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The magnetism caused by the spin of odd electrons can indeed influence the attractive force between the atomic nucleus and other particles. This effect is known as spin-spin coupling or hyperfine coupling.

In atoms, the atomic nucleus has its own intrinsic angular momentum or spin, and so do the electrons. When the spin of an electron interacts with the spin of the atomic nucleus, it can affect the overall magnetic properties of the atom.

The hyperfine coupling between the electron and the nucleus can lead to different energy levels or states for the atom. These energy levels depend on the relative alignment of the electron and nuclear spins. As a result, the attractive force experienced by the atomic nucleus can be influenced.

The strength of the hyperfine coupling can either increase or decrease the attractive force, depending on the specific circumstances. In some cases, the coupling can increase the attractive force between the electron and the nucleus, leading to a lower energy state. This is known as a diamagnetic effect, where the atom or molecule is weakly repelled by a magnetic field.

On the other hand, in certain situations, the coupling can decrease the attractive force, resulting in an increased energy state. This is referred to as a paramagnetic effect, where the atom or molecule is weakly attracted to a magnetic field.

It's important to note that the overall effect of spin-spin coupling on the attractive force depends on the specific electron and nuclear configurations, as well as external factors such as the presence of magnetic fields. Therefore, the influence can vary from atom to atom or molecule to molecule.

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