PoS(NIC-IX)010 http://pos.sissa.it/ ∗ [email protected] Speaker. The of far fromwell as stability nuclear provide structure information that is on crucial decay forshort modeling and stellar half-lives, reaction . and Low production the as rates, inherentclear precision quantity required to measure. make The masses minuteness perhaps ofing the the binding brave most attempts has difficult at also reliable nu- contributed to theoretical confound- massney, Pearson, predictions. Thibault, In Rev. the Mod. spirit Phys. 75, of 1021,this previous 2003 reviews paper [Lun- and introduces Lunney, the Eur. role Phys. played J. by Aparing masses 25, the in 3, (growing) astrophysics 2005], multitude and of and -measurement provides programsuation an now process update, active worldwide. com- that The links eval- creation reaction, of decay the mass and table: binding anucleosynthesis energies benchmark networks. is for the also development described of the as the well mass models as required its by ∗ Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. c ° International Symposium on —June Nuclei 25-30 in 2006 the Cosmos —CERN, IX Geneva, Switzerland Centre de Spectrométrie Nucléaire et de(CSNSM-IN2P3/CNRS), Spectrométrie Université de de Masse Paris Sud, Orsay,E-mail: David Lunney Mass measurements of exotic nuclei andimportance their for PoS(NIC-IX)010 ]. The 6 David Lunney at the time), discov- 3 − 10 ] and winning the Nobel prize (for ], whose memory was honored at the 3 4 ]. The mass measurement, performed 5 , was quite recently tested using a radia- 2 2 mc = ray was measured as well as the mass difference E − kilogram, whose definition continues to be com- 2 γ the , represents an eight-order-of-magnitude improvement in ]. Thus, the link between mass measurements and stellar 11 ]. Though much debated, there are definitely implications of 2 − 7 10 Arthur Eddington realized that if the sun could use the energy-equivalent of 1 ]. 1 ] for the top quark mass) in order to see if the Higgs boson might be found at CERN 8 The story of “How the sun shines” is brilliantly recounted by John Bahcall [ Aston went on to measure the masses of over 200 nuclides, establishing what he termed the “packing fraction” By far the most vigorous mass measurement activity is found in since radioac- Finally, the ultimate in microscopy - particle physics, at the highest energy frontier - seeks to Another interesting application of mass measurements that relates to astrophysics is the deter- Interestingly enough, the relation in question, This valley was first explored during the 1920’s by Francis Aston at Cambridge, who, in taking The landscape of the chart of nuclides is often described as having a , formed Nuclear astrophysics is much about studying the infinitely small to understand the infinitely 2 1 Chemistry) in 1922. NiC-IX conference. now shown in all nuclear physics textbooks as the per [ tive, -capture reaction where the emitted promised by a variations in cleanliness (and as such, is accompanied by a cleaning recipe) [ tive nuclides may be ashave much no as way of 300 predicting times their more masses numerous with any than certainty. the 300 stable ones and we still glimpse the beginning of the universe andquarks one (see key element [ of that iswith in the mass LHC measurements (see of J. Ellis, this volume). nucleosynthesis goes back to the beginning of the field. mination of fundamental constants, notably such variations in cosmology (see A. Coc, this volume). the art of mass spectroscopy into the realm of precision measurements ( this mass difference to(and hence, its age) combustion, would the be hotly resolved debated [ question of the sun’s reason for worrying about accuracy ofthat fundamental they may constants have comes varied from with astronomical time assertions [ by the nuclear (the negative bindingpath energy). that Stable resembles nuclides lie a along river anuclides meandering running with along high the neutron- bottom (anddrip of lines, vice-versa) a at ratios valley. which are the Each less internal side energy bound, of reaches reaching the zero; nuclides the valley beyond rises ridges, this as or precipice are unbound. large. The properties of atomic nucleiprocesses. are