High-accuracy mass spectrometry of fission products with Penning traps

Mass measurements of fission products based on Penning-trap technique are reviewed in this article. More than 300 fission products have been measured with JYFLTRAP, ISOLTRAP, CPT, LEBIT and TITAN Penning traps with a typical precision of δm/m ≈ 10−7 − 10−8. In general, the results agree well with each other. The new data provide a valuable source of information and a challenge for the future development of theoretical mass models as well as for obtaining a deeper insight into microscopic properties of atomic nuclei as measured, for example, via key mass differentials. Shape transitions around N = 60, subshell closure at N = 40 and shell closures at N = 50 and N = 82 have been investigated in the trend of the precisely measured two-neutron separation energies. The evolution of two-neutron and two-proton shell gaps has been studied and compared to theoretical models for Z = 50, N = 50 and N = 82. Proton–neutron pairing effect in separation energies and odd–even staggering of masses are shortly discussed. In addition to nuclear structure, many experiments have been motivated by nuclear astrophysics. (Some figures may appear in colour only in the online journal)


Introduction
Accurate mass measurements of exotic nuclei are required e.g. for studies of nuclear structure and astrophysics as well as for tests of the standard model [1,2]. In addition to the absolute mass or binding energy determination, the first and second order differentials of the masses are often the most important indicators of local and global changes of structures [3]. Such differentials offer challenging objects for precision mass measurements of nuclear ground states and lowenergy isomers. Since the accuracy of the ground state mass measurements is now approaching that of the excited states it offers interesting perspectives for studying the binding energy systematics for the excited states as well. In general, the mass measurements of neutron-rich nuclei far from stability require a relative precision of δm/m < 10 −6 , corresponding to about 100 keV at A = 100, for probing the evolution of shell structure, collectivity and shell closures [1]. These are normally studied by using the systematics of one-and two-nucleon separation energies over long isotopic or isotonic chains. A higher accuracy of δm/m < 10 −7 (e.g. 10 keV at A = 100) is typically needed for the binding energies of extremely neutron-rich halo nuclei. Relative mass accuracies below 10 −7 are also required for studying second-order differentials, such as odd-even staggering of binding energy related to the nature of pairing in neutron-rich nuclei [4], its possible isospin dependence and role near the neutron drip-line. The same argument holds for a specific class of double differences of nuclear masses termed δV pn [5][6][7], which isolates the proton-neutron interaction of the last two valence protons and neutrons, and has been shown, for example, to possess correlation with octupole effects in nuclear structure [8].
Indirect applications of nuclear masses are important both in fundamental as well as in applied physics. The bulk of nuclear structure studies far from the valley of stability is still based on beta-decay spectroscopy. There, reliable data on the decay Q-values are crucial, for example, when extracting the transition strengths for individual beta transitions or analysing the delayed neutron data. Nuclear data of neutron-rich nuclides, and especially for fission products, is a crucial input for network calculations in nuclear astrophysics and nuclearenergy related applications. The latter concerns decay heat, delayed neutron emission, fission yields and isomeric yields for current and future fission reactor concepts. Also, in the nuclear security front the production of pure isomeric sources for applications such as required by the Comprehensive Test Ban Treaty Organization [9] are becoming increasingly important.
The introduction of Penning traps to radioactive isotope mass measurements has changed the scope of direct mass measurements significantly. Combining them with the buffer-gas cooling [10] in a radio frequency quadrupole (RFQ) trap has made it possible to employ very fast injection of ions into a Penning trap. When coupled to a traditional ISOL system, such as ISOLDE at CERN [11], a bottle neck has become due to slow extraction, especially for refractory elements. This problem has been solved in the ion guide isotope separator on-line (IGISOL) technique [12] and its successor technique called ion catcher. The combination of all the above mentioned approaches have opened up a possibility for high-precision mass measurements of radioactive isotopes of all chemical elements with half-lives down to less than 100 ms. In this review, we give an overview of recent mass measurements of neutron-rich nuclei produced in fission reactions and discuss their implications on nuclear structure physics.

Experimental method
Two main production methods have been used to provide neutron-rich nuclei in the fission product region for Penning trap mass measurements (see figure 1). They are both based on ISOL technique. The ISOLTRAP mass spectrometer [13] is coupled to the ISOLDE mass separator facility and the JYFLTRAP [14][15][16] is connected to the universal IGISOL mass separator [12]. ISOLDE is using high-energy proton beams to produce the wanted nuclides in fission and spallation reactions whereas the IGISOL production is based on low-energy nuclear reactions.
