Electromagnetic transition rates of Carbon-12 and Oxygen-16 in rotational-vibrational models

The union of rotational and vibrational modes in generator-coordinate-type calculations, with application to neutrinoless double-beta decay

Good many-body methods for medium and heavy nuclei are important. Here we combine ideas from standard generator-coordinate methods (GCM) and the so-called Monte Carlo shell model, and set forth a novel approach: starting from a mean-field solution (Hartree-Fock-Bogoliubov), we create a set of non-orthogonal basis states, by using low-lying vibrational quasiparticleTamm-Dancoff modes, and then project onto states of good angular momentum and particle number. The results we benchmark against full shell model calculations. Even with just a few such modes we find improvement over standard GCM calc…

Evidence for rotational to vibrational evolution along the yrast line in the odd-A rare-earth nuclei

The phase transition of nuclei to increasing angular momentum (or spin) and excitation energy is one of the most fundamental topics of nuclear structure research. The odd-N nuclei with A equal 160 are widely considered belonging to the well-deformed region, and their excitation spectra are energetically favored to exhibit the rotational characteristics. In the present work, however, there is evidence indicating that the nuclei can evolve from rotation to vibration along the yrast lines while increasing spin. The simple method, named as E-Gamma Over Spin (E-GOS) curves, would be used to discern…

Changes in rotational characters of one- and two-phonon $γ$-vibrational bands in $^{105}$Mo

The $γ$ vibration is the most typical low-lying collective motion prevailing the nuclear chart. But only few one-phonon rotational bands in odd-$A$ nuclei have been known. Furthermore, two-phonon states, even the band head, have been observed in a very limited number of nuclides not only of odd-$A$ but even-even. Among them, that in $^{105}$Mo is unique in that Coriolis effects are expected to be stronger than in $^{103}$Nb and $^{105}$Nb on which theoretical studies were reported. Then the purpose of the present work is to study $^{105}$Mo paying attention to rotational character change of th…

Rotational-vibrational coupling in the BPS Skyrme model of baryons

We calculate the rotational-vibrational spectrum in the BPS Skyrme model for the hedgehog skyrmion with baryon number one. The resulting excitation energies for the nucleon and delta Roper resonances are slightly above their experimental values. Together with the fact that in the standard Skyrme model these excitation energies are significantly lower than the experimental ones, this provides strong evidence for the conjecture that the inclusion of the BPS Skyrme model is necessary for a successful quantitative description of physical properties of baryons and nuclei.

Rotational constants of multi-phonon bands in an effective theory for deformed nuclei

We consider deformed nuclei within an effective theory that exploits the small ratio between rotational and vibrational excitations. For even-even nuclei, the effective theory predicts small changes in the rotational constants of bands built on multi-phonon excitations that are linear in the number of excited phonons. In 166Er and 168Er, this explains the main variations of the rotational constants of the two-phonon gamma vibrational bands. In 232Th, the effective theory correctly explains the trend that the rotational constants decrease with increasing spin of the band head. We also study the…

Infinitesimal cranking for triaxial angular-momentum-projected configuration-mixing calculation and its application to the gamma vibrational band

Inclusion of time-odd components into the wave function is important for reliable description of rotational motion by the angular-momentum-projection method; the cranking procedure with infinitesimal rotational frequency is an efficient way to realize it. In the present work we investigate the effect of this infinitesimal cranking for triaxially deformed nucleus, where there are three independent cranking axes. It is found that the effects of cranking about three axes on the triaxial energy spectrum are quite different and inclusion of all of them considerably modify the resultant spectrum fro…

Evidence for Tetrahedral Structure of Calcium-40

More than 100 excited states of the Calcium-40 nucleus, with isospin 0, are classified into rotational-vibrational bands of an intrinsic tetrahedral structure. Almost all observed states below 8 MeV can be accommodated, as well as many high-spin states above 8 MeV. The bands have some similarity to those classifying states of Oxygen-16, but the A-mode vibrational frequency is lower relative to the E-mode and F-mode frequencies than in Oxygen-16. Previously identified rotational bands up to spin 16 and energy above 20 MeV are unified here into a smaller number of tetrahedral bands.

Oxygen-16 Spectrum from Tetrahedral Vibrations and their Rotational Excitations

A reinterpretation of the complete energy spectrum of the Oxygen-16 nucleus up to 20 MeV, and partly beyond, is proposed. The underlying intrinsic shape of the nucleus is tetrahedral, as in the naïve alpha-particle model and other cluster models, and A, E and F vibrational phonons are included. The A- and F-phonons are treated in the harmonic approximation, but the E-vibrations are extended into a two-dimensional E-manifold of D2-symmetric, four-alpha-particle configurations, following earlier work. This allows for the underlying tetrahedral configuration to deform through a square configurati…

相互作用玻色子模型中的双中子分离能、binding energies和相变

Two-neutron separation energies, binding energies and phase transitions in the interacting boson model

在相互作用玻色子模型的框架下，重新分析了三个过渡区（转动-振动、转动- $γ$ -不稳定和振动- $γ$ -不稳定跃迁）。本文提出了一种新的研究有限系统（如原子核）中相变的方法。结合能分析的重要性，而不仅仅是能谱和电磁跃迁，描述过渡区强调。最后，我们讨论一些现实的例子。

在计算形变偶偶核基态转动带时考虑β和γ振动

Including beta- and gamma- Vibrations in Evaluating the Ground State Rotational Band of Deformed Even-Even Nuclei

从Bohr-Mottelson的半经验形式出发，发展了一个新的模型，该模型考虑了β和γ头能量的影响以及转动惯量的变化，可以计算几乎所有形变e-e核的基态转动带.该模型可以调整与实验可用的β-和γ-振动能量的核，以及为那些未测量的β-和γ-振动。

Transition from vibrational to rotational characters in low-lying states of hypernuclei

In order to clarify the nature of hypernuclear low-lying states, we carry out a comprehensive study for the structure of $^{144-154}_{~~~~~~~~Λ}$Sm-hypernuclei, which exhibit a transition from vibrational to rotational characters as the neutron number increases. To this end, we employ a microscopic particle-core coupling scheme based on a covariant density functional theory. We find that the positive-parity ground-state band in the hypernuclei shares a similar structure to that of the corresponding core nucleus. That is, regardless of whether the core nucleus is spherical or deformed, each hyp…