# Meson theory of nuclear force

In this particular article Meson theory of nuclear force, we are going to discuss the meson theory in detail.In order to explain the existence of nuclear force, Heisenberg in 1932 proposed that there is the fast exchange of electron and positron in between neutron-proton of the nucleus. For example, neutron emits the electron and then it becomes the proton. And thereafter proton absorbs the electron and then becomes the neutron.

As a resulting exchange of electron and positron produces a nuclear force in between the proton-neutron. But the force produced by this type of exchange is found to be very weak (of the order of ≅ 10^-14)in comparison of nuclear force. Hence this proposal fails to explain nuclear force.

Again in 1935 Japanese scientists, Yukawa proposed a meson theory of nuclear force. According to this theory, each nucleon continuously emits and simultaneously absorbs pion particle. The old name of pion particle (π) is pai-meson (π-meson).

## Types of pion

Pion may be of three types;

1. positively charged pion(π^+ or pi plus)
2. negatively charged pion (π^-1 or pi minus)
3. neutral pion(π^0 or pi zero)

If a nucleon exists near another nucleon, then pion emitted by a nucleon may be absorbed by another nearest nucleon.

In this process, momentum is transferred, as a result, nuclear force is generated.

### The exchange of pion between the nucleons

The exchange of pion between the nucleons can be explained as follows-

1. When a proton emits a pi meson, then it is converted into the neutron. If there is another neutron near to the proton, it absorbs the emitted meson and converts into the proton.

p + n→(n + π^+) + n → n + (π^+ + n)→ n + p

2. When a neutron emits a pi minus meson, then it is converted into the proton. If there is another proton near to the neutron, it absorbs the emitted meson and converts into the neutron.

n + p →(p + π^-) + p →  p + (π^- + p) → p + n

3. Exchange of pi zero mesons can also generate nuclear force.

p + p → (p + π^0) + p→ p + (π^0 + p) → p+ p

n + n → (n + π^0) + n → n + (π^0 + n) → n + n

From the exchange theory of meson particle, the presence of repulsive force at the comparatively very short distance and attractive force at the short distance in the nucleus can be explained and this can be understood by the following illustration-

#### Example

Let us consider two boys are exchanging balls. If the exchange of balls takes place by throwing balls towards one another, then the momentum of the ball is transferred towards the boys. And this would generate the repulsive force. If the same boy snatches the balls from another boy, then they pull the balls from each other and it would generate attractive force.

##### Estimation of the mass of meson particle-

For the estimation of the mass of meson particle, let us use the Heisenberg uncertainty principle which is assumed valid in this exchange of points. According to it,

ΔE Δt ∼ h

In general, the range of nuclear force is about R∼ 1.7 * 10^-15m. If the velocity of pion exchanging between the nucleons is equal to that of light, then the time taken by the pion in the exchange between nucleons which exist in this range,

Δt ∼ R/c

Now if assume uncertainty in energy due to pion exchange equivalent to the mass-energy of the pion, then

ΔE ∼ m c²

From the Heisenberg uncertainty principle,

m c² R/c ∼ h

And m ∼ h/ Rc

Hence, m ∼ (1.05 * 10^-34)/(1.7 * 10^-15 *3 * 10*8)∼ 2.06 * 10^-28 kg

m ∼ (2.06 * 10^-28)/ (9.1 * 10^-31) ∼226 me

Where me is the mass of an electron.

###### Conclusion

In this particular article Meson Theory of Nuclear Force, we have studied about Meson theory and Estimation of the mass of meson particle in the easiest way possible.

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