At IGISOL, the ions of interest are produced in proton-induced fission reactions by bombarding natural uranium target with proton or deuteron beams with energies between 20 and 30 MeV and intensity between 10 and 30 μA. The targets are 15 mg cm −2 thick metallic foils tilted to 7 • angle with respect to the beam axis resulting in effective thickness of 120 mg cm −2 . The fission reaction products are thermalized in a helium-filled gas cell at a pressure of about 100-400 mbar. Resulting from charge-exchange processes with helium  [17] are denoted by open grey squares and the new nuclei identified recently at RIKEN [18] by crosses. atoms and impurities in the gas, the majority of ions are singly charged. Fast helium flow transports the ions out of the gas cell within about 10 ms whereby they are guided through the sextupole ion guide [19] and accelerated to 30 keV energy. A combination of a 55 • bending magnet and a slit allows only the ions with the selected mass number to pass towards a gas-filled RFQ cooler and buncher [20]. The RFQ cooler is used to cool and store the ions before releasing them in a short bunch into the JYFLTRAP Penning trap setup. Typical highest independent nuclide yields have been measured to be 10 5 ions s −1 . With the minimum required production rate of 10 ions s −1 about 400 short-lived neutron-rich isotopes are within reach for the mass measurement experiments with JYFLTRAP. A schematic layout of the facility is shown in figure 2.
The mass measurements of fission fragments discussed in this paper have been performed with the JYFLTRAP Penning trap [14][15][16] at IGISOL, ISOLTRAP [13] at ISOLDE/CERN, Canadian Penning trap (CPT) [21] at Argonne National Laboratory and LEBIT [22] at Michigan State University. Recently, some neutron-rich Rb and Sr isotopes have also been measured [23] with TITAN [24] at TRIUMF. In the following, we describe the experimental method performed at JYFLTRAP. JYFLTRAP consists of two cylindrical Penning traps inside a 7 T superconducting solenoid. The ions in a Penning trap have three different eigenmotions: axial motion with a frequency ν z , radial magnetron (ν − ) and reduced cyclotron motions (ν + ). According to the invariance theorem [25], the sideband frequency ν − + ν + corresponds to the true cyclotron frequency with a high precision even in a non-ideal Penning trap: where B is the magnetic field, and q and m are the charge and the mass of the ion. The first trap of JYFLTRAP is called purification trap. It is used for beam purification via mass-selective buffer-gas cooling technique [10]. With a typical mass resolving power of around m/ m ≈ 3 × 10 4 neighbouring isobars can usually be separated in the first trap before injecting them through a narrow diaphragm towards the second trap, precision trap.  shows an example of a mass scan performed with the purification trap. Peaks corresponding to different isobars-Mo, Tc and Ru-are clearly visible and separable. By setting a correct first trap frequency only the ions of interest can be selected for precision mass measurements or the ions can be sent through the second trap for e.g. post-trap spectroscopy measurements.  . Independent isotopic yields of Rh isotopes. The yields are given as percentages of the height of the fitted Gaussian peak. 109 Rh and 115 Rh were used as references for the Rh isotopes. See [27] for details of yield determination.
The first trap has also been used to study independent fission yields [26,27]. Figure 4 gives an example of isotopic yield distribution for rhodium measured at IGISOL. Sometimes purification with the first trap leaves some unwanted ions (from an isomeric state or neighbouring isobar) to the ion bunch. With a so-called Ramsey cleaning technique [28] a mass resolving power up to m/ m ≈ 10 6 can be achieved. In that method, the purified ions from the first trap are further cleaned by applying dipolar excitation at reduced cyclotron frequency of the contaminant ion in the form of time-separated oscillatory fields [29][30][31] in the precision trap. This drives the unwanted species to a larger orbit but the ions of interest stay unaffected. After the dipolar excitation, only the ions of interest can pass through the 2 mm diaphragm back to the purification trap for recooling and recentring before actual mass measurement in the precision trap. This dipolar cleaning method is useful both for mass measurements and for trap-assisted spectroscopy if the normal first trap purification is not sufficient to produce clean ion bunches.
High-precision mass measurements are performed employing the time-of-flight ion cyclotron resonance technique [32,33] in the precision trap. There, a dipole excitation is firstly applied to ions to increase their magnetron radius. A subsequent quadrupole excitation converts the magnetron motion into a reduced cyclotron motion periodically. When the excitation frequency matches with the sideband frequency, the radial energy of the ions reaches its maximum value after one full conversion from initially pure magnetron motion to reduced cyclotron motion. The gain in radial energy is observed as a shorter time-of-flight to the microchannel plate detector when extracted from the trap in the strong magnetic field gradient. Figure 5(a) shows a TOF spectrum for 134 Sb obtained by applying a continuous quadrupolar excitation of 800 ms without Ramsey-cleaning. A contribution from the isomeric state at 279(1) keV [34] is clearly seen in this spectrum. When Ramsey cleaning is applied, the ground and the isomeric state can be measured separately. If the quadrupolar excitation is applied as time-separated oscillatory fields [35,31], e.g. as two pulses separated by a longer waiting time, the sideband minima are steeper and the resonance is narrower. As a result, the cyclotron frequency can be determined more precisely. This can be seen from the TOF resonances for the ground and the isomeric state of 134 Sb (figures 5(b) and (c)) for which a Ramsey-excitation pattern of 25 ms-350 ms-25 ms (on-off-on) has been applied: the resonance width is roughly similar to the 800 ms excitation and the sideband minima are much steeper. With a continuous excitation of 400 ms the line width should have been doubled from the 800 ms excitation since the width is inversely proportional to the excitation time.
The magnetic field B is calibrated with a reference ion whose mass is well-known. At JYFLTRAP, the ions have typically a charge state q = +e. Thus, the mass of the nuclide of interest can be determined as: where r = ν c,ref ν c,meas is the cyclotron frequency ratio between the reference ion and the ion of interest, m ref is the atomic mass of the reference and m e is the electron mass.
