# Comprehensive mass measurement study of 252Cf fission fragments
with MRTOF-MS and masses of neutron-rich Ce isotopes

S. Kimura<EMAIL_ADDRESS>Wako Nuclear Science Center (WNSC), Institute of
Particle and Nuclear Studies (IPNS), High Energy Accelerator Research
Organization (KEK), Wako 351-0198, Japan  RIKEN Nishina Center for
Accelerator-Based Science, Wako 351-0198, Japan  M. Wada  Wako Nuclear Science
Center (WNSC), Institute of Particle and Nuclear Studies (IPNS), High Energy
Accelerator Research Organization (KEK), Wako 351-0198, Japan  H. Haba  RIKEN
Nishina Center for Accelerator-Based Science, Wako 351-0198, Japan  S.
Ishizawa  Institute for Materials Research (KINKEN, IMR), Tohoku University,
Sendai 980-8577, Japan  New Industry Creation Hatchery Center (NICHe), Tohoku
University, Sendai 980-8579, Japan.  Y. Ito  Advanced Science Research Center,
Japan Atomic Energy Agency (JAEA), Tokai, 319-1195, Japan.  RIKEN Nishina
Center for Accelerator-Based Science, Wako 351-0198, Japan  T. Niwase
Department of Physics, Kyushu University, Fukuoka, 819-0395, Japan  M.
Rosenbusch  RIKEN Nishina Center for Accelerator-Based Science, Wako 351-0198,
Japan  P. Schury  Wako Nuclear Science Center (WNSC), Institute of Particle
and Nuclear Studies (IPNS), High Energy Accelerator Research Organization
(KEK), Wako 351-0198, Japan  A. Takamine  RIKEN Nishina Center for
Accelerator-Based Science, Wako 351-0198, Japan

###### Abstract

We report the mass measurements of neutron-rich isotopes produced via
spontaneous fission of ${}^{252}{\rm Cf}$ using a multi-reflection time-of-
flight mass spectrograph. The mass of ${}^{155}{\rm Ce}$ is determined
experimentally for the first time. A discrepancy between the experimental and
literature values was found for the mass of ${}^{127}{\rm Sb}$, which was
previously deduced through indirect measurements. In comparison with several
theoretical predictions, both the values and the trend of the mass excesses of
${}^{152-155}{\rm Ce}$ cannot be consistently explained. The wide-range and
simultaneous mass measurements of the multi-reflection time-of-flight mass
spectrograph enable us to reexamine existing mass data. The new measurements
suggest corrections to the present values, including data from previous
Penning trap mass measurements.

##  I Introduction

Figure 1: Location of the observed nuclides on the nuclear chart. The observed
nuclides are indicated with orange-colored squares. The black squares
represent the stable nuclides. The nuclides mentioned in this paper are marked
with red-colored squares. The contour map shows the fission yield of 252Cf
[1].

Atomic mass measurements provide essential data for nuclear physics to reveal
the underlying nuclear structure and to understand the nuclear reactions [2,
3]. Particularly for nuclear astrophysics, a large set of accurate and precise
mass data is required to understand the origin of elements. The rapid neutron-
capture ($r$-) process path is governed by the balance between the
$\beta^{-}$-decay rate and neutron-capture rate. In the neutron-capture
process, $({\rm n},\gamma)-(\gamma,{\rm n})$ equilibrium will be established,
and the net neutron-capture rate strongly depends on the $Q$-value. Nuclear
masses are crucial in determining the final isotopic abundance of the
$r$-process. Access to the $r$-process nuclei is difficult due to their
locations far from stability; thus, theoretical predictions are needed to
obtain the final isotopic abundances. A mass precision better than $\sim$50
keV is required to determine the isotopic abundance ratio to be better than a
factor of 2 [4]. However, in the regions without experimental data on nuclear
masses, there is a wide variance amongst the masses predicted by various
theoretical models [5].

