Abstract
The nuclear shell structure, which originates in the nearly independent motion of nucleons in an average potential, provides an important guide for our understanding of nuclear structure and the underlying nuclear forces. Its most remarkable fingerprint is the existence of the so-called magic numbers of protons and neutrons associated with extra stability. Although the introduction of a phenomenological spin–orbit (SO) coupling force in 1949 helped in explaining the magic numbers, its origins are still open questions. Here, we present experimental evidence for the smallest SO-originated magic number (subshell closure) at the proton number six in 13–20C obtained from systematic analysis of point-proton distribution radii, electromagnetic transition rates and atomic masses of light nuclei. Performing ab initio calculations on 14,15C, we show that the observed proton distribution radii and subshell closure can be explained by the state-of-the-art nuclear theory with chiral nucleon–nucleon and three-nucleon forces, which are rooted in the quantum chromodynamics.
Highlights
The nuclear shell structure, which originates in the nearly independent motion of nucleons in an average potential, provides an important guide for our understanding of nuclear structure and the underlying nuclear forces
The first series—2, 8, 20—is attributed to the harmonic-oscillator (HO) potential, while the second one—28, 50, 82 and 126—is due to the spin–orbit (SO) coupling force. It was the introduction of this phenomenological SO force—a force that depends on the intrinsic spin of a nucleon and its orbital angular momentum, and the socalled j–j coupling scheme that helped explain[1,2] completely the magic numbers, and won Goeppert-Mayer and Jensen the Nobel Prize
We present experimental evidence for a prevalent Z = 6 subshell closure in 13–20C, based on a systematic study of proton radii obtained from our recent experiments as well as the existing nuclear charge radii[12], electric quadrupole transition nrautcelseiB3(0E, 2a)nbdetwateoemn itch-em2aþ1ssanddatgar3o1u. nWd e0þgsshoswta, tebsyofpeevrefonr–mevineng coupled-cluster calculations, that the observations are supported by the ab initio nuclear model that employs the nuclear forces derived from the effective field theory of the quantum chromodynamics
Summary
The nuclear shell structure, which originates in the nearly independent motion of nucleons in an average potential, provides an important guide for our understanding of nuclear structure and the underlying nuclear forces. The theoretical study[6] of the SO splitting of the 1p1/2 and 1p3/2 single-particle states in 15N has suggested possible roles of two-body SO and tensor forces, as well as three-body forces, the discovery of a prevalent SO-type magic number 6 is expected to offer unprecedented opportunities to understand its origins. In her Nobel lecture, Goeppert-Mayer had mentioned the magic numbers 6 and 14—which she described as hardly noticeable—but surmised that the energy gap between the 1p1/2 and 1p3/2 orbitals due to the SO force is fairly small[7]. The small B(E2) values indicate small proton contributions to the transitions, and together with the theoretical predictions may imply the existence of a proton-subshell closure
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