Particle number conserving BCS approach in the relativistic mean field model and its application to ^32–74 Ca

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. *

Charge radii of potassium isotopes in the RMF(BCS)* approach

“…In comparison with the charge radii of calcium isotopes, the amplitude of the parabolic-like shape between 39 K and 47 K is smaller due to the last unpaired proton [12,[15][16][17][18]. Meanwhile, the rapid increase of charge radii is also found across the N = 28 shell closure [19].…”

“…The quantity ∆D = |D n − D p | represents the difference of Cooper pair condensations for neutrons and protons. It is calculated self-consistently by solving the state-dependent BCS equations with a δ force [37,39]. One should note that although the correction is introduced as an empirical approximation of neutron-proton pairing correlations, it is calculated using the outputs of the microscopic RMF(BCS) approach.…”

Neutron drip line of $Z=9-11$ isotopic chains

“…To deal with pairing correlations, we use the variational BCS approach [81,82]. To restore the particle number conservation, we adopt the variation after projection BCS method or the so-called FBCS method, which is recently implemented in the RMF model [70]. The corresponding FBCS equation reads…”

“…Based on these considerations, in the present work, we study the fluorine, neon, sodium, and magnesium isotopes in the relativistic mean field model and employ the recently developed particular number conservation BCS (FBCS) approach to deal with pairing correlations [70]. We focus on the differences between the results obtained in the RMF+BCS approach and those in the RMF+FBCS approach to explore the relevance of the latter in the description of neutron-rich nuclei and in predicting the location of the neutron drip line.…”

Novel ansatz for charge radii in density functional theories

“…In doing so, slight readjustment of the mean-field parameters might be needed as well. Furthermore, as the ansatz is based on the BCS theory, where particle number is not conserved, one may wish to study how its restoration affects the description of charge radii using, e.g., the FBCS method [38]. The fact that our ansatz performed slightly worse for nuclei with magic numbers, such as N = 28 and N = 126, indeed indicates such an necessity.…”