In the region of neutron-rich lanthanoid isotopes, many nuclear masses have
been determined with the Penning trap mass spectrometers (PT-MSs). Among these
measurements of the neutron-rich isotopes, which can be produced by the
spontaneous fission of ${}^{252}{\rm Cf}$, there is a significant contribution
from the Canadian Penning trap (CPT) at the CARIBU facility [6, 7, 8, 9]. A
mass measurement study focusing on the same region with JYFLTRAP at Jyväskylä
has also been reported [10]. The three nuclides, 156Nd, 158Nd, and 162Sm, are
reported in both studies with JYFLTRAP and CPT [8]. For 162Sm, the extracted
mass excesses of both studies are in agreement. However, for the two Nd
isotopes, one can find that the differences in their mass excess values are
$\Delta{\rm ME}_{\rm CPT-JYFL}({}^{156}{\rm Nd})=7.9(2.4)~{}{\rm keV}$ and
$\Delta{\rm ME}_{\rm CPT-JYFL}({}^{158}{\rm Nd})=62(37)~{}{\rm keV}$. While
the inconsistency for 156Nd is less than 10 keV, the 158Nd case shows more
than 50 keV, but its deviation remains at a level of $1.7\sigma$ due to the
larger uncertainty provided by JYFLTRAP. This is significantly large
considering the requirement of the $r$-process calculation. For most isotopes
in the neutron-rich lanthanoid region, the presently accepted masses, as
determined by the 2020 Atomic Mass Evaluation (AME20) [11, 12], are based on
single mass measurement. Thus, cross-checking the existing results with the
measurements via other techniques is desired to improve the accuracy of the
nuclear mass data.

Figure 1 shows the observed isotopes in the study of 252Cf fission fragment
with a multi-reflection time-of-flight mass spectrograph (MRTOF-MS). More than
250 isotopes covering 29 elements have been extracted from the gas cell and
observed in the time-of-flight (TOF) spectra. We report the results of these
measurements, a highlight of which are neutron-rich lanthanoid isotopes
extending to 155Ce.

##  II Experiment

Figure 2 shows a schematic of the experimental setup of the present study. The
experimental setup comprises a cryogenic He gas cell (GC), an ion transport
suite, and the MRTOF-MS. A 9.25 MBq 252Cf source (spontaneous fission branch:
3.1% [13]) with a 6-$\mu$m Ti degrader is installed in front of the GC. The GC
has a 1.5-$\mu$m Mylar window and is cryogenically cooled to $\sim$$70~{}{\rm
K}$ throughout all measurements. The He gas pressure is regulated to maintain
a density equivalent to 150 mbar at room temperature. The emitted fission
fragments from the 252Cf source will be stopped and thermalized inside the GC.
The thermalized ions are manipulated by an RF-carpet [14] toward the exit of
the GC and further transported to a planar geometry radio-frequency quadrupole
(RFQ) trap (flat trap) [15], which works as an ejection device to the MRTOF-
MS, via the ion transport system having two linear RFQ traps. The second
linear RFQ trap can be used as a quadrupole mass filter and enable the removal
of the intense contaminants produced inside the GC via ionization with the
$\alpha$-particles emitted by the 252Cf source.

The transported analyte ions are perpendicularly ejected from the flat trap to
the MRTOF-MS. The ejection trigger signals are also used as the start signal
of a time-to-digital converter (TDC) start trigger. The ejected ions are
captured by temporarily lowering the entrance mirror potential of the MRTOF-MS
and raising it before the ions return to the entrance mirror. After the ions
make a certain number of reflections, making the time focus condition, their
TOFs are measured by lowering the exit mirror potential and allowing the ions
to fly to the TOF detector.

The flat trap has a wide mass acceptance, making it capable of accumulating
and storing across a wide range of $A/q$ values simultaneously, while the
MRTOF-MS similarly has a broad acceptance to capture ions spanning a wide
$A/q$ range. This can lead to a contaminated TOF spectrum with many unwanted
ion species. To avoid this, an in-MRTOF deflector (IMD) [16] has been
installed at the middle point, the drift part of the MRTOF-MS. The IMD
consists of a pair of two planar electrodes and can remove unwanted ions by
applying a voltage of 20 V when the analyte ions are not passing through the
IMD. The operation condition of the IMD is determined with ${}^{85}{\rm
Rb}^{+}$ ions from an offline ion source to calibrate the timing of the IMD
pulses and ensure that desired ion species are not disturbed.

Figure 2: Schematic view of the experimental setup.

