I've held off on getting involved in this as long as I could,
but you are so definitive in your comment.  I could make the
same argument that the unit of electron density is "1" because,
after all, the volume is just the count of the number of Å^3 and
a count is not a unit.  In fact, as Dr. Holton pointed out,
every unit is just a count of something, length is the count of
wavelengths of a particular beam of light, mass is the number
of blocks of metal from Paris that total to the same mass, etc.

   We put units in our discussion of numbers because it aids in
our ability to communicate meaning to one another.  Yes, electrons
are like apples and are simply counts, but we have the old saying
that you can't add apples and oranges, which means you have to
keep track of which numbers are counts of apples and which are
counts of oranges.  Where this different is important it is
convenient to label the counts with a note as to the appleness
or orangeness of each number.

   For maps it is important for people to know if their map is
in e/Å^3 or sigma/Å^3.  Both maps are commonly encountered in
this field and both are called electron density maps.  I could
put a note on my home page stating that whenever I talk about
a map I give numbers in e/Å^3 but it is more convenient for the
reader if I just put the convention next to the number.

   You have a subset of quantities that you use as labels (I'm
guessing cm, sec, Kg and others.).  I find it convenient to
use additional labels when certain quantities arise in my work. It
isn't a matter of you being right and me being wrong or the other
way around.  The only logically consistent solution is to have
no units at all, and that would be terribly confusing to everyone.

Dale Tronrud

[email protected] wrote:
> I fully agree with Ian and would again point to the authoritative
> documentation :
> 
> http://www.bipm.org/en/si/derived_units/2-2-3.html
> 
> The quantities f^0, f' and f" are unitless, i.e. simply numbers (or
> rather: their unit is the number one, which is usually omitted).
> 
> The unit of the electron density is really just 1/Å^3. To see this,
> consider that the electron density is defined to be
> 
> \rho = (Number of electrons)/volume
> 
> The numerator is simply a count, and thus unitless (or rather: its unit
> is the number one).
> 
> In practice, we like to a remind ourselves that these values refer to
> electrons and therefore like to think of e/Å^3 as the unit of electron
> density, but this is somewhat incoherent, if not incorrect. The fact
> that we are dealing with electrons (as opposed to apples) is contained
> in the definition of the quantity "electron density". It does not need
> to be explicitly specified in the unit.
> 
> 
> Marc
> 
> 
> 
> 
> Quoting Bernhard Rupp <[email protected]>:
> 
>> <NOTATION>
>> Notation
>> ========
>>
>> f0: atomic scattering factor for normal scattering, defined as the ratio
>> of scattered amplitude to that for a free electron.
>> </NOTATION>
>>
>> ----------------------------------------------------------------------
>> Hmmm...where does the 'electron' in electron density then come from after
>> integration/summation over the structure factors?
>> ----------------------------------------------------------------------
>>
>> BR
>>

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