Spin-orbit and orbit-orbit strengths for the radioactive neutron-rich doubly magic nucleusSn132in relativistic mean-field theory

Abstract

Relativistic mean-field (RMF) theory is applied to investigate the properties of the radioactive neutron-rich doubly magic nucleus 132 Sn and the corresponding isotopes and isotones. The two-neutron and two-proton separation energies are well reproduced by the RMF theory. In particular, the RMF results agree with the experimental single-particle spectrum in 132 Sn as well as the Nilsson spin-orbit parameter C and orbit-orbit parameter D thus extracted, but remarkably differ from the traditional Nilsson parameters. Furthermore, the present results provide a guideline for the isospin dependence of the Nilsson parameters.The concept of magic numbers is one of the most fundamental ingredients for understanding the nature of atomic nuclei. Due to the strong spin-orbit couplings, the magic numbers for stable nuclei are shown as 2, 8, 20, 28, 50, and 82 for both protons and neutrons as well as 126 for neutrons [1,2], which are no longer simply the shell closure of the harmonic oscillators. Thus it is quite sophisticated to predict the next proton and neutron magic numbers [3,4], which are, nevertheless, critical for guiding the superheavy element synthesis. The phenomenon of shell closure is also crucial for determining the waiting points of the rapid neutron-capture process (r process), which is responsible for the production of more than half of the elements heavier than iron.With both proton and neutron magic numbers, the so-called doubly magic nuclei form a very small and exclusive club. These nuclei are rigidly spherical and particularly stable compared to their neighbors. Along the β stability line, only five nuclei are included: 4 He, 16 O, 40 Ca, 48 Ca, and 208 Pb. Furthermore, by simply combining these traditional magic numbers, one will also end up with the neutron-deficient nuclei 48 Ni, 56 Ni, and 100 Sn, neutron-rich nuclei 78 Ni and 132 Sn, as well as the extreme neutron-rich nucleus 70 Ca that is predicted as a giant halo nucleus [5]. It has been shown that the shell structures existing in the single-particle spectra can change in the nuclei far away from the stability line [6]. For example, the N = 28 shell closure disappears when the proton number decreases, and thus the nucleus 44 S is found to have prolate-spherical shape coexistence [7] and 42 Si is well deformed [8]. Therefore, whether the potentially doubly magic nuclei far away from the stability line are indeed doubly magic is a hot and fundamental topic.Since 56 Ni was confirmed as a radioactive doubly magic nucleus on the neutron-deficient side [9], the potentially doubly magic nucleus 132 Sn on the neutron-rich side has been paid much attention both experimentally and theoretically in the past years. However, pinning down whether 132 Sn is doubly magic or not was not so straightforward. By using the Sn(α,t) reactions, it was found that outside the Z = 50 core the energy gap between the proton single-particle states 1h 11/2 and 1g 7/2 increases with neutron excess [10], which suggests a decrease in the nuclear spin-orbit interaction. This was r...

Hidden pseudospin and spin symmetries and their origins in atomic nuclei

“…The observed single-particle energies obtained by pickup or knockout reactions contain polarization effects, except for the cases where the spectroscopic factors of the single-particle states are close to one [303,373]. Therefore, one should take into account the particle-vibration coupling and polarization effects [374,375].…”

“…First of all, let us start with the neutron-rich doubly magic nucleus 132 Sn as an example, which shows that the selfconsistent CDFT or RMF theory can nicely reproduce its ground-state properties including the single-particle spectra [303].…”

Role of residual interaction in the relativistic description of M1 excitation

“…One of the fundamental properties of the SP energy levels is the spin-orbit (SO) splitting, which is essential to explain the so-called magic numbers in nuclei [9,10]. In modern nuclear physics, one open question is how the SO splitting and the respective shell effects evolve from the valley of stability toward exotic nuclei with large neutron-to-proton number ratios [11][12][13]. It is also essential in description of nuclear processes that involve unstable nuclei of relevance for nuclear astrophysics, e.g., in modeling supernova explosion and neutron-star mergers, including the r-process nucleosynthesis , which is responsible for the production of about half of chemical elements heavier than iron [14,15].…”

Hidden pseudospin and spin symmetries and their origins in atomic nuclei

“…First of all, let us start with the neutron-rich doubly magic nucleus 132 Sn as an example, which shows that the self-consistent CDFT or RMF theory can nicely reproduce its ground-state properties including the single-particle spectra [303].…”

“…The experimental verification of the pseudospin symmetry can also be done from the single-particle energies. The observed single-particle energies obtained by pickup or knockout reactions contain polarization effects, except for the cases where the spectroscopic factors of the single-particle states are close to one [303,373]. Therefore, one should take into account the particle-vibration coupling and polarization effects [374,375].…”