原子核质量的测量和评估

质量是原子核的基本性质之一,在核物理和核天体物理中都有重要的应用。原子核质量测量是目前核物理研究的一个前沿热点课题,国际上各个核物理实验室积极发展新设备和新技术,在短寿命放射性核素测量和超高精度质量测量方面取得了重要进展,本文对此进行了总结评述。在兰州重离子加速器冷却储存环（HIRFL-CSR）上利用等时性质量谱仪测量了一些原子核的质量,本文对其在测量精度、核态最短寿命等前沿进展做了简要介绍,并介绍了正在发展的双飞行时间质量谱仪。原子质量评估收集所有与原子核质量相关的实验数据,经过评估后推荐出质量值及相应误差。原子质量评估AME2016于2017年3月发表,为科技工作者提供基准数据。Mass is a fundamental property of the atomic nucleus. Nuclear mass data play an important role in nuclear physics and nuclear astrophysics. Thanks to the developments of novel mass spectrometers and radioactive nuclear beam facilities, the experimental knowledge of nuclear masses has been continuously expanding along two main directions, including:measurements aimed at high-precision mass values and at the most exotic nuclei far from the stability. The latest progress are reviewed in the paper. In the past few years, mass measurements of short-lived nuclides were performed using isochronous mass spectrometry based on the Cooler Storage Ring at the Heavy Ion Research Facility in Lanzhou(HIRFL-CSR). The progresses on the frontiers of short half-life and high precision are introduced. The Atomic Mass Evaluation (AME) is the most reliable source for the comprehensive information related to the atomic (nuclear) masses. The latest version of the AME, i.e., AME2016, was published in March, 2017, serving the research community with the benchmark data.     

ISOLTRAP: An on-line Penning trap for mass spectrometry on short-lived nuclides

ISOLTRAP is a Penning trap mass spectrometer for high-precision mass measurements on short-lived nuclides installed at the on-line isotope separator ISOLDE at CERN. The masses of close to 300 radionuclides have been determined up to now. The applicability of Penning trap mass spectrometry to mass measurements of exotic nuclei has been extended considerably at ISOLTRAP by improving and developing this double Penning trap mass spectrometer over the past two decades. The accurate determination of nuclear binding energies far from stability includes nuclei that are produced at rates less than 100 ions/s and with half-lives well below 100ms. The mass-resolving power reaches 10⁷ corresponding to 10keV for medium heavy nuclei and the uncertainty of the resulting mass values has been pushed down to below 10^-8. The article describes technical developments achieved since 1996 and the present performance of ISOLTRAP.     

A Proposed Storage Ion Trap of an ‘In-Flight Capture’ Type for Precise Mass Measurement of Radioactive Nuclear Reaction Products and Fission Fragments

Data on nuclear masses provide a basis for creating and testing various nuclear models. A tandem system comprised of the U-400M cyclotron, the COMBAS magnetic separator and the mass spectrometric ion trap of an ‘in-flight capture’ type is considered as a complex for producing of the short-lived nuclei by heavy ions in fragmentation reactions and for precise mass measurement of this nuclei. The FLNR plan scientific and technical research includes a project DRIBs for producing accelerated beams of radioactive nuclear reaction products and photofission fragments. This project proposes also precise mass measurements with the help of ion trap. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Use of Multi-Pass Time-of-Flight Mass Analyzers for Nuclear-Decay Spectroscopy of Mass Identified Nuclei

The masses of ions of some keV can be determined in multi-pass time-of-flight mass analyzers [1,2] with high precision. The mass accuracies thus achieved are sufficient to determine the proton and neutron numbers for most short-lived and stable nuclei [3,5]. Recording α- or γ-radiation of the investigated nuclei in delayed coincidence to the ion arrival, one thus can perform nuclear spectroscopy of selected nuclei. This revised version was published online in July 2006 with corrections to the Cover Date.     

High-precision mass measurements of hydrogen-like <Superscript>24</Superscript>Mg<Superscript>11+</Superscript> and <Superscript>26</Superscript>Mg<Superscript>11+</Superscript> ions in a Penning trap

For the determination of the bound-electron g factor in hydrogen-like heavy ions the mass of the ion is needed at a relative uncertainty of at least 1 ppb. With the SMILETRAP Penning trap mass spectrometer at the Manne Siegbahn Laboratory in Stockholm several mass measurements of ions with even-even nuclei at this level of precision have been performed so far, exploiting the fact that the mass precision increases linearly with the ion charge. Measurements of masses of the hydrogen-like ions of the two Mg-isotopes ²⁴Mg and ²⁶Mg are reported. The masses of the hydrogen-like ions are 23.979011054(14) u and 25.976562354(34) u, corresponding to the atomic masses 23.985041690(14) u and 25.982592986(34) u, respectively. The possibility to use these two isotopes for the first observation of an isotope effect in the bound-electron g factor in hydrogen-like heavy ions is discussed.     