##  III Analysis

The analysis strategy is similar to the previous work with the MRTOF-MS [17].
The measured TOF value for an ion, having mass $m$ and charge $q$, which
undergoes $n$ laps in the MRTOF-MS device, can be represented by

$t_{\rm obs}=(a+b\cdot n)\sqrt{m/q}+t_{0}$ (1)

where $a$ and $b$ are constants related to the non-reflection flight path and
the path between consecutive reflections, respectively, and $t_{0}$ represents
an electronic delay between the TDC start signal and the ion’s actual ejection
from the flat trap. The single reference method [18], which needs only one
reference mass, is adopted to determine the mass of analyte ions. In this
method $m_{\rm X}$, the ionic mass of nuclide X, is given by Eq. 2:

$m_{\rm X}=\rho^{2}m_{\rm ref}=\left(\frac{t_{\rm X}-t_{0}}{t_{\rm
ref}-t_{0}}\right)^{2}m_{\rm ref},$ (2)

where $\rho$ is the TOF ratio, $t_{\rm X}$ and $t_{\rm ref}$ are the TOF of
nuclide X and the reference ion, respectively, $m_{\rm ref}$ is the mass of
the reference ion, $t_{0}$ is the constant time offset within the measurement
system mentioned above. The systematic mass error resulting from the
uncertainty of the constant time offset $\delta t_{0}$ is estimated to be
$\delta(\rho^{2})/\rho^{2}\sim 10^{-9}$ when employing isobaric references
[19] and is negligible in the present study. As the mass reference, we select
the nuclide, which has no known long-lived isomeric states and shows the
highest intensity spectral peak.

Collecting sufficient numbers of the more exotic nuclides in an isobar chain,
the required measurement time was over twelve hours for each. During this
time, the TOF could vary considerably due to the thermal expansion of the
MRTOF-MS device and minor instabilities in the high-voltage power supply
system for the mirror electrodes [20]. In all measurements of the present
study, the fission fragment and the ${}^{85}{\rm Rb}$ ions provided from an
offline ion source were alternately measured in 25-ms cycles. Then, these TOF
drifts can be compensated by the use of ${}^{85}{\rm Rb}$ ions. The TOF
corrections were performed within each subset, obtained by dividing the raw
data set into ${\cal N}$ parts. For ions in each subset $i$ the corrected TOF
$t_{\rm corr,i}$ is calculated using the following relation:

$t_{\rm corr,i}=t_{\rm raw,i}\left(\frac{t_{\rm 85Rb}}{t_{\rm
85Rb,i}}\right),$ (3)

where $t_{\rm raw,i}$ is the uncorrected TOF of each ion in subset $i$, while
$t_{\rm 85Rb}$ and $t_{\rm 85Rb,i}$ are the standard TOF of ${}^{85}{\rm Rb}$
and the fitted TOF center of the $i^{th}$ spectral subset, respectively. This
correction method was applied to all the data presented here.

To fully preclude accidental misattribution in identifying the ions in the TOF
spectra, the measurements were performed at two different numbers of laps, 602
and 604, for each $A/q$ series. The final results of two measurements
belonging to the same $A/q$ series were obtained as their weighted average,

$\displaystyle\overline{\rho^{2}}$ $\displaystyle=$
$\displaystyle\frac{w^{2}_{602}\rho^{2}_{602}+w^{2}_{604}\rho^{2}_{604}}{w^{2}_{602}+w^{2}_{604}},$
(4) $\displaystyle\delta(\overline{\rho^{2}})$ $\displaystyle=$
$\displaystyle\frac{1}{\sqrt{w^{2}_{602}+w^{2}_{604}}},$ (5)

where $w_{i}$ is a weight of each measurement and is defined by $w_{i}\equiv
1/\delta(\rho_{i}^{2})$.

The atomic mass of nuclide X, $M_{\rm X}$, observed as the $q_{\rm X}+$ ions,
is given by

$M_{\rm X}=q_{\rm X}(m_{\rm ref}\overline{\rho^{2}}+m_{\rm e}),$ (6)

where $m_{\rm ref}$ and $m_{\rm e}$ are the ionic masses of the references and
the electron rest mass, respectively.

Figure 3: TOF spectra of $A/q=77.5$ series. Red lines show the fit results
with the phenomenological fitting function. The enlarged spectra around the
predicted positions of 155Ce are indicated in the top-left panels.

Figure 4: TOF spectra of $A/q=75.5-77.0$ series. Red lines show the fit
results with the phenomenological fitting function.

