AHL Nuclear radius

  2. Atomic, nuclear and particles
  3. Nuclear physics
  4. AHL Nuclear radius
    5. 10'

The structure of matter can be investigated using scattering experiments, both of whole nuclei and of electrons.

Knowledge of the radius of one nuclear isotope can be used to calculate the radius of any other.

Key Concepts

There are two techniques to measure the radius of a nucleus.

Rutherford scattering

The Rutherford scattering experiment can be used to determine the radius of a nucleus.

As the angle is increased from the initial beam direction, the number of alpha particles decreases. This is due to the repulsive elecric forces between the alpha particles and the nucleus, which increases in magnitude with shorter distances. The scattering distribution can be predicted by an equation devised by Rutherford (not required for the course).

In high energy scattering experiments, the alpha particles move close enough to the nucleus to be within the range of the strong nuclear force. This means that the scattering distribution is affected. The point at which the Rutherford scattering equation no longer applies can be used to find the effective nuclear radius. 

Eisberg, R. M. and Porter, C. E., Rev. Mod. Phys. 33, 190 (1961)

Eisberg, R. M. and Porter, C. E., Rev. Mod. Phys. 33, 190 (1961)

 

Electron diffraction

An alternative method for finding the nuclear radius uses the diffraction of electrons and the angle of the first minimum intensity in the scattering pattern:

  • Electrons may interact with matter as a wave when the nucleus is comparable in size to the de Broglie wavelength (Wave particle duality)
  • The diffraction pattern around a spherical object leads to an approximate equation for the angle of the first minimum intensity in the scattering pattern: \(\sin\theta\approx{\lambda\over D}\), where \(D\) is the nuclear diameter. The small angle approximation is usually not appropriate.

Electron microscopes are more effective than optical microscopes for imaging small objects due to the small wavelengths that can be achieved.

 

The strong nuclear force is short range; unlike gravitation, the magnitude of force does not vary as an inverse square law. Nuclear density is approximately the same for all nuclei. The consequence is that the radius of any nucleus is related only to the number of nucleons:

\(R=R_0A^{1\over 3}\)

  • \(R\) is the radius of a nucleus (m)
  • \(R_0\) is a constant (m)
  • \(A\) is the number of nucleons

The only macroscopic objects with the same density as nuclei are neutron stars.

 

Essentials

Nuclear energy levels

Just like electrons, the nucleus has energy levels for different excited states. Experimental evidence for these nuclear energy levels is the specific energies of gamma photons during radioactive decay.

 

Neutrino

The neutrino is a fundemental particle in the lepton family. Electron neutrinos (\(\nu_e\)), muon neutrinos (\(\nu_\mu\)) and tau neutrinos (\(\nu_\tau\)) are affected by the weak nuclear force. Their mass and charge are zero (thus, their interactions with matter are limited) and their spin is \(1\over 2\). Neutrinos also have antiparticles, antineutrinos.

Neutrinos were discovered when beta particle energies were measured following \(\beta^-\) decay. The particles had a range of energies, which should not have been the case for just one particle from a nucleus.

Instead, the neutrino was consuming some of the energy, but was undetected in isolation.

 

 

 

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