首次系统地研究了83 \leq Z \leq 101范围内奇偶核α衰变精细结构。所用的模型是最近提出的变形核的库仑和邻近势模型（CPPDN），它采用变形库仑势，变形两项邻近势和离心势。计算的部分半衰期，总半衰期和分支比与实验数据进行了比较，是在良好的协议。部分半衰期的标准差为1.08，分支比的标准差为1.21。我们的形式主义也成功地预测角动量阻碍和结构阻碍的转变。本文的研究表明，CPPMDN是一个统一的理论，它成功地解释了基态和同质异能态的α衰变，以及偶偶核、偶奇核和奇偶核的α精细结构。我们的研究表明，母核和子核表面的差异或形变参数的变化以及母核和子核壳层结构的变化，都会影响α衰变几率。
英文摘要：
Systematic study on α-decay fine structure is presented for the first time in the case of odd-even nuclei in the range 83 \leq Z \leq 101. The model used for the study is the recently proposed Coulomb and proximity potential model for deformed nuclei (CPPMDN), which employs deformed Coulomb potential, deformed two term proximity potential and centrifugal potential. The computed partial half lives, total half lives and branching ratios are compared with experimental data and are in good agreement. The standard deviation of partial half-life is 1.08 and that for branching ratio is 1.21. Our formalism is also successful in predicting angular momentum hindered and structure hindered transitions. The present study reveals that CPPMDN is a unified theory which is successful in explaining alpha decay from ground and isomeric state; and alpha fine structure of even-even, even-odd and odd-even nuclei. Our study relights that the differences in the parent and daughter surfaces or the changes in the deformation parameters as well as the shell structure of the parent and daughter nuclei, influences the alpha decay probability.
采用Fayans { \it et al}的EDF方法，在自洽的TFFS中计算了100多个球奇核的基态和激发态的磁矩.我们把自己限制在有一个中子和一个质子粒子（空穴）的原子核中，这些粒子被添加到魔法或半魔法的核心中。一个简单的模型，没有相互作用的奇核子。在大多数情况下，我们分析，得到了良好的协议与实验数据。考虑了几种情况下，这种简单的模型不工作，有必要超越。对许多不稳定奇核和奇-奇核的磁矩的未知值进行了预测，其中包括60个激发态奇-奇核的磁矩。
We develop a novel theoretical method for calculating spectroscopic properties of those nuclei with odd number of nucleons, that is based on the nuclear density functional theory and the particle-boson coupling scheme. Self-consistent mean-field calculation based on the DFT is performed to provide microscopic inputs to build the Hamiltonian of the interacting boson-fermion systems, which gives excitation spectra and transition rates of odd-mass nuclei. The method is successfully applied to identify the quantum shape phase transitions and the role of octupole correlations in odd-mass nuclei, an…
We present a method to calculate spectroscopic properties of odd-odd nuclei within the framework of the Interacting Boson-Fermion-Fermion Model based on the Gogny energy density functional. The $(β,γ)$-deformation energy surface of the even-even (boson-)core nucleus, spherical single-particle energies and occupation probabilities of the odd neutron and odd proton, are provided by the constrained self-consistent mean-field calculation within the Hartree-Fock-Bogoliubov method with the Gogny-D1M functional. These quantities are used as a microscopic input to fix most of the parameters of the IBF…
We show that the lowest-energy solution of the Hartree-Fock-Bogoliubov (HFB) equation has the even particle-number parity as long as the time-reversal symmetry is conserved in the HFB Hamiltonian without null eigenvalues. Based on this finding, we give a rigorous foundation of a method for solving the HFB equation to describe the ground state of odd-mass nuclei by employing a time-reversal anti-symmetric constraint operator to the Hamiltonian, where one obtains directly the ground state as a self-consistent solution of the cranked-HFB-type equation. Numerical analysis is done for the neutron-r…
Spectroscopic Amplitudes (SA) in the Interacting Boson Fermion Fermion Model (IBFFM) are necessary for the computation of $0νββ$ decays but also for cross sections of heavy-ion reactions, in particular, Double Charge Exchange reactions for the NUMEN collaboration, if one does not want to use the closure limit. We present for the first time: i) the formalism and operators to compute in a general case the spectroscopic amplitudes in the scheme IBFFM from an even-even to odd-odd nuclei, in a way suited to be used in reaction code, i.e., extracting the contribution of each orbital; 2) the odd-odd …
Nuclear level density at low excitation energies is proposed as an indicator of the first order phase transitions in nuclei. The new signature, a maximum value of the level density at the critical point, appears to be sensitive to the detailed way the phase transition takes place in different nuclear regions: it is consistent with phase coexistence in the N=90 region, and with a rapid crossing of the two phases, without their coexistence/mixing at the critical point in the N=60 region, respectively. Candidates for critical point nuclei are proposed for odd-mass and odd-odd nuclei, using correl…
The low-energy excitations and $β$ decays of odd-A nuclei are studied within the interacting boson-fermion model (IBFM), based on the Gogny-D1M nuclear energy density functional (EDF). The constrained Hartree-Fock-Bogoliubov (HFB) approximation is employed to compute potential energy surfaces in terms of triaxial quadrupole degrees of freedom for even-even Xe and Ba nuclei in the mass $A\approx 130$ region. The mean field approximation also provides spherical single-particle energies and occupation probabilities for the neighboring odd-A nuclei. Those quantities represent a microscopic input f…
We investigate the prolate-to-oblate shape phase transitions in the neutron-rich Pt, Os and Ir nuclei in the mass $A\approx 190$ region. The Hamiltonian of the interacting boson-fermion model, used to describe the odd-mass $^{185-199}$Pt, $^{185-193}$Os and $^{185-195}$Ir isotopes, is partially constructed by using as a microscopic input the results of constrained self-consistent mean-field calculations within the Hartree-Fock-Bogoliubov method with the Gogny force. The remaining few parameters are adjusted to experimental data in the odd systems. In this way the calculations reasonably descri…