Nowadays data acquisition is done interleavedly [36] at JYFLTRAP: after one or two frequency sweeps for the reference ion, a few frequency sweeps are collected for the ion of interest and this pattern is repeated as long as required for sufficient statistics. The files are divided into smaller parts in such a way that a proper count-rate class analysis [37] can be applied for the datasets. The interleaved scanning reduces the uncertainty due to time-dependent fluctuations in the magnetic field, which for JYFLTRAP have been determined as δ where t is the time between the two reference measurements. This error is quadratically added to the statistical uncertainty of each frequency ratio. The weighted mean of the measured frequency ratios is calculated and used as the final value. The inner and outer errors [38] of the data sets are compared and the larger value of these two is taken as the error of the mean. The mass-dependent uncertainty of JYFLTRAP and remaining residual relative error have been thoroughly investigated via carbon cluster measurements [39]. The uncertainty due to mass-dependent shift δ m,lim (r)/r = (7.5 ± 0.4 × 10 −10 /u) × m [39] and an additional residual relative uncertainty δ res,lim (r)/r = 7.9 × 10 −9 [39] are quadratically added to the error. More details of the JYFLTRAP facility can be found from [16].
Before the Penning-trap era, most of the mass values of fission fragments were based on beta-decay endpoint energies. This indirect method tend to underestimate the mass values due to unobserved feeding to higher lying excited states in the daughter nucleus (pandemonium effect [70]). Direct Penning-trap measurements have revealed large discrepancies to tabulated mass values based mainly on beta-decay energies. The effect accumulates and is more pronounced towards more neutron-rich members of an isobaric chain. The pandemonium effect is seen in figure 6 where the deviation between the Penning trap measurement of fission fragments to the Atomic Mass Evaluation 2003 (AME03) [71] values have been plotted as a function of isospin projection T Z = (N − Z)/2. In general, the difference from the AME03 values largely based on beta-decay experiments is bigger for more neutron-rich nuclei (higher T Z ). Some of the earliest ISOLTRAP results have already been included in the AME03. Therefore, they deviate less from the AME03 than the other experimental results.
The dramatic influence of the Penning-trap measurements on the atomic mass evaluation is seen in figure 6. The deviations of the Penning-trap values compared to the preview of the forthcoming Atomic Mass Evaluation called here as AME11 [17] are much smaller than to the AME03 values. Most of the results have been included in the AME11 except the latest results from JYFLTRAP [48,49] and CPT [65]. Nevertheless, the new results [48,49,65] deviate less from the AME11 values than the Penning-trap measurements in general from the AME03. For example, the results of [48,49] are in agreement with the extrapolated values of AME11 when the error bars are taken into account. There are only a few cases where the Penning trap data included in the AME11 show a more than 1σ deviation to the evaluation. These are 95 Rb, 95 Y, 106 Tc and 115 Ru (JYFLTRAP), 65 Ni, 72 Ga, 91 Sr, 95 Sr, and 136,137 Cs (ISOLTRAP), 146 La and 148 Pr (CPT), and 64 Co (LEBIT). For these nuclides, the absolute deviations to AME11 are generally small the biggest deviations being around 100 keV ( 64 Co, 115 Ru, 148 Pr). An isomeric state has been suggested to explain the large discrepancy for 64 Co [66]. Also 148 Pr has a long-lived isomeric state. 115 Ru should be further investigated to find out an explanation for the deviation.
Most of the Penning-trap mass measurements have been performed with JYFLTRAP and ISOLTRAP Penning traps. The IGISOL method used to produce ions for JYFLTRAP experiments is chemically insensitive but the primary beam intensity is much lower compared to ISOLDE. At ISOLTRAP, the experiments have focused on noble gases (Kr and Xe) for which a plasma ion source with a cooled transfer line is ideal, on elements for which resonant laser ionization can be applied (Ni, Cu, Zn, Ag) and on elements for which surface ionization can be exploited (Cr, Ga, Rb, Sr, Cd, Cs, Ba). At JYFLTRAP, the majority of experiments have focused on refractory elements between Y and Pd not studied elsewhere but also several isotopes from Ni to Br and from Cd to Te have been studied.
There are 19 common isotopes, mainly of Zn, Cd and Sn, investigated both at JYFLTRAP and ISOLTRAP (see figure 7). The overall agreement between ISOLTRAP and JYFLTRAP measurements is good. The only deviations occur at 123 Cd and 133 Sn. The difference for 133 Sn is close to 1σ and can be explained by statistics (the probability to lie beyond the 1σ band is around 32%). The discrepancy at 123 Cd is most likely due to the 11/2 − isomer in 123 Cd. At JYFLTRAP, both the ground and the isomeric state of 123 Cd have been measured [49,50] and found to agree with earlier beta-decay experiments and disagree with the previously deduced excitation energy for the isomer. The ISOLTRAP value not corrected by the possible isomer contribution is above the mass-excess value measured for the isomeric state at JYFLTRAP. Thus, ISOLTRAP has most likely measured the 11/2 − isomer although the value is higher than measured for the isomeric state at JYFLTRAP. At CPT, a combination of a strong 252 Cf source and a gas catcher has been employed and the measurements have focused on heavier isotopes from Sb to Gd [64,65]. Six antimony and tellurium isotopes have been measured both at CPT and JYFLTRAP (see figure 8). In general, the results agree with each other. The deviation at 137 Te is rather small (1.3σ ) and the discrepancy at 134 Sb can be explained if the isomeric state 134 Sb m has been measured at CPT. The agreement between the ISOLTRAP and CPT results is also good (see figure 9). Of the 11 nuclides measured both at CPT and ISOLTRAP, the only significant deviation is found at 138 Xe (1.7σ ).

