12. Reactioins, Fusion, Nucleosynthesis

Question 1

State the equation for the reaction rate per unit time, and define the components of the equation

Answer 1

W = JNσ
J - Flux = n_b v_i where n_b is the number density of the particles in the incoming beam, v_i is the velocity of the beam
N - Number of nuclei in the target illuminated by beam
σ - Mean cross section

Question 2

What is the motion of the target particle in nuclear physics

Answer 2

Always stationary

Consider non-relativistic mechanics

Question 3

What are the two classes of reactions

Answer 3

Direct reactions and compound nuclear reactions

Question 4

What is a direct reaction?

Answer 4

Occurs on a short time scale of 10^-22s

- Time in which the projectile passes the target nucleus

Question 5

What is a nuclear compound reaction?

Answer 5

Longer timescale

- Projectile absorbed and a compound nucleus is created which later decays

Question 6

What are the four types of direct reactions?

Answer 6

1. Elastic
2. Inelastic
3. Pick up
4. Stripping

Question 7

State all the properties of an elastic direct reaction

Answer 7

a + A -> a + A

Target and projectile remain the same, just exchange of energy and momenta

Question 8

State all the properties of an inelastic direct reaction

Answer 8

a + A -> a + A*

Target nucleus is excited, but remains as the same nuclide

Question 9

State all the properties of an pick up direct reaction

Answer 9

A1 a + A2 A -> (A1 + n) b + (A2 - n) B

- Projectile picks up one or more target nucleons

Question 10

State all the properties of an stripping direct reaction

Answer 10

A1 a + A2 A -> (A1 - n) b + (A2 + n) B

- Projectile loses one or more nucleons to the target

Question 11

Describe the graph of cross-section neutron energy for neutron absorption

Answer 11

• Low energy, X-sec falls as 1/v
• Then get resonance peaks reflecting shell structure of nucleus with decreasing amplitude
• At high energy, slow smooth decrease

Question 12

State the equation for the PP chain

Answer 12

H + H -> 2H + e+ + electron neutrino + 0.42MeV
H + 2H -> 3He + photon + 5.49 MeV
3He 3He -> 4He + 2H + 12.86MeV

Question 13

What type of temperature do we need for fusion, and what is the biggest problem with this?

Answer 13

Need to heat plasma to 10^7 - 10^8 K

- Difficult to confine

Question 14

State the total released energy in the PP chain, and how much of it is carried away?

Answer 14

Used 4 protons to produce 1 He
E = 24.68 + 2.04 (Annihilation)
0.26 MeV carried away

Question 15

What is another process for fusion?

Answer 15

CNO
Again 4p fuse to 4He with the same energy budget
12C acts as a catalyst of the reaction

Question 16

How does fusion occur in the sun when the energy needed to overcome V_c is 10^10K?

Answer 16

Sun temp is 10^7K. Quantum tunneling due to the large size of the sun

Question 17

Describe and explain the cross section energy graph for fusion in our sun

Answer 17

Bell curve centered about E_0, FWHM = E_0
- At low E(velocity), fusion cross section is too small to contribute
- Large energy there are too few nuclei pairs to contribute significantly
Middle part contributes to fusion.

Question 18

When does nuclear burning continue until, and why?

Answer 18

Until Iron (A = 56) as it is the peak BE/nucleon

Question 19

Why do we need a different mechanism to go beyond A = 56 to form heavier nuclei, and what is this mechanism?

Answer 19

As when we increase A, we are now decreasing the binding energy per nucleon

• Not energetically favourable
• Need neutron or proton capture from a large flux of particles which is typically available in exploding stars

Question 20

What are the two types of neutron capture?

Answer 20

The s process and the r process

Question 21

Describe the neutron capture s process

Answer 21

When neutron capture is slow compared to beta decay, so the atomic number increases

Question 22

Describe the neutron capture r process

Answer 22

When neutron capture is fastcompared to beta decay, so we get an increase in the mass number while the atomic number stays the same