The mathematical treatment of such states, being long range potential fields, differ from other short range potentials ( for example Yukawa Potential ).
12.
The Coulomb potential of electromagnetism is an example of a Yukawa potential with e & minus; " kmr " equal to 1 everywhere.
13.
The screened 1 / " r " function is often encountered in physics as a screened Coulomb potential, also called a " Yukawa potential ".
14.
:: : : : It might be a good idea to add something about units to Yukawa potential . talk ) 22 : 02, 16 September 2011 ( UTC)
15.
However, the nuclear force acts only over relatively short ranges ( a few nucleon diameters ), since it follows an exponentially decaying Yukawa potential which makes it insignificant at longer distances.
16.
However, the residual strong force has a limited range because it decays quickly with distance ( see Yukawa potential ); thus only nuclei smaller than a certain size can be completely stable.
17.
The pion was first proposed to exist by Yukawa in the 1930s as the primary force carrying boson of the Yukawa Potential in nuclear interactions, and was later observed at nearly the same mass that he originally predicted for it.
18.
Massive fields instead satisfy " �� = m�� where m is a nonzero constant, and the solutions to that look like ? ( r ) " ( 1 / r ) e " mr ( a Yukawa potential ).
19.
An even more convincing calculation is the derivation of Regge trajectories ( and hence eigenvalues ) of the radial Schr�dinger equation with Yukawa potential by both a perturbation method ( with the old l ( l + 1 ) factor ) and independently the derivation by the WKB method ( with Langer replacement )-- in both cases even to higher orders.
20.
On the other hand, if we relax the conditions, and require only that the field everywhere outside a spherically symmetric body is the same as the field from some point mass at the centre ( of any mass ), we allow a new class of solutions given by the Yukawa potential, of which the inverse square law is a special case.
