Background: Understanding nuclear shape is a crucial problem in nuclear physics. In particular, determining the sign of quadrupole deformation, i.e., whether prolate or oblate, remains a challenging problem. Purpose: Our aim is to propose a method for determining the sign of quadrupole deformation using $α$ inelastic scattering data and to demonstrate its effectiveness. Method: Our approach is the standard coupled-channel method based on the macroscopic model. We utilize the nuclear reorientation effect, a phenomenon associated with the self coupling of excited states, as a probe sensitive to the sign of deformation. Results: We first provide an overview of how the reorientation effect influences inelastic scattering cross sections, and numerically confirm its validity in realistic cases. We then demonstrate that the sign of deformation can be uniquely determined from inelastic scattering cross section data. Conclusion: Our technique offers a systematic approach for determining the sign of deformation in both stable and unstable nuclei. The broad applicability of $α$ inelastic scattering will make it a valuable tool to study shape of nuclei, especially unstable nuclei.
The yrast lines in Kr isotopes with $N=42$, 44, and 46 are investigated in a beyond mean field framework with both prolate-oblate coexistence and quasiparticle alignment taken into account. Quasiparticle orbitals with high-$j$ and low-$Ω$ on the oblate side are shown to be responsible for the sharp backbending observed in $^{82}$Kr, by driving the yrast shape from prolate to oblate. This suggests that quasiparticle alignment may not be neglected in the investigation of the shape evolution along the yrast line.
Prolate-oblate shape competition and impact on charge radii in Bk isotopes
School of Physics, Zhengzhou University（郑州大学物理学院）；State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University（北京大学物理学院核物理与核技术国家重点实验室）
The shape of a nucleus is one of fundamental nuclear properties. We perform a systematic investigation of bubble nuclei that also exhibit shape coexistence in Hf, W, Os, Pt and Hg even-even isotopes using the deformed relativistic Hartree-Bogoliubov theory in continuum. For a systematic study, we first consider nuclear bubble structures and shape coexistence separately. We confirm that deformations and pairing correlations hinder bubble structures by comparing our results with those from relativistic continuum Hartree-Bogoliubov theory that assumes spherical symmetry in nuclei. We then predict…
The consequences of the short range nature of the nucleon-nucleon interaction, which forces the spatial part of the nuclear wave function to be as symmetric as possible, on the pseudo-SU(3) scheme are examined through a study of the collective deformation parameters beta and gamma in the rare earth region. It turns out that beyond the middle of each harmonic oscillator shell possessing an SU(3) subalgebra, the highest weight irreducible representation (the hw irrep) of SU(3) has to be used, instead of the irrep with the highest eigenvalue of the second order Casimir operator of SU(3) (the hC i…
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。
The phenomena of shape evolution and shape coexistence in even-even $^{88-126}$Zr and $^{88-126}$Mo isotopes is studied by employing covariant density functional theory (CDFT) with density-dependent point coupling parameter sets DD-PCX and DD-PC1, and with separable pairing interaction. The results for rms deviation in binding energies, two-neutron separation energy, the differential variation of two-neutron separation energy, and rms charge radii, as a function of neutron number, are presented and compared with available experimental data. In addition to the oblate-prolate shape coexistence i…
Temperature and angular momentum induced shape changes in the well deformed 100 Nb have been investigated within the theoretical framework of Statistical theory combined with triaxially deformed Nilson potential and Strutinsky prescription. Two shape coexistence, one in the ground state of 104 Nb between oblate and triaxial shapes and another one between oblate and rarely seen prolate non-collective shapes in excited hot rotating 100 Nb at the mid spin values around 14-16h are reported for the first time. The level density parameter indicates the influence of the shell effects and changes dras…
We consider several variants of SU(3) partial dynamical symmetry in relation to quadrupole shapes in nuclei. Explicit construction of Hamiltonians with such property is presented in the framework of the interacting boson model (IBM), including higher order terms, and in its proton-neutron extension (IBM-2). The cases considered include a single prolate-deformed shape with solvable ground and $γ$ or $β$ bands, coexisting prolate-oblate shapes with solvable ground bands, and aligned axially-deformed proton-neutron shapes with solvable symmetric ground and $γ$ bands and mixed-symmetry scissors an…
Exclusive cross sections for the $^{43}$P$(-1p)^{42}$Si reaction to the lowest $0^+$ and $2^+$ states, measured at NSCL with GRETINA and the S800, are interpreted in terms of a two-level mixing (collective) model of oblate and prolate co-existing shapes. Using the formalism developed for deformed nuclei we calculate the spectroscopic amplitudes and exclusive cross-sections in the strong coupling limit, where for $^{43}$P the schematic wavefunction includes the coupling of the Nilsson [211]$\frac{1}{2}$ proton orbit. Good agreement with the experimental data is obtained when the amplitude of th…
