We examine the general nature of nuclear odd-even mass differences by employing neutron and proton mass relations that emphasize these effects. The most recent mass tables are used. The possibility of a neutron excess dependence of the staggering is examined in detail in separate regions defined by the main nuclear shells, and a clear change in this dependency is found at $Z=50$ for both neutrons and protons. A further separation into odd and even neutron (proton) number produces very accurate local descriptions of the mass differences for each type of nucleons. These odd-even effects are combined into a global phenomenological expression, ready to use in a binding energy formula. The results deviate from previous parametrizations, and in particular found to be significantly superior to a recent two term, $A^{-1}$ dependence.
We have studied odd-even nuclear mass staggering with the Skyrme-Hartree-Fock-Bogoliubov theory by employing isoscalar and isovector contact pairing interactions. By reproducing the empirical odd-even mass differences of the Sn isotopic chain, the strengths of pairing interactions are determined. The optimal strengths adjusted in this work can give better description of odd-even mass differences than that fitted by reproducing the experimental neutron pairing gap of $^{120}$Sn.
Partial dynamical symmetry (PDS) is shown to be relevant for describing the odd-even staggering in the $γ$-band of $^{156}$Gd while retaining solvability and good SU(3) symmetry for the ground and $β$ bands. Several classes of interacting boson model Hamiltonians with SU(3) PDS are surveyed.
In this work, new recursion relations for the number of spin-J states for identical particles in a single-j shell are presented. Such relations are obtained using the generating-function technique, which enables one to exhibit an odd-even staggering in the spin distribution of an even number of fermions in a single-j shell: the number of states with an even value of J is larger than the number of states with an odd value of J. An analytical expression of the excess of states with an even value of J is provided, and its asymptotic behavior for large values of j is discussed.
The fragmentation of thermalized sources is studied using a version of the Statistical Multifragmentation Model which employs state densities that take the pairing gap in the nuclear levels into account. Attention is focused on the properties of the charge distributions observed in the breakup of the source. Since the microcanonical version of the model used in this study provides the primary fragment excitation energy distribution, one may correlate the reduction of the odd-even staggering in the charge distribution with the increasing occupation of high energy states. Thus, in the frame- wor…
The existing nuclear masses formula and nuclear masses model has undoubtedly achieved very good results, but it is still not satisfactory for some nuclear masses. Although there are many studies in Odd-Even staggering (OES) of nuclear masses, but the research on nuclear masses by using the systematicness of OES is indeed very few. Our purpose in this paper is to describe an empirical formula for Odd-Even staggering of nuclear masses that can be useful in describing and predicting nuclear masses. We empirically obtained the formula of odd-Z (odd-N) nuclei and even-Z (even-N) nuclei based on stu…
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…
We discuss the role of pairing anti-halo effect in the observed odd-even staggering in reaction cross sections for $^{30,31,32}$Ne and $^{36,37,38}$Mg isotopes by taking into account the ground state deformation of these nuclei. To this end, we construct the ground state density for the $^{30,31}$Ne and $^{36,37}$Mg nuclei based on a deformed Woods-Saxon potential, while for the $^{32}$Ne and $^{38}$Mg nuclei we also take into account the pairing correlation using the Hartree-Fock-Bogoliubov method. We demonstrate that, when the one-neutron separation energy is small for the odd-mass nuclei, a…
A Universal Four-Fermion Formation Framework and Odd-Even Staggering in $α$ Decay
Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-sen University（中山大学中法核工程与技术学院）；Department of Physics, Royal Institute of Technology（皇家理工学院物理系）
Survival of Pairing Correlations and Shell Effects at Scission in Finite-Temperature Nuclear Fission: Implications for Odd-Even Staggering
National Centre for Nuclear Research（国家核研究中心）；China Institute of Atomic Energy, Nuclear Data Center（中国原子能科学研究院核数据中心）；Department of Theoretical Physics, Maria Curie-Skłodowska University（玛丽亚·居里-斯克沃多夫斯卡大学理论物理系）；Department of Physics, Tsinghua University（清华大学物理系）
The properties of neutron matter are integral to the correct description of neutron stars as well as the description of neutron-rich nuclei. One key property of neutron matter is its superfluid behaviour in a range of densities relevant to the inner crust of neutron stars. This work investigates the finite-size effects in the pairing gap of a pure neutron matter superfluid system at densities found in the inner crust of cold neutron stars. The BCS (Bardeen-Cooper-Schrieffer) treatment of superfluidity gives rise to the mean-field pairing gap while a projection after variation (PBCS Theory) can…
The odd fermion at the edge: odd-even staggering in the trapped, unitary Fermi gas
University of Washington（华盛顿大学）；INFN sezione di Torino（都灵意大利国家核物理研究所）；Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern（伯尔尼大学爱因斯坦基础物理中心理论物理研究所）
Isospin Dependence in the Odd-Even Staggering of Nuclear Binding Energies
GSI的FRS-ESR设施为在一次实验中精确测量核物质表面的大面积提供了独特的条件。得到了604个缺中子核素（30 ≤ Z ≤ 92）的质量值，典型的不确定度为30微单位。首次测定了114种核素的质量。系统地研究了Z=50和Z=82质子壳层闭合之间的同位素链的核质量奇偶交错（OES）。结果与现代核模型的预测进行了比较。比较表明，OES的测量趋势是不能复制的理论拟合的质量只。从调整到质量和密度相关的核观测量的模型中提取的光谱配对间隙与实验数据吻合得更好。
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…
The mean-square charge radii of $^{207,208}$Hg ($Z=80, N=127,128$) have been studied for the first time and those of $^{202,203,206}$Hg ($N=122,123,126$) remeasured by the application of in-source resonance-ionization laser spectroscopy at ISOLDE (CERN). The characteristic \textit{kink} in the charge radii at the $N=126$ neutron shell closure has been revealed, providing the first information on its behavior below the $Z=82$ proton shell closure. A theoretical analysis has been performed within relativistic Hartree-Bogoliubov and non-relativistic Hartree-Fock-Bogoliubov approaches, considering…
The positive-parity states of even-even Xe nuclei are investigated within the framework of modified O(6) limit of the interacting boson model (IBM1). The effective three-body interaction [QQQ] where Q is the IBM O(6) quadrupole operator is introduced to exhibit the triaxiality nature. The shape of nuclear surface is described by the deformation parameters beta, gamma by using the intrinsic coherent state. The potential energy surfaces (PES) of the transition U(5)-Triaxiality-O(6) are calculated and analyzed and the critical phase transition points are identified. For each nucleus a fitting pro…
We study the fine structure of nuclear rotational spectra on the basis of both dynamical and discrete symmetry approaches. In this framework we show that the odd--even (Delta I = 1) staggering effects observed in various rotational bands carry detailed information about the collective band-mixing interactions and the collective shape properties of heavy nuclei.