A phenomenological fitting function, based on an exponential-Gaussian hybrid
function [18, 20, 21], was used to fit non-Gaussian-shape peaks accurately. In
the present study, we employed the function:

$\displaystyle
f(\tau)=\left\\{\begin{array}[]{l}\left(\kappa/\sigma\right)\exp\left[\frac{t_{\rm
s1}(t_{\rm s1}-2\tau)}{2\sigma^{2}}\right]\ \left({\rm for}\ \tau<t_{\rm
s1}\right),\\\ \\\
\left(\kappa/\sigma\right)\exp\left[-\frac{\tau^{2}}{2\sigma^{2}}\right]\
\left({\rm for}\ t_{\rm s1}\leq\tau<t_{\rm s2}\right)\\\ \\\
\left(\kappa/\sigma\right)\exp\left[\frac{t_{\rm s2}(t_{\rm
s2}-2\tau)}{2\sigma^{2}}\right]\ \left({\rm for}\ \tau\geq t_{\rm
s2}\right),\end{array}\right.$ (12)

where $t_{{\rm s}i}$ denotes the range of each sub-function. The variable
$\tau$ is defined as $\tau\equiv t-\mu$, where $\mu$ is the peak center used
in the mass determinations.

Herein, we set an assumption about the peak shape: the peaks of the ions
belonging to the same $A/q$ series have an identical shape. Based on this
assumption, the only free parameters for each peak in the fitting function are
the peak center $\mu$ and the peak height $\kappa$ for the species of
interest. In the fitting algorithm, to improve the mass precision, the $\tau$
parameter was treated as a function of $t$, $t_{\rm ref}$, and $\rho$, where
$\rho$ is the TOF ratio from Eq. 2. Then, the fitting function $F$ for $N$
peaks was described by

$\displaystyle F(t,t_{\rm ref},\rho_{1},\cdots,\rho_{\rm
N},,\kappa_{1},\cdots,\kappa_{\rm N})=\hskip 80.00012pt$
$\displaystyle\sum_{i=1}^{N}f(t,t_{\rm ref},\rho_{i},\kappa_{i},\sigma,t_{{\rm
s}1},t_{{\rm s}2}).$ (13)

The ROOT package [22] was used for peak fitting. There is an ambiguity in the
degree of freedom in the binning process to fit: the width and offset of the
center. To take their influence into account, the systematic error of
$\delta\rho_{\rm sys,bin}=10^{-8}$ [17] was added to the error of each
measured $\rho$ as an additional error.

##  IV Results and Discussion

In the present paper, we focus on the five $A/q$ series: $A/q=75.5$, 76.0,
76.5, 77.0, and 77.5. The TOF spectra of $A/q=77.5$ series at 602 and 604 laps
are shown in Fig. 3. Other $A/q$ series’ TOF spectra are given in Fig. 4. If
the relative positions and intensities of a given set of peaks remain constant
at different numbers of laps, we can infer that they are isobaric with each
other. In the TOF spectra, we observed not only atomic but also molecular
adduct ions with the same/different charge states, $e.g.$, ${}^{14}{\rm
N}_{2}$-attached $2+$ ions and ${}^{40}{\rm Ar}_{2}$-attached $3+$ ions, and
stable molecular ions. Thus, many ions with different mass numbers $A$ can be
included in the same TOF spectrum. This allows us to confirm a mass
correlation between not only two ion species but also all mass correlations
with all other observed species simultaneously. This is an excellent advantage
of the MRTOF-MS for achieving accurate measurements.

In the present measurements, the mass resolving power was $R_{\rm m}\sim
500,000$. Some observed isotopes have low-lying isomeric states with an
excitation energy of $E_{\rm X}\lesssim 100~{}{\rm keV}$. They cannot be
resolved based on the present mass resolving power; we treated them as one
peak with a single component.

The accuracy of mass determination by the MRTOF-MS is at the $3.5\times
10^{-8}$ level when an accurate isobaric reference is used, as in the previous
study [17]. In this study, however, the most intense peak of the fission
products, i.e., a nuclide previously measured with PT-MS, was used as the
reference for each $A/q$. Specifically, 151Pr ($\delta m_{\rm ref}=12$ keV),
152Pr (9.8 keV), 153Nd (2.7 keV), 154Nd (1.0 keV), and 155Pm (4.7 keV) were
used as the mass references. We found that if the uncertainty of a reference
is smaller than a few keV, it can cause as much as a $3\sigma$ discrepancy for
the mass value of another previously measured isobar. The high linearity of
the MRTOF-MS suggests a problem with the error evaluation of one of the
measurements. However, at this point, it is unclear which one is correct, so
we reexamined the uncertainties of the mass references to avoid the
discrepancy, i.e., reaching a $1\sigma$ agreement. They are specifically 153Nd
($\delta m_{\rm ref}=2.7$ keV$\rightarrow$16 keV), 154Nd (1.0
keV$\rightarrow$13 keV), and 155Pr (4.7 keV$\rightarrow$7.1 keV).

