α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character

Abstract

A long-standing crucial question with atomic nuclei is whether or not α clustering occurs there. An α particle (helium-4 nucleus) comprises two protons and two neutrons, and may be the building block of some nuclei. This is a very beautiful and fascinating idea, and is indeed plausible because the α particle is particularly stable with a large binding energy. However, direct experimental evidence has never been provided. Here, we show whether and how α(-like) objects emerge in atomic nuclei, by means of state-of-the-art quantum many-body simulations formulated from first principles, utilizing supercomputers including K/Fugaku. The obtained physical quantities exhibit agreement with experimental data. The appearance and variation of the α clustering are shown by utilizing density profiles for the nuclei beryllium-8, -10 and carbon-12. With additional insight by statistical learning, an unexpected crossover picture is presented for the Hoyle state, a critical gateway to the birth of life.

An alternating quark ball-and-stick model of nuclear structure

“…The next stable nuclide is 6 Li, and it has 18 quarks. The AQM radius prediction again employs formula (2), except 𝑛 =18, yielding a predicted radius value of 2.42 fm.…”

“…Surprisingly, the 6 Li radius prediction (2.42 fm) is quite close to the experimental radius of 7 Li (2.44 fm), even though 7 Li contains an additional neutron. The smaller diameter of 7 Li relative to 6 Li is understandable if the additional neutron (diameter roughly 1.6 fm) falls within the center of the 6 Li (diameter of approximately 4.8 fm), wherein the additional neutron essentially "inflates" the predicted oval structure of 6 Li into the more circular shape of 7 Li. Concealed within the structure of 7 Li, the additional neutron would not affect its predicted radius of rotation.…”

“…The diameter of an alpha particle ( 4 He nucleus) is 3.36 fm. The internal diameter of 6 Li's central space is 4.86 fm (assuming a regular octadecagon shape), so an alpha particle fits within 6 Li with a 0.75 fm margin. A similar approach applies to 11 B, accepted radius of 2.41 fm, which accommodates an alpha particle within the 11 B central space, and a neutron (diameter ≈1.6 fm) within the space inside the alpha particle (diameter ≈3.2 fm) leaving a margin of 0.8 fm around the neutron.…”

“…Larger structures beginning with 12 C comprise stacked 6 Li rings. The reference standard for the distance between adjacent parallel rings was derived from the distance between the two stacked 6-nucleon rings of 12 C, owing to its perfect point symmetry and small uncertainty in measurement (∆tot R = 0.0022 fm).…”

“…[4] The binding energy per nucleon for the smallest 4n nuclei is higher than those of neighboring nuclei, indicating the unusual stability of alpha-cluster nuclei [5], a hypothesis that continues to attract attention. [6] The discovery of the quark in 1968 led to the introduction of quantum chromodynamics (QCD) in 1974, a description of the strong force in terms of quark-to-quark interactions. Primarily a theory of nuclear force, the arrival of QCD did not immediately advance the cause of nuclear structure.…”