No abstract

A particle number conserving BCS approach (FBCS) is formulated in the relativistic mean field (RMF) model. It is shown that the so-obtained RMF+FBCS model can describe the weak pairing limit. We calculate the ground-state properties of the calcium isotopes 32−74 Ca and compare the results with those obtained from the usual RMF+BCS model. Although the results are quite similar to each other, we observe an interesting phenomenon, i.e., for 54 Ca, the FBCS approach can enhance the occupation probability of the 2p 1/2 single particle level and slightly increases its radius, compared with the RMF+BCS model. This leads to an unusual scenario that although 54 Ca is more bound with a spherical configuration but the corresponding size is not the most compact one. We anticipate that such a phenomenon might happen for other neutron rich nuclei and should be checked by further more systematic studies. *

No abstract

No abstract

No abstract

We apply the recently proposed RMF(BCS)* ansatz to study the charge radii of the potassium isotopic chain up to $^{52}$K. It is shown that the experimental data can be reproduced rather well, qualitatively similar to the Fayans nuclear density functional theory, but with a slightly better description of the odd-even staggerings (OES). Nonetheless, both methods fail for $^{50}$K and to a lesser extent for $^{48,52}$K. It is shown that if these nuclei are deformed with a $\beta_{20}\approx-0.2$, then one can obtain results consistent with experiments for both charge radii and spin-parities. We argue that beyond mean field studies are needed to properly describe the charge radii of these three nuclei, particularly for $^{50}$K.

The systematic trend in nuclear charge radii is of great interest due to the universal shell effects and odd-even staggering (OES). Modified root mean square (rms) charge radius formula, which phenomenologically accounts for the formation of neutron-proton ($np$) correlations, is firstly applied to study the odd-$Z$ copper and indium isotopes. Theoretical results obtained by relativistic mean field (RMF) model with NL3, PK1 and NL3$^{*}$ parameter sets are compared with the experimental data. Our results show that both OES and the abrupt changes across $N=50$ and $82$ shell closures are reproduced evidently in nuclear charge radii. The inverted parabolic-like behaviors of rms charge radii can also be remarkably described between two neutron magic numbers, namely $N=28$ to $50$ for copper isotopes and $N=50$ to $82$ for indium isotopes. This implies the fact that the $np$-correlations play an indispensable role in quantitatively determining the fine structures of nuclear charge radii along odd-$Z$ isotopic chains. Meanwhile, our conclusions have almost no dependence on the effective forces.

A recent experimental breakthrough identified the last bound neutron-rich nuclei in fluorine and neon isotopes. Based on this finding, we perform a theoretical study of Z = 9, 10, 11, 12 isotopes in the relativistic mean field (RMF) model. The mean field parameters are assumed from the PK1 parameterization, and the pairing correlation is described by the particle number conservation BCS (FBCS) method recently formulated in the RMF model. We show that the FBCS approach plays an essential role in reproducing experimental results of fluorine and neon isotopes. Furthermore, we predict 39Na and 40Mg to be the last bound neutron-rich nuclei in sodium and magnesium isotopes.