Isomeric states
Many fission fragments have long-lived excited states, isomers, which have to be taken into account in Penning-trap mass measurements. Very short-lived isomers (T 1/2 100 ms) do not disturb the experiments. Isomers with excitation energies of more than around 100 keV can be resolved from the ground state. More than 20 isomers of fission fragments have been measured with JYFLTRAP and ISOLTRAP. Figure 10 shows the mass-excess values for the measured isomers compared to the NUBASE 2003 evaluation [72]. The large deviations can be mainly explained by the uncertainties related to beta-decay experiments which tend to underestimate the mass-excess values, as was shown already in figure 6. The NUBASE data for 82 As m , 96 108 Rh m , 125 Cd m , 129 In m , 131 In m and 134 Sb m , from which the JYFLTRAP measurements differ most, are based on beta-decay energies. For 97 Y, the ground-state is based on beta-decay energy. For 123 Cd m , the NUBASE value is also based on beta-decay experiments but there, some of the beta-gates used to determine the ground-state endpoint energy belonged to the isomeric state [50]. This has led to an overestimation of the ground-state mass value in NUBASE. For many nuclides, both the ground and the isomeric state of a nucleus have been measured with a Penning trap and the excitation energy has been determined. Figure 11 shows the excitation energies of the isomers compared to the NUBASE values. For 71 Zn, 90 Rb, 97 Y and 118 Ag, the ground-state has not been measured with a trap and the value has been adopted   113 Ru, 110,112,114,116 Rh, 115,117,119,121,122,123,124 Ag and 131 Sn. If the excitation energy is too low to be separated from the ground state, a correction to the measured value has to be made. There, the production ratio of the states is crucial and a simple assumption of 1:1 production ratio may lead to inaccurate mass values. In future, post-trap spectroscopy should be employed to identify the measured state.  [49] and CPT data [65]. The star denotes the deviation to the mass excess value of 134 Sb m measured at JYFLTRAP. Note the difference in vertical scale before and after the axis break.

Comparison to different mass models
We compared the masses of the fission fragments measured with Penning traps to different mass models. Three selected models that gave the best agreement were the Finite Range Droplet Model (FRDM95 [73]), which is a microscopic-macroscopic model applying shell model corrections onto liquid-drop model, the model by Duflo and Zuker [74], which separates the Hamiltonian into monopole and multipole terms, and a mean-field model HFB-21 [75]. Whereas the comparison of the new experimental data to AME03 revealed larger deviations for more neutron-rich nuclei, the trend is relatively flat for FRDM, Duflo-Zuker and HFB-21 (see figure 12). Three models based on energy density functionals were also compared to our dataset: SLy4 [76,77], SkP [76,77]  correlations (GCM J=0) [3]. Typical rms deviations of these functionals have been around 3.14 MeV (SkP) [78], 5.10 MeV (SLy4) [78] and 5.33 MeV (GCM) [3]. For the dataset used here, the rms deviations are around 2 − 3 MeV for these models. There is a clear trend when moving towards higher T Z nuclei: the model values increase more than the experimental data (see figure 13). The GCM (J=0) and SkP models show the largest deviations to experimental data at low T Z whereas the model SLy4 gives the worst predictions for the most neutron-rich nuclei. Both the GCM (J=0) and SkP models underestimate the masses by around 1 − 2 MeV whereas SLy4 overestimates the mass values by around 2 MeV. The results do not change much when the updated mass values are used instead of AME03.

