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Register a new userPermutation symmetry and magic numbers of few-electron systems
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This paper has been withdrawn by Wenji Deng (e-mail: [email protected]) for further modification at Oct. 12, 1998. {PACS: 03.75.Fi, 05.30.Jp.64.60.-i, 32.80.Pj}
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We consider the problem of distinguishing convex subsets of $n$-cyclotomic model sets $varLambda$ by (discrete parallel) X-rays in prescribed $varLambda$-directions. In this context, a `magic number $m_{varLambda}$ has the property that any two convex subsets of $varLambda$ can be distinguished by their X-rays in any set of $m_{varLambda}$ prescribed $varLambda$-directions. Recent calculations suggest that (with one exception in the case $n=4$) the least possible magic number for $n$-cyclotomic model sets might just be $N+1$, where $N=operatorname{lcm}(n,2)$.
The nuclear shell model is a benchmark for the description of the structure of atomic nuclei. The magic numbers associated with closed shells have long been assumed to be valid across the whole nuclear chart. Investigations in recent years of nuclei far away from nuclear stability at facilities for radioactive ion beams have revealed that the magic numbers may change locally in those exotic nuclei leading to the disappearance of classic shell gaps and the appearance of new magic numbers. These changes in shell structure also have important implications for the synthesis of heavy elements in stars and stellar explosions. In this review a brief overview of the basics of the nuclear shell model will be given together with a summary of recent theoretical and experimental activities investigating these changes in the nuclear shell structure.
We discuss our recently proposed S3(down)xS3(up) flavour-permutation-symmetric mixing observables, giving expressions for them in terms of (moduli-squared) of the mixing matrix elements. We outline their successful use in providing flavour-symmetric descriptions of (non-flavour-symmetric) lepton mixing schemes. We develop our partially unified flavour-symmetric description of both quark and lepton mixings, providing testable predictions for CP-violating phases in both B decays and neutrino oscillations.
Influence of magic numbers on nuclear radii is investigated via the Hartree-Fock-Bogolyubov calculations and available experimental data. With the $ell s$ potential including additional density-dependence suggested from the chiral effective field theory, kinks are universally predicted at the $jj$-closed magic numbers and anti-kinks (textit{i.e.} inverted kinks) are newly predicted at the $ell s$-closed magic numbers, both in the charge radii and in the matter radii along the isotopic and isotonic chains where nuclei stay spherical. These results seem consistent with the kinks of the charge radii observed in Ca, Sn and Pb and the anti-kink in Ca. The kinks and the anti-kinks could be a peculiar indicator for magic numbers, discriminating $jj$-closure and $ell s$-closure.
The interplay between magic number stabilities and superfluidity of small para-hydrogen clusters with sizes $N = 5$ to 40 and temperatures $0.5 K leq T leq 4.5 $K is explored with classical and quantum Path Integral Monte Carlo calculations. Clusters with $N < 26$ and T $leq 1.5 K$ have large superfluid fractions even at the stable magic numbers 13, 19, and 23. In larger clusters, superfluidity is quenched especially at the magic numbers 23, 26, 29, 32, and 37 while below 1 K, superfluidity is recovered for the pairs $(27,28)$, $(30,31)$, and $(35,36)$. For all clusters superfluidity is localized at the surface and correlates with long exchange cycles involving loosely bound surface molecules.
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