important Here ingredients we for will modeling various concentrateexotic astrophysical on one: gives the us mass. importantstructure Like information as observing well due a as to distant the , the energy weighing available binding for an energy decays and that reactions. determines nuclear between the initial and final nuclides using a Penning trap [ the 80 years since Aston established the field. Masses of exotic nuclides for astrophysics 1. Introduction ered that the mass of(four was ) less [ than the total mass of what he thought were its constituents with a relative accuracy of almost PoS(NIC-IX)010 - ] γ 14 ). In , n S 13 , ) the left- 12 David Lunney ] and [ ] and discussion in freeze out 11 , 17 10 , 9 process propels it along the r tells us how easily that happens. Since we n process, see C. Froehlich, this volume. For process under given astrophysical conditions S r r 3 ) process and its mass requirements, see H. Schatz, this volume.) The rp process is that a large fraction of the heaviest elements are produced and , derived from the mass difference of adjacent ) of essentially all n r S process and why it requires mass measurements r -decay towards stable isotopes - like water trickling down the valley hillside after a ]. Here, the rapid process is recalled along with the reasons it re- β 18 , 17 , 16 To eventually determine the trajectory of the The rapid neutron-capture nucleosynthesis process (see Figure 1) is thought to be associated Modeling astrophysical processes is challenging not only because we cannot build a stellar Stellar nucleosynthesis requires a detailed knowledge of the structure of a huge range of nu- , 15 rain storm. rays that strip off the loosely held and the Sec. 5). neutron-rich nuclides. Gorged on neutrons, the nucleus becomes an easy target for marauding with supernovae when seed nuclei feedevent. on an (For enormous details neutron flux and produced other in contributions this to cataclysmic the including references therein. The[ importance of nuclear data for nucleosynthesis is discussed in 2. The stellar laboratory but also because stellar timegreat scales uncertainty so regarding greatly astrophysical eclipse sites our anddata own. for events, reaction Consequently, not cross there helped sections is at by a low a energy and lack nuclear of properties nuclear (like the physics mass) of exotic nuclei. (and hence, the abundancesseparation produced), energy ( we need to know (amongst other things) thealso neutron- need to know about neutron-capturethe cross-sections, nuclides we in need question to (as know statisticaladdition the models to level may densities mass not of spectrometry, be all detailed applicablepability in nuclear for this delayed spectroscopy region neutrons is of and therefore small fission.is required, needed And including regarding if nuclear ca- it potentials wasn’tnuclear and already data giant enough, required, dipole even there more resonances. is information currently Notmost no only radioisotope of facility is the on a the isotopes huge planet in amountsufficiently that question! microscopic can of even character produce This that can difficult provide situation the must many be properties (see remedied [ by nuclear models of the rapid ( Masses of exotic nuclides for astrophysics clides, sometimes to thedecisive limits effects on of nuclear stability. structure (shells,myriad The deformation, effects of pairing) mass the but binding is also energy on particularly for nuclear energy structure important, release. are discussed not The in only [ for its quires us to measureintroduced masses and of compared, exotic reviewing nuclides. theShort numerous sections Then, on (new) the the measurement Atomic various programs Mass measurement Evaluation in and techniques the mass are process. models precede the conclusion. consequence of the ejected into the .steep grade The of general the path nuclear taken valleyof where by neutrons. very the short-lived, After neutron-rich the nuclei temperature batheover falls in isotopes and this hot the broth neutron flood subsides (called PoS(NIC-IX)010 O) 16 ) neutron ]). r 3 David Lunney ) and rapid ( s 200) ∼ ∼ ∼∼ A ( 126 At Stellar Nucleosynthesis decay Po ββ ββ 4 Bi - -isotope -isotope -delayed p s r