The Mass Programme at GANIL Using the CSS2 and CIME Cyclotrons

The mass-measurement programme at GANIL aims to measure the masses of heavy nuclei close to the N=Z line which is the ideal region to study neutron-proton pairing. An original direct time-of-flight mass-measurement method was developed at GANIL which uses the CSS2 cyclotron as a high-resolution spectrometer. The masses of ions of A=68,76,80 and 100 have been measured with a precision of a few 10⁻⁶. Mass measurements will be performed with the new CIME cyclotron of SPIRAL using a similar method based on the measurement of the phase of the accelerated ions for different radio-frequencies. A recently approved experiment will help develop this new technique and aims to measure the mass of ³¹Ar radioactive nuclei with a precision of 10⁻⁶. This revised version was published online in July 2006 with corrections to the Cover Date.     

Isospin dependence in the odd-even staggering of nuclear binding energies

The FRS-ESR facility at GSI provides unique conditions for precision measurements of large areas on the nuclear mass surface in a single experiment. Values for masses of 604 neutron-deficient nuclides (30 < or = Z < or = 92) were obtained with a typical uncertainty of 30 microu. The masses of 114 nuclides were determined for the first time. The odd-even staggering (OES) of nuclear masses was systematically investigated for isotopic chains between the proton shell closures at Z = 50 and Z = 82. The results were compared with predictions of modern nuclear models. The comparison revealed that the measured trend of OES is not reproduced by the theories fitted to masses only. The spectral pairing gaps extracted from models adjusted to both masses, and density related observables of nuclei agree better with the experimental data.     

Direct mass measurements of the neutron-rich isotopes of fluorine through chlorine

The masses of 34 neutron-rich isotopes of fluorine through chlorine are reported. These measurements more fully delineate the mass surface in the region of deformed nuclei centered around ³¹Na and, in addition, provide the first mass values of several silicon through sulfur nuclei. We compare our data to recent shell model and mass model calculations     

Ability of the radial basis function approach to extrapolate nuclear mass

The ability of the radial basis function(RBF) approach to extrapolate the masses of nuclei in neutron-rich and superheavy regions is investigated in combination with the Duflo-Zuker(DZ31), Hartree–Fock-Bogoliubov(HFB27), finite-range droplet model(FRDM12) and Weizs?cker-Skyrme(WS4) mass models. It is found that when the RBF approach is employed with a simple linear basis function, different mass models have different performances in extrapolating nuclear masses in the same region, and a single mass model may have different performances when it is used to extrapolate nuclear masses in different regions. The WS4 and FRDM12 models(two macroscopic–microscopic mass models), combined with the RBF approach, may perform better when extrapolating the nuclear mass in the neutron-rich and superheavy regions.     

Weizsäcker-Skyrme核质量模型的统计误差研究

基于最大值近似估算的方法,系统地研究了Weizsäcker-Skyrme（WS4）核质量模型的参数不确定性,并计算了WS4核质量模型理论预言值的统计误差。WS4核质量模型的理论预言值与实验值的偏差基本都小于模型的统计误差,表明采用最大值近似估算法对WS4核质量模型理论预言的统计误差的分析是简捷而有效的。进一步研究了WS4核质量模型理论计算中最敏感的参数,结果表明,对称能系数相关的两个参数c_sym和κ对中子滴线附近的原子核质量有重要影响。此外还对WS4模型与WS*模型的参数不确定性及统计误差进行了对比研究,WS4模型中各模型参数的不确定性比WS*模型中相应模型参数的不确定性降低了10%~ 50%。The statistical uncertainties of 15 model parameters in the Weizsäcker-Skyrme(WS4) mass model are investigated with an efficient approach, and the propagated errors in the predicted masses are estimated. The discrepancies between the predicted masses and the experimental data are almost all smaller than the model errors. The most sensitive model parameter which causes the largest statistical error is analyzed for all bound nuclei. We find that the two coefficients of symmetry energy term significantly influence the mass predictions of extremely neutron-rich nuclei. In addition, the parameter uncertainties and statistical errors of the WS4 mass model and the WS* mass model are compared. The uncertainties of model parameter in the WS4 mass model is reduced by 10% ~ 50% compared with the WS* mass model.     

