This document discusses the liquid drop model of nuclear structure. It describes the liquid drop model as treating the nucleus like a drop of incompressible liquid with short-range nuclear forces between nucleons. The liquid drop model uses a semi-empirical mass formula to predict nuclear binding energies based on volume, surface tension, Coulomb repulsion, and other terms. It provides coefficients that were fitted to experimental nuclear binding energy data and can estimate energies for many stable and unstable nuclei.

1. NUCLEAR MODELS
CHAPTER 2

2. 2.1 The Liquid Drop Model
◦ Nucleus - statistical assembly of
neutrons and protons with an effective
surface tension - similar to a drop of
liquid.
◦ Explain the spherical shape of most
nuclei.
◦ Predict the binding energy of nucleus.
◦ Nucleons interacting – make frequent
collision with one another.
◦ Similar with movement of thermally
agitated molecules in liquid.

3. ◦ Rationale;
◦ Volume of nucleus ∝ number of nucleons
◦ Nuclear matter is incompressible
◦ Binding energy of nucleus ∝ number of nucleons
◦ Nuclear force must have a saturation character, i.e each nucleon only interacts
with nearest neighbors
◦ Binding energy = Volume energy + Surface energy + Coulomb energy

4. ◦ Semi-empirical mass formula – apply to atomic masses.
◦ Atomic mass M(Z,A) – sum of 6 terms.
1. Mass of the constituent nucleons and electrons;
2. Volume term;
3. Surface term;
Strong nuclear force – short range
Strong nuclear force – short range
Independent of nucleus’s size
Overestimate the nuclear force
Correct the volume term
Proportional to surface area
Decrease the binding energy

5. 4. Coulomb term;
5. Asymmetry term;
6. Pairing term;
Coulomb energy of charged nucleus
– protons repel each other
Due to Pauli principle
There are no stable nuclei with very
large neutron/proton excesses
Observed tendency for nuclei to have
Z=N
Maximizes binding when Z and N is
even
f5
(A)= -f(A); Z & N even
f5
(A)=0 ; Z even, N odd or Z odd, N even
f5
(A)= f(A); Z & N odd

6. ◦ To remember the term - notation VSCAP;
Binding energy
◦ a1
= av
= 15.56 MeV/c2
◦ a2
= as
= 17.23 MeV/c2
◦ a3
= ac
= 0.697 MeV/c2
◦ a4
= aa
= 93.14 MeV/c2
◦ a5
= ap
= 12.0 MeV/c2
One commonly used value

7. The data fitting remarkably
good, but not exact
Gives accurate values for some
200 stable and many more
unstable nuclei.

8. ◦ Contribution of each term to binding energy per nucleon;
Volume term increases
the ΔEbe
, the other term
reduce ΔEbe
Curve total SEMF – Binding
energy after all terms
have been considered

9. Where En
= Energy needed to remove a neutron from a nucleus,
Ep
= Energy needed to remove a proton from a nucleus
◦ To remove a neutron,
◦ To remove a proton,
ΔEbe
≠ En
≠ Ep

10. Example
◦

11. ◦

12. Solution
◦

13. Exercises
◦

14. DEC 2019 (Q1.c)
Ans : 519.83 MeV

15. DEC 2019 (Q1.d)
JUN 2019

16. JUN 2018 (Q2.b)
DEC 2016 (Q1.d)

17. JUN 2016 (Q1.c)
JUN 2015 (Q1.b)

18. JUN 2015 (Q1)