ββ ββ showing possible paths for the slow ( one / two neutron decay Pb 126 -values, or energy differences; and direct (or inertial) methods = Q ], fragmentation (or fusion-evaporation) of thin targets with in- N 23 Tl Hg neutronnumber Au decay path

− -process path -process path Hf Lu Yb Tm Er Pt Ir Os Re W Ta stable isotopes stable s r β known masses Very recently, ANL, MSU and JYFL have made their first direct mass measurements The nuclear chart around 3 Mass measurement programs have been underway for quite some time at GANIL, GSI and TOFI at LANL was also active but ceased operation in the 1990’s. Traditionally, two categories of mass measurements exist: so-called indirect techniques – re- Determining the binding energy of exotic nuclides is easily one of the most difficult challenges 3 C (with which the mass unit is defined). Aston’s measurements (defined with respect to capture processes. Also shown is the area delimiting nuclides for which the mass is measured. and realization of new setups are wellof underway at (direct) MAFF and mass TRIUMF. Fig. measurement 2 program shows a locations. global view A comprehensive review is given by Lunney, ISOLDE. flight separation (FIFS) and thick-target, isotope separation on-line (ISOL). actions and decays – that produce 3. How exotic nuclides are weighed (and where) of experimental nuclear physics. Massesthe fall exhaustive under examination the of class all of possible precision sourcesproduction of measurements, rates (systematic) requiring (down error. to This a is few combinedto per with operate second), low further in compounded the by harsh requiringusing environment precision of two apparatus accelerator canonical facilities. methods Such [ facilities produce radionuclides – –species where are time-of-flight performed or12 with cyclotron-frequency respect measurements to of well-known the reference exotic masses, ultimately linking them to Figure 1: pioneered the direct scheme, for which he invented the double-focusing technique (see [ Masses of exotic nuclides for astrophysics PoS(NIC-IX)010 ] 20 ] and Blaum David Lunney 21 ]). 24 in [ et al. values or proton/neutron-separation RIKENRING − Q ]. The proceedings of the APAC (Atomic 14 JYFLTRAP 5 SMILETRAP (MSI) SMILETRAP MAFFTRAP ESR (GSI) ESR (GSI) SHIPTRAP ] in 2000 provide a comprehensive collection (in a single 19 TITAN (TRIUMF) SPEG CSS2 (GANIL) UW-PTMS CPT (ANL) CPT MISTRAL (CERN) MISTRAL ] for information on indirect techniques. ], with an update by Lunney [ 20 12 ISOLTRAP (CERN) ISOLTRAP , LEBIT LEBIT (NSCL) 19 FSU- TRAP , 12 ]). An illustrative view of the different mass measurement programs worldwide is 63 Global view of active mass measurement programs. In light type are programs that use Penning , 62 At GANIL, attempts were made to improve time-of-flight measurements by lengthening the With TOFI gone, SPEG at GANIL is now the grand-daddy of mass programs. Using frag- It might be argued that there is no need for the masses themselves of nuclei very far from ] for recent reviews. 22 energies (especially in the case ofare unbound other nuclides, for considerations example). that Whilea this make strong is the indeed constraint true, (direct) on there determination anuclei). theoretical of This shell-correction point a is term mass of (especially particular(see important, in interest [ for the for mean-field-based example case mass of formulasshown doubly-magic under in development Fig. 2.referred to Below, the is [ a summary of the direct measurement programs only. The reader is flight path using the many turns that result from injection of fusion-evaporation products into the mented projectiles, measurements ofmass. time-of-flight Although and the resolving rigidity powerthem are is to modest, reach combined the the to drip tremendous line sensitivity determine for of the many their light method species allows (see Savajols issue) of the details of the various techniques. Recently, a special issue devoted to H.