Abstract
We investigate the neutron number $(N)$ dependence of root mean square radii of point proton distribution (proton radii) of Be, B, and C isotopes with the theoretical method of variation after spin-parity projection in the framework of antisymmetrized molecular dynamics (AMD). The proton radii in Be and B isotopes changes rapidly as $N$ increases, reflecting the cluster structure change along the isotope chains, whereas, those in C isotopes show a weak $N$ dependence because of the stable proton structure in nuclei with $Z=6$. In neutron-rich Be and B isotopes, the proton radii are remarkably increased by the enhancement of the two-center cluster structure in the prolately deformed neutron structure. We compare the $N$ dependence of the calculated proton radii with the experimental ones reduced from the charge radii determined by isotope shift and those deduced from the charge changing interaction cross section. It is found that the $N$ dependence of proton radii can be a probe to clarify enhancement and weakening of cluster structures.
Highlights
In light unstable nuclei, various exotic structures such as magic number breaking, new cluster structures, and neutron halo structure have been discovered
In a series of Be isotopes, it has been revealed that the structure changes rapidly with the increase of the neutron number N and the cluster structure develops in neutron-rich Be isotopes as discussed in many theoretical and experimental studies [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26]
The experimental matter radii are those deduced from the interaction cross section [50]
Summary
Various exotic structures such as magic number breaking, new cluster structures, and neutron halo structure have been discovered. ΞA }, indicating single-nucleon Gaussian centroids and spin orientations for all nucleons These parameters are determined by the energy variation after spin-parity projection to obtain optimized AMD wave functions for J π states. I choose the width parameter ν for single-nucleon Gaussian wave packets to minimize energies of stable nuclei (9 Be, 11 B, and 12 C) and use the fixed ν value in each series of isotopes. Different width parameters for protons and neutrons or independent widths for all nucleons should be adopted as done in the method of fermionic molecular dynamics (FMD) [40,41] and an extended version of AMD [42]. The. AMD+VAP method better describes structures of the ground and excited states of light nuclei and useful to investigate details of the structure change between shell-model-like states and cluster states than the simple AMD. Note that the AMD wave function is similar to the wave function used in FMD calculations [41], though some differences exist in the width parameter and variational procedure, as well as adopted effective interaction
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