Exercise 1: Masses and binding energies

The data on binding energies can be found in the file bedata.dat at the github address of the course

a) Write a small program which reads in the proton and neutron numbers and the binding energies and make a plot of all neutron separation energies for the chain of oxygen (O), calcium (Ca), nickel (Ni), tin (Sn) and lead (Pb) isotopes, that is you need to plot $$ S_n= BE(N,Z)-BE(N-1,Z). $$ Comment your results.

b) Include in the same figure(s) the liquid drop model results of Eq. (2.17) of Alex Brown's text, namely $$ BE(N,Z)= \alpha_1A-\alpha_2A^{2/3}-\alpha_3\frac{Z^2}{A^{1/3}}-\alpha_4\frac{(N-Z)^2}{A}, $$ with \( \alpha_1=15.49 \) MeV, \( \alpha_2=17.23 \) MeV, \( \alpha_3=0.697 \) MeV and \( \alpha_4=22.6 \) MeV. Comment your results

c) Make a plot of the binding energies as function of the number of nucleons \( A \) using the data in the file on bindingenergies and the above liquid drop model. Make a figure similar to figure 2.5 of Alex Brown where you set the various parameters \( \alpha_i=0 \). Comment your results.

d) Use the liquid drop model to find the neutron drip lines for Z values up to 120. Analyze then the fluorine isotopes and find, where available the corresponding experimental data, and compare the liquid drop model predicition with experiment. Comment your results. A program example in C++ and the input data file bedata.dat can be found found at the github repository for the course