Before the lab. exercise you should read the following parts in the Krane textbook (K.S. Krane, Introductory Nuclear Physics).

- Angular Momentum and Parity Selection Rules for Decay (Krane, chapter 9.4)
- Angular Momentum and Parity Selection Rules for Decay (Krane, chapter 10.4)
- Internal Conversion (Krane, chapter 10.6)
- Auger Effect (Any textbook in Atomic Physics, for example: Ch. 18.7 in Haken & Wolf, The Physics of Atoms and Quanta.)
- Semiconductor Detectors (Krane, chapter 7.4)

The general expression for the change in energy per distance, , for a charged particle slowing down in a material is called Bethe-Blochs formula and is given by:

(1) |

- is the electron charge
- is the permeability in vacuum
- is the incoming particle's charge in
- is the density of the material
- is the electron mass
- is the shell correction parameter
- is the speed of light
- is for the incoming particle
- is the molar mass of the material
- is the mean excitation potential
- is a density correction term

Note that is proportionated to . This means for example that an alpha particle will stop much faster compared to a proton in a given material.

Apart from the inelastic scattering against other electrons, another
mechanism will also be important, namely emission of Bremsstrahlung.
This emission of electromagnetic radiation is due to the deceleration
of the electrons when they enter the material. The cross section
for Bremsstrahlung is dependent on the mass as:

(2) |

- Photo absorption
- Compton scattering
- Pair production

To find information about the different states of a nucleus we study the transitions between the states. A transition from one state to a energetically lower state will result in the emission of energy from the nucleus. This energy is usually emitted in the form of a photon, but the nucleus can also interact with the electrons of its atom to release the excess energy.

A photon emitted from a nucleus will have an energy corresponding to the difference in energy between the initial and final state of the nucleus. The multipolarity of the photon corresponds to the angular momentum that the photon carries away from the nucleus. If we know the spin and parity of one of the states, we can learn something about the spin and parity of the other state by measuring the multipolarity of the emitted photon.

The multipolarity of a nuclear transition can be measured in various ways. One striking difference between different multipolarities is the angular intensity distribution of the radiation. The distribution is given by the Legendre polynomials of the corresponding order. The distribution of the radiation for one transition will only give us information about the order of the transition, it is not possible to see if the transition is magnetic or electric. To do this we also need to measure the polarisation of the radiation.

To get an non-isotropic intensity distribution, the magnetic sub-levels must be unevenly populated. Assuming, see figure 1 that an I=1 state is de-excited into an I=0 state, we have three possible transitions corresponding to the three magnetic sublevels for I=1. Each transition have a different m, and therefore a different angular intensity distribution. The problem is that is is not trivial to separate the three transitions. We can split up the levels by applying an external magnetic field, but even a very large field will not make it possible to separate the transitions with a normal -ray detector. We will therefore see a sum of the three angular distributions, and if the sub-levels are evenly populated the sum will be isotropic. One way to solve the problem is to lower the temperature of the source so that the Boltzmann distribution will give an uneven distribution of the population of the sub-levels. To do this, the temperature must be as low as about 0.01 K.

We see that there are several difficulties in using the intensity distribution for measuring the multipolarity of a nuclear transition. There are however other ways of solving these difficulties, like using so-called angular correlation measurements (Krane, ch. 10.4).

In this laboration we will use another technique to measure the
multipolarity of a transition. This method does not depend on
the angular intensity distribution of the radiation.
Instead, we use the fact that
the the relative intensity of internal conversion
depend on the multipolarity of the transition (the intensity
does also depend on other factors, see Krane, page 346).
By measuring the internal
conversion intensity, we can therefore deduce the multipolarity of the
transition.

(3) |

(4) |

Another problem is that we must compensate for the efficiency
of the detector. This efficiency is energy dependent, so an
efficiency curve can be plotted by measuring the intensities
of some -ray peaks for a number of calibration sources. Using
the efficiency curve, the ratio between the detector efficiencies
for the X-rays and -rays of interest can be measured as:

(5) |

By combining the relations above we can now calculate .
Diagrams that relate to energy and multi-polarity can be
found in the laboratory.
From this multi-polarity we can conclude the spin and parity
for the 662 keV state of Ba by using the selection rules.

- What is internal conversion?
- How is the internal conversion coefficient defined?
- What parameters does it depend on?
- What is the meaning of the multipolarity of a electro-magnetic transition?
- What selection rules are valid for the electro-magnetic transitions?
- Why can there be no M0-transitions?
- How can a E0-transition be realised?
- How does the germanium detector work?
- What is limiting the speed of the germanium detector?
- Why is an alpha-particle stopped faster that a proton when entering materials?
- Electrons are different from the other charged particles when it comes to detection methods. In what way?
- What is the big advantage of the germanium detector over the NaI detector?
- Does the NaI detector have any advantage over the germanium detector?
- What kind of statistics determine both the radioactive decay and the detection process?
- What can be read from the so-called Bragg curve?
- What is a single-escape peak and what is a double-escape peak?

Appendix A

Appendix B

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