Examples of the change of neutron shell-structure in both weakly-bound and resonant neutron one-particle levels in nuclei towards the neutron drip line are exhibited. It is shown that the shell-structure change due to the weak binding may lead to the deformation of those nuclei with the neutron numbers $N \approx$ 8, 20, 28 and 40, which are known to be magic numbers in stable nuclei. Nuclei in the "island of inversion" are most easily and in a simple manner understood in terms of deformation. As an example of spectroscopic properties other than single-particle energies, magnetic moments of some weakly-bound possibly deformed odd-N nuclei with neutron numbers close to those traditional magic numbers are given, which are calculated using the wave function of the last odd particle in deformed Woods-Saxon potentials.
The location of the neutron drip line, currently known for only the lightest elements, remains a fundamental question in nuclear physics. Its description is a challenge for microscopic nuclear energy density functionals, as it must take into account in a realistic way not only the nuclear potential, but also pairing correlations, deformation effects and coupling to the continuum. The recently developed deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) aims to provide a unified description of even-even nuclei throughout the nuclear chart. Here, the DRHBc with the successful d…
The predictive power of the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) for nuclear mass is examined in the superheavy region, $102 \le Z \le 120$. The accuracy of predicting the 10 (56) measured (measured and empirical) masses is $0.635$ ($0.642$) MeV, in comparison with $0.515$ ($1.360$) MeV by WS4 and $0.910$ ($2.831$) MeV by FRDM. Possible stability against multineutron emission beyond the two-neutron drip line is explored by the DRHBc theory, which takes into account simultaneously the deformation effects, the pairing correlations, and the continuum effects. Nucle…
We have done systematic Hartree-Fock-Bogoliubov calculations in coordinate space on the one-quasi-particle energies and binding energy odd-even staggering (OES) in semi-magic nuclei with the zero-range volume, mixed and surface pairing forces in order to explore the influence of their density dependence. The odd-$N$ isotopes are calculated within the blocking scheme. The strengths for the pairing forces are determined in two schemes by fitting locally to reproduce pairing gap in $^{120}$Sn and globally to all available data on the OES of semi-magic nuclei with $Z\geq8$. In the former calculati…
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 investigate ground states properties of Pb isotopes located between neutron and proton drip-lines estimated by two-neutron (two-proton) separation energies and Fermi energies within the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc). First, we report some candidates of nuclear shape coexistence in the isotope chain. They are accessed by calculating total energy as a function of the deformation parameter $β_2$, and for the coexistence candidates we take a couple of the deformation region bringing about minima of the energy within energy difference $ΔE < $ 1 MeV. Second,…
The exotic phenomenon of two-neutron halos and 2n-radioactivity are explored in the neutron-rich $^{40,42,44}$Mg by employing various variants of the relativistic mean-field approach. The extended tail of spatial density distributions including the enhanced neutron radii and skin thickness, pairing correlations, single-particle spectrum and wave functions predict $^{40,42,44}$Mg to be strong candidates for deformed neutron halos. Weakening of magicity at N$=$28 plays a significant role in the existence of a weakly bound halo in $^{40}$Mg which is currently the heaviest isotope of Mg accessible…
The recently observed weakly-bound 39Na provides a stringent theoretical constraint on the neutron drip-line. We studied the properties of drip-line nuclei around 39Na with the Hartree-Fock-Bogoliubov method and various Skyrme interactions. We adopted the extended SkM*-ext1 parameterization which can properly describe two-neutron separation energies of oxygen and fluorine isotopes and deformations at the center of the "island of inversion". Systematic calculations of drip lines of O, F, Ne, Na, Mg, and Al isotopes have been performed. We infer that 42Mg is weakly bound and 45Al is less weakly …
Relativistic mean-field description of nuclei at the drip lines
本文综述了近年来相对论平均场论在近滴线核结构研究中的应用。对于具有极端同位旋值的系统，相对论哈特里-博戈留波夫模型提供了一个统一的和自洽的平均场和配对关联的描述。该模型已应用于结构现象的研究，包括：在s-d中子壳层上方的质量区域中，轻核中中子皮和中子晕的形成，有效自旋-轨道相互作用的强同位旋依赖性和由此导致的表面性质的改变，对于丰中子核的球形N=28壳层间隙的抑制以及变形和形状共存的相关现象，球形核$14\leq Z \leq 28$中的质子滴线和变形核$59 \leq Z \leq 69$区域中的基态质子放射性。
We studied the charge radius ($r_{c}$), neutron radius ($r_n$), and neutron skin-thickness ($Δr=r_n-r_p$) over a chain of isotopes from C to Zr with the stable region to the neutron drip line. Theoretical calculations are done with axially deformed self-consistent relativistic mean-field theory (RMF) with effective nonlinear NL3 and NL3* interactions. The theoretically estimated values are compared with available experimental data and a reasonable agreement are noted. We additionally assessed the two-neutron separation energy ($S_{2n}$) to mark the drip line nuclei of the considered isotopic s…
Fayans energy density functional (EDF) FaNDF^0 has been applied to the nuclei around uranium region. Ground state characteristics of the Th, U and Pu isotopic chains, up to the two-neutron drip line, are found and compared with predictions from several Skyrme EDFs. The two-neutron drip line is found for FaNDF^0, SLy4 and SkM^* EDFs for a set of elements with even proton number, from Pb up to Fm.
