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Single particle spin-orbit interaction energy problem in nuclear shell structure is solved through negative harmonic oscillator in the self-similar-structure shell model (SSM) [4] and considering quarks contributions on single particle spin and orbit momentum. The paper demonstrates that single particle motion in normal nuclei is described better by SSM negative harmonic oscillator than conventional shell model positive harmonic oscillator[1][2][3]. The proposed theoretical formula for spin orbit interaction energy agrees well to experiment measurements.
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We address consequences of strong tensor and weak spin-orbit terms in the local energy density functional, resulting from fits to the $f_{5/2} - f_{7/2}$ splittings in $^{40}$Ca, $^{48}$Ca, and $^{56}$Ni. In this study, we focus on nuclear binding energies. In particular, we show that the tensor contribution to the binding energies exhibits interesting topological features closely resembling that of the shell-correction. We demonstrate that in the extreme single-particle scenario at spherical shape, the tensor contribution shows tensorial magic numbers equal to $N(Z)$=14, 32, 56, and 90, and that this structure is smeared out due to configuration mixing caused by pairing correlations and migration of proton/neutron sub-shells with neutron/proton shell filling. Based on a specific Skyrme-type functional SLy4$_T$, we show that the proton tensorial magic numbers shift with increasing neutron excess to $Z$=14, 28, and 50.
The Self-similar-structure shell model (SSM) comes from the evolution of the conventional shell model (SM) and keeps the energy level of SM single particle harmonic oscillation motion. In SM, single particle motion is the positive harmonic oscillation and in SSM, the single particle motion is the negative harmonic oscillation. In this paper a nuclear evolution equation (NEE) is proposed. NEE describes the nuclear evolution process from gas state to liquid state and reveals the relations among SM, SSM and liquid drop model (DM). Based upon SSM and NEE theory, we propose the solution to long-standing problem of nuclear shell model single particle spin-orbit interaction energy . We demonstrate that the single particle motion in normal nuclear ground state is the negative harmonic oscillation of SSM[1][2][3][4] Key words: negative harmonic oscillation, nuclear evolution equation, self-similar shell model
We first give an overview of the shell-correction method which was developed by V. M. Strutinsky as a practicable and efficient approximation to the general selfconsistent theory of finite fermion systems suggested by A. B. Migdal and collaborators. Then we present in more detail a semiclassical theory of shell effects, also developed by Strutinsky following original ideas of M. Gutzwiller. We emphasize, in particular, the influence of orbit bifurcations on shell structure. We first give a short overview of semiclassical trace formulae, which connect the shell oscillations of a quantum system with a sum over periodic orbits of the corresponding classical system, in what is usually called the periodic orbit theory. We then present a case study in which the gross features of a typical double-humped nuclear fission barrier, including the effects of mass asymmetry, can be obtained in terms of the shortest periodic orbits of a cavity model with realistic deformations relevant for nuclear fission. Next we investigate shell structures in a spheroidal cavity model which is integrable and allows for far-going analytical computation. We show, in particular, how period-doubling bifurcations are closely connected to the existence of the so-called superdeformed energy minimum which corresponds to the fission isomer of actinide nuclei. Finally, we present a general class of radial power-law potentials which approximate well the shape of a Woods-Saxon potential in the bound region, give analytical trace formulae for it and discuss various limits (including the harmonic oscillator and the spherical box potentials).
We discuss two conditions needed for correct computation of $2 u betabeta$ nuclear matrix-elements within the realistic shell-model framework. An algorithm in which intermediate states are treated based on Whiteheads moment method is inspected, by taking examples of the double GT$^+$ transitions $mbox{$^{36}$Ar}rightarrowmbox{$^{36}$S}$, $mbox{$^{54}$Fe}rightarrowmbox{$^{54}$Cr}$ and $mbox{$^{58}$Ni} rightarrowmbox{$^{58}$Fe}$. This algorithm yields rapid convergence on the $2 ubetabeta$ matrix-elements, even when neither relevant GT$^+$ nor GT$^-$ strength distribution is convergent. A significant role of the shell structure is pointed out, which makes the $2 ubeta beta$ matrix-elements highly dominated by the low-lying intermediate states. Experimental information of the low-lying GT$^pm$ strengths is strongly desired. Half-lives of $T^{2 u}_{1/2}({rm EC}/{rm EC}; mbox{$^{36}$Ar}rightarrowmbox{$^{36}$S})=1.7times 10^{29}mbox{yr}$, $T^{2 u}_{1/2}({rm EC}/{rm EC};mbox{$^{54}$Fe}rightarrow mbox{$^{54}$Cr})=1.5times 10^{27}mbox{yr}$,$T^{2 u}_{1/2}({rm EC} /{rm EC};mbox{$^{58}$Ni}rightarrowmbox{$^{58}$Fe})=6.1times 10^{24}mbox{yr}$and $T^{2 u}_{1/2}(beta^+/{rm EC};mbox{$^{58}$Ni} rightarrowmbox{$^{58}$Fe})=8.6times 10^{25}mbox{yr}$ are obtained from the present realistic shell-model calculation of the nuclear matrix-elements.
We study the role of the tensor term of the Skyrme effective interactions on the spin-orbit splittings in the N=82 isotones and Z=50 isotopes. The different role of the triplet-even and triplet-odd tensor forces is pointed out by analyzing the spin-orbit splittings in these nuclei. The experimental isospin dependence of these splittings cannot be described by Hartree-Fock calculations employing the usual Skyrme parametrizations, but is very well accounted for when the tensor interaction is introduced. The capability of the Skyrme forces to reproduce binding energies and charge radii in heavy nuclei is not destroyed by the introduction of the tensor term. Finally, we also discuss the effect of the tensor force on the centroid of the Gamow-Teller states.
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