Question

In neutron stars, which are roughly \(90 \%\) neutrons and are held together almost entirely by nuclear forces, which of the following terms become(s) relatively dominant for the binding energy, compared to that energy in an ordinary nucleus? a) the Coulomb term b) the asymmetry term c) the pairing term d) all of the above e) none of the above

Short answer

Answer: The asymmetry term (b) is dominant in the binding energy of a neutron star compared to an ordinary nucleus.

Step-by-step solution

Analyze the Coulomb term

In an ordinary nucleus, the Coulomb term arises due to the electrostatic repulsion between protons. In a neutron star, which is primarily composed of neutrons, the Coulomb term would not be a significant contributor to the binding energy as there are very few protons. Therefore, the Coulomb term is not dominant in a neutron star compared to an ordinary nucleus.

Analyze the asymmetry term

The asymmetry term takes into account the imbalance between the number of protons and neutrons in a nucleus. In an ordinary nucleus, the number of protons and neutrons are relatively balanced, while in a neutron star, there is a significant imbalance, with a much higher percentage of neutrons. This indicates that the asymmetry term is dominant in the binding energy of a neutron star compared to an ordinary nucleus.

Analyze the pairing term

The pairing term accounts for the energy gained or lost when nucleons (protons or neutrons) are paired together. In both an ordinary nucleus and a neutron star, the pairing term is influenced by the number of nucleons and their arrangement. It is not immediately clear if the pairing term would be dominant in a neutron star compared to an ordinary nucleus without performing a detailed calculation. However, given that the majority of the nucleons in a neutron star are neutrons, it is expected that the pairing term plays a more significant role in the binding energy of a neutron star.

Conclusion

Considering the analysis of each term, the asymmetry term (b) is dominant in the binding energy of a neutron star compared to an ordinary nucleus due to the significant imbalance in the number of protons and neutrons. The pairing term (c) might also play a more significant role in a neutron star, but without a detailed calculation, it is not certain. The Coulomb term (a) is not dominant in a neutron star due to the small number of protons. Thus, the answer is (b) the asymmetry term.