Shell structure of low-lying neutron resonant levels in axially-symmetric quadrupole-deformed potentials is discussed, which seems analogous to that of weakly-bound neutrons. As numerical examples, nuclei slightly outside the neutron-drip-line, $^{39}_{12}$Mg$_{27}$ and $^{21}_{6}$C$_{15}$, are studied. For the lowest resonance I obtain $I^π$ = $Ω^π$ = 5/2$^{-}$ for $^{39}$Mg which is likely to be prolately deformed, while $I^π$ = $Ω^π$ = 1/2$^{+}$ may be assigned to the nucleus $^{21}$C which may be oblately deformed. Consequently, $^{21}$C will not be observed as a recognizable resonant stat…
Possible bound nuclei beyond the two-neutron drip line in the $50\leqslant Z \leqslant 70$ region are investigated by using the deformed relativistic Hartree-Bogoliubov theory in continuum with density functional PC-PK1. Bound nuclei beyond the drip lines of $_{56}$Ba, $_{58}$Ce, $_{62}$Sm, $_{64}$Gd and $_{66}$Dy are predicted, forming peninsulas of stability in nuclear landscape. Near these peninsulas, several multi-neutron emitters are predicted. The underlying mechanism of the peninsulas of stability is investigated by studying the total energy, Fermi surface, quadrupole deformation and th…
Based on the relativistic calculations of the nuclear masses in the transfermium region from No $(Z=102)$ to Ds $(Z=110)$ by the deformed relativistic Hartree-Bogoliubov theory in continuum, the possible existence of the bound nuclei beyond the neutron drip lines is studied. The two-neutron and multi-neutron emission bound nuclei beyond the primary neutron drip line of $N=258$ are predicted in $Z=106,108$ and $110$ isotopes. Detailed microscopic mechanism investigation reveals that nuclear deformation plays a vital role in the existence of the bound nuclei beyond the drip line. Furthermore, no…
Proton rich nuclei at and beyond the proton drip line in the Relativistic Mean Field theory
用相对论平均场理论研究了$55\le Z \le 73$区富质子奇$Z$核的基态性质。RMF方程在谐振子基下用展开法求解。在粒子-粒子通道中，我们采用了具有零程$δ$力的状态相关BCS方法，该方法已被证明对丰中子核也是有效的。计算了所有的基态性质，包括单质子分离能、基态形变、最后占据的质子轨道和质子滴线的位置。与现有的实验数据和预测的RHB方法得到了很好的协议。
Deformed Hartree-Fock Calculation of Proton-Rich Nuclei
我们对2 ≤ Z ≤ 82的偶偶核进行了Hartree-Fock+BCS计算，N的范围从质子滴线外到丰中子侧的实验前沿。得到了737个核的基态解和480个核的形状共存解。我们的方法的特点是笛卡尔网格表示的单粒子波函数，这是有利于处理核子皮肤和奇异的形状。计算结果与Moller等人的有限范围液滴模型及实验值进行了比较。
We use the finite amplitude method (FAM), an efficient implementation of the quasiparticle random phase approximation, to compute beta-decay rates with Skyrme energy-density functionals for 3983 nuclei, essentially all the medium-mass and heavy isotopes on the neutron rich side of stability. We employ an extension of the FAM that treats odd-mass and odd-odd nuclear ground states in the equal filling approximation. Our rates are in reasonable agreement both with experimental data where available and with rates from other global calculations.
We have investigated the Gamow-Teller transitions from ${}^{22}\textrm{Ne}$ to ${}^{22}\textrm{Na}$ by applying the isospin projected antisymmetrized molecular dynamics combined with generator coordinate method. We have found that the GT strength from $^AZ(J^πT)={}^{22}\textrm{Ne}(0_1^+1)$ is fragmented into two final states ${}^{22}\textrm{Na}(1_{1,2}^+0)$, which belong to $K=0$ and $K=1$ bands constructed by a prolately deformed $^{20}$Ne core with a $S=1$ proton-neutron ($pn$) pair. Coupling of the intrinsic-spin of the $pn$ pair with the core deformation play an important role in the GT fr…
After identifying the nuclei in the regions near A =80 and A = 160 for which beta-decay rates have the greatest effect on weak and main r-process abundance patterns, we apply the finite-amplitude method (FAM) with Skyrme energy-density functionals (EDFs) to calculate beta-decay half-lives of those nuclei in the quasiparticle random-phase approximation (QRPA). We use the equal filling approximation to extend our implementation of the charge-changing FAM, which incorporates pairing correlations and allows axially symmetric deformation, to odd-A and odd-odd nuclei. Within this framework we find d…
