Using Woods-Saxon potentials and the eigenphase formalism for one-particle resonances, one-particle bound and resonant levels for neutrons as a function of quadrupole deformation are presented, which are supposed to be useful for the interpretation of spectroscopic properties of some light neutron-rich nuclei with weakly-bound neutrons. Compared with Nilsson diagrams in text books which are constructed using modified oscillator potentials, we point out a systematic change of the shell structure in connection with both weakly-bound and resonant one-particle levels related to small orbital angular momenta $\ell$. Then, it is seen that weakly-bound neutrons in nuclei such as $^{15-19}$C and $^{33-37}$Mg may prefer to being deformed as a result of Jahn-Teller effect, due to the near degeneracy of the 1d$_{5/2}$-2s$_{1/2}$ levels and the 1f$_{7/2}$-2p$_{3/2}$ levels in the spherical potential, respectively. Furthermore, the absence of some one-particle resonant levels compared with the Nilsson diagrams in text books is illustrated.
It is argued that there exist natural shell model spaces optimally adapted to the operation of two variants of Elliott' SU3 symmetry that provide accurate predictions of quadrupole moments of deformed states. A selfconsistent Nilsson-like calculation describes the competition between the realistic quadrupole force and the central field, indicating a {\em remarkable stability of the quadruplole moments}---which remain close to their quasi and pseudo SU3 values---as the single particle splittings increase. A detailed study of the $N=Z$ even nuclei from $^{56}$Ni to $^{96}$Cd reveals that the reg…
Oblate deformation of light neutron-rich even-even nuclei
轻中子丰富的偶偶核，其基态是扁形变，寻找，检查尼尔森图的基础上现实的伍兹-撒克逊潜力。Nilsson图的单粒子能量是通过求解由坐标空间中的薛定谔方程得到的耦合微分方程来计算的，其中$r \rightarrow \infty$对于单粒子束缚能级和共振能级都具有适当的渐近行为。本征相位形式主义用于计算单粒子共振能量。在Nilsson图的扁方一侧的大的能隙被发现与频率比（$ω_{\perp} : ω_{z}$）是简单有理数的谐振子势的扁方变形的幻数有关。与此相反，对于扁长形变，从谐振子势的（$ω_{\perp} : ω_{z}$）的简单有理数比获得的幻数几乎与粒子数无关，在基于实际Woods-Saxon势的Nilsson图中，在该粒子数处出现大的能隙。给出了$^{42}_{14}$ Si $_{28}$为扁球形的论据。在轻核中，发现核$^{20}_{6}$ C $_{14}$是具有扁圆基态的良好候选者。在质量数$A \approx 70$的区域中，除了$^{64}_{28}$ Ni $_{36}$之外，还可以在$^{76}_{28}$ Ni $_{48}$周围的核中发现扁扁基态。
Background: Microscopic calculations of heavy nuclei face considerable difficulties due to the sizes of the matrices that need to be solved. Various approximation schemes have been invoked, for example by truncating the spaces, imposing seniority limits, or appealing to various symmetry schemes such as pseudo-SU(3). This paper proposes a new symmetry scheme also based on SU(3). This proxy-SU(3) can be applied to well-deformed nuclei, is simple to use, and can yield analytic predictions. Purpose: To present the new scheme and its microscopic motivation, and to test it using a Nilsson model calc…
An approximate SU(3) symmetry appears in heavy deformed even-even nuclei, by omitting the intruder Nilsson orbital of highest total angular momentum and replacing the rest of the intruder orbitals by the orbitals which have escaped to the next lower major shell. The approximation is based on the fact that there is a one-to-one correspondence between the orbitals of the two sets, based on pairs of orbitals having identical quantum numbers of orbital angular momentum, spin, and total angular momentum. The accuracy of the approximation is tested through calculations in the framework of the Nilsso…
Systematic investigation of the rotational bands in nuclei with $Z \approx 100$ using a particle-number conserving method based on a cranked shell model
One-particle properties of deformed N $\approx$ 28 odd-N nuclei with weakly-bound or resonant neutrons
利用基于变形Woods-Saxon势的Nilsson图研究了含N $\approx$ 28的奇N核向中子滴线方向的可能变形.在正确的边界条件下，直接求解空间坐标网格中的薛定谔方程，得到了弱束缚和共振单粒子能级。如果我们使用与$β$稳定核相同的扩散势，中子2 p $_{3/2}$和1f $_{7/2}$能级之间的能量差变得非常小，或者N=28的能隙几乎消失，因为这些能级的结合能接近于零。这表明，这些中子滴线核的基态可能会变形。特别地，研究了奇N核$^{43}_{16}$ S $_{27}$和$^{45}_{16}$ S $_{29}$基态的自旋宇称和磁矩.此外，还提出了在位于滴线外的$^{39}_{12}$ Mg $_{27}$中，如果N=28能隙几乎为零，则最低共振态可能具有5/2 $^{-}$。
We propose a new quantum mechanical method to evaluate complete and incomplete fusion in collisions of weakly bound nuclei. The method is applied to the $^{7}{\rm Li}+^{209}{\rm Bi}$ system and the results are compared to experimental data. The overall agreement between theory and experiment is very good, above and below the Coulomb barrier.