Influence of binding energies of electrons on nuclear mass predictions

Nuclear mass contains a wealth of nuclear structure information, and has been widely employed to extract the nuclear effective interactions. The known nuclear mass is usually extracted from the experimental atomic mass by subtracting the masses of electrons and adding the binding energy of electrons in the atom. However,the binding energies of electrons are sometimes neglected in extracting the known nuclear masses. The influence of binding energies of electrons on nuclear mass predictions are carefully investigated in this work. If the binding energies of electrons are directly subtracted from the theoretical mass predictions, the rms deviations of nuclear mass predictions with respect to the known data are increased by about 200 ke V for nuclei with Z, N 8. Furthermore, by using the Coulomb energies between protons to absorb the binding energies of electrons, their influence on the rms deviations is significantly reduced to only about 10 ke V for nuclei with Z, N 8. However, the binding energies of electrons are still important for the heavy nuclei, about 150 ke V for nuclei around Z = 100 and up to about 500 ke V for nuclei around Z = 120. Therefore, it is necessary to consider the binding energies of electrons to reliably predict the masses of heavy nuclei at an accuracy of hundreds of ke V.     

Mass measurements of relativistic projectile fragments in the storage ring ESR

Two experimental methods of measuring masses of exotic nuclei in the storage ring ESR are presented. Bismuth and nickel fragments were produced via projectile fragmentation, separated and investigated with the combination of the fragment separator FRS and the ESR: (i) Direct mass measurements of relativistic projectile fragments were performed using Schottky mass spectrometry (SMS), i.e., exotic nuclei were stored and cooled in the ESR. Applying electron cooling, the relative velocity spread of circulating low intensity beams can be reduced below 10⁻⁶. Under this condition a mass resolving power of up to m/Δm=6.5·10⁵ (FWHM) was achieved in a recent measurement. Previously unknown masses of more than 100 neutron-deficient isotopes have been measured in the range of 60≤Z≤84. Using known Q _α values the area of known masses could be extended to more exotic nuclei and to higher proton numbers. The results are compared with mass models and extrapolations of experimental values. In a second experiment with ²⁰⁹Bi projectiles the area of the measured masses was extended to lower proton numbers. Due to various improvements at the ESR the precision of the measurements could be raised. (ii) Exotic nuclei with half-lives shorter than the time needed for SMS (present limit: T _1/2 ≈ 5 sec) can be investigated by time-of-flight measurements whereby the ESR is operated in the isochronous mode. This novel experimental technique has been successfully applied in first measurements with nickel and neon fragments where a mass resolving power of m/Δm=1.5·10⁵ (FWHM) was achieved.     

A Physics Case for SHIPTRAP: Measuring the Masses of Transuranium Elements

SHIPTRAP will allow direct measurement of masses of transuranium nuclides. The method of choice is a Penning trap spectrometer coupled to the SHIP (Separator for Heavy Ion Products) facility at GSI, Darmstadt. In this paper the impact of the SHIPTRAP facility, with its capability of systematic mass measurements with high precision, is explored. Rather few masses of nuclides above uranium are presently known experimentally. In the region of nuclides above Z=100 no ground state masses were measured directly. SHIPTRAP will play an important role in systematically mapping out this area. Possible candidates for direct mass measurements, even with small or very small production cross sections, are presented. This revised version was published online in July 2006 with corrections to the Cover Date.     

The First Isochronous Mass Measurements at CSRe

With the commissioning of the Cooler Storage Ring at the Heavy Ion Research Facility in Lanzhou (HIRFL-CSR),a pilot experiment operating the CSRe in isochronous mode to test the power of HIRFL-CSR for measuring the mass of the short-lived nucleus was performed in December of 2007.The fragments with A/q=2 of ~(36) Ar were injected into CSRe and their revolution frequencies were measured with a fast time pick-up detector with a thin foil in the circulating path of the ions.The preliminary result is presented.The result shows the potential of CSRe for mass measurements of short-lived nuclei.     

Mass measurements in the endpoint region of the rp-process at SHIPTRAP

The Penning-trap mass spectrometer SHIPTRAP was designed for precision mass measurements of radionuclides produced in fusion–evaporation reactions. The latest measurement campaign covered heavy nuclei (A>90) related to the astrophysical rapid proton capture process. The masses of 34 neutron-deficient radionuclides have been measured since February 2006 with relative uncertainties between 5×10⁻⁸ and 1×10⁻⁷. Furthermore, the use of an octupolar RF excitation for the time-of-flight ion-cyclotron-resonance technique was investigated and an increase of the resolving power by a factor of ten was observed in agreement with simulations. This will allow to resolve isomeric states with excitation energies of a few 10 keV only.      