-J. Kluge [ stability since what is important for are Figure 2: traps. In italic type are facilities that are under construction. Pearson and Thibault [ has appeared which is a[ valuable (and needed) update. See also Scheidenberger [ Physics at Accelerators) conference [ Masses of exotic nuclides for astrophysics PoS(NIC-IX)010 ]. In ]. The 39 ]). More 30 37 David Lunney ]. Recently, a ] 30 28 ]) with an accuracy of 40 ]). MISTRAL is located at the mother ] and Herlert, this volume) has pioneered 20 4 ]. 44 ]. Relativistic fragments are filtered through in [ ]. For a recent status report on ESR work see 38 29 ]. An enormous volume of mass data has now 31 34 6 et al. ], Delahaye [ Sm was performed which should provide a large harvest Li (a “superlarge” nuclide - see [ ]. These were done using 24-GeV protons from the PS 24 11 152 36 in [ ] and Lunney et al. 24 in [ et al. ]. Some difficulties were experienced initially but recently the technique has 26 ]. The same technique has been used with the new cyclotron CIME, which offers more 27 ]. ISOLTRAP (see Herfurth According to the original ISOLDE Users’ Guide, edited by H.-J. Kluge (1986), “The first four letters of the MISTRAL is a good example of a technique that combines good accuracy and sensitivity. Perhaps the most distinguishing difference between ISOL and In-flight Fragmentation facili- No place on earth operates more storage rings than CERN, site of this conference. Though The same idea of lengthening the time of flight can be realized by storing the in a ring, as 33 4 , 32 2003 MISTRAL measured the mass of most of the trap-based methods now being used for measuring masses of radioactive species (al- of proton-rich masses in the medium-mass range [ acronym ISOLDE have a rational explanation:the they reader stand to for complete the Isotope interpretation, Separator if On-Line. necessary.” It is left to the imagination of second method, used tomode measure where short-lived the species, revolution requiresthis frequency operating case is the the (to ring ions are first inderived monitored from order) isochronous in-beam matching independent with successive of time a signals the thin-foil [ detector velocity the spread. theexperiment revolution In using frequency the is fragmentation of 5 keV (see Bachelet As a transmission, time-of-flighttechnique spectrometer is using very a fast allowing radiofrequency access “clock”, to the its shortest-lived measurement nuclides produced at ISOLDE [ ties is the the lowISOLDE, energy the and mother superior of all optical ISOL properties facilitiesmeasurements: of possesses MISTRAL two the and permanent resultant experiments ISOLTRAP, both beam dedicated of to ofistics which mass exotic of rely ISOL nuclides. on beams. the particular optical character- used for the primary beams,measurements CERN using storage rings a were spectrometer instrumental [ in the very first on-line mass been produced by the ESR, spanning a sizeable portion of the[ nuclear chart [ recently, 1.4-GeV protons from the PSworld’s Booster premier ring ISOL have facility been ISOLDE used (see to Fig. create 3) exotic [ nuclides at the of all ISOL facilities: ISOLDE,mother where of a all few on-line meters Penning-trap installations of . beamline separate it from ISOLTRAP, the flexibility regarding acceleration frequency. The first tests are quite promising [ with the Experimental Storage Ring (ESR)a at mass GSI separator and [ injected intomeasured the ring two operated ways. with a One given istime rigidity where by it their detecting passes masses the an can so-called be electrodedo Schottky and this, signal obtaining however, the of the ions a evolution must charged frequency bespread. particle from cooled since each the This the Fourier is fragmented transform. beam done has To with a an relatively large velocity cooler but the process requires several seconds [ (synchrotron) ring. The PS also serves as injector for the AD, SPS and LHC (see [ Masses of exotic nuclides for astrophysics CSS2 cyclotron [ been improved and the newly-measured resultsall and cases revised [ errors now provide good agreement in PoS(NIC-IX)010 in et al. isomeric David Lunney MISTRAL ISOL- TRAP REX-ISOLDE HRS ]). 7 24 targets 10 m GPS ]). Another interesting application of traps is obtaining different ], generally dedicated to stable species produced with high charge ]. 42 50 [ , 43 49 to Starting with a gas-filled, linear RFQ trap, low-energy bunches are SPS et al.

