Deals with various models of nuclie

1. Presented by:
Syedah Noorul sabah
Nuclear
models
Presented by :
Syedah Noorul Sabah

2. Nuclear models can be classified into two main groups.
a) Strong-interaction, or statistical models,
b) Independent- particle models,
Strong -interaction model or statistical model : This model is based on the
assumption that the protons and neutrons are mutually coupled to each other and
behave cooperatively in a way that reflects the short-ranged strong nuclear force
between them. Examples : Liquid Drop model and Compound Nucleus Model.
Independent -particle Model : This model is based upon main assumption that
there is little or no interaction between the individual particles that
constitute nuclei; each proton and neutron moves in its own orbit and behaves as if
the other nuclear particles were passive participants.

3. Examples: Nuclear Shell Model and its variations.
Other nuclear models:
a) Collective Model
b) Optical Model
Collective Model put forwarded by Aage Bohr (son of Neils Bohr),
incorporate aspects of both groups, that is ,it is a combination of the shell
model and the liquid-drop model.
Optical Model In this model nucleus is assumed as a medium having
complex refractive index.

4. Liquid Drop Model
This model was first proposed by George Gamow along with Weizsacher in
1935 who have recognized some experimental evidences and found
resemblance of nucleus with a liquid drop and then developed by Niels
Bohr and John Wheeler later on.
The liquid drop model treats the nucleus as a drop of incompressible nuclear
fluid of very high density.

5. ● Like the molecules in a drop of liquid, the nucleons are imagined to interact strongly
with each other with almost same force.
fn-n ~fn-p ~ fp-p
● Just like liquid molecules can collide with each other due to thermal agitation like wise
nucleons collide frequently with each other in the nuclear interior, its mean free path as
it moves about is substantially less than the nuclear radius.
● The liquid drop is assumed as incompressible meaning its density can’t be changed
similar is the case for nucleus also where the density of the nucleus is constant for all
the nuclei.
● The liquid drop is spherical because of surface tension similarly the nucleus is spherical
because of the strong nuclear force.
● Heat of vaporization in liquid is comparable to binding energy of the nucleons in a
nucleus.

6. ● Evaporation of a liquid drop corresponds to radioactive emission from a
radioactive isotope.
● Surface tension in the liquid arises from the fact that surface molecules in a drop
are not so tightly bound as are the molecules in the interior. There is evidence to
show that is so in the case of nucleons present in a nucleus as well.
● In a liquid drop , molecules are influenced by only by those which lie in
immediate neighbourhood. This means that intermolecular forces are short
range forces only. The same is the case in a nucleus. The nucleon -nucleon
forces operate within short ranges only.
● A nucleus may capture high energy particle to form compound nucleus in a
similar manner as liquid drop may get excited , the excess of energy of captured
particle being shared by all the particles of the nucleus or the drop.

7. Modes of de-excitation in compound nucleus and
liquid drop
Compound Nucleus Liquid Drop
By emission of radiation By Cooling
By emission of a nucleon By Evaporation
By Nuclear fission By breaking into droplets
Just as two liquid drops may undergo fusion to form a bigger drop , similarly two
light nuclie may undergo fusion to form a bigger nucleus.
As the model justifies the similarities between a liquid drop and a nucleus one can
then construct a semiempirical model (half theory/half data) also known as Bethe-
Weizacker Semi-empirical Mass Formula to account for the total nuclear binding
energy, the most basic of nuclear properties. The values are in good agreement with
experimental data.

8. Bethe-Weisacker’s SEMF:
where, av = 14.1 MeV, as = 13.0 MeV, ac = 0.595 MeV, aa = 19.0 MeV, ap =
33.5 MeV.

9. Explanation of Nuclear fission on the basis of liquid
Drop Model
We know that the atomic nucleus behaves like the
molecules in a drop of liquid. But in this nuclear
scale, the fluid is made of nucleons (protons and
neutrons), which are held together by the strong
nuclear force. The interior nucleons are completely
surrounded by other attracting nucleons just like
molecules did in case of a liquid drop. In the ground
state the nucleus is spherical. If the sufficient kinetic
or binding energy is added, this spherical nucleus
may be distorted into a dumbbell shape and due to
positive charge repulsion on the two ends splits into
two fragments hence, forming two daughter nuclei.
This process is what we call nuclear fission.

10. Achievements of this model
1. It predicts the atomic masses and binding energies of various
nuclei to a larger accuracy.
2. It predicts emission of alpha and beta particles in
radioactivity.
3. The theory of compound nucleus, which is based on this
model, explains the basic features of the nuclear fission process.

11. Failures of this model
1. It fails to explain the extra stability of certain nuclei, with the
numbers of protons or neutrons are 2, 8, 20, 28, 50, 82 or 126 etc
2. It fails to explain the measured magnetic moments of many
nuclei.
3. It also fails to explain the spin and parity of nuclei.
4. It is also not successful in explaining the excited states in most
of the nuclei.