Nuclear Physics
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[edit] Units and Conventions
We shall use natural units. So, we shall choose 
where
is the Plank's constant and c is the velocity of light.
Because the product of length and momentum has dimensions of ,
the units of length and momentum are inverse of each other. Similarly
length/time has dimensions of velocity and therefore the units of
length and time are same. Einstein's mass energy relation is E = mc2
and the energy-momentum relation is 
. These relations
imply that the units of energy, momentum and mass are same. The angular
momentum has same dimensions as the Plank's constant so it is
dimensionless. The dimensions of all the physical quantities in
natural units can be fixed using such arguments.
The natural length scale in nuclear physics is set by the typical size
of nuclei. It is chosen to be 1fm = 10 − 13cm. The unit of time
can be chosen to be same. In cgs units 1fm of time is 
. The energy, momentum and mass can
then be measured in inverse fm. Alternatively, we can choose to
measure energy, momentum and mass in units of MeV, which is a typical
energy scale in nuclear physics. Then the length and time is measured
in inverse MeV. The product of and c has the dimension of
energy times time and its value is 197.3 MeV fm. We can use this fact
to convert energy units into length units. That is, 197.3MeV = 1fm − 1. For back-of-the envelop calculations we can take 200MeVfm = 1. This introduces an error of about a percent in the calculations.