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p 1 The ISOLDE facility at CERN. Shown are the two target stations, one feeding the General Purpose to AD ] as well as Clark, this volume). It is the first instrument of its kind making use of “the ISOLDE 25 Now starting to produce results (and broughtThe invention to of you the Penning by trap the for precision makers measurements of earned H. ISOLTRAP) Dehmelt is a SHIP- share of the 1989 Nobel prize. The superior performance of the versatile Penning trap has naturally triggered new experimen- CERN,Geneva 5 ], [ LINAC 24 states. The next projectand was excommunication the from Canadian Canada, Penning is Trap now (CPT) in which, full-fledged after operation at a ANL difficult (see early Clark life chemical species (sometimes not available asion ISOLDE beams) to by decay waiting to for its a daughter trapped [ radioactive tal programs. The first “clone”Laboratory in of Stockholm ISOLTRAP [ was SMILETRAP, located at the Manne Siegbahn [ best of both worlds”; the advantages ofapparatus high-energy - production linked reactions by and a low-energy gas precision cell (see Savard in [ Figure 3: Separator and the other, theline High and Resolution experiments. Separator, followed Inset by upperand the left PS merging shows Booster switchyard, the ring central that 200-meter alternately beam the diameter sends PS pioneering the ring on-line 1.4-GeV complex, mass protons including to measurementsmass the ISOLDE measurement in Linac and experiments the ISOLTRAP the and 1970’s). PS MISTRAL (which currently Also was at used shown ISOLDE. for are photographs of themost) permanent everywhere else. injected into a large-volume, cylindricalterest Penning is trap retained for and isobaric sentand purification. measured to by The the time of precision flight of Penningto after in- trap bear ejection. where By (requiring bringing its storage an cyclotron times enormousstates, frequency of reserve resulting of in is over resolving unambiguous one excited power identification, second), otherwisefor impossible ISOLTRAP example, by is nuclear C. able spectroscopy Weber to (see, weigh even Masses of exotic nuclides for astrophysics PoS(NIC-IX)010 ]. in 61 et al. David Lunney ]). Also under test and Rykov 24 ]). Overcoming great ] is the amount of new 24 ]) and the University of in [ 14 et al. 46 in [ et al. et al. ] and Hager, this volume). ] and Dilling 57 ]. Further results, on stable species, have , 60 and Sun ]. LEBIT has reached a great milestone in ] for description). The most striking feature 58 56 , ) of the masses of stable nuclides: the “Tal- 59 12 [ ], formerly at MIT [ 11 Ca [ 55 8 et al. − , 38 48 − 8 ] and the 2005 version [ , 10 54 10 12 47 ], [ ] and Vorobyev, this volume), a new-generation instru- ]. 24 , Ringle 53 45 in [ ], [ ] for those), it is clear to see that achieving good accuracy is et al. 24 24 ] with promising results recorded on very neutron-rich species 35 et al. in [ et al. shows an interesting comparison of the different techniques devoted to radioactive 4 Figure In addition to SMILETRAP, two other Penning trap spectrometers continue in the pursuit of Two other Penning traps are being commissioned. One is MAFFTRAP which will enjoy Not content at MSU only measuring masses with a Penning trap, a new experiment has been Another interesting (non-Penning-trap!) development was made at ORNL where masses of The newest arrival is LEBIT at MSU, the first Penning trap to be filled with products of a JYFLTRAP in Jyvaskyla was built almost essentially as a twin to SHIPTRAP using a two- ]). 24 (compared to the 2003 version of the figure [ validated LEBIT’s accuracy to a few parts in [ Washington Penning trap (UWPTMS) [ difficult to very short-lived nuclides. However, greataccessing progress more is exotic being nuclides. made in the case of traps for the ultimate precision (currently approaching species: the obtained measurement uncertainty (for somedistance recent from results) stability as a of function the of measured the nuclide isobaric (see [ the copious production ratesusing of the neutron-rich FRM-2 species reactor, now offered operating by near thermal Garching neutron-induced (see fission Habs lahassee Trap” (at Florida State University [ commissioned, inspired by SPEG at GANIL,fragmented coupling beams time-of-flight and (see rigidity Matos