Liquid Drop Model
Liquid Drop Model of Nuclear Binding Energy

The most important concept in physics is that of energy. It governs and limits the transformation of all physical systems including nuclei. The first theory of nuclear energy was the liquid drop model proposed in the 1930's. The famous liquid-drop formula for nuclear binding energies is
B = av A + as A2/3 + aa |N-Z|2/A + ac Z2/A1/3 + ap (mod(N,2)+mod(Z,2)-1)/A1/2
where A is the number of nucleons in the nucleus, Z is the number of protons, and N=A-Z is the number of neutrons. The five terms are known as the volume,surface,symmetry,Coulomb,and pairing energies,respectively. The parameters in the formula are usually determined by a least squares fit to known binding energies. This web site allows you to modify the formula and make your own fit. You can also fit neutron and proton separation energies instead of the total binding energies. The results screen gives you the option to download the entire table and your fit. Before you make any changes, try the fit using the default settings. The rms error in the binding energy should come out to 2.82 MeV. The most poorly fit nucleus should come out to be (Z,N,A) = (50,82,132). The formula can be modified in several ways. Often Z2 in the Coulomb term is replaced by Z(Z-1). Another functional change is to replace |N-Z|2/4 in the asymmetry term by the expression T(T+1) where T=|N-Z|.

-----------------------------------------------------------------------------

1. Energy to fit:

Binding Energy B(Z,A); or Neutron Separation Energy; or Proton Seperation Energy

2. Experimental data to be fit


All nuclei in mass table
Only nuclei with even N and Z
Other selection

3. Terms to include in the Liquid Drop Formula


Standard Terms:

av volume; as surface

ac Coulomb: -Z**2.0/A**(1.0/3.0) or -Z*(Z-1.0)/A**(1.0/3.0)

aa symmetry: -(N-Z)**2.0/(1.0*A) or -4.0*T*(T+1)/A   Danielewicz's parameterization

ap pairing: (mod(N,2)+mod(Z,2)-1) * A**(-1/2.) other:

User Specified terms (one or two): new1: ; new2:

Shell effects?

4. Select fitting method

1. Least-square Fit
2. Minimax Fit

-------------------------------------------------------------
April 2012--version 1.3
Produced by G.F. Bertsch: bertsch@uw.edu
With credits to M. Uusnakki, A. Bulgac, A. Luo, S. Reddy, and A. Steiner