Penning-trap mass measurements on 92, 94-98, 100Mo with JYFLTRAP

Penning-trap measurements on stable 92, 94-98, 100Mo isotopes have been performed with relative accuracy of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\ensuremath 1\cdot 10^{-8}$\end{document} with the JYFLTRAP Penning-trap mass spectrometer by using 85Rb as a reference. The Mo isotopes have been found to be about 3keV more bound than given in the Atomic Mass Evaluation 2003 (AME03). The results confirm that the discrepancy between the ISOLTRAP and JYFLTRAP data for 101-105Cd isotopes was due to an erroneous value in the AME03 for 96Mo used as a reference at JYFLTRAP. The measured frequency ratios of Mo isotopes have been used to update mass-excess values of 30 neutron-deficient nuclides measured at JYFLTRAP.


Introduction
Recently, a discrepancy was found between cadmium mass measurements performed at JYFLTRAP, where 96 Mo + was used as a reference [1], and SHIPTRAP [2] and ISOLTRAP results, where 85 Rb + was used as a reference ion [3]. Earlier JYFLTRAP has shown to be capable of performing very accurate mass measurements. Therefore, it was assumed that the 96 Mo mass-excess value would be about 3 keV off in the Atomic Mass Evaluation 2003 (AME03) [4]. The mass evaluation done in ref. [3] showed that there is a −3.2 keV shift between the AME03 value and the evaluated value for 96 Mo. In this work, we wanted to confirm this evaluation result by a direct mass measurement of 96 Mo. If the mass of 96 Mo is off by 3 keV, also the neighbouring isotopes connected by (n, γ) reactions in the AME03 are likely to be off. Thus, we decided to check the mass-excess values of all stable molybdenum isotopes and investigate where the possible 3 keV offset could come from. These measurements have a direct effect on previous JYFLTRAP results since stable molybdenum isotopes ( 94,96,97,98 Mo) have been used as references for 30 neutrondeficient nuclides at JYFLTRAP.
The first trap of JYFLTRAP (purification trap) is used for the isobaric purification of the injected ion bunches by using the buffer-gas cooling technique [10]. The mass measurement is carried out in the second Penning trap (precision trap). The measurement is based on the determination of the sideband frequency of the ions of interest ν + + ν − , where ν + and ν − are the reduced cyclotron frequency and the magnetron frequency, respectively. In an ideal Penning trap, this sideband frequency matches with the true cyclotron frequency ν c = 1 2π q m B of ions with charge state q and mass m in the magnetic field B [11]. The frequency determination was done by using the time-of-flight ion-cyclotron-resonance (TOF-ICR) technique [12]. In this method, the ion's radial energy is increased in the trap by using an azimuthal quadrupole radio-frequency (RF) field with the cyclotron frequency of the ions. Since the radial energy of the ions is converted to axial energy in the gradient of the magnetic field when extracted from the trap, the increased energy leads to a shorter flight time to the micro-channel plate (MCP) detector. In this experiment, a Ramsey-type ion motion excitation was used [13,14] with two 25 ms long fringes separated by a 750 ms long waiting time. Figure 2 shows two examples of Ramsey TOF resonances for 85 Rb + and 96 Mo + . The cyclotron frequency of an ion and its uncertainty are obtained from the experimental TOF data by fitting the theoretical fit function. The mass measurement in a Penning trap is based on the measurement of the frequency ratio r between a reference ion with a well-known mass and an ion of interest: This frequency ratio and its uncertainty are used to deduce the mass of the ion of interest by using the equation where m meas is the mass of the atom of interest, m ref is the mass of the reference atom and m e is the mass of the electron. Thus, the uncertainty in the mass of the reference atom contributes to the final mass value, and it can be reevaluated by using the most accurate knowledge for the mass of the reference atom.