measurements [ of neutron-rich species produced bybetween an known and ISOL unknown-mass isobars, fission dispersed target atfollowing the were the image 25 of measured MV the as tandem energy-analyzing magnet post-accelerator, position and identified differences by an energy-loss measurement [ opening the world offuture. fragmentation to the Penning trap and will be of great importance for the produced by fragmentation of a Kr beam (see Estrade, this volume). data and new programs.going into All details in (see all, Lunney in the [ different techniques are quite complementary. Without fragmentation reaction (see Schury ment reaching for the bestevaporation of residues that both issue worlds forth by from trapping a gas trans- cell. elements created byin-one fusion- design where thecase isobaric separator of trap ISOLTRAP and –the precision are host hyperbolic located of trap in neutron-rich – the refractorycomplementing separated the elements same in elements produced that magnet. the at can ISOLDE. The beis One initial truly fed production great impressive of to (see this advantage Jokinen it young experiment of by the JYFLTRAP is IGISOL facility, greatly Masses of exotic nuclides for astrophysics TRAP at GSI (see Block difficulties with contamination from thecell, rather LEBIT has violent now stopping produced of its first the result, fragmented on beam in a gas is TITAN, a Penninghigh-charge trap states at of radioactive TRIUMF species (bred incyclotron in Vancouver, frequencies) an which with EBIT) shorter to will trapping achieve be higher times accuracy (see the (i.e., [ first higher installation to use PoS(NIC-IX)010 ]; 25 et al. ] and , 53 52 David Lunney ]; CPT: [ 24 in [ ]; SHIPTRAP: [ 57 , et al. 56 , 55 , 54 C , the mass of every other nuclide 12 value. Thus, the ensemble of all reaction, − Q ]; MISTRAL: Bachelet ]; JYFLTRAP: [ 9 30 24 ]. ] for description where a 2003 version is shown - note that in [ 61 12 et al. ]; ESR-SMS: [ ]; ORNL: [ 34 58 and Guénaut et al. ]; ESR-IMS: [ 27 Experimental uncertainty of mass results (published in only the last 3-4 years) versus isobaric ]; CSS2: [ For many years now, we have been privileged to have two grand inquisitors for atomic masses It is important to distinguish the AME from a simple compilation of data. Since the atomic 24 (G. Audi and A.H. Wapstra) whose careful evaluation of the various input data produced the atomic in [ ISOLTRAP: Herfurth is ultimately linked. Dueaccuracy, the to masses measured the by inherent direct (inertial)known difficulty methods reference of are always measured measuring given the with magnetic respect samemass fields to way. is a with well- not In sufficient usually the given case but of a indirect decay (energy) or methods, reaction an absolute 4. The Atomic-Mass Evaluation: not just a mass table mass unit has been defined as one twelfth the mass of the Figure 4: distance from stability for eachthe nuclide programs (see in [ brackets correspond to older data shown for comparison). Data from SPEG: Savajols Vorobyev, this volume; LEBIT: [ decay and spectrometry data possesses many crossdata, links. a In detailed order evaluation to must produce be a(e.g., mass performed. the table half Note from life) this that that this can is be unlike directly any inserted other into physical a compilation. quantity Masses of exotic nuclides for astrophysics PoS(NIC-IX)010 ]. 64 David Lunney ] contains 2228 experimental ]. The FRDM has pushed the 10 65 [ et al. ]). 19 10 6 process, leaving no choice but to resort to theory. ]). This class of models is known as microscopic-macroscopic due their r 12 The formula also gives a prediction for the location of the drip lines in astonishing concordance with that of a Some handy algebraic relations exist that have been formulated from the symmetry of the nu- For the last 60 years, mass formulas have been based on this type of liquid-drop formula Attempts at (and needs for) the prediction of the nuclear mass date from not so long after the Despite the impressive developments in mass spectrometry, and those with associated radioac- 6 microscopic mean-field model (see Fig.2 by J.M. Pearson in [ clear charge and (taking into account thecalculation easily-determined of Coulomb locally-unknown component) masses allow surrounded reasonable by knownMultiplet ones. Equation Examples (IMME) are, with