The interacting boson-fermion model (IBFM), with parameters determined from the microscopic Hartree-Fock-Bogoliubov (HFB) approximation, based on the parametrization D1M of the Gogny energy density functional (EDF), is employed to study the structural evolution in odd-mass $γ$-soft nuclei. The deformation energy surfaces of even-even nuclei, single-particle energies and occupation probabilities of the corresponding odd-mass systems have been obtained within the constrained HFB approach. Those building blocks are then used as a microscopic input to build the IBFM Hamiltonian. The coupling const…
The low-energy structure and $β$ decay properties of neutron-rich even- and odd-mass Pd and Rh nuclei are studied using a mapping framework based on the nuclear density functional theory and the particle-boson coupling scheme. Constrained Hartree-Fock-Bogoliubov calculations using the Gogny-D1M energy density functional are performed to obtain microscopic inputs to determine the interacting-boson Hamiltonian employed to describe the even-even core Pd nuclei. The mean-field calculations also provide single-particle energies for the odd systems, which are used to determine essential ingredients …
The spectroscopic properties of the odd-odd isotopes $^{124-132}$Cs have been studied within the interacting boson-fermion-fermion model based on the Gogny-D1M energy density functional framework. Major ingredients to build the interacting boson-fermion-fermion Hamiltonian, such as the ($β,γ$)-deformation energy surfaces for the even-even core nuclei $^{124-132}$Xe as well as single-particle energies and occupation probabilities of the odd nucleons, have been computed microscopically with the constrained Hartree-Fock-Bogoliubov method. A few coupling constants of the boson-fermion and residual…
For $N=Z$ odd-odd nuclei, a three-body model assuming two valence particles and an inert core can provide an understanding of pairing correlations in the ground state and spin-isospin excitations. However, since residual core-nucleon interactions can have a significant impact on these quantities, the inclusion of core excitations in the model is essential for useful calculation to be performed. The effect of core excitations must be included in order to gain a detailed understanding of both the ground state and spin-isospin properties of these systems. To this end, we include the vibrational e…
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 compute the $β$-decay $ft$-values within the frameworks of the energy density functional (EDF) and the interacting boson model (IBM). Based on the constrained mean-field calculation with the Gogny-D1M EDF, the IBM Hamiltonian for an even-even nucleus and essential ingredients of the interacting boson-fermion-fermion model (IBFFM) for describing the neighboring odd-odd nucleus are determined in a microscopic way. Only the boson-fermion and residual neutron-proton interaction strengths are determined empirically. The Gamow-Teller (GT) and Fermi (F) transition rates needed to compute the $β$-d…
In this contribution, we present the cluster shell model which is analogous to the Nilsson model, but for cluster potentials. Special attention is paid to the consequences of the discrete symmetries of three alpha-particles in an equilateral triangle configuration. This configuration is characterized by a special structure of the rotational bands which can be used as a fingerprint of the underlying geometric configuration. The cluster shell model is applied to the nucleus 13C.
A systematic study of $γ$-bands observed in atomic nuclei is performed using the triaxial projected shell model (TPSM) approach. The staggering phase between the even and odd spin members of the $γ$-band for most the nuclei investigated in the present work is found to have even-I-below-odd-I, which in the framework of the collective model is considered as a signature of $γ$-softness. It is observed that out of twenty-three systems studied, only four nuclei, namely, $^{76}$Ge, $^{112}$Ru, $^{170}$Er and $^{232}$Th depict staggering phase with odd-I-below-even-I, which is regarded as an indicati…
The self-consistent model, developed previously to describe phonon coupling (PC) effects in magnetic moments of odd magic and semi-magic nuclei, is extended to quadrupole moments. It is based on the theory of finite Fermi systems with the use of the perturbation theory in $g_L^2$, where $g_L$ is the vertex creating the $L$-phonon. Accounting for the phonon tadpole diagrams is an important ingredient of this model. The calculation scheme is based on the Fayans energy density functional DF3-a and does not contain any adjusted parameters. The odd In and Sb isotopes are considered, which are the p…
A unified theoretical model reproducing charge radii of known atomic nuclei plays an essential role in making extrapolations for unknown nuclei. Recently developed new ansatz which phenomenologically takes into account the neutron-proton short-range correlations ($np$-SRCs) can describe the discontinuity properties and odd-even staggering (OES) effect of charge radii along isotopic chains remarkably well. In this work, we further review the modified root-mean-square (rms) charge radii formula in the framework of relativistic mean field (RMF) theory. The charge radii are calculated along variou…
