Week 1 - Introduction, revision and nuclear models

Question 1

Saturation

Answer 1

For medium to large nuclei, the internuclear force felt by each nucleon is constant.

Question 2

From PHYS30121, the nuclear force is found to be?

Answer 2

Charge symmetric, charge independent, spin dependent and displays saturation (in nuclei).

Question 3

What are mirror nuclei?

Answer 3

They are analogue partners of one another with just the number of protons and neutrons interchanged.

Question 4

For a mirror system of two nucleons, explain why there are six possible combinations for s-state systems?

Also explain why two of these states are forbidden.

Answer 4

(s-state so L=0) The possible combinations are: nn, np, pp. Each are these are spin-1/2 fermions so each combination can either couple to S=0 or S=+1. Therefore the are 6 combinations (3x2=6).

Two of the states are forbidden due to Pauli. Cannot have two identical protons or neutrons in the same state. (S=0 nn or pp)

Question 5

How is the charge independence of the strong force formalised?

Answer 5

By assigning a new spin, Isospin, to the nucleon.

Question 6

For any nucleon, what is the value of isospin?

Answer 6

t = 1/2

Question 7

What is the z-projection of isospin for a neutron?

Answer 7

tz = +1/2

Question 8

What is the z-projection of isospin for a proton?

Answer 8

tz = -1/2

Question 9

Two nucleon states have T values of?

What states do these T values signify.

Answer 9

T = 0 or 1.

1 = Triplet state
0 = Singlet state

Question 10

What is the formula for mean-squared radius?

Answer 10

(1)

Question 11

What is the formula for the classical cross section for an interaction of two spheres? define all terms.

Answer 11

(2)

b = impact parameter

R1 = Radius of sphere 1.

R2 = Radius of sphere 2.

Question 12

What is the value of 1 barn in metres squared?

Answer 12

1b = 10 ^ -28 m^2

Question 13

How can the cross section of an interaction be found from the differential cross section?

Answer 13

(3)

Question 14

What is the definition of the differential cross section?

Answer 14

The effective area of the nucleus that scatters a particle into a cone of solid angle d(Omega) in a direction defined by theta and phi.

In the absence of a polarised beam or target, the differential cross section is independent of phi and is just reliant on theta.

Question 15

What is the formula for nuclear radius?

Answer 15

r = r0 * A^1/3

Question 16

What is the formula for coulomb barrier?

Answer 16

Vc = 1.44 (MeV) Z1 * Z2/r (fm)

Question 17

What is the formula for reaction rate?

Answer 17

Rate = n * sigma * phi

n = No. atoms per m^2.

sigma = cross section

phi = Beam current in ions/s.