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Register a new userMeasuring the surface thickness of the weak charge density of nuclei
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The present PREX-II and CREX experiments are measuring the rms radius of the weak charge density of $^{208}$Pb and $^{48}$Ca. We discuss the feasibility of a new parity violating electron scattering experiment to measure the surface thickness of the weak charge density of a heavy nucleus. Once PREX-II and CREX have constrained weak radii, an additional parity violating measurement at a momentum transfer near 0.76 fm$^{-1}$ for $^{208}$Pb or 1.28 fm$^{-1}$ for $^{48}$Ca can determine the surface thickness.
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We present and discuss numerical predictions for the neutron density distribution of $^{208}$Pb using various non-relativistic and relativistic mean-field models for the nuclear structure. Our results are compared with the very recent pion photoproduction data from Mainz. The parity-violating asymmetry parameter for elastic electron scattering at the kinematics of the PREX experiment at JLab and the neutron skin thickness are compared with the available data. We consider also the dependence between the neutron skin and the parameters of the expansion of the symmetry energy.
The initial energy density produced in heavy ion collisions can be estimated with the Bjorken energy density formula after choosing a proper formation time $tau{_{rm F}}$. However, the Bjorken formula breaks down at low energies because it neglects the finite nuclear thickness. Here we include both the finite time duration and finite longitudinal extension of the initial energy production. When $tau{_{rm F}}$ is not too much smaller than the crossing time of the two nuclei, our results are similar to those from a previous study that only considers the finite time duration. In particular, we find that at low energies the initial energy density has a much lower maximum value but evolves much longer than the Bjorken formula, while at large-enough $tau{_{rm F}}$ and/or high-enough energies our result approaches the Bjorken formula. We also find a qualitative difference in that our maximum energy density $epsilon^{rm max}$ at $tau{_{rm F}}=0$ is finite, while the Bjorken formula diverges as $1/tau{_{rm F}}$ and the previous result diverges as $ln (1/tau{_{rm F}})$ at low energies but as $1/tau{_{rm F}}$ at high energies. Furthermore, our solution of the energy density approximately satisfies a scaling relation. As a result, the $tau{_{rm F}}$-dependence of $epsilon^{rm max}$ determines the $A$-dependence, and the weaker $tau{_{rm F}}$-dependence of $epsilon^{rm max}$ in our results at low energies means a slower increase of $epsilon^{rm max}$ with $A$.
We show that the charge radii of neighboring atomic nuclei, independent of atomic number and charge, follow remarkably very simple relations, despite the fact that atomic nuclei are complex finite many-body systems governed by the laws of quantum mechanics. These relations can be understood within the picture of independent-particle motion and by assuming neighboring nuclei having similar pattern in the charge density distribution. A root-mean-square (rms) deviation of 0.0078 fm is obtained between the predictions in these relations and the experimental values, i.e., a comparable precision as modern experimental techniques. Such high accuracy relations are very useful to check the consistence of nuclear charge radius surface and moreover to predict unknown nuclear charge radii, while large deviations from experimental data is seen to reveal the appearance of nuclear shape transition or coexsitence.
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.
The effects of an additional $K^-$ meson on the neutron and proton drip lines are investigated within Skyrme-Hartree-Fock approach combined with a Skyrme-type kaon-nucleon interaction. While an extension of the proton drip line is observed due to the strongly attractive $K^-p$ interaction, contrasting effects (extension and reduction) on the neutron drip line of Be, O, and Ne isotopes are found. The origin of these differences is attributed to the behavior of the highest-occupied neutron single-particle levels near the neutron drip line.
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