Splitting pattern of equivalent spins.

Ampl = equivsplit(I,n)

Computes the line intensity pattern of an EPR spectrum due to an electron spin-1/2 coupled to n equivalent nuclear spins with quantum number I. First-order perturbations are assumed.

Five spins-1/2 give a first-order splitting pattern given by

Ampl = equivsplit(1/2,5)

Ampl =
     1     5    10    10     5     1

The 5 spins-1/2 give rise to 6 lines with intensity ratio 1:5:10:10:5:1.

5 spins-1/2 give rise to a first-order splitting pattern Ampl = [1 5 10 10 5 1] according to the Pascal triangle

               1              0 spins
             1   1            1 spin-1/2
           1   2   1          2 spins-1/2
         1   3   3   1        3 spins-1/2
       1   4   6   4   1      4 spins-1/2
     1   5  10  10   5   1    5 spins-1/2

Any number in a given column is the sum of its two closest neighbors in the preceding row.

For spin with S>1/2, a generalized Pascal triangle is used. E.g. for spin-1

             1                0 spins
          1  1  1             1 spin-1
       1  2  3  2  1          2 spins-1
    1  3  6  7  6  3  1       3 spins-1

In general, for a spin S, any number in a given column is the sum of its 2S+1 closest neighbors in the preceding row.

The splitting pattern is calculated by (n-1)-fold convolution of a (2I+1)-element vector of ones.

equivcouple, garlic