

L = neutron lifetime
“Neutron emission from fission, progressing/aging through a succession of scattering collisions, and ending with absorption”

Question 8

Derive the neutron multiplication equation

Answer 8

@ t=0 N(0) neutrons
Next generation will have k•N(0)
The i’th generation will have k^i•N(0)

t=i•l where t is time and l is neutron lifetime

Hence the number of neutrons present at N(t) = N(0)•k^(t/l)

x = exp(lnx)

N(t) = N(0)•exp[(t/l)•lnk]

If K is close to 1 —> |k-1| &laquo_space;1 then ln(k) ~~ k-1

Final, N(t) = N(0)•exp[(k-1)*t/l]

Question 9

Why are fission fragments unstable?

Answer 9

High neutron to proton ratio

N/Z increases for larger nuclei (larger A)

Fragments have smaller A but same N/Z ratio hence beta decay and gamma decay

The N/Z ratio for these fragments is much higher than the line of stability

Question 10

Principle fuel types and energy gain (BE/A). How to calculate total BE gain

Answer 10

Th233 - 5.1MeV
U234 - 6.8MeV
U236 - 6.5MeV
U239 - 5.0MeV
Pu240 - 6.7MeV

Reactants(BE/A A) - products(BE/AA)

Question 11

Min and max Z^2/A for spontaneous fission to occur

Answer 11

Min: > 18

Max: < ~66

Upper limit as this would be higher than the coulomb potential and just would exist for a fraction of a second.

Delta M > 0 for a decay to occur

Question 12

What is the roughly timeline for decay heat of a fully running reactor?

Answer 12

1% of max power approx 6hours

0.1% of max power approx 1 month

1600MW reactor
1% = 16MW
0.1% = 1.6MW

Question 13

How does the cross-section for x-ray as a function of Z^2 differ from neutrons?

Answer 13

X-Rays
• cross section increases as Z increases

Neutrons
• varies massively on size of Z

More likely to interact with nuclei of similar size, also more likely to interact if KE lower

Question 14

How to calculate total cross-section, sigma_t and its constituents

Answer 14

Sigma_t = sigma_s + sigma_a

Sigma_s (scattering) = sigma_n (elastic) + sigma_n’ (inelastic)
•inelastic conserves momentum but not KE

Sigma_a (absorption) = sigma_n,Gamma (absorption and remission of a gamma/ capture) + sigma_f (fission cross-section)

Same summations and subscripts apply to macroscopic cross-sections

Question 15

How come neutrons travel far in a material before interacting? Think size of atoms

Answer 15

Size of atom = 10^-8
Size of nucleus = 10^-12

Fraction of the cross-sectional area perpendicular to a neutrons flight path blocked by a single tightly packed layer of atoms would be roughly
(10^-12)2/(10-8)2 = 10^-8 (small probability)