Now that you have determined both aV and aA, we can investigate the effect of the pairing term (aP).

Semi-Empircal Mass Formula

Figure 2 shows the difference between the experimentally measured and theoretically calculated binding energies (last column in Table 2, shown previously), using the current model parameters (from Table 1). If you have optimised aV and aA correctly, the line should be close to zero. (Look at the scale of the y-axis if you change the values of aV and aA)

Table 1: Constants of liquid drop formula (MeV)
Symbol Value
aV
aS 18.3
aC 0.714
aA
aP

3(a) Keeping aV and aA as your optimised parameters (filled in from activities 1 and 2), make sure the pairing term (aP) is set to zero. In Figure 2, you should see a ‘stepping’ effect depending on whether there is an odd or even number of neutrons in the oxygen isotope with masses 13 to 17. This is the effect of the pairing term.

What is the scale of the stepping you see in Figure 2?
keV

3(b) Now try changing the value of aP to see how it affects the 'stepping'? What value of aP minimises this 'stepping'?

3(c) Leave your value for aP in the Table to use it for the next activity.