# Properties of nuclear force - What are Nuclear forces - eSaral

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## What are Nuclear forces?

The strong forces of attraction which firmly hold the nucleons in the small nucleus and account for the stability of the nucleus are called nuclear forces.

## Properties of Nuclear Forces

### The nuclear force is a short-range force.

1. They are appreciable when the distance between nucleons is of the order of $2.2 \times 10^{-15} \mathrm{~m}$
2. They become negligible when the distance between nucleons is greater than $4.2 \times 10^{-15} \mathrm{~m}$
3. When the distance between two nucleons is less than $1 \times 10^{-15}$ m the nuclear forces become strongly repulsive

### Nuclear forces are charge independent

The force between a pair of protons, a pair of neutrons, and a pair of neutrons and protons are equal.

$F(n-n)=F(p-p)=F(n-p)$

The net force between pair of neutrons and a pair of neutron and proton is equal. This is slightly greater than the force between pair of protons because force between protons is reduced due to electrostatic repulsion

Net force F (n — n) = Net force F(n — p) > Net force F (p — p)

### Nuclear forces are spin dependent

1. The nuclear force depends on the relative orientation of spins between two interacting nucleons
2. The force of attraction between two nucleons with parallel spin is greater than the force between nucleons with antiparallel spin.
3. Deutron is formed in a bound state only if spins of neutron and proton are parallel.

### Nuclear forces show saturation property

1. The nucleon in the nucleus interacts with its nearest neighbor only.
2. It remains unaffected by the presence of other surrounding nucleons.
3. The nuclear force between a pair of nucleons in light and a heavy nucleus is equal.

### Nuclear forces are non-central forces

1. They do not act along line joining the center of two nucleons
2. The non-central component depends on the orientation of spins relative to the line joining the center of two nucleons.

### Nuclear forces are exchange forces

1. The nuclear forces originate by exchange of mesons $\left(\pi^{+}, \pi^{\circ}, \pi^{-}\right)$ between the nucleons

2. mass of meson = 0.15 amu = 140 MeV = 280 × mass of electron

3. $p-p$ force $\mathrm{p}+\pi^{\circ} \longleftrightarrow \mathrm{p}$

n – n force $\mathrm{n}+\pi^{\circ} \longleftrightarrow \mathrm{n}$

n – p force $\mathrm{p}+\pi^{-} \longleftrightarrow \mathrm{n}$

$\mathrm{n}+\pi^{+} \longleftrightarrow \mathrm{p}$

4. The theory of exchange forces was given by Yukawa

5. The potential energy of a particle in this force field is given by Yukawa potential $U(r)=U_{0} e^{-r / r_{0}}$ where

$\mathrm{r}_{0}$ & $\mathrm{U}_{0}$ are constants.

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