Shell Evolution Study for New Magic Number N =32 via Isochronous Mass Spectrometry

Recent results and progress of mass measurements of neutron-rich nuclei utilizing Isochronous Mass Spectrometry (IMS) based on the HIRFL-CSR complex at Lanzhou are reported. The nuclei of interest were produced through projectile fragmentation of primary 86Kr ions at a realistic energy of 460.65 MeV/u. After in-flight separation by the fragment separator RIBLL2, the fragments were injected and stored in the experimental storage ring CSRe, and their masses were determined from measurements of their revolution times. The re-determined masses were compared and evaluated with other mass measurements, and the impact of these evaluated masses on the shell evolution study is discussed.     

High precision mass measurement and LPT

A Penning trap, which can measure the atomic masses with the highest precision, is one of the most important facilities in nuclear physics research nowadays. The precision mass data play an important role in the studies of nuclear models, mass formulas, nuclear synthesis processes in the nuclear astrophysics, symmetries of the weak interaction and the conserved vector current (CVC) hypothesis. The status of high precision mass measurement around the world, the basic principle of Penning trap and the basic information about the LPT (Lanzhou Penning Trap) are introduced.     

The AME2016 atomic mass evaluation (Ⅰ).Evaluation of input data;and adjustment procedures

This paper is the first of two articles(Part Ⅰ and Part Ⅱ) that presents the results of the new atomic mass evaluation,AME2016.It includes complete information on the experimental input data(also including unused and rejected ones),as well as details on the evaluation procedures used to derive the tables of recommended values given in the second part.This article describes the evaluation philosophy and procedures that were implemented in the selection of specific nuclear reaction,decay and mass-spectrometric results.These input values were entered in the least-squares adjustment for determining the best values for the atomic masses and their uncertainties.Details of the calculation and particularities of the AME are then described.All accepted and rejected data,including outweighted ones,are presented in a tabular format and compared with the adjusted values obtained using the least-squares fit analysis.Differences with the previous AME2012 evaluation are discussed and specific information is presented for several cases that may be of interest to AME users.The second AME2016 article gives a table with the recommended values of atomic masses,as well as tables and graphs of derived quantities,along with the list of references used in both the AME2016 and the NUBASE2016 evaluations(the first paper in this issue).     

The AME2012 atomic mass evaluation (I). Evaluation of input data, adjustment procedures

This paper is the first of two articles (Part I and Part II) that presents the results of the new atomic mass evaluation, AME2012. It includes complete information on the experimental input data (including not used and rejected ones), as well as details on the evaluation procedures used to derive the tables with recommended values given in the second part. This article describes the evaluation philosophy and procedures that were implemented in the selection of specific nuclear reaction, decay and mass-spectrometer results. These input values were entered in the least-squares adjustment procedure for determining the best values for the atomic masses and their uncertainties. Calculation procedures and particularities of the AME are then described. All accepted and rejected data, including outweighed ones, are presented in a tabular format and compared with the adjusted values (obtained using the adjustment procedure). Differences with the previous AME2003 evaluation are also discussed and specific information is presented for several cases that may be of interest to various AME users. The second AME2012 article, the last one in this issue, gives a table with recommended values of atomic masses, as well as tables and graphs of derived quantities, along with the list of references used in both this AME2012 evaluation and the NUBASE2012 one (the first paper in this issue).     

The AME2016 atomic mass evaluation (Ⅱ).Tables,graphs and references

This paper is the second part of the new evaluation of atomic masses,AME2016.Using least-squares adjustments to all evaluated and accepted experimental data,described in Part Ⅰ,we derive tables with numerical values and graphs to replace those given in AME2012.The first table lists the recommended atomic mass values and their uncertainties.It is followed by a table of the influences of data on primary nuclides,a table of various reaction and decay energies,and finally,a series of graphs of separation and decay energies.The last section of this paper lists all references of the input data used in the AME2016 and the NUBASE2016 evaluations(first paper in this issue).     

