# Lesson 6 - General specifications of radiation sources

## Types of sources

In this course, we will be working with four spatial layouts of sources.  In this lesson, we want to introduce them and get a little practice in converting from one type to the other.  The four are

1. Point sources,
2. Line sources,
3. Area (or surface) sources,
4. Volumetric sources,

NOTE: Notice that I have simplified the notation somewhat from the book, taking out the spatial and angular dependence.  This is because we will be dealing almost exclusively with uniform, isotropic sources.

### Point sources,

These are sources that denote particles that are spontaneously emitted from a single point, with no physical source modeled:

This is a mathematical simplification, of course, of a physical source.  The book gives two general requirements for assuming this:

1. Volume of physical source sufficiently small in comparison with the dimensions between source and detector; and
2. Negligible interaction of radiation with the matter in the source volume.

and then states that Requirement 2 can be relaxed if source characteristics are modified to account for source self-absorption.  This relaxation is generally made by performing a stand-alone calculation of a physical source, carefully collecting information about the number and energy profile of particles (of all types) that escape the source, and then attributing the escaping particles to the mathematical point source in a subsequent calculation.

This allows the analyst to model the effects of the source without having to model the source material in the calculation.

### Line sources,

The line source, which has the addition dimension "per unit length," is a similar mathematical simplification of a physical source, but one in which all dimensions but one of the physical source are small in comparison with the dimensions between source and detector.  In other words, it is long and skinny ("pencil-like").  We call the dimension we keep the "length", L:

Notice that a differential length of the source emits , therefore acts like a small point source.   The total particle emission rate from the line sources is .

NOTE:  If one is given a line source and -- either because you think the length is really not significant or just to be conservative in your analysis or just to get an approximate answer to save time -- you can reduce the line source to a point source with this strength.  (You would probably want to locate the point source at the midpoint of the line.)

### Area (or surface) sources,

The analogy continues with the area source.  If two dimensions cannot be ignored, we model the source as a flat source and the dimension has a "per unit area" in it.  A differential area on the surface, then, acts like a mini-point-source, and the total particle emission rate from the area source becomes .

Example:  In two dimensions, we have an additional possibility for reducing the complexity of the source. For example, as the detector gets further away from the surface, the analysis might first decide that the W dimension is no longer significant but the L dimension is still significant; therefore, the analyst might approximate the area source as a line source of length L (located, in the figure, vertically centered left and right) with a strength

.

Then, as the detector is withdrawn further and the analyst considers the L dimension to be insignificant as well, the source might become a point source located at the center of the originalsurface, with strength

.

### Volumetric sources,

The final, and most general, form of the source that we will use is a full three dimensional source, where all three spatial dimensions are significant.  As an example, consider as a parallelepiped (i.e., block) shaped source:

A volumetric source can also be reduced to the previous, simpler forms: area source, line source, and point source.  The exercise at the end of the lesson will give you practice doing this.

## Curie vs. Becquerel

The standard, preferred unit of activity is the  Becquerel (Bq), which is 1 disintegration/sec.  Us old guys still use the Curie (Ci), which is .  You are caught in the middle and have to know both.

## Activity vs. particle production rate

Be sure to recognize the difference between these two.  Sources are often specified in terms of the disintegration rate of decaying isotopes; it is up to the analyst to figure out the resulting particle source rate.

Appendix H in the book gives gamma and x-ray emission information for selected radionuclides.  This can be useful.

Example:  What would be the source terms associated with a 2 cm radius by 5 cm high cylindrical source of 90-day-old ruthenium-103 labeled as having an activity 0.1 microcurie on a date 90 days ago?

Answer: From the Appendix H data, the half-life of Ru103 is 36.4 days, which gives us a decay constant of:

The current activity will be:

Since Ru-103 decays with release of a 497.1 keV photon 90.9% of the time and a 610.3 keV photon 5.73% of the time, the associated total gamma production rate would be:

This would be the appropriate source strength if the source is represented as a point source.

If the 62.83 cc volume of the source is modeled in the problem, then the appropriate volumetric source terms are:

and