The results are summarized in Table 1 and 2. In the following parts, we will
discuss the details of the results of each $A/q$ series.

Table 1:  Measured values of the squares of time-of-flight ratio $\rho^{2}$ and the mass excess values ME. The nuclides used as atomic mass references are shown in column “Ref.”. MElit indicates the literature’s mass excess values, and $\Delta{\rm ME}$ represents the differences between MElit and the mass excess values of the present study: $\Delta{\rm ME}\equiv{\rm ME}-{\rm ME}_{\rm lit}$. The reference of MElit is indicated in column “Ref. of lit.”; AME20 [11, 12] and CPT [9]. The $\delta$m/m column provides relative mass precisions of the present measurements. The mass reference’s reexamined uncertainty is presented with an arrow connected to the original value. Species | $\rho^{2}$ | $\delta(\rho^{2})/\rho^{2}$ | ME (keV) | MElit. (keV) | Ref. of lit. |  $\Delta{\rm ME}$ (keV)
---|---|---|---|---|---|---
$A/q=75.5$ |  |  |  |  |  |
${}^{111}{\rm Pd}$${}^{40}{\rm Ar}^{2+}$111Admixture of the ground state and the isomeric state(s) | 0.99961500(13) | $1.3\times 10^{-7}$ | $-120\,906(30)$ | $-121\,025.79(73)$ | AME20 | $120(30)$
${}^{111}{\rm Rh}$${}^{40}{\rm Ar}^{2+}$ | 0.999640390(47) | $4.7\times 10^{-8}$ | $-117\,336(24)$ |  $-117\,343.7(6)$.9) | AME20 | $7(25)$
${}^{111}{\rm Ru}$${}^{40}{\rm Ar}^{2+}$ | 0.999679667(46) | $4.6\times 10^{-8}$ | $-111\,815(24)$ |  $-111\,825.2(9)$.7) | AME20 | $11(26)$
${}^{151}{\rm Pm}^{2+}$ | 0.999953012(47) | $4.7\times 10^{-8}$ | $-73\,386(24)$ |  $-73\,386.3(4)$.6) | AME20 | $1(25)$
${}^{151}{\rm Nd}^{2+}$ | 0.999970367(18) | $1.8\times 10^{-8}$ | $-70\,946(23)$ |  $-70\,943.2(1)$.1) | AME20 | $-3(24)$
${}^{151}{\rm Pr}^{2+}$ | 1 |  |  | $-66\,780(12)$ | AME20 |
${}^{151}{\rm Ce}^{2+}$11footnotemark: 1 | 1.000039526(19) | $1.9\times 10^{-8}$ | $-61\,223(24)$ | $-61\,225(18)$ | AME20 | $2(29)$
${}^{150}{\rm Ce}$${}^{1}{\rm H}^{2+}$ | 1.000065422(20) | $2.0\times 10^{-8}$ | $-57\,582(24)$ | $-57\,558(12)$ | AME20 | $-24(26)$
${}^{151}{\rm La}^{2+}$ | 1.000094199(89) | $8.9\times 10^{-8}$ | $-53\,537(26)$ | $-53\,310(435)$ | AME20 | $-226(436)$
${}^{150}{\rm La}$${}^{1}{\rm H}^{2+}$ | 1.000126206(35) | $3.5\times 10^{-8}$ | $-49\,037(24)$ |  $-49\,022.1(2)$.5) | AME20 | $-15(24)$
$A/q=76.0$ |  |  |  |  |  |
${}^{112}{\rm Rh}$${}^{40}{\rm Ar}^{2+}$11footnotemark: 1 | 0.999640920(55) | $5.5\times 10^{-8}$ | $-114\,600(21)$ | $-114\,771(44)$ | AME20 | $171(49)$