核素等时性质量测量实验中一种基于离子速度纯化次级束的方法

等时性质量谱仪（Isochronous Mass Spectrometry,IMS）是测量短寿命核素质量的有效实验装置。在IMS核素质量测量实验过程中,目标核素通过弹核碎裂反应产生,并被次级束流线分离、传输后注入到储存环内。由于远离稳定线的目标核素产额非常低,经常伴随大量杂质核素产生,这些杂质离子会加重飞行时间探测器（Time of Flight,TOF）系统的工作负担。在HIRFL-CSR利用IMS进行核素质量测量实验过程中,发展了一种进一步纯化筛选次级离子的方法,以减轻TOF系统的工作负担。基于次级离子在束流线中飞行速度的差异性,利用HIRFL-CSR踢轨磁铁（Kicker）系统,调节次级束流注入CSRe的时间,使次级离子得到进一步筛选和纯化后注入到CSRe内。在实验中,我们测试并验证了该方法的可行性,并讨论了它在纯化次级束流方面的作用。The isochronous Mass Spectrometry (IMS) is a powerful experimental instrument for measuring masses of short-lived nuclides.In the IMS,the nuclides of interest are produced via the projectile fragmentation reaction,then injected into the storage ring after the in-flight separation with beam line.The yields of the nuclides of interest are usually very small accompanying a huge amount of contaminant nuclides,aggravating the load of time-of-flight (TOF) detector.In the IMS nuclear mass measurement experiment conducted at the HIRFL-CSR,we developed a method of purifying the secondary beam fragments to ease the burden of the TOF detector,which is based on the differences of the ions' velocities in the beam line and realized by adjusting the injection time of secondary fragments using the Kicker system of the HIRFL-CSR.We tested and verified the method in an online experiment,and its performance is discussed in this paper.     

The AME2012 atomic mass evaluation (II). Tables, graphs and references

This paper is the second part of the new evaluation of atomic masses, AME2012. From the results of a leastsquares calculation, described in Part I, for all accepted experimental data, we derive here tables and graphs to replace those of AME2003. The first table lists atomic masses. It is followed by a table of the influences of data on primary nuclides, a table of separation energies and reaction energies, and finally, a series of graphs of separation and decay energies. The last section in this paper lists all references to the input data used in Part I of this AME2012 and also to the data included in the NUBASE2012 evaluation (first paper in this issue).     

PERIODIC TABLE OF THE ELEMENTS

<正>Table 4.1.Revised 2011 by D.E.Groom(LBNL),and E.Bergren.Atomic weights of stable elements are adapted from the Commission on Isotopic Abundances and Atomic Weights,"Atomic Weights of the Elements 2007,"http://www.chem.qmul.ac.uk/iupac/AtWt/.The atomic number(top left)is the number of protons in the nucleus.The atomic mass(bottom)of a stable elements is weighted by isotopic abundances in the Earth's surface.If the element has no stable isotope,the atomic mass(in parentheses)of the most stable isotope currently known is given.In this case the mass is from http://www.nndc.bnl.gov/amdc/masstables/Ame2003/mass.mas03 and the longest-lived isotope is from www.nndc.bnl.gov/ensdf/zajform.jsp.The exceptions are Th,Pa,and U,which do have characteristic terrestrial compositions.Atomic masses are relative to the mass of 12C,defined to be exactly 12 unified atomic mass units(u)(approx.g/mole).Relative isotopic abundances often vary considerably,both in natural and commercial samples;this is reflected in the number of significant figures given for the atomic mass.IUPAC does not accept the claims for elements 113,115,117,and 118 as conclusive at this time.     

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.     

Statistical errors in Weizscker-Skyrme mass model

The statistical uncertainties of 13 model parameters in the Weizscker-Skyrme(WS*) mass model are investigated for the first time with an efficient approach,and the propagated errors in the predicted masses are estimated.The discrepancies between the predicted masses and the experimental data,including the new data in AME 2016,are almost all smaller than the model errors.For neutron-rich heavy nuclei,the model errors increase considerably,and go up to a few MeV when the nucleus approaches the neutron drip line.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,and the deformation energy coefficients play a key role for well-deformed nuclei around the β-stability line.     

The AME2016 atomic mass evaluation (I). Evaluation of input data; and adjustment procedures

This paper is the first of two articles (Part I and Part II) that presents the results of the new atomic mass evaluation, AME2016. It includes complete information on the experimental input data (also including unused and rejected ones), as well as details on the evaluation procedures used to derive the tables of recommended values given in the second part. This article describes the evaluation philosophy and procedures that were implemented in the selection of specific nuclear reaction, decay and mass-spectrometric results. These input values were entered in the least-squares adjustment for determining the best values for the atomic masses and their uncertainties. Details of the calculation and particularities of the AME are then described. All accepted and rejected data, including outweighted ones, are presented in a tabular format and compared with the adjusted values obtained using the least-squares fit analysis. Differences with the previous AME2012 evaluation are discussed and specific information is presented for several cases that may be of interest to AME users. The second AME2016 article gives a table with the recommended values of atomic masses, as well as tables and graphs of derived quantities, along with the list of references used in both the AME2016 and the NUBASE2016 evaluations (the first paper in this issue).     