Two-nucleon binding energies
The study of the evolution and interplay of shell structure and collective properties as a function of proton and neutron numbers requires accurate knowledge of the fine structure of the mass surface. The fine structure is best viewed in the systematic evaluation of mass differentials as a function of proton and neutron number. Typical mass differentials are one-and two-nucleon separation energies and decay Q-values. A similar request holds for second order differentials such as the shell gap energies and odd-even staggering (OES) of masses related to pairing effects. With the present-day ion-trap spectrometry these quantities are typically available with accuracies of the order of 10 keV or better. This offers accuracy comparable to that of excited states spectroscopy far from stability in the outskirts of the known nuclear landscape. The two-neutron separation energy S 2n can be obtained by using the following formulae: where E and Mc 2 stand for the binding energy and mass, respectively. Two-proton separation energies are determined analogously. In the following sections, two-nucleon binding energies of neutron-rich nuclei are presented in a few selected regions. Firstly, the behaviour of S 2n values between the closed shells in the deformed region around N = 60 and at subshell closure   In particular, the neutron-rich isotopes around A = 100 have been investigated for a shape transition and coexistence of shapes around Z = 40 and N = 60, see [79] and references therein. While the ground states of the strontium and zirconium isotopes below N ≈ 60 appear to be only weakly deformed or nearly spherical, the heavier isotopes display mainly axially symmetric deformed shapes. In 1994 spectroscopic studies of Lhersonneau et al [80] showed that nuclei with N > 60 have large ground state quadrupole deformations, while the intermediate N = 59 isotones of strontium, yttrium and zirconium still have nearly spherical ground states. This interpretation has since then been confirmed by a series of collinear laser spectroscopy experiments in the form of a sudden increase of the mean-square charge radii around N = 60 [81]. When moving towards higher Z, molybdenum isotopes are, however, found to be already less deformed or even posses triaxial shapes. Two-neutron separation energies shown in figure 14 highlight the influence of strong ground state deformation on masses as a deep dip below N = 61 which corresponds to a distinct local maximum in twoneutron binding. The behaviour of charge radii together with two-neutron binding energies is shown in figure 15. In their recent theoretical paper Takahara et al [82] showed that the spin-orbit potential plays a decisive role in the predominance of prolate deformation of ground states. This is also the case for neutron-rich nuclei above N = 60 where neutrons start to occupy deformed orbits deriving from the g 7/2 having considerable overlap with the spin-orbit partner proton orbits deriving from the g 9/2 single-particle level. The correlation between the relevant neutron and proton orbits drives the nucleus to large deformations for nuclides with Z = 38 − 41 and N > 60. This picture is also supported by the recent mass measurements of neutron-rich Kr  isotopes (Z = 36) [62] where protons are not yet occupying the g 9/2 orbit resulting in a nearly monotonically decreasing trend in S 2n .
Local maxima in two-nucleon separation energy curves can be related to energy gaps due to shell stabilization effects. In order to probe the existence of such gaps one can plot S 2n values for isotones as function of the proton number as shown in figure 16 for neutron-rich nuclei studied with the JYFLTRAP. A distinct energy gap is observed when crossing the N = 58 neutron number which coincides with the onset of deformation. For Zr, one observes even a crossing of the curves corresponding to N = 60 and 62. Otherwise, the curves show a smooth nearly monotonic behaviour indicating only weak structural effects over a broad range of proton and neutron numbers. Figure 17. Two-neutron separation energies for even-Z isotopes as a function of neutron number in comparison with semiempirical liquid drop model (see [85]).
For nuclei with larger proton and or neutron numbers, the situation becomes more complex with the mixing of many configurations and less pronounced axial deformation. Two-neutron separation energies show behaviour which signals either their non-sensitivity to structural changes or appearance of weak structural changes in the ground states. It is tempting to view the values compared to a simple liquid drop model approach based on the semiempirical mass formula [83,84]. Using the formula for two-neutron separation energy and the coefficients from [85] two-neutron separation energies for neutron-rich Zr, Mo, Ru, Pd and Cd isotopes were calculated and are plotted with the experimental values in figure 17. Except for the discontinuities around N = 60, the overall trend in the slopes for Zr and Mo isotope chains is produced. However, when moving towards higher-Z isotope chains and N = 82 neutron number, an increasing shift in the trends of S 2n energies as compared to the droplet model is seen. It is obvious that a more refined theoretical approach is needed.
The mean-field calculations presented in [48] provide a reasonable starting point to describe the underlying structural evolution accounting for the systematics of S 2n . In particular, both Gogny-D1S and Gogny-D1N energy density functionals predict a very similar evolution of the ground-state shapes as a function of the neutron number for a given isotopic chain. The agreement between the experiment and the theory is rather good in the D1S calculation, in particular for Ru and Pd isotopes. The calculation predicts appearance of a new discontinuity beyond N = 72 for Ru, Mo and Zr isotopes along the change of structure towards spherical shape. This would be a challenging task for future experiments to confirm or not.
Nevertheless, a close inspection of the potential energy surfaces reveals the presence of several low-lying competing configurations for the considered nuclei as well as γ -softness. This already indicates that correlations beyond the static mean-field picture, i.e. symmetry restoration and/or configuration mixing [86,87], may play a role in the description of the considered nuclei.  Penning traps on the landscape of masses in this region is important. Generally, S 2n decreases smoothly with neutron number and shell effects appear as a discontinuity, most visibly at the N = 50 shell closure for neutrons. Smaller effects as discontinuities from a smooth trend are observed as an increased binding for 67 Ni 39 and 68 Ni 40 . These small deviations coincide with the earlier proposed spherical sub-shell closure at N = 40 observed in various spectroscopic studies, although being a rather small effect compared to major shell closures of the doubly magic nuclei. However, recent measurement of g factors and quadrupole moments of the odd-A Cu isotopes support an apparent magic behaviour at N = 40. According to this study the effect is related to the parity change between the pf-shell orbits and the g 9/2 level. Therefore, this magic behaviour cannot be interpreted only in terms of the energy gap at N = 40 [88].