${}^{112}{\rm Ru}$${}^{40}{\rm Ar}^{2+}$ | 0.999668761(51) | $5.1\times 10^{-8}$ | $-110\,660(21)$ | $-110\,670.7(96)$ | AME20 | $11(23)$
${}^{12}{\rm C}{}^{32}{\rm S}_{2}^{1+}$ | 0.999715477(32) | $3.3\times 10^{-8}$ | $-52\,024(10)$ | $-52\,031.0743(26)$ | AME20 | $7(10)$
${}^{58}{\rm Ni}{}^{16}{\rm O}{}^{1}{\rm H}_{2}^{1+}$ | 0.999738692(29) | $2.9\times 10^{-8}$ | $-50\,382(10)$ | $-50\,387.93(35)$ | AME20 | $6(10)$
${}^{148}{\rm Ce}$${}^{40}{\rm Ar}_{2}^{3+}$ | 0.99978904(12) | $1.2\times 10^{-7}$ | $-140\,456(39)$ | $-140\,478(11)$ | AME20 | $22(41)$
${}^{152}{\rm Pm}^{2+}$11footnotemark: 1 | 0.999947464(25) | $2.5\times 10^{-8}$ | $-71\,217(20)$ | $-71\,254(26)$ | AME20 | $37(33)$
${}^{152}{\rm Nd}^{2+}$ | 0.999955016(17) | $1.7\times 10^{-8}$ | $-70\,148(20)$ | $-70\,150(25)$ | AME20 | $1(31)$
${}^{152}{\rm Pr}^{2+}$ | 1 |  |  | $-63\,782.2(98)$ | CPT |
${}^{152}{\rm Ce}^{2+}$ | 1.000034560(18) | $1.8\times 10^{-8}$ | $-58\,891(20)$ | $-58\,878.3(23)$ | CPT | $-13(20)$
${}^{151}{\rm Ce}$${}^{1}{\rm H}^{2+}$11footnotemark: 1 | 1.000069506(20) | $2.0\times 10^{-8}$ | $-53\,945(20)$ | $-53\,936(18)$ | AME20 | $-9(27)$
${}^{151}{\rm La}$${}^{1}{\rm H}^{2+}$ | 1.000123838(62) | $6.2\times 10^{-8}$ | $-46\,256(22)$ | $-46\,021(435)$ | AME20 | $-235(436)$
$A/q=76.5$ |  |  |  |  |  |
${}^{113}{\rm Pd}$${}^{40}{\rm Ar}^{2+}$ | 0.99963982(15) | $1.5\times 10^{-7}$ | $-118\,639(39)$ | $-118\,630.4(70)$ | AME20 | $-8(40)$
${}^{113}{\rm Rh}$${}^{40}{\rm Ar}^{2+}$ | 0.999673917(48) | $4.8\times 10^{-8}$ | $-113\,781(34)$ | $-113\,806.8(71)$ | AME20 | $26(34)$
${}^{113}{\rm Ru}$${}^{40}{\rm Ar}^{2+}$11footnotemark: 1 | 0.99972269(20) | $2.0\times 10^{-7}$ | $-106\,833(44)$ | $-106\,908(38)$ | AME20 | $75(58)$
${}^{125}{\rm Sn}^{\rm m}$${}^{14}{\rm N}_{2}^{2+}$11footnotemark: 1 | 0.99991043(16) | $1.6\times 10^{-7}$ | $-80\,089(40)$ | $-80\,139.3(13)$ | AME20 | $23(40)$
${}^{125}{\rm In}$${}^{14}{\rm N}_{2}^{2+}$11footnotemark: 1 | 0.99994834(18) | $1.8\times 10^{-7}$ | $-74\,690(42)$ |  $-74\,685.5(1)$.8) | AME20 | $-5(42)$
${}^{153}{\rm Sm}^{2+}$ | 0.999963232(36) | $3.6\times 10^{-8}$ | $-72\,568(33)$ | $-72\,560.1(10)$ | AME20 | $-8(33)$
${}^{153}{\rm Pm}^{2+}$ | 0.999976473(18) | $1.8\times 10^{-8}$ | $-70\,682(33)$ | $-70\,648.0(91)$ | AME20 | $-34(34)$
${}^{153}{\rm Nd}^{2+}$ | 1 |  |  |  $-67\hskip 1.99997pt330.4(27\rightarrow 160)$ | AME20 |
${}^{153}{\rm Pr}^{2+}$ | 1.000040537(15) | $1.5\times 10^{-8}$ | $-61\,556(33)$ | $-61\,547.5(24)$ | AME20 | $-8(33)$
