Central depressions in the charge density profiles of the nuclei around $^{46}$Ar

The occurrence of the proton bubble-like structure has been studied within the relativistic Hartree-Fock-Bogoliubov (RHFB) and relativistic Hartree-Bogoliubov (RHB) theories by exploring the bulk properties, the charge density profiles and single proton spectra of argon isotopes and $N = 28$ isotones. It is found that the RHFB calculations with PKA1 effective interaction, which can properly reproduce the charge radii of argon isotopes and the $Z=16$ proton shell nearby, do not support the occurrence of the proton bubble-like structure in argon isotopes due to the prediction of deeper bound proton orbit $pi2s_{1/2}$ than $pi1d_{3/2}$. For $N = 28$ isotones, $^{42}$Si and $^{40}$Mg are predicted by both RHFB and RHB models to have the proton bubble-like structure, owing to the large gap between the proton $pi2s_{1/2}$ and $pi1d_{5/2}$ orbits, namely the $Z=14$ proton shell. Therefore, $^{42}$Si is proposed as the potential candidate of proton bubble nucleus, which has longer life-time than $^{40}$Mg.

Proton radioactivity described by covariant density functional theory with Similarity Renormalization Group method

Half-life of proton radioactivity of spherical proton emitters is studied within the scheme of covariant density functional (CDF) theory, and for the first time the potential barrier that prevents the emitted proton is extracted with the similarity renormalization group (SRG) method, in which the spin-orbit potential along with the others that turn out to be non-negligible can be derived automatically. The spectroscopic factor that is significant is also extracted from the CDF calculations. The estimated half-lives are found in good agreement with the experimental values, which not only confirms the validity of the CDF theory in describing the proton-rich nuclei, but also indicates the prediction power of present approach to calculate the half-lives and in turn to extract the structural information of proton emitters.

A Comparison Theorem and A Sharp Bound via the Ricci Flow

We prove a comparison theorem for the compact surfaces with negative Euler characteristic via the Ricci flow.

A Class of Monotonic Quantities along the Ricci Flow

We construct a class of monotonic quantities along the normalized Ricci flow on closed n-dimensional manifolds.

Some Asymptotic Behavior of the first Eigenvalue along the Ricci Flow

We study some asymptotic behavior of the first nonzero eigenvalue of the Lalacian along the normalized Ricci flow and give a direct short proof for an asymptotic upper limit estimate.