Nuclear clustering-manifestations of non-uniformity in nuclei

Abstract

Well-developed [Formula: see text] clusters are known to exist in light [Formula: see text] nuclei, and their properties are reasonably well described with modern nuclear structure theories. However, 'modestly' developed clusters in medium to heavy nuclei remain little understood, both theoretically and experimentally. Extension of the focus to include modestly developed clusters leads us to a concept of 'generalized clusters' and 'cluster ubiquitousness'. The former includes clusters more weakly bound than an [Formula: see text] cluster, such as deuteron, triton and [Formula: see text], and even clusters partially broken owing to nuclear medium effects. The latter means the existence of clusters in any nuclei, where cluster development was not previously discussed. Effects of the tensor and the spin-orbit interactions on the coexistence of clusters with independent nucleons are discussed using recent nuclear theoretical models. A mixture of the clusters with shell-like components plays an essential role in the synthesis of elements in the universe and the origin of life, together with an [Formula: see text] decay. It is also pointed out that clustering in heavy nuclei may accelerate fission and fusion processes. Future experimental plans using cluster knockout reactions, which have the potential to extract information of 'generalized clusters' in a variety of nuclei including stable and unstable nuclei, are also discussed. This article is part of the theme issue 'The liminal position of Nuclear Physics: from hadrons to neutron stars'.

Keywords: alpha decay; knockout reaction; nuclear cluster; origin of elements; spin–orbit interaction; tensor interaction.

Figure 1.

Constant-density contours for ${}^8\mathrm{Be}$ in the laboratory (left) and the intrinsic (right) frames calculated with the quantum Monte Carlo theory. Reprinted from [11]. ©2000 with permission from the American Physical Society.

Figure 2.

Density profiles of $\alpha$ and ${}^{12}\mathrm{C}$ nuclei obtained with the ab initio Monte Carlo shell model. (a) Colour code of the density. (b) Density of the $\alpha$ -particle ground state. (c–e) Density of three $0^{+}$ states of ${}^{12}\mathrm{C}$ . (f–i) Decomposition into the region I (‘liquid drop’) and II (‘clustering’). Reprinted from [20]. ©https://creativecommons.org/.

Figure 3.

Triple-differential cross-section of the ${\displaystyle {}^{48}\mathrm{T}\mathrm{i}(\mathit{p},\mathit{p}\alpha {)}^{44}\mathrm{C}\mathrm{a}}$ reaction. Experimental data from [24]. are compared with DWIA calculations. Reprinted from [26]. ©2021 with permission from the American Physical Society.

Figure 4.

Schematic figure for the formation of ${}^{12}\mathrm{C}$ : The triple- $\alpha$ reaction through a formation of the ${}^8\mathrm{Be}$ resonance state populates the Hoyle state at 7.654 MeV. The Hoyle state decays to three $\alpha$ s (~99.95%) and the ${}^{12}\mathrm{C}$ ground state via electromagnetic transitions (~0.05%).

Figure 5.

$\alpha$ preformation factors in the model presented in [47] versus the neutron number of parent nuclei for the decays of even–even isotopes with $Z=84-104$ . Reprinted from [47]. ©2018 with permission from the American Physical Society.

Figure 6.

The proton localization functions $C_p$ (left) and a nucleon density $\rho$ (right) at $t=$ 1150, 1200 and 1250 fm/c in the fission of ${}^{240}\mathrm{Pu}$ . Reprinted from [49]. ©2022 with permission from the American Physical Society.

Figure 7.

Separation energy spectra of the $(p,p\alpha )$ reactions at $E_p=100$ MeV for ${}^{40}\mathrm{Ca}$ , ${}^{48}\mathrm{Ti}$ , ${}^{54}\mathrm{Fe}$ and ${}^{66}\mathrm{Zn}$ . Reprinted from [24]. ©1984 with permission from the American Physical Society.

Figure 8.

The neutron-number dependence of the ${}^{112-124}\mathrm{Sn}(p,p\alpha )$ cross-section integrated over transitions to low-lying states of the residual Cd isotopes. Data are taken from [55].

Figure 9.

Theoretical predictions of cluster fractions in nuclear matter at finite temperature ( $T$ ) at different proton factions ( $Y_p$ ). Left: predictions of the generalized relativistic mean-field model at $T=10$ MeV and $Y_p$ =0.4. Full and dashed lines indicate predictions with and without nucleon–nucleon scattering correlations. Reprinted from [58]. ©2013 with permission from Springer. Right: predictions of the generalized nonlinear relativistic mean-field theory at $T=3$ MeV and $Y_p$ = 0.1, 0.5. Reprinted from [59]. ©2017 with permission from the American Physical Society.