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Register a new userNonlocalized Clustering: A New Concept in Nuclear Cluster Structure Physics
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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.
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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.
We present a very brief description of the Hartree-Fock method in nuclear structure physics, discuss the numerical methods used to solve the self-consistent equations, and analyze the precision and convergence properties of solutions. As an application we present results pertaining to quadrupole moments and single-particle quadrupole polarizations in superdeformed nuclei with A~60.
Using many-body perturbation theory and coupled-cluster theory, we calculate the ground-state energy of He-4 and O-16. We perform these calculations using a no-core G-matrix interaction derived from a realistic nucleon-nucleon potential. Our calculations employ up to two-particle-two-hole coupled-cluster amplitudes.
The prospects of extracting new physics signals in a coherent elastic neutrino-nucleus scattering (CE$ u$NS) process are limited by the precision with which the underlying nuclear structure physics, embedded in the weak nuclear form factor, is known. We present microscopic nuclear structure physics calculations of charge and weak nuclear form factors and CE$ u$NS cross sections on $^{12}$C, $^{16}$O, $^{40}$Ar, $^{56}$Fe and $^{208}$Pb nuclei. We obtain the proton and neutron densities, and charge and weak form factors by solving Hartree-Fock equations with a Skyrme (SkE2) nuclear potential. We validate our approach by comparing $^{208}$Pb and $^{40}$Ar charge form factor predictions with elastic electron scattering data. In view of the worldwide interest in liquid-argon based neutrino and dark matter experiments, we pay special attention to the $^{40}$Ar nucleus and make predictions for the $^{40}$Ar weak form factor and the CE$ u$NS cross sections. Furthermore, we attempt to gauge the level of theoretical uncertainty pertaining to the description of the $^{40}$Ar form factor and CE$ u$NS cross sections by comparing relative differences between recent microscopic nuclear theory and widely-used phenomenological form factor predictions. Future precision measurements of CE$ u$NS will potentially help in constraining these nuclear structure details that will in turn improve prospects of extracting new physics.
This contribution gives a short review of recent theoretical advances in most topics of nuclear cluster physics concentrating, however, around {$alpha$} particle clustering. Along the route, the point of view will be critical mentioning not only progress but also failures and open problems.
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