the which Isospin Mass thecan mass be of remarkably a reproduced nuclide using only forming a an quadraticrelation, isobaric function. uses analog Another multiplet a scheme, the similar Garvey-Kelson ideamasses but are by determined constructing iteratively a using sortrelations, the of broadly neighboring finite-difference classified known as grid masses local, in as canquired which boundary be unknown (for values. useful example, where Such near specific, locally-unknown the masses proton are drip re- line) but generally show gross systematic deviations in with “modern” refinements from microscopicgeneral effects description such in as [ shell closureshybrid nature. and deformation Such (see models aresometimes, widely other used nuclear since properties. they provide Thethe extended most Finite-Range data well-known Droplet sets microscopic-macroscopic Model for approach (FRDM) masses is of and Moeller, Nix very discovery of the bindingThe energy. same formula The is first still massat used formula mass today was predictions with that but various mostly of refinementsIt for Von – Weizsaecker is illustrating sometimes [ the instructive in effects to (dubious) of considerparameters attempts shell that (volume, closures surface, Von that Weizsaecker symmetry, were initially and notknown formulated Coulomb) included. at which his the he model time. fit using The toerror only same the of four exercise 200 only today, or 4.25 using MeV. so the Giventhis mass 2228 the is values masses absence a now of remarkable known, shell achievement. achieves effects an (unknown rms in Von Weizsaecker’s time), mic-mac approach to its limitmicroscopic and is part, exemplary though for somewhat thesingle-particle, uncoupled generalized folded data from Yukawa sets potential the and which liquid-drop availability. canstrength part, The also functions, is be fission used barriers constructed and to using nuclear generate deformation a beta-decay parameters half-lives, in addition to the mass. 5. Mass models (and chaos) tive beam production andnuclides handling involved in techniques, the it is still not yet possible to reach many of the Masses of exotic nuclides for astrophysics mass table. The evaluation ensurestermined that independently. the The mass most determined recent in atomic any mass one evaluation way [ is coherent when de- masses and another 951 estimated frombination systematic of trends. 7773 These masses experimental are datasolving the 1381 (of result equations of which with the 374 847 com- are parametersa in rejected unique order case as to of a produce providing result themodels. a mass of global table. careful starting The point evaluation), mass - table and is benchmark - for the development of mass PoS(NIC-IX)010 , et al. David Lunney ]). Due to the availability of co- 12 ]. 12 ]). Moreover, no auxiliary nuclear properties can 11 ]. Though still a parametrization, (in order to em- 12 error of model predictions compared to experimental 66 rms for incorporating different effects. This causes disaster for ] where references to the previous mass tables can be found. 63 souplesse error of various models. On the left are the global models. On the right ] to suggest that perhaps the idea of chaos, or fluctuations in the periodic 67 rms ] and the reader is referred there for the results and discussion. It is interesting 12 error can be viewed as a scalar indication. Perhaps more important, due to the fact rms The The local models generally provide a better fit, simply because they have a very large parame- Fig. 5 shows the One benchmark of importance is the The question that we obviously need to ask is: What is the best mass model? Alas, it will be Mass tables have – at last – been constructed using a nucleon-nucleon interaction: the Skyrme- A microscopically-rooted approach worth mentioning is an evolution by Duflo and Zuker, ] who have exploited the non-physics of the Garvey-Kelson relations to lower this limit to about 24 that we develop models in orderrms to error extrapolate, for is a new vector data,performed approach. in which For [ have this not we can been calculate used the in the adjustment procedure. This study was extrapolations, however. In the case of theexperimental Garvey-Kelson masses relations could (GK in be Fig. reproduced,With 5) since only the going 60% exception farther of of the caused