Data analysis and results
To minimize frequency shifts coming from the drifting magnetic field, the measurements were performed by running 2 scan cycles of the ion of interest (Mo + ) and then 2 scan cycles of the reference ion ( 85 Rb + ) and repeating this pattern. The measured data were divided into 15cycle-long runs. A count-rate class analysis [15], where the data were divided into classes according to the number of detected ions, was carried out. The frequency was extrapolated to 0.6 ions in the trap due to the 60% detection efficiency.
The average frequency ratios were calculated by using the weighted means. The internal errors (σ int , statistical uncertainties of the weighted means) were compared to external errors (σ ext , weighted standard deviations) and so-called Birge ratios R = σ ext /σ int were determined [16]. In the ideal case, the ratio should be close to 1. For the uncertainty of r we took always the larger one of the internal and external uncertainties. For this value σ r , a massdependent uncertainty σ m (r) = (7.5 · 10 −10 /u) · Δm · r [17] and a residual uncertainty σ res (r) = (7.9 · 10 −9 ) · r [17] were added quadratically. Measured frequency ratios and their uncertainties are shown in table 1. Birge ratios were close to 1 in each mass measurement set. This means that the deviations in the data are statistical. The used atomic mass unit is u = 931 494.009 0(71) keV [18], the electron mass m e = 510.998910(13) keV [19], and the value for 85 Rb mass excess ME = −82167.331 (11) keV [4]. An example of the measured frequency ratios is shown in fig. 3.
In fig. 4 all the links influencing the Mo mass-excess values in the AME03 are shown. Since the JYFLTRAP values disagreed with the AME03 values (except for 92 Mo), a thorough comparison to earlier measurements was carried out and all possible links from and to the Mo isotopes in the AME03 were checked out in this work. The results are given below nuclide by nuclide.
The main result is that the values from Bishop et al. [23] disagree with the JYFLTRAP values and explain most of the difference between the JYFLTRAP results and the AME03 values. Deviations were also found to C 7 H 10 -94 Mo [22], 95 Nb(β − ) 95 Mo [24], 98 Mo(n, γ) 99 Mo [20,21], and 100 Mo( 3 He, p) 102 Tc [37]. The (n, γ) results between 94 Mo and 98 Mo agree nicely with the JYFLTRAP values. JYFLTRAP mass-excess values for Mo isotopes suggest that these Mo isotopes are systematically too weakly bound in the AME03. This will also have an effect on the nuclides which have main influences coming from these isotopes, such as for neighbouring Nb and Tc nuclides or 101 Mo.

Mo
The JYFLTRAP mass value for 92 Mo agrees with the values from C 7 H 8 -92 Mo [22] [20]) and AME03 [4]. Bishop (1963)* employs the AME03 mass value [4] for 94 Mo instead of the value from this work.
fig. 5, where the deviation from different experiments (ME LIT ) to the JYFLTRAP mass-excess value (ME JYFL ) is shown.

Mo
The mass value measured for 94 Mo at JYFLTRAP disagrees with the AME03 value by −3.0 (21) keV. Similarly to 92 Mo, there is a 6.3 (22) keV difference between the  . 6). Actually, even bigger disgareement is found when the AME03 value for 92 Mo is used. In addition, the value from C 7 H 10 -94 Mo [22] gives a 5.3(31) keV higher mass-excess value for 94 Mo than measured at JYFLTRAP. The beta-decay experiments [26][27][28] agree with the JYFLTRAP value but the value from (p, n) reactions [32] disagrees with it. The

Mo
The JYFLTRAP mass value for 95 Mo is 3.3(21) keV lower than the AME03 value. The AME03 value is mainly based on the 94 Mo(n, γ) 95 Mo [20] and 95 Mo(n, γ) 96 Mo [20] values, which agree well with the JYFLTRAP results for 94 Mo, 95 Mo, and 96 Mo. A shift is observed when the AME03 value is applied for 94 Mo and 96 Mo, again indicating that these Mo isotopes are systematically less bound in the AME03 (see fig. 7). Also the value based on the beta decay 95 Nb(β − ) 95 Mo [24] disagreeing with the JYFLTRAP value has an influence on the 95 Mo value in the AME03.

Mo
The JYFLTRAP mass-excess value for 96 Mo is 2.9 (22) keV lower than the AME03 value. All reaction links in the AME03 agree with the JYFLTRAP value when JYFLTRAP mass-excess values for 95 Mo and 97 Mo are used (see fig. 8). The disagreement between the AME03 value and the JYFLTRAP value comes from the erroneous mass values of 95 Mo and 97 Mo in the AME03.

Mo
The JYFLTRAP mass-excess value slightly disagrees with the AME03 value for 100 Mo. An almost perfect agreement is found with the value based on C 7 H 16 -100 Mo [22],    [37] influencing the AME03 value of 100 Mo, deviate from our Penning-trap mass measurement (see fig. 11). In addition, the value derived from the 100 Mo(n, γ) 101 Mo [44] reaction gives a similar deviation as the AME03 value. This suggests that the AME03 value for 101 Mo should be about 6.6 keV lower in order to agree with the (n, γ) data.