Sub
Moreover, a well-established change of the slope above N = 40 is observed for Ni and Cu isotopic chains in figure 18. This change could be due to the action of a tensor force [89]. Filling more neutrons in the 1g 9/2 orbit results in the pulling-down of the orbit. In addition, with more neutrons occupying the 1g 9/2 orbit the 1f 5/2 and 2p 3/2 orbits are crossing each other above N = 40. The result of these two effects will increase the S 2n energies and results in a reduced slope beyond N = 40. A similar explanation has been given for neutron-rich Ga isotopes above 71 Ga [90].

4.2.3.
Shell closure at N = 50. For quantitative insight into the question of the change of masses around shell closures, one can study the two-nucleon gaps for neutrons or protons. For this purpose, we have plotted in figure 19 two-neutron separation energies for N = 46, 48, 50, 52, 54 and 56 isotones as a function of the proton number with the latest mass values. The energy difference between the N = 50 and 52 isotones corresponds to a two-neutron shell gap across N = 50. When moving down in Z from the semi doubly magic 90 Zr there is an obvious trend for lowering the value having a minimum at Ge (Z = 32). This corresponds also to a minimum in the systematics of the first 2 + energies of known even-A N = 50 isotones suggesting maximum impact from core polarization effects. The isotone curves also indicate that the gap at N = 50 opens up towards the doubly magic Ni core (Z = 28). For magic nuclei the two-nucleon gap energy is approximately twice the gap of the single-particle spectrum providing a signature for the magicity [3].
Beyond the energy difference of N = 50 and N = 52 isotones, it is of interest to notice that the otherwise smooth trend of S 2n values for each isotone is broken for the N = 48 and 50 isotones between Z = 32 and 36. This may arise from two-particle and two-hole excitations across the shell gap. Otherwise, a rather flat behaviour indicating smoothness in energies of the g 9/2 and d 5/2 (or s 1/2 ) neutron states across the entire range of the studied proton numbers is observed.
In [46], experimental N = 50 shell gap energies were compared with two spherical mean-field calculations by Otsuka et al [91,92] employing a D1S or a GT3 tensor interaction as well as three different self-consistent mean field calculations in the frame of the density functional theory [3,77,76] were used to calculate the N = 50 shell gap energies. Both calculations of Otsuka overpredicted the gap by at least a factor of 2 over the experimentally known range. The use of the tensor-based interaction brought the gap clearly down to 78 Ni. The two calculations of Stoitsov et al with Sly4 energy density functionals [76,77] agreed in trends but differed in magnitude rather strongly depending on the inclusion of correlations. It is remarkable that the models based on the density functional theory reproduced qualitatively the trend in experimental values: a monotonic reduction from Z = 40 down and a minimum at Z = 32. They also predicted the increase in the gap energy and therefore the strengthening of the magicity towards 78 Ni in compliance with the concept of mutual support of magicities [93]. Figure 20 shows the experimental two-neutron gap energies for N = 50 in comparison with a few selected theoretical models in the region around Z = 28 − 40. The evolution of the shell gap over a broader range of proton numbers is shown in figure 25. The nuclear shell model clearly overpredicts the gap energies and yields a rather flat trend in shell-gap energies. The HFB Gogny with correlations [94] shows also a relatively flat trend in the gap energies and underestimates them, particularly closer to stability. The energy density functional in the   defined as a difference between the S 2p values of the Z = 28 and Z = 30 isotopic chains increases up to N = 39 after which it starts to decrease (see figure 22). The reduction in the shell gap energy has been explained by tensor force calculations [89,91]. As more neutrons are occupying 1g 9/2 orbit, 1f 7/2 and 1f 5/2 orbits are coming closer to each other resulting in a reduction of the proton shell gap energy at Z = 28 from N = 40 to N = 50. In order to understand the experimental data of copper isotopes and the decrease in the shell gap energies, it was shown in [95] that proton core excitations play an important role when approaching N = 50. As these theoretical calculations suggest that the Z = 28 shell gap becomes rather small at N = 50, more experimental data are required to determine the trend in experimental shell gap energies closer to N = 50.

4.2.5.
The Z = 50 and N = 82 shell closures. The shell closure at Z = 50 and N = 82 has long been known to exhibit features of exceptional purity for its spherical single particle structure [96,97]. This has been the result of intensive explorations by nuclear spectroscopy of excited states in this region. However, only recently the precise direct measurements of masses have become available and extended the knowledge of the ground state binding energies beyond N = 82 for Sn and above. The most recent results coming from JYFLTRAP and ISOLTRAP cover the masses of isotopic chains up to 135 Sn, 136 Sb, 140 Te and 146 Xe. In addition, the Penning trap mass measurements at ISOLTRAP and CPT cover heavier fission products from Cs up to Gd. All available data are summarized in the two-neutron separation energy plot shown in figure 23. A rather smooth trend is observed for all curves except when crossing the N = 82 shell closure. A distinct drop in binding energy is observed signalling a large and nearly constant drop in energy between N = 82 and N = 84. Beyond N = 84, the trends are again smooth until the deformed rare earth region around N = 90 is reached. Here, for the Pr isotopes a similar but less dramatic jump in S 2n is observed as compared to the N = 60 region (see figure 14).