The mesoscopic nature of the atomic nucleus gives rise to a wide array of macroscopic and microscopic phenomena. The size of the nucleus is a window into this duality: while the charge radii globally scale as $A^{1/3}$, their evolution across isotopic chains reveals unanticipated structural phenomena [1-3]. The most ubiquitous of these is perhaps the Odd-Even Staggering (OES) [4]: isotopes with an odd number of neutrons are usually smaller in size than the trend of their even-neutron neighbours suggests. This OES effect varies with the number of protons and neutrons and poses a significant cha…
Two fits of the pairing residual interaction in the rare-earth region are independently performed. One is made on the odd-even staggering of masses by comparing measured and explicitly calculated three-point binding-energy differences centered on odd-even nuclei. Another deals with the moments of inertia of the first 2+ states of well deformed even-even nuclei upon comparing experimental data with the results of Inglis-Belyaev moments (supplemented by a crude estimate of the so-called Thouless-Valatin corrections). The sample includes 24 even-even and 31 odd-mass nuclei selected according to t…
We present the mass excesses of 52-57Sc, obtained from recent time-of-flight nuclear mass measurements at the National Superconducting Cyclotron Laboratory at Michigan State University. The masses of 56Sc and 57Sc were determined for the first time with atomic mass excesses of -24.85(59)(+0 -54) MeV and -21.0(1.3) MeV, respectively, where the asymmetric uncertainty for 56Sc was included due to possible contamination from a long-lived isomer. The 56Sc mass indicates a small odd-even mass staggering in the A = 56 mass-chain towards the neutron drip line, significantly deviating from trends predi…
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…
Neutron-deficient $^{177-185}$Hg isotopes were studied using in-source laser resonance-ionization spectroscopy at the CERN-ISOLDE radioactive ion-beam facility, in an experiment combining different detection methods tailored to the studied isotopes. These include either alpha-decay tagging or Multi-reflection Time-of-Flight gating to identify the isotopes of interest. The endpoint of the odd-even nuclear shape staggering in mercury was observed directly by measuring for the first time the isotope shifts and hyperfine structures of $^{177-180}$Hg. Changes in the mean-square charge radii for all…
In this work, we study the odd-even effect in binding energies and charge radii, and systematic behavior of differential radii, to identify the underlying components of the effective nuclear interaction. We apply nuclear density functional theory using a family of Fayans and Skyrme energy density functionals fitted to similar datasets but using different optimization protocols. We inspect various correlations between differential charge radii, odd-even staggering in energies and radii, and nuclear matter properties. Detailed analysis is carried out for medium-mass and heavy semi-magic nuclei w…
Charge radii are one of the most fundamental properties of atomic nuclei characterizing their charge distributions. Though the general trend as a function of the mass number is well described by the $A^{1/3}$ rule, some fine structures, such as the evolution along the calcium isotopic chain and the corresponding odd-even staggerings, are notoriously difficult to describe both in density functional theories and ab initio methods. In this letter, we propose a novel ansatz to describe the charge radii of calcium isotopes, by adding a correction term, proportional to the number of Cooper pairs, an…
Fission fragments' charge and mass distribution is an important input to applications ranging from basic science to energy production or nuclear non-proliferation. In simulations of nucleosynthesis or calculations of superheavy elements, these quantities must be computed from models, as they are needed in nuclei where no experimental information is available. Until now, standard techniques to estimate these distributions were not capable of accounting for fine-structure effects, such as the odd-even staggering of the charge distributions. In this work, we combine a fully-microscopic collective…
$α$ decay is usually associated with both ground and low-lying isomeric states of heavy and superheavy nuclei, and the unpaired nucleon plays a key role on $α$ decay. In this work, we systematically studied the $α$ decay half-lives of odd-$A$ nuclei, including both favored and unfavored $α$ decay within the two-potential approach based on the isospin dependent nuclear potential. The $α$ preformation probabilities are estimated by using an analytic formula taking into account the shell structure and proton-neutron correlation, and the parameters are obtained through the $α$ decay half-lives dat…
Two types of average neutron-proton interaction formulas are compared: In the first type, neutron-proton interactions for even-even and odd-$A$ nuclei extracted from experimental binding energies show a smooth behavior as a function of mass number $A$ and are dominated by the contribution from the symmetry energy. Whereas in the second type large systematic staggering is seen between even-$A$ and odd-$A$ nuclei. This deviation is understood in term of the additional neutron-proton interaction in odd-odd nuclei relative to the neighboring even-even and odd-$A$ systems. We explore three possible…
