Abstract

GUPTA, R.  and  SUNDER MALIK, S.. Single particle spectrum of a nucleon in the harmonic oscillator mean field with spin-orbit coupling - a semiclassical view. Rev. mex. fis. [online]. 2020, vol.66, n.1, pp.82-90.  Epub Nov 27, 2020. ISSN 0035-001X.  https://doi.org/10.31349/revmexfis.66.82.

We have presented the single, particle spectrum for a particle in a mean-field of an isotropic harmonic oscillator with $\overrightarrow{I}\bullet \overrightarrow{s}$ coupling based on our semiclassical approach. It has been seen that this spectrum, without $\overrightarrow{I}\bullet \overrightarrow{s}$ coupling, exactly matches with the quantum mechanical one (without nuclear constraints). In this case, periodicity conditions give only pendulating orbits coinciding with l ≥ 0 axis, which fully supports the observations reported by Bohr and Mottelson (28). The orbits with l _ 0 are generated by reflecting the particle from the nuclear surface, R0, instead of infinity, which is the usual nuclear constraint. The mean-field strength is fixed by virial theorem. The resulting spectrum compares reasonably with the quantum spectrum for a particle enclosed in a perfectly reflecting walls. The variation of particle number withenergy helps us to identify the significant quantum numbers ‘n’ and ‘l’ in this semiclassical method. Finally, the $\overrightarrow{I}\bullet \overrightarrow{s}$ coupling splits each level and the splitting width of these levels compares well with that of nuclear splitting. Thus the complete nuclear shell model (with magic numbers) is reproduced without any fitting parameter.

Keywords : Semiclassical methods; periodic orbit theory; trace formula; spherical cavity; 03.65.Sq; 03.65.Bz; 71.20.Ad; 05.45.+b.

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