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Register a new userNuclear Shell Structure Evolution Theory
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Zhengda Wang
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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
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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.
The atomic nucleus is a quantum many-body system whose constituent nucleons (protons and neutrons) are subject to complex nucleon-nucleon interactions that include spin- and isospin-dependent components. For stable nuclei, already several decades ago, emerging seemingly regular patterns in some observables could be described successfully within a shell-model picture that results in particularly stable nuclei at certain magic fillings of the shells with protons and/or neutrons: N,Z = 8, 20, 28, 50, 82, 126. However, in short-lived, so-called exotic nuclei or rare isotopes, characterized by a large N/Z asymmetry and located far away from the valley of beta stability on the nuclear chart, these magic numbers, viewed through observables, were shown to change. These changes in the regime of exotic nuclei offer an unprecedented view at the roles of the various components of the nuclear force when theoretical descriptions are confronted with experimental data on exotic nuclei where certain effects are enhanced. This article reviews the driving forces behind shell evolution from a theoretical point of view and connects this to experimental signatures.
The goal of nuclear structure theory is to build a comprehensive microscopic framework in which properties of nuclei and extended nuclear matter, and nuclear reactions and decays can all be consistently described. Due to novel theoretical concepts, breakthroughs in the experimentation with rare isotopes, increased exchange of ideas across different research areas, and the progress in computer technologies and numerical algorithms, nuclear theorists have been quite successful in solving various bits and pieces of the nuclear many-body puzzle and the prospects are exciting. This article contains a brief, personal perspective on the status of the field.
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.
The shapes of neutron-rich exotic Ni isotopes are studied. Large-scale shell model calculations are performed by advanced Monte Carlo Shell Model (MCSM) for the $pf$-$g_{9/2}$-$d_{5/2}$ model space. Experimental energy levels are reproduced well by a single fixed Hamiltonian. Intrinsic shapes are analyzed for MCSM eigenstates. Intriguing interplays among spherical, oblate, prolate and gamma-unstable shapes are seen including shape fluctuations, $E$(5)-like situation, the magicity of doubly-magic $^{56,68,78}$Ni, and the coexistence of spherical and strongly deformed shapes. Regarding the last point, strong deformation and change of shell structure can take place simultaneously, being driven by the combination of the tensor force and changes of major configurations within the same nucleus.
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