The Evaluation of Atomic Masses

The ensemble of experimental data on the 2830 nuclides which have been observed since the beginning of Nuclear Physics are being evaluated, according to their nature, by different methods and by different groups. The two ‘horizontal’ evaluations in which I am involved: the Atomic Mass Evaluation AME and the NUBASE evaluation belong to the class of ‘static’ nuclear data. In this tutorial lecture I will explain and discuss in detail the philosophy, the strategies and the procedures used in the evaluation of atomic masses. This revised version was published online in July 2006 with corrections to the Cover Date.     

The AME 2020 atomic mass evaluation (I). Evaluation of input data,and adjustment procedures

This is the first of two articles(Part I and Part II)that presents the results of the new atomic mass evaluation,Ame2020.It includes complete information on the experimental input data that were used to derive the tables of recommended values which are given in Part II.This article describes the evaluation philosophy and procedures that were implemented in the selection of specific nuclear reaction,decay and mass-spectrometric data which were used in a least-squares fit adjustment in order to determine the recommended mass values and their uncertainties.All input data,including both the accepted and rejected ones,are tabulated and compared with the adjusted values obtained from the least-squares fit analysis.Differences with the previous Ame2016 evaluation are discussed and specific examples are presented for several nuclides that may be of interest to Ame users.     

Precision mass measurements of short-lived nuclides at HIRFL-CSR in Lanzhou

In recent years, extensive short-lived nuclear mass measurements have been carried out at the Heavy- Ion Research Facility (HIRFL) in Lanzhou using Isochronous Mass Spectrometry (IMS). The obtained mass values have been successfully applied to nuclear structure and astrophysics studies. In this contribution, we give a brief introduction to the nuclear mass measurements at HIRFL-CSR facility. Main technical developments are described and recent results are summarized. Furthermore, we envision the future perspective for the next-generation storage ring facility HIAF in Huizhou.     

Examination of n-T_9 conditions required by N=50,82,126 waiting points in r-process

We examined the conditions of neutron density(n) and temperature(T_9) required for the N = 50, 82,and 126 isotopes to be waiting points(WP) in the r-process. The nuclear mass based on experimental data presented in the AME2020 database(AME and AME ±Δ) and that predicted using FRDM,WS4, DZ10, and KTUY models were employed in our estimations. We found that the conditions required by the N = 50 WP significantly overlap with those required by the N = 82 ones, except for the WS4 model. In addition, the upper(or lower) bounds of the n-T_9 conditions based on the models are different from each other due to the deviations in the two-neutron separation energies.The standard deviations in the nuclear mass of 108 isotopes in the three N = 50, 82, and 126 groups are about rms = 0.192 and 0.434 Me V for the pairs of KTUY-AME and WS4-KTUY models,respectively. We found that these mass uncertainties result in a large discrepancy in the nn-T_9 conditions, leading to significant differences in the conditions for simultaneously appearing all the three peaks in the r-process abundance. The newly updated FRDM and WS4 calculations can give the overall conditions for the appearance of all the peaks but vice versa for their old versions in a previous study. The change in the final r-process isotopic abundance due to the mass uncertainty is from a few factors to three orders of magnitude. Therefore, accurate nuclear masses of the r-process key nuclei, especially for ~(76) Fe,~(81)Cu,~(127)Rh,~(132)Cd,~(192)Dy, and ~(197)Tm, are highly recommended to be measured in radioactive-ion beam facilities for a better understanding of the r-process evolution.     

A validity test of E = m ? c2

The comparison of mass and energy variation in a nuclear reaction allows an experimental verification of Einstein’s energy - mass equivalence principle. Mass measurements are performed in a high precision Penning trap and yield values in unified atomic mass units. The energies of emitted gamma radiation are determined via Laue-diffraction with perfect crystals. The according values of the gamma ray wave lengths are expressed in units of the crystal lattice constant. The comparison of masses and wave lengths requires a conversion factor, which represents the unified atomic mass unit within the SI unit system. The latter is given by the molar Planck constant N _A h, which itself is known via its relation to the fine structure constant. In the present paper we report on measurements carried out until 2003 with an uncertainty level of 4 ⋅ 10^-7. We discuss the main limitations of these experiments and outline the possibilities for future measurements at the 10^-8 level. Such measurements would allow a direct representation of the unified atomic mass unit in terms of a Compton frequency and are of utmost importance for a future re-definition of the kilogram mass unit.