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Register a new userIrregularities in nuclear radii at magic numbers
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H. Nakada
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Influence of magic numbers on nuclear radii is investigated via the Hartree-Fock-Bogolyubov calculations and available experimental data. With the $ell s$ potential including additional density-dependence suggested from the chiral effective field theory, kinks are universally predicted at the $jj$-closed magic numbers and anti-kinks (textit{i.e.} inverted kinks) are newly predicted at the $ell s$-closed magic numbers, both in the charge radii and in the matter radii along the isotopic and isotonic chains where nuclei stay spherical. These results seem consistent with the kinks of the charge radii observed in Ca, Sn and Pb and the anti-kink in Ca. The kinks and the anti-kinks could be a peculiar indicator for magic numbers, discriminating $jj$-closure and $ell s$-closure.
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The main purpose of the present manuscript is to review the structural evolution along the isotonic and isotopic chains around the traditional magic numbers 8; 20; 28; 50; 82 and 126. The exotic regions of the chart of nuclides have been explored during the three last decades. Then the postulate of permanent magic numbers was de nitely abandoned and the reason for these structural mutations has been in turn searched for. General trends in the evolution of shell closures are discussed using complementary experimental information, such as the binding energies of the orbits bounding the shell gaps, the trends of the rst collective states of the even-even semi-magic nuclei, and the behavior of certain single-nucleon states. Each section is devoted to a particular magic number. It describes the underlying physics of the shell evolution which is not yet fully understood and indicates future experimental and theoretical challenges. The nuclear mean eld embodies various facets of the Nucleon- Nucleon interaction, among which the spin-orbit and tensor terms play decisive roles in the shell evolutions. The present review intends to provide experimental constraints to be used for the re nement of theoretical models aiming at a good description of the existing atomic nuclei and at more accurate predictions of hitherto unreachable systems.
Radii of charge and neutron distributions are fundamental nuclear properties. They depend on both nuclear interaction parameters related to the equation of state of infinite nuclear matter and on quantal shell effects, which are strongly impacted by the presence of nuclear surface. In this work, by studying the dependence of charge and neutron radii, and neutron skin, on nuclear matter parameters, we assess different mechanisms that drive nuclear sizes. We apply nuclear density functional theory using a family of Skyrme functionals obtained by means of different optimization protocols targeting specific nuclear properties. By performing the Monte-Carlo sampling of reasonable functionals around the optimal parametrization, we study correlations between nuclear matter paramaters and observables characterizing charge and neutron distributions. We demonstrate the existence of the strong converse relation between the nuclear charge radii and the saturation density of symmetric nuclear matter and also between the neutron skins and the slope of the symmetry energy. For functionals optimized to experimental binding energies only, proton and neutron radii are weakly correlated due to canceling trends from different nuclear matter parameters. We show that by requiring that the nuclear functional reproduces the empirical saturation point of symmetric nuclear matter practically fixes the charge (or proton) radii, and vice versa. The neutron skin uncertainty primarily depends on the slope of the symmetry energy. Consequently, imposing a constraint on both $rho_0$ and $L$ practically determines the nuclear size, modulo small variations due to shell effects.
A new paradigm for nuclear structure that includes blocking effects of tensor interactions is proposed. All of the recently discovered magic numbers (N=6, 14, 16, 32 and 34) in neutron-rich nuclei can be explained by the blocking effects. A large amount of binding energy is gained by high-momentum correlated pairs of nucleons produced by the tensor interaction. Such tensor correlations strongly depend on the configuration space available for exciting nucleons to 2p-2h states. When additional neutrons occupy a new orbital, the previously available configuration may be lost, resulting in a sudden loss of binding energy otherwise gained by the 2p-2h excitations. Such tensor blocking effects enlarge the energy gaps at all observed new magic numbers. Tensor blocking also explains consistently the observed peculiar configurations of neutron-rich nuclei at the borders of shells.
A unified theoretical model reproducing charge radii of known atomic nuclei plays an essential role to make extrapolations in the regions of unknown nuclear size. Recently developed new ansatz which phenomenally takes into account the neutron-proton short-range correlations (np-SRCs) can describe the discontinuity properties and odd-even staggering (OES) effect of charge radii along isotopic chains remarkably well. In this work, we further review the modified rms charge radii formula in the framework of relativistic mean field (RMF) theory. The charge radii are calculated along various isotopic chains that include the nuclei featuring the $N=50$ and $82$ magic shells. Our results suggest that RMF with and without considering correction term give almost similar trend of nuclear size for some isotopic chains with open proton shell, especially the shrink phenomena of charge radii at strong neutron closed shells and the OES behaviors. This suggests that the np-SRCs has almost no influence for some nuclei due to the strong coupling between different levels around Fermi surface. The weakening OES behavior of nuclear charge radii is observed generally at completely filled neutron shells and this may be proposed as a signature of magic indicator.
A novel shape evolution in the Sn isotopes by the state-of-the-art application of the Monte Carlo Shell Model calculations is presented in a unified way for the 100-138Sn isotopes. A large model space consisting of eight single-particle orbits for protons and neutrons is taken with the fixed Hamiltonian and effective charges, where protons in the 1g9/2 orbital are fully activated. While the significant increase of the B(E2; 0+1 -> 2+1) value, seen around 110Sn as a function of neutron number (N), has remained a major puzzle over decades, it is explained as a consequence of the shape evolution driven by proton excitations from the 1g9/2 orbital. A second-order quantum phase transition is found around N=66, connecting the phase of such deformed shapes to the spherical pairing phase. The shape and shell evolutions are thus described, covering topics from the Gamow-Teller decay of 100Sn to the enhanced double magicity of 132Sn.
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