San José State University

applet-magic.com
Thayer Watkins
Silicon Valley
USA

 The Quarkic Source of the Mutual Repulsion of Like Nucleons and Attraction of Unlike Nucleons

There is considerable evidence, given elsewhere, that neutrons repel each other under the nuclear strong force. Likewise there is also evidence that under the strong force, as well as the electrostatic force, protons repel each other. On the other hand there is under the strong force an attraction between a proton and a neutron. This, along with the formation of spin pairs of nucleons, is what holds nuclei together. It is the familiar case of like particles repelling each other and unlike ones being attracted.

This behavior can be represented in terms of nucleons having a nucleonic charges, let us say +1 for the proton and −1 for the neutron. Then the force F between two nucleons having nucleonic charges of n1 and n2 and separated by a distance s would be

#### F = n1n2f(s)

where f(s) gives the functional relationship between the force and the separation distance of the centers of the nucleons. Elsewhere it is argued that the function form of f(s) is

#### f(s) = H*exp(−s/s0)/s²

where H is a constant and s0 is a scale parameter which arises from the decay of the π mesons which carry the strong force.

The force being proportional to the product of the nucleonic charges results in force for like particles being the opposite of the force between unlike particles.

## The Quarkic Composition of the Nucleons

The proton is believed to be composed of two up quarks and one down quark; the neutron of two down quarks and one up quark. Let un and dn be the nucleonic charge of the up quark and down quark, respectively. With the nucleon charge of the proton being +1 and that of the neutron being −1, un and dn must satisfy the relations

#### 2un + dn = +1 un + 2dn = −1

Multiplying the second equation by 2 results in

#### 2un + dn = +1 2un + 4dn = −2

Subtracting the first equation from the second gives

#### 3dn = −3 and hence dn = −1

From this it follows that

#### un = +1

This is the same process by which it is determined that the electrostatic charges, uc and dc, are (2/3)e and −(1/3)e, respectively, from the charge of the proton being +1e and that of the neutron being 0.

## The Nucleonic Charges of Other Particles

Mesons, such as the π mesons (pions), are thought to be composed of an up quark and a down quark. The nucleon charge of the π mesons is therefore un+dn=0. Thus they are not subject to the strong force, which makes sense because they are the carriers of the strong force.

There is not yet information to use as a basis for determining the nucleonic charge of the other quarks.

## Other Assignments of Nucleonic Charge

In another webpage, nucleoniccharge2.htm, the case is made that the square of the nucleonic charge of the proton is twice that of the neutron and opposite in sign. This would mean that if the nucleonic charge of a proton is assigned a value of 2 then the nucleonic charge of a neutron would be −1.4. In this case the equations to be satisfied are:

#### 2un + dn = +2 un + 2dn = −1.4

These equations have the solution

#### un = +3.27/2 = +1.67 dn = −3.8/3 = − 1.27

The fractional values cannot be entirely eliminated, but if the proton were said to have a nucleonic charge of 6 and the neutron one of −4.2 the significance of the fractional part can be greatly reduced. However, the choice of +2 for the proton and −1.4 for the neutron is reasonable.

Mesons being the combination of a quark and an antiquark would have a nucleonic charge of ±0.4 or ±2.94 depending upon whether the nucleonic charge is the same for an antiquark as for the quark or reversed in sign. Intuitively the ±0.4 seems more plausible.

The net nucleonic charge of an alpha particle would be 2(2)+2(−1.4)= 1.2, about 0.6 of that of a proton.

(To be continued.)

## Conclusions

The attraction or repulsion of pairs of nucleons can be explained by the nucleons having a nucleonic charge. The charges of nucleons with respect to the strong force can be derived from the corresponding charges of their constituent quarks. Mesons, being made up of two differnt types of quarks, are then neutral with respect to the strong force.