To investigate in more details the evolution of the shell structure two-neutron separation energies are plotted as a function of proton number in figure 24. The N = 82 and 84 isotonic chains are separated by a large energy gap with a maximum value of about 6.5 MeV at   [3], the most recent Skyrme HFB mean-field calculations HFB-21 [75], and Gogny HFB mass model HFB-D1M [94].  [3] and Goriely et al [94]. The calculation of Bender et al employs SLy4 [81] energy density functional in the deformed basis with dynamical quadrupole correlations. A relatively good agreement with the experimental values has been obtained although the model is not able to explain the reduction sufficiently, unlike in the case of N = 50 [46]. The calculation without correlations gives a rather constant or slightly increasing value as a function of proton number. This confirms the importance of correlations due to core polarization. Another similar mean-field approach of Goriely et al [94] employs the HFB framework with a Gogny interaction taking into account all the quadrupole correlations self-consistently and microscopically. However, this model provides too strong reduction for the energy gap with increasing Z but reproduces the gap near Z = 50 equally well with the other two calculations. In conclusion, it is obvious that the mean-field models such as those in [3,94] rather successfully describe the binding energies near the shell closure. At Z = 50 and N = 82 the over-prediction of the gap is only about 0.5 MeV. Our present mass data provide no information on the behaviour of the N = 82 shell closure below Sn which remains a major challenge for future experiments.
Of equal importance in probing the possible shell evolution outside of the doubly magic 132 Sn is the systematics of two-proton separation energies. They are plotted for five isotopic chains around Z = 50 in figure 26. The gap is well pronounced at N = 82 and is about twice larger than the gap in the middle of the shell signalling the importance of mutual magicity in 132 Sn binding. The changing energy gap highlights the role of correlations along the isotopic chain as seen in figure 25 where a comparison is made against the model calculations with and without correlations.  existence, but their variations with proton and neutron numbers contain also information on valence particle properties of ground states and are characterized by pairing effects due to pp, nn and pn interaction. The latter has a relatively weak effect on binding energy. Therefore, their study requires highest possible accuracies for the mass measurements. As an example, we show one-neutron separation energy for Sn, Sb and Te isotopes as a function of the neutron number in figure 27. In addition to the large drop in binding between N = 82 and N = 83, the curves are characterized by the prevailing odd-even effects. In particular, the proton-neutron pairing effect seen as an increased binding of odd-odd isotopes is obvious. For example, by adding a proton to the odd-neutron nucleus 133 Sn increases its neutron binding energy by about 0.8 MeV. To demonstrate the effect, we plotted neutron separation energies for the N = 83 as a function of proton number (see figure 28). This phenomenon is common over the entire nuclear mass table and has not been treated/solved by any systematic theory so far.
A possible explanation for the increased binding was offered by Friedman and Bertsch [98] within the density functional theory, at its spherical or strongly deformed limit. In the spherical limit the odd-neutron goes into spherical j n shell with an energy of n and proton to a j p shell. The enhancement due pn pairing can now be estimated empirically from the spectrum of the odd-odd nucleus as: Here E J are the measured energies of the levels of the multiplet in the odd-odd nucleus. One of the best examples to test this formulation is 134 Sb where all the members of the π g 7/2 νf 7/2 multiplet from the 0 − ground state to the 7 − isomer at 279 keV are known [34]. Employing the above formula we get the empirical value of 0.48 MeV for δ s . This should be compared with the value extracted from the neutron separation energies of nuclei with proton numbers Z, Z + 1 and Z + 2. Following the procedure of [98] and standard angular momentum recoupling results in the value of 0.43 MeV in excellent agreement with the empirical shell-model estimate.

Odd-even staggering of masses and pairing gap.
High-accuracy mass measurements with Penning traps are opening a new vision for studies of fine structure effects in nuclear binding energies. An excellent and important application is the study of pairing effects which represent relative contribution to a total mass energy in the level of the order of 10 −5 to 10 −6 . Pairing energy gaps gain particular importance in weakly bound nuclei far from the valley of stability. Their formulation represents an important task for nuclear theory. Empirically, pairing energies can be studied by measuring odd-even mass differences along the isotopic or isotonic chains. OES has been largely attributed to BCS pairing but there are also other mechanisms, such as those due to mean-field effects, that can contribute (see e.g. [4,[99][100][101]). The simplest approach for studying the pairing effect is the three-point odd-even mass staggering formula, written here for neutrons: where ME is mass excess and Z and N denote proton and neutron numbers. One advantage of this formula is that it can be applied to more experimental data than the higher order formulae. As pointed out in the above mentioned references the three-point formula presents contributions from both pairing and mean-field effects. The odd-neutron values of (3) N can be considered to be a measure of pairing effects only whereas the even-N values are more sensitive to the splitting of the single-particle spectrum around the Fermi level [4,101]. Figure 29 presents (3) N for Sn, Te and Xe isotopes and shows a rather uniform overall pattern and odd-even variation. For Sn isotopes the small dip at N = 65 and the large one at N = 83 could be attributed to a neutron subshell at N = 64 and the neutron shell closure at N = 82. The mean-field calculations of [102] employing the pairing functional with mixed surface and volume pairing were able to reproduce the overall trend of OES for Sn isotopes rather well up to 133 Sn. No results were presented for Te or Xe isotopes in this reference. However, their behaviour is similar to Sn except above N = 82. It is obvious that there is an asymmetry in the OES values when crossing the N = 82 shell closure.