Duflo-Zuker instabilitythe (DZ in global the in models algorithm. Fig. all 5), giveBohigas who and practically Leboeuf show the [ an same impressive fitorbits fit of of of about particles only 700 in 375 keV. keV, thenuclear This binding nuclear observation energy. potential, prompted This contrive interesting to[ idea limit has been the taken possibilities up in by80 calculation others, keV. of notably Hirsch the et al. in to note that there is no consensus amongst the different models concerning extrapolation. The are local models for whichthese models essentially and all their calculated (number of) masses parameters, are see [ adjustable. Forter more space details and on as such, more impossible to answer given thereality. apparent However, failure the of problem theory is and thatdrip the line experiment need and is for we in are experiment no forced, to positionmight in help confirm to a us determine vicious judge the circle, the location to different of rely approaches. on the theory. Let us examinedata. some This criteria that quantity is athis first is indication since one the of modelstheory, the are by fundamental providing all common adjusted contributions starting to that point the and the same benchmark Atomic data. data for Mass Indeed, meaningful Evaluation comparison. makes to nuclear Hartree-Fock-Bogoliubov appraoch (see detailed discussion in [ inspired by the Shell-Modelpirically Hamiltonian [ bypass the problematicinvolves monopole solving the term Schroedinger equation which that is producesproperties wave may responsible functions be from for consistently which derived nuclear other in nuclear saturation), addition to it a full mass table. Masses of exotic nuclides for astrophysics distant, unknown territory (see discussion in [ be computed. pious computing power, systematic variations ofusing Skyrme-force parameters the can experimental now mass behas performed, data been as systematically studied a through diagnostic. theHFB9, elaboration was The of tailored a to sensitivity total satisfy of of constraintsto 13 the of the mass ensemble neutron interaction tables, of . parameters known one These nuclides of tables thatsometimes) which, now rival discuss all provide the other residual HFB-13 approaches. fits in Goriely, [ Samyn, Pearson, (


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0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 The root-mean-square difference between experimental masses (of the AME1995) and different rms error (MeV) error rms A. S. Eddington, Nature 106 (1920) 14 F. W. Aston, “Mass Spectra and Isotopes – 2ndJ.N. edition” Bahcall, (Edward “How Arnold, the London, Sun 1942) shines,” http://nobelprize.org/nobel_prizes/physics/articles/fusion/index.html S. Rainville R. Davis, Metrologia 40 (2004) 299; M. Glaeser, Metrologia 40 (2004) 376 F. W. Aston, Nature 105 (1920) 617 Nuclear Astrophysics, or Astronuclear physics, as some refer to it [ We have seen that CERN, [4] [5] [6] [1] [2] [3] Masses of exotic nuclides for astrophysics the deepest cosmological questionsmeasurements are of probed exotic nuclei (at were the(at performed LHC) ISOLDE), (at producing but the the PS) also most and accurate where where results the that of fine the very age. tradition first continues mass mass models (global approaches on the left and local, on the right). See [ 6. Epilog Figure 5: question indeed becomes existential, invoking thetrue idea expressed for by me.” Kierkegaard: “...a truth that is gle due to considerable uncertaintiesrole that (and exotic impossibilities) nuclides regarding will observations.ments play, the will Whatever not impressive be the feats to and blame! progress in the field of massReferences measure- PoS(NIC-IX)010 David Lunney , (W.A. Benjamin, Inc., New York, 1969) 13 Nuclear Structure, Volume 1 , J. Phys. G: Nucl. Part. Phys. 31 (2005) S1869 et al. ], p.35 , Nucl. Phys. A 756 (2005) 3 19 , arXiv:nucl-ex/0509019 (2005) Proceedings VL National Conference on Nuclear , Phys. Rev. Lett. 31 (1973) 118 , J. Phys. G: Nucl. Part. Phys. 31 (2005) S1771 , AIP Conf. Proc. 831 (2006) 108 , Nucl. Phys. A 685 (2001) 115c et al. , Int. J. Mass Spectrom. 251 (2006) 252 et al. et al. et al. et al. et al. et al. M. Stadlmann et al., Phys. Lett. B 586M. (2004) Matos, 27 AIP Conf. Proc. 819 (2006) 164 R. 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