${}^{152}{\rm Pr}$${}^{1}{\rm H}^{2+}$ | 1.00007585(15) | $1.5\times 10^{-7}$ | $-56\,526(39)$ | $-56\,493.2(98)$ | CPT | $-33(40)$
${}^{153}{\rm Ce}^{2+}$ | 1.000088541(34) | $3.4\times 10^{-8}$ | $-54\,718(33)$ | $-54\,711.5(24)$ | CPT | $-6(33)$
${}^{152}{\rm Ce}$${}^{1}{\rm H}^{2+}$ | 1.000110410(36) | $3.6\times 10^{-8}$ | $-51\,602(33)$ |  $-51\,589.3(2)$.3) | CPT | $-13(33)$
Table 2: Continue of Table 1. The extrapolation value of AME20 is indicated with the # symbol. Species | $\rho^{2}$ | $\delta(\rho^{2})/\rho^{2}$ | ME (keV) | MElit. (keV) | Ref. of lit. |  $\Delta{\rm ME}$ (keV)
---|---|---|---|---|---|---
$A/q=77.0$ |  |  |  |  |  |
${}^{151}{\rm Nd}$${}^{40}{\rm Ar}_{2}^{3+}$ | 0.999801672(55) | $5.5\times 10^{-8}$ | $-141\,025(42)$ | $-141\,023.0(11)$ | AME20 | $-2(42)$
${}^{151}{\rm Pr}$${}^{40}{\rm Ar}_{2}^{3+}$ | 0.999821116(45) | $4.5\times 10^{-8}$ | $-136\,843(41)$ | $-136\,860(12)$ | AME20 | $17(43)$
${}^{1}{\rm H}{}^{12}{\rm C}{}^{32}{\rm S}_{2}^{1+}$ | 0.99983314(13) | $1.3\times 10^{-7}$ | $-44\,752(16)$ | $-44\,742.1032(26)$ | AME20 | $-10(16)$
${}^{151}{\rm Ce}$${}^{40}{\rm Ar}_{2}^{3+}$ | 0.999846972(52) | $5.2\times 10^{-8}$ | $-131\,282(41)$ | $-131\,305(18)$ | AME20 | $23(45)$
${}^{126}{\rm Sn}$${}^{14}{\rm N}_{2}^{2+}$ | 0.999897482(56) | $5.6\times 10^{-8}$ | $-80\,279(28)$ | $-80\,288(11)$ | AME20 | $9(30)$
${}^{154}{\rm Sm}^{2+}$ | 0.999952088(25) | $2.5\times 10^{-8}$ | $-72\,449(27)$ | $-72\,455.6(13)$ | AME20 | $6(27)$
${}^{154}{\rm Pm}^{2+}$ | 0.999981007(15) | $1.5\times 10^{-8}$ | $-68\,303(27)$ | $-68\,267(25)$ | AME20 | $-36(37)$
${}^{154}{\rm Nd}^{2+}$ | 1 |  |  |  $-65\hskip 1.99997pt579.6(10\rightarrow 130)$ | AME20 |
${}^{154}{\rm Pr}^{2+}$ | 1.000052825(16) | $1.6\times 10^{-8}$ | $-58\,005(27)$ | $-58\,000.7(25)$ | CPT | $-5(27)$
${}^{153}{\rm Pr}$${}^{1}{\rm H}^{2+}$ | 1.000078794(75) | $7.5\times 10^{-8}$ | $-54\,282(29)$ | $-54\,258.5(24)$ | CPT | $-23(29)$
${}^{154}{\rm Ce}^{2+}$ | 1.000094033(58) | $5.8\times 10^{-8}$ | $-52\,097(28)$ | $-52\,068.9(24)$ | CPT | $-28(28)$
${}^{153}{\rm Ce}$${}^{1}{\rm H}^{2+}$ | 1.000126684(44) | $4.4\times 10^{-8}$ | $-47\,415(27)$ |  $-47\,422.5(2)$.4) | CPT | $7(27)$
$A/q=77.5$ |  |  |  |  |  |
${}^{115}{\rm Cd}^{\rm m}$${}^{40}{\rm Ar}^{2+}$111Admixture of the ground state and the isomeric state(s) | 0.999611874(70) | $7.0\times 10^{-8}$ | $-122\,952(17)$ | $-123\,124.38(65)$ | AME20 | $-9(17)$
${}^{115}{\rm Pd}^{\rm m}$${}^{40}{\rm Ar}^{2+}$11footnotemark: 1 | 0.999664409(26) | $2.6\times 10^{-8}$ | $-115\,370(15)$ | $-115