等时性质量谱仪中N=Z核质量测量的方法探索

N=Z核的质量数据对于研究rp-和νp-过程至关重要。此外,N=Z原子核的质量数据将会帮助我们解决与核结构有关的许多关键问题。结合碎片分离器的等时性质谱仪（Isochronous mass spectrometry,IMS）是十分快速有效而且高分辨的质量测量工具。由于N=Z核的m/q值非常接近,目前国际上的储存环质量谱仪CSRe/IMP和ESR/GSI还无法实现对N=Z核运用飞行时间谱进行鉴别,因而无法对它们进行质量测量。在日本理化学研究所的仁科加速器中心新建了专用的等时性质谱仪（IMS）,即稀有放射性同位素储存环"Rare-RI Ring"（R3）,以确定短寿命的放射性原子核的质量,其目标质量相对精度为10-6。R3质谱仪与高分辨的碎片分离器BigRIPS的组合,运用束流线的高分辨的离子鉴别,使得R3上的IMS方法对N=Z核进行质量测量成为可能。本文设计了专用的等时性束流光学设置,模拟了124Xe的主束经过碎裂反应产生的N=Z核在束流线中穿过各焦平面的径迹、能量、速度等信息,同时检验了这些次级束在环内的飞行时间相对于动量的变化关系。模拟的结果表明:当储存环的等时性光学设置在某一个N=Z核时,所有其它N=Z核在环内的回旋时间也与动量弥散无关,说明了这些核也满足等时性条件。基于N=Z核的这种等时性的特点,本文对R3上刻度N=Z核的方法也进行了讨论。     

Technical Improvements in the Experiment of Isochronous Mass Measurement of 58Ni Projectile Fragments

 The combination of in-flight fragment separator and the isochronous mass spectrometry(IMS) in storage rings have been proven to be a powerful tool for the precision mass measurements of shortlived exotic nuclei. In IMS, the mass-over-charge ratio is only related to the revolution period of stored ions, and the relative mass resolution can reach up to the order of 10−6. However, the instability of the magnetic field of storage ring deteriorates the resolution of revolution period, making it very difficult to distinguish the ions with very close mass-over-charge ratio via their revolution periods. To improve the resolution of revolution periods, a new method of weighted shift correction (WSC) has been developed to accurately correct the influence of the magnetic field instabilities in the isochronous mass measurements of 58Ni projectile fragments. By using the new method, the influence of unstable magnetic fields can be greatly reduced, and the mass resolution can be improved by a factor up to 1.7. Moreover, for the ions that still cannot be distinguished after correcting the magnetic field instabilities, we developed a new method of pulse height analysis for particle identification. By analyzing the mean pulse amplitude of each ion from the timing detector, the stored ions with close mass-over-charge ratios but different charge states such as 34Ar and 51Co can be identified, and thus the mass of 51Co can be determined. The charge-resolved IMS may be helpful in the future experiments of isochronous mass measurement even for N =Z nuclei.     

Prompt neutron emission spectra and multiplicities in the thermal neutron induced fission of235U

The emission spectra of prompt fission neutrons from mass and kinetic energy selected fission fragments have been measured in²³⁵U(n _th,f). Neutron energies were determined from the measurement of the neutron time of flight using a NE213 scintillation detector. The fragment energies were measured by a pair of surface barrier detectors in one set of measurements and by a back-to-back gridded ionization chamber in the second set of measurements. The data were analysed event by event to deduce neutron energy in the rest frame of the emitting fragment for the determination of neutron emission spectra and multiplicities as a function of the fragment mass and total kinetic energy. The results are compared with statistical model calculations using shell and excitation energy dependent level density formulations to deduce the level density parameters of the neutron rich fragment nuclei over a large range of fragment masses.     

Direct mass measurements of exotic nuclei at the FRS-ESR facility at GSI

An overview of direct mass measurements of exotic nuclei at the FRS-ESR facility at GSI is given. The nuclides are produced at relativistic energies by projectile fragmentation and fission, separated in-flight at the fragment separator FRS and injected into the storage ring ESR. Mass measurements are performed using Schottky and Isochronous Mass Spectrometry, which both allow for high precision measurements with single-ion sensitivity. Recent experimental developments are summarized, and examples for measurement results are given, including applications in nuclear structure physics and astrophysics, comparisons with mass predictions, and the search for new isotopes and isomers. Further research potential will be available at next-generation fragment-separator-storage-ring facilities such as the Super-FRS-CR-NESR complex at the future FAIR facility.