Updated mass values of the nuclides measured at JYFLTRAP using Mo references
Up to date, 30 neutron-deficient nuclides have been measured with respect to molybdenum reference ions at JYFLTRAP (see refs. [1,45,46]). Thus, the results of this paper have an effect on these mass-excess values. The values can be easily updated by multiplying the old frequency ratio measured against a molybdenum isotope (r old ) by the frequency ratio of the corresponding molybdenum ion to 85 Rb + measured in this work (r Mo-Rb ):  [48]). 3 The original values of −66273(7) keV (old) and −66275.4(6.0) keV (new) were modified for an unknown mixture of isomeric states ( 85 Nb m at E x ≥ 69 keV [49]). 4 Possible contribution from an isomer at 250(160)# keV [47] has not been taken into account. 5 The original values of −73868(7) keV (old) and −73871.1(6.4) keV (new) were modified for an unknown mixture of isomeric states ( 87 Nb m at 3.84 (14) keV [47]). 6 The original values of −76149(7) keV (old) and −76151. 5 (14) keV [47]), and 88 Nb m (E x = 40(140) keV [47]) have been taken into account according to eq. (14) of ref. [50] and added quadratically to the experimental uncertainties. No correction due to the isomer in 86 Nb (E x = 250(160)# keV [47]) has been done since this isomer is considered as uncertain. It should also be noted that for 85 Nb, the energy of the isomer is only a lower limit [49]. The previous values for 91 Tc and 91 Ru were published in ref. [46], which was a joint publication of JYFLTRAP and SHIPTRAP. Here, the JYFLTRAP values measured against 94 Mo have been updated and new weighted means of JYFLTRAP and SHIPTRAP values have been calculated for 91 Tc and 91 Ru. As can be seen from table 2, the updated values are on the average about 2.8 keV lower than the old values. This is well within the error bars.
Although the 3 keV shift in the mass excesses of Mo isotopes is less than 1σ, it is important to take it into account. For example, the Cd isotopes have been measured at SHIPTRAP [2] and ISOLTRAP [3] by using 85 Rb as a reference. The mass-excess values determined with JYFLTRAP for Cd isotopes employing 96 Mo as a reference [1] disagreed in some cases with ISOLTRAP and SHIPTRAP (see fig. 12). The shift from the AME03 value in the mass of 96 Mo was already observed in the mass evaluation performed in ref. [3]. In this work, we have experimentally determined this mass value. The updated Cd values (see table 2) agree within one standard deviation with the ISOLTRAP data. However, the SHIPTRAP values for 101,102,104 Cd still deviate from the ISOLTRAP and JYFLTRAP data.

Conclusions
In this paper, we have reported frequency ratios between 92,94-98,100 Mo and 85 Rb measured with the JYFLTRAP setup. The mass-excess values of the Mo isotopes have been determined with about 1 keV precision, which is at least by a factor of 2 more precise than in the AME03. In addition, all measured stable Mo isotopes have been found to be more bound than given in the AME03. This will also have an effect on the nuclides which have main influences coming from these Mo isotopes in the AME03, such as for neighbouring Nb, Mo and Tc nuclides.
94,96,97,98 Mo have been used as references for 30 neutron-deficient nuclides measured at JYFLTRAP, and thus, these values have been updated with the new molybdenum values. Although the difference to the previous values is less than 1σ, it is worthwhile to take it into account for example when comparing to results from other facilities. In addition, proton-capture rates relevant for astrophysical rp [51,52] and νp [53,54] processes depend exponentially on proton separation energies, and already a small change will have an effect on the rate. In any case, the stable molybdenum isotopes are now more accurate references for future mass measurements of neutron-deficient nuclides.
This measurement was motivated by the discrepancy in the cadmium mass-excess values between JYFLTRAP, ISOLTRAP and SHIPTRAP. An inaccurate mass-excess value of 96 Mo in the literature has now been confirmed to be the reason for the deviation. This gives a perfect example why the main result from a Penning-trap measurement should be rather the frequency ratio between the reference ion and the ion of interest and its uncertainty rather than the mass-excess value itself. This way one can always use the most accurate value for the mass of the reference ion and recalculate the mass values of ions of interest.