To highlight the asymmetry across N = 82 the experimental neutron OES for Sn, Te, and Xe isotopes is shown in figure 30. To emphasize pairing effects, for each isotopic chain the points with odd neutron numbers are connected by solid lines. The difference between the values for N = 81 and 83 shows a large asymmetry for Sn but a much smaller one for Te and Xe. For comparison we show in the lower part of figure 30 the OES for Pb and Po isotopes across N = 126. Here the symmetric behaviour is obvious around N = 125. Contrary to this, the upper figure indicates a considerably stronger quenching in pairing gap for Sn than for Te and Xe suggesting importance of core polarization effects. This is in somewhat discrepant to the behaviour of the shell gap energy shown in figure 25. Therefore this behaviour remains somewhat puzzling. However, concerning the question of asymmetry itself, it is of interest to note that a similar asymmetry has been observed for the B(E2) values of neutron-rich Te isotopes. It was also traced to reduced neutron pairing above the N = 82 shell closure [103].
In order to probe this question theoretically self-consistent calculations were recently performed by using the Sly4 [104] energy density functional and contact pairing force. The pairing channel was described within the HFB approximation and the blocking and filling approximations [101,105] were used to treat odd nuclei. Figure 31 shows the neutron (3) N staggering calculated within the spherical approximation [106]. The experimental decrease of OES when crossing the N = 82 gap in Sn is very well reproduced with the volume or mixed pairing forces [107], whereas the data exclude the pure surface-localized pairing force. As discussed in a previous paper [103], such pairing decrease is due to a lower level density above the N = 82 gap. However, in the N = 83 isotones, the disagreement with data for Te and Xe remains a puzzle, unresolved within the current state of the art theoretical approaches. It cannot be explained by the combined pairing and static-deformation correlation effects. Study of higher-order correlations, such as the configuration mixing of deformed states, requires an implementation of methods for odd nuclei that are presently not available, see [49].  [17,48,49] and two different r-process paths [113,114] for conditions T = 1.5 GK and N n = 10 24 cm −3 and T = 1.0 GK and N n = 10 28 cm −3 . The new nuclei identified recently at RIKEN [18] are denoted by grey crosses.

Nuclear astrophysics
Masses play a key role in the modelling of the astrophysical r process since they affect neutroncapture, beta-decay and photodisintegration rates as well as fission probabilities of the involved nuclei [108][109][110][111][112]. Therefore, masses have to be known accurately enough in order to reliably compare the calculated r-process abundances to the observations. In the region of the studied fission fragments (see figure 32), the r process moves along the N = 50 neutron shell via subsequent beta decays and neutron captures up to around Z = 30. Then, it runs away towards more neutron-rich nuclei until it reaches the neutron shell N = 82 after around Z = 40. The r-process path depends strongly on the used astrophysical model and the environment (temperature and neutron density). If fission and the resulting cycling of the matter is taken into account, more nuclides in a broader region are involved in the process.
Penning-trap mass measurements have reached the r-process path for nuclides around 80 Zn 50 and 132 Sn 82 . More than 50 nuclides, whose masses have been measured either with JYFLTRAP or ISOLTRAP, are located at the r-process path (T = 1.5 GK, N n = 10 24 cm −3 ) plotted in red in figure 32. As a result, the uncertainties of the mass-excess values in the AME11 have been reduced below 10 keV for most of these nuclides. Although many of the r-process nuclei will remain unreachable for current facilities, the large number and superior precision of Penning-trap mass measurements help in constructing more reliable mass extrapolations and models to be used for r-process studies.
Isomeric states have to be taken into account in the r-process modelling. Namely, isomers and low-lying excited states can be thermally populated if the r-process operates at high temperatures, and thus, the beta-decay rates can be significantly different from the terrestrial rates [112]. On the other hand, if the r-process operates at such low temperatures that thermal equilibrium cannot be achieved, it becomes necessary to independently describe the population of different isomers after neutron capture and the rates for neutron capture and decay of each isomer. Mass uncertainties related to nuclei having isomers can be reduced via post-trap decay spectroscopy which helps in identifying the measured state as the ground state or an isomer or a mixture of states.

Conclusions
High-precision Penning-trap mass measurements of fission fragments have increased our knowledge of neutron-rich nuclei and their properties. The measurements have also been accurate: results obtained at different Penning-trap facilities agree generally well with each other. Typically, neutron-rich nuclei have been found to be less bound than evaluated in AME03. The deviation accumulates when moving towards more neutron-rich nuclei. Penning traps provide also a new way to measure masses or excitation energies of isomeric states. The precisely measured masses of fission fragments and their derivatives have been essential for studying e.g. evolution of shell gaps, deformation, OES and pairing effects. New mass data offer also a good database to test different theoretical mass models. Accurate mass values and theoretical estimates are needed for more reliable modelling of the astrophysical r-process. In future, Penning traps aim towards more exotic neutron-rich nuclei. They are also essential facilities to purify radioactive beams for spectroscopic studies of neutron-rich nuclei.