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The nonlocalized clustering approach is generalized to $$^{8-11}$$ Be isotopes with isospin dependent spin–orbit potential. A new form of the Tohsaki-Horiuchi-Schuck-Ropke (THSR) wave function is introduced to provide a correct description for the $$\sigma $$ -binding neutron in $$^{11}$$ Be. Systematic calculations for $$^{8-11}$$ Be isotopes are performed and results fit well with experimental values. The low energy spectrum of $$^{11}$$ Be is also obtained, especially the correct spin-parity $$1/2^{+}$$ is reproduced for the intruder ground state. The exotic neutron halo structure of $$^{11}$$ Be is studied by calculations of root-mean-square radii and density distribution. The spectroscopic factor is also calculated and discussed for the $$1/2^+$$ ground state of $${}^{11}$$ Be.

Quartetting ( $$\alpha $$ -like clustering) occurs in low-density matter ( $${\le }0.03$$ fm $$^{-3}$$ ) which exists, e.g., at the surface of nuclei. It is of interest for the $$\alpha $$ preformation to calculate the $$\alpha $$ decay of heavy nuclei such as $$^{212}$$ Po, but also in light nuclei (e.g., $$^{20}$$ Ne) which shows strong signatures of quartetting. We analyze the intrinsic structure of the $$\alpha $$ -like cluster and the center-of-mass motion of the quartet, in particular the role of Pauli blocking. The Thomas–Fermi model for the (daughter) core nucleus is improved introducing quasiparticle nucleon states. Calculations performed for harmonic oscillator basis states show that the effective potential for the quartet center-of-mass motion remains nearly constant within the core nucleus. The relation to the (Tohsaki–Horiuchi–Schuck–Ropke) THSR approach is discussed.

We explain how to treat a microscopic wave function of α-condensation taking a 3α-nucleus as a typical example. The wave function has been originally proposed ten years before by Horiuchi, Ropke, Schuck and the present author (Phys. Rev. Lett., 2001, 87: 192501). The microscopic model, which fully takes into account the Pauli principle between all the constituent nucleons, effective internucleon forces and the Coulomb force, can play an important role in reproducing an α-gas nature thanks to α-condensation as an excited state of α-like nuclei. An essential point of the wave function is to describe their ground state simultaneously. We study its typical features by giving an analytical formula of the norm kernel and the kernel concerning the one-body operator for 3α-condensation.