8. The Nuclear Force Flashcards
What does the deuteron consist of?
1 proton and 1 neutron
What is the electric charge of the deuteron?
+1e
What is the nuclear spin of the deuteron?
I = 1
What is the observed magnetic dipole moment of the deuteron?
µ = 0.857 µ_N
What parity does the deuteron have?
Even parity (π = 1)
What is the binding energy of the deuteron?
B = 2.224 MeV
Does the deuteron have excited states?
No
What does the deuteron spin quantum number represent?
The total angular momentum of the nucleus
Give the equation for the total angular momentum of a nucleus
Describe the vector diagram that can be used to represent the total angular momentum
What are the allowed values of spin for a deuteron?
s = 1 or s = 0
What are the allowed values of total angular momentum, I, for a deuteron?
I must ultimately equal 1
Describe the s = 0 case for the total angular momentum of a deuteron
There is only one combination in this case.
Describe the s = 1 case for the total angular momentum of a deuteron (if ℓ = 0)
Describe the s = 1 case for the total angular momentum of a deuteron (if ℓ = 1)
Describe the s = 1 case for the total angular momentum of a deuteron (if ℓ = 2)
Give the equation for the parity of a 2 particle (proton and neutron) system
State the observed parity of the deuteron, proton, and neutron
Deuteron: +1
Proton: +1
Neutron: +1
These are all even
Which deuteron spin states are allowed based on the parity of a 2 particle system?
ℓ must be EVEN so any ℓ = 1 states can be excluded.
The ℓ = 0, s = 1 and the ℓ = 2, s = 1 states are allowed.
Based on the observed magnetic moment of deuteron, how much time does it spend in the s = 1, ℓ = 0 and s = 1, ℓ = 2 states?
ℓ = 0: 96%
ℓ = 2: 4%
Describe the strength of the strong nuclear force
Strong: ~100x stronger than electromagnetic interactions
Describe the range of the strong nuclear force
Short range: cuts off at ~ 2 fm
Describe the direction of the strong nuclear force
Attractive but with a repulsive core at very short distances
Is the strong nuclear force charge dependent?
No
Is the strong nuclear force spin dependent?
Yes
What model is used to describe the nuclear potential of a deuteron?
A 3D square well model of radius, R, and depth, V0.
r = distance between the proton and neutron
Does the square well model of the deuteron have a Coulomb barrier?
No since there is only a proton and a neutron.
State the time-independent Schrödinger equation for a particle with mass, m, in a potential, V(r)
State the time-independent Schrödinger equation for a particle with mass, m, in a potential, V(r), in spherical polar co-ordinates
What is the radial component of the time-independent Schrodinger equation?
Give the equation for the reduced mass of a two-body system
m = reduced mass
m_n = neutron mass
m_p = proton mass
What is the radial component of the time-independent Schrödinger equation in terms of u(r)?
State the solution to the time-independent Schrödinger equation for the square well model when r < R
Oscillatory solution
B = 0 for ψ(r) to remain finite
State the solution to the time-independent Schrödinger equation for the square well model when r > R
Exponential solution
D = 0 for ψ(r) to remain finite
What is the radius and depth of the square well for a deuteron
R ~ 2.1 fm
V0 ~ 35 MeV
Is deuteron in a tightly bound state?
No, it is only just bound
What is a singlet state?
A state with only one z-component of spin. The spins of the two particles are equal and opposite (i.e. they are antiparallel and the z-component is 0).
Example: The s = 0 state has m_s = 0
What is a triplet state?
A state with three z-components of spin. The spins of the two particles can both be up, both be down, or be equal and opposite.
Example: The s = 1 state has m_s = -1, 0, +1
The spin dependence of the strong nuclear force means that is is _______ when the nuclear spins are anti-parallel.
Weaker
Where is there evidence for the spin-dependence of the nuclear force?
In the scattering of neutrons incident on proton targets.
The theoretical calculation of the overall cross section only matches experimental data when both the triplet and singlet states are considered with the appropriate probability for each.
Give the equation for the overall cross section of proton-neutron scattering
σ_T = overall cross section
σ_triplet = triplet cross section
σ_singlet = singlet cross section
What is the overall cross section for proton-neutron scattering?
20.4 b
What are exchange particles?
Virtual particles that carry discrete quanta of information. For spin 1/2 nucleons to interact, the exchange particles must have integer spin (0 or 1) and a charge of -1e, 0, +1e.
What is a virtual particle?
One that only exists for a short period of time, ∆t. During this time they ‘borrow energy’ from the vacuum according to the constraints of the Heisenberg Uncertainty Principle (∆E∆t ~ℏ).
Give the equation for the rest mass energy of an exchange particle
m_ex = exchange particle mass
c = speed of light
R = range
Give the example of a type of exchange particle
Pions: they have spin 0 and come in three varieties (π+, π0, π-).
Describe the three types of nucleon-nucleon interaction (pion exchange)
