An analytic phenomenological shell model mass formula for light nuclei is constructed. The formula takes into account the non locality of the self consistent single particle potential and the special features of light...An analytic phenomenological shell model mass formula for light nuclei is constructed. The formula takes into account the non locality of the self consistent single particle potential and the special features of light nuclei, namely： （a） charge and mass distributions are closer to a Gaussian shape than to the shape characteristic in medium and heavy nuclei; （b） the central charge and mass densities are larger than, and decrease towards, the ＂asymptotic＂ values that are the reference parameters for nuclear matter; and （c） after a shell closure, the next level has a larger orbital angular momentum and a noticeably larger mean square radius. Only then a good numerical fit is obtained with parameters consistent with optical model analysis and empirical spin-orbit couplings. A correlation between the ＂skin effect＂ and the symmetry dependence of the optical potential is established. Towards the neutron drip line the potential well depth, the spin-orbit splitting of the single particle levels and the gap between major shells decrease, as has been observed. The ensuing shift and contraction of the single particle level scheme may lead to： （a） to strong configuration mixing and new magic numbers, and （b） the onset of the halo effect, to avoid the expulsion of single particle levels to the continuum.展开更多
由于在轻核中质子与中子处于同一壳,当用相互作用玻色子模型(IBM)描述轻核时,必须引入同位旋.这时 IBM 就叫 IBM 4,系统的对称群为U_(36).它有七条群链,其中群链U_36(?)U_6(sd)×U_6(ST)(?)SU_3(sd)×SU_3(S)×SU_3(T)(?)SU...由于在轻核中质子与中子处于同一壳,当用相互作用玻色子模型(IBM)描述轻核时,必须引入同位旋.这时 IBM 就叫 IBM 4,系统的对称群为U_(36).它有七条群链,其中群链U_36(?)U_6(sd)×U_6(ST)(?)SU_3(sd)×SU_3(S)×SU_3(T)(?)SU_3(sdS)×SU_3(T)(?)O_3(J)×O_3(T)叫强耦合 SU(3)极限。由于 E2跃迁算符 T(E2)q 是由群 U_(36),V_6(sd),SU_3(sd),SU_3(s)与 SU_3(s dS)的生成元构成的,故不必构造出强耦合 SU(3)极限的波函数,利用 Elliott 波函数妒φ((λμ)KJM)就可以得到 E2跃迁.展开更多
文摘An analytic phenomenological shell model mass formula for light nuclei is constructed. The formula takes into account the non locality of the self consistent single particle potential and the special features of light nuclei, namely： （a） charge and mass distributions are closer to a Gaussian shape than to the shape characteristic in medium and heavy nuclei; （b） the central charge and mass densities are larger than, and decrease towards, the ＂asymptotic＂ values that are the reference parameters for nuclear matter; and （c） after a shell closure, the next level has a larger orbital angular momentum and a noticeably larger mean square radius. Only then a good numerical fit is obtained with parameters consistent with optical model analysis and empirical spin-orbit couplings. A correlation between the ＂skin effect＂ and the symmetry dependence of the optical potential is established. Towards the neutron drip line the potential well depth, the spin-orbit splitting of the single particle levels and the gap between major shells decrease, as has been observed. The ensuing shift and contraction of the single particle level scheme may lead to： （a） to strong configuration mixing and new magic numbers, and （b） the onset of the halo effect, to avoid the expulsion of single particle levels to the continuum.