The coordinate-space Hartree-Fock-Bogoliubov (HFB) approach with quasiparticle blocking has been applied to study the odd-A weakly bound nuclei $^{17,19}$B and $^{37}$Mg, in which halo structures have been reported in experiments. The Skyrme nuclear forces SLy4 and UNEDF1 have been adopted in our calculations. The results with and without blocking have been compared to demonstrate the emergence of deformed halo structures due to blocking effects. In our calculations, $^{19}$B and $^{37}$Mg have remarkable features of deformed halos.
Rotational Feshbach resonances in the deformed halo nucleus $^{31}$Ne
National Institute of Technology (KOSEN), Gifu College（岐阜工业高等专门学校）；RIKEN Nishina Center（理化学研究所仁科加速器中心）；Department of Physics, Kyushu University（九州大学物理学系）；Research Center for Nuclear Physics (RCNP), Osaka University（大阪大学核物理研究中心）
Collisions between complex nuclei may give rise to their total or partial fusion. The latter case is found experimentally to gain importance when one of the colliding nuclei is weakly bound. It has been commonly assumed that the partial fusion mechanism is a two-step process, whose first step is the dissociation of the weakly bound nucleus, followed by the capture of one of the fragments. To assess this interpretation, we present the first implementation of the three-body model of inclusive breakup proposed in the 1980s by Austern et al. [Phys. Rep. 154, 125 (1987)] that accounts for both the …
Experimental studies of nuclear collisions involving light weakly-bound nuclei show a systematic suppression of the complete fusion cross section by $\sim$30\% with respect to the expectation for tightly bound nuclei, at energies above the Coulomb barrier. Although it is widely accepted that the phenomenon is related to the weak binding of these nuclei, the origin of this suppression is not fully understood. In here, we present a novel approach that provides the complete fusion for weakly bound nuclei and relates its suppression to the competition between the different mechanisms contributing …
The incomplete fusion dynamics of $^6$Li + $^{209}$Bi collisions at energies above the Coulomb barrier is investigated. The classical dynamical model implemented in the {\sc platypus} code is used to understand and quantify the impact of both $^6$Li resonance states and transfer-triggered breakup modes (involving short-lived projectile-like nuclei such as $^8$Be and $^5$Li) on the formation of incomplete fusion products. Model calculations explain the experimental incomplete-fusion excitation function fairly well, indicating that (i) delayed direct breakup of $^6$Li reduces the incomplete fusi…
In this work, we identify a unique and novel feature of central density depletion in both proton and neutron named as doubly bubble nuclei in 50$\leq$Z(N)$\leq$82 region. The major role of 2d-3s single-particle (s.p.) states in the existence of halo and bubble nuclei is probed. The occupancy in s.p. state 3s$_{1/2}$ leads to the extended neutron density distribution or halo while the unoccupancy results in the central density depletion. By employing the Relativistic Mean-Field (RMF) approach along with NL3* parameter, the separation energies, single-particle energies, pairing energies, proton,…
