The proton distribution is well-studied via the nuclear charge density distribution derived from electron scattering experiments. Electron scattering is popularly used to estimate nuclear charge distributions, as the electromagnetic interactions are well understood theoretically. Since electron scattering primarily relies on electric charge, it is minimally sensitive to neutrons, which are electrically neutral, making it difficult to study neutron distribution.

However, to understand the structure of unstable nuclei and the problem of the size of the neutron star, knowing the neutron distribution is critical. To estimate this, scientists have attempted longitudinally polarized-electron scattering, which gives a ratio of weak charge form factor (contributed by neutrons) to the electromagnetic form factor (contributed by the charge density). But this experiment is difficult, time-consuming, and shows about 10% error, making the calculation of the root mean square radius (rms) of the point neutron distribution (R_n) almost impossible.

To address this challenge, a study published in the Progress of Theoretical and Experimental Physics demonstrates a novel approach that utilizes the fourth moment of the nuclear charge density distribution—derived from electron scattering, to extract information ofR_n. This study received ‘The Outstanding Paper Award of the Physical Society of Japan’ for the authors’ contributions to nuclear physics. The study estimated the mean square radius (msr) of neutrons (R_n) and that of protons (R_p) and the neutron skin thickness (δR = R_n − R_p) using relativistic and non-relativistic mean field models.

Recent studies show that the msr of the nuclear charge density is contributed by , while the mean fourth-order moment of the charge density depends on  as well. Further, nuclear models suggest that  strongly correlates with through . Using these facts, the relationship between various moments in the nuclear models was studied for neutron-dense nuclei like ²⁰⁸Pb and ⁴⁸Ca, to extract values of R_p and R_n from the intersection of the theoretical and experimental values for or obtained via electron scattering.

With minimal experimental errors and reduced reliance on complex models, this new method to estimate neutron distributions has found potential applications across neutron-rich systems in nuclear and astrophysics research.

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