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We explain various facets of the THSR (Tohsaki-Horiuchi-Schuck-Ropke) wave function. We first discuss the THSR wave function as a wave function of cluster-gas state, since the THSR wave function was originally introduced to elucidate the 3$alpha$-condensate-like character of the Hoyle state ($0_2^+$ state) of $^{12}$C. We briefly review the cluster-model studies of the Hoyle state in 1970s in order to explain how there emerged the idea to assign the $alpha$ condensate character to the Hoyle state. We then explain that the THSR wave function can describe very well also non-gaslike ordinary cluster states with spatial localization of clusters. This fact means that the dynamical motion of clusters is of nonlocalized nature just as in gas-like states of clusters and the localization of clusters is due to the inter-cluster Pauli principle which is against the close approach of two clusters. The nonlocalized cluster dynamics is formulated by the container model of cluster dynamics. The container model describes gas-like state and non-gaslike states as the solutions of the Hill-Wheeler equation with respect to the size parameter of THSR wave function which is just the size parameter of the container. When we notice that fact that the THSR wave function with the smallest value of size parameter is equivalent to the shell-model wave function, we see that the container model describes the evolution of cluster structure from the ground state with shell-model structure up to the gas-like cluster state via ordinary non-gaslike cluster states. For the description of various cluster structure, more generation of THSR wave function have been introduced and we review some typical examples with their actual applications.
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We investigate the $alpha$+oo cluster structure in the inversion-doublet band ($K^pi=0_{1}^pm$) states of ene with an angular-momentum-projected version of the Tohsaki-Horiuchi-Schuck-R{o}pke (THSR) wave function, which was successful in its original form for the description of, e.g., the famous Hoyle state. In contrast with the traditional view on clusters as localized objects, especially in inversion doublets, we find that these {it single} THSR wave functions, which are based on the concept of nonlocalized clustering, can well describe the $K^{pi}=0_1^-$ band and the $K^{pi}=0_1^+$ band. For instance, they have 99.98% and 99.87% squared overlaps for $1^-$ and $3^- $ states (99.29%, 98.79% and 97.75% for $0^+, 2^+$ and $4^+$ states), respectively, with the corresponding exact solution of the $alpha$+oo resonating group method. These astounding results shed a completely new light on the physics of low energy nuclear cluster states in nuclei: The clusters are nonlocalized and move around in the whole nuclear volume, only avoiding mutual overlap due to the Pauli blocking effect.
We review recent studies of the cluster structure of light nuclei within the framework of the algebraic cluster model (ACM) for nuclei composed of k alpha-particles and within the framework of the cluster shell model (CSM) for nuclei composed of k alpha-particles plus x additional nucleons. The calculations, based on symmetry considerations and thus for the most part given in analytic form, are compared with experiments in light cluster nuclei. The comparison shows evidence for Z_2, D_{3h} and T_d symmetry in the even-even nuclei 8Be (k=2), 12C (k=3) and 16O (k=4), respectively, and for the associated double groups Z_2 and D_{3h} in the odd nuclei 9Be, 9B (k=2, x=1) and 13C (k=3, x=1), respectively.
The atomic nucleus is a quantum many-body system whose constituent nucleons (protons and neutrons) are subject to complex nucleon-nucleon interactions that include spin- and isospin-dependent components. For stable nuclei, already several decades ago, emerging seemingly regular patterns in some observables could be described successfully within a shell-model picture that results in particularly stable nuclei at certain magic fillings of the shells with protons and/or neutrons: N,Z = 8, 20, 28, 50, 82, 126. However, in short-lived, so-called exotic nuclei or rare isotopes, characterized by a large N/Z asymmetry and located far away from the valley of beta stability on the nuclear chart, these magic numbers, viewed through observables, were shown to change. These changes in the regime of exotic nuclei offer an unprecedented view at the roles of the various components of the nuclear force when theoretical descriptions are confronted with experimental data on exotic nuclei where certain effects are enhanced. This article reviews the driving forces behind shell evolution from a theoretical point of view and connects this to experimental signatures.
We investigate emission of bremsstrahlung photons during scattering of $alpha$-particles off nuclei. For that, we construct bremsstrahlung model for $alpha$-nucleus scattering, where a new formalism for coherent and incoherent bremsstrahlung emissions in elastic scattering and mechanisms in inelastic scattering is added. Basing of this approach, we analyze experimental bremsstrahlung cross-sections in the scattering of $alpha$-particles off the isotope[59]{Co}, isotope[116]{Sn}, isotope[rm nat]{Ag} and isotope[197]{Au} nuclei at 50 MeV of $alpha$-particles beam measured at the Variable Energy Cyclotron Centre, Calcutta. We observe oscillations in the calculated spectra for elastic scattering for each nucleus. But, for isotope[59]{Co}, isotope[116]{Sn} and isotope[rm nat]{Ag} we obtain good agreement between calculated coherent spectrum with incoherent contribution for elastic scattering with experimental data in the full photon energy region. For heavy nucleus isotope[197]{Au} we find that (1) Oscillating behavior of the calculated spectrum of coherent emission in elastic scattering is in disagreement with experimental data, (2) Inclusion of incoherent emission improves description of the data, but summarized spectrum is in satisfactory agreement with the experimental data. To understand unknown modification of wave function for scattering, we add new mechanisms of inelastic scattering to calculations and extract information about unknown new amplitude of such mechanisms from experimental data analysis. This amplitude has maxima at some energies, that characterizes existence of states of the most compact structures (clusters) in nucleus-target. We explain origin of oscillations in the bremsstrahlung spectra for elastic scattering (at first time). New information about coherent and incoherent contributions is extracted for studied reactions.
We review recent experimental and theoretical progress in understanding the microscopic details of clustering in light nuclei. We discuss recent experimental results on $alpha$-conjugate systems, molecular structures in neutron-rich nuclei, and constraints for ab initio theory. We then examine nuclear clustering in a wide range of theoretical methods, including the resonating group and generator coordinate methods, antisymmetrized molecular dynamics, Tohsaki-Horiuchi-Schuck-Ropke wave function and container model, no-core shell model methods, continuum quantum Monte Carlo, and lattice effective field theory.
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