Semimicroscopic algebraic description of α clustering in Ne isotopes

The α-cluster states of20Ne,19Ne and18Ne have been analyzed as members of a supermultiplet predicted by the U(4|12) cluster supersymmetry scheme. The analysis of B(E2) data and one-nucleon transfer reactions seem to support the validity of this scheme. The α-cluster states of the22Ne nucleus have been analyzed independently, and were compared with DAMD and GCM calculations. Based on these results, a similar study of21Ne seems worthwhile.


Introduction
Nuclei in the neighborhood of 20 Ne are known to possess marked α cluster bands. Among them, some Ne isotopes are in the forefront of investigations: α-clustering in 19 Ne is known to play an important role nuclear astrophysical processes in stars [1], while Ne isotopes with A > 20 serve as examples for systems with molecular orbitals [2].
The semimicroscopic algebraic cluster model (SACM) [3] has been applied to many p-and sd-shell nuclei assuming core+α or other types of clustering (see e.g. the references of [4]). This model makes heavy use of the SU(3) algebra, which appears in the desciption of both the relative motion and that of the internal cluster structure, where it accounts for the orbital structure in terms of Elliott's SU(3) model. The semimicroscopic nature of the SACM is manifested by the fact that it combines a microscopic model space with effective interactions. Due to the former one the model gives rigorous account of the Pauli exclusion principle between the nucleons, while the latter one allows a relatively simple parametrization of the physical operators.
The systematic application of the SACM to neighbouring core+α-type cluster systems revealed correlations in the model parameters with the mass number [5]. This finding later inspired the extension of the formalism of the SACM to a supersymmetry scheme that allows the unified description of the α-cluster states of neighbouring nuclei [6]. Supersymmetry links bosonic and fermionic degrees of freedom, which appear naturally in the SACM as the excitation of the relative motion, and that of the internal structure of non-closed-shell clusters, respectively. In this scheme the α-cluster states of 20 Ne (0 fermion), 19 F, 19 Ne (1 fermion) and 18 O, 18 F, 18 Ne (2 fermions) belong to the same U(4|12) supermultiplet.
More recently the SACM was appied to describe α-clustering in the 22 Ne nucleus [4]. Besides the interpretation of the experimental energy levels and E2 transitions, the results were also compared with the predictions of two other models, the generator-coordinate method (GCM) and the deformed-basis antisymmetrized molecular dynamics (DAMD) approach.  Table 1. α-cluster bands in A=20, 19, and 18 nuclei up to two major shell excitations.
The basis states associated with the chain (1) are labelled by the same quantum numbers as in the SACM [3], plus the fermion number N F and the total particle number N = N B + N F [6]: One important implication of the Pauli blocking between the nucleons of the clusters is that n π , and thus N B and N are restricted from below. The predictions of the cluster SUSY scheme involving the six nuclei displayed in Table 1 were tested in two ways: comparing the calculated and experimental values for electric quadrupole transition intensities for the six nuclei, and checking the one-nucleon transfer intensities in six known reactions between five of them.
The comparison of the experimental and theoretical B(E2) values was done by adjusting the three model parameters to the most precisely measured transitions in two different ways. First the fitting procedure was carried out for each nucleus separately, then a global fit was done, involving the available electric quadrupole transition data for all six nuclei.
There were altogether 52 experimental B(E2) values with well defined mean values and errors, and a few more with lower or upper limits. There were 5, 5 an 2 experimental B(E2) data for 20 Ne (in two bands assigned to (λ, µ) = (8, 0) and (9, 0)), 19 Ne (with (6, 0) and (8,1)) and 18 Ne (with (4, 0)). It was found that the parameters determined for the six nuclei individually did not differ much from the parameters extracted from the fit to the experimental data of all six nuclei, indicating the approximate validity of the SUSY scheme.  Table 2. α-cluster bands in 22 Ne and 21 Ne up to two major shell excitations.

22
Ne and 21 Ne: candidates for molecular orbital structures In some N > Z systems the neutrons can be pictured as moving on molecular orbitals around the core+α configuration [2], which, for Neon isotopes is 16 O + α. This development inspired us to apply the SACM to the 22 Ne nucleus [4]. The SACM α-cluster model space of 22 Ne and 21 Ne is displayed in Table 2.
The low-lying positive-parity part of the experimental 22 Ne spectrum is dominated by the 0 + 1 and 2 + bands, while the 0 + 2 band with large prolate deformation starts at 6.23 MeV. In the SACM these bands correspond to n π (λ, µ)κ =8(8,2)0, 8(8,2)2 and 10(14,0)0. For negative parity the 1 − , 0 − 1 and 2 − bands are known at low energy, which correspond to n π (λ, µ)κ =9(11,1)1, 9(9,2)0 and 9(9,2)2. The energy spectrum was fitted with the SACM Hamiltonian containing five parameters, and good agreement was found for the positive-parity spectrum. The calculated E2 transitions agreed well with the handful of known experimental data . The model predicted further bands, but the available experimental data was insufficient for assigning experimental states to the model ones. However, these predictions generally compared well with the results of two microscopic models, the deformed-basis antisymmetrized molecular dynamics (DAMD) [7] approach and the generator-coordinate method (GCM) [8]. The low-lying bands were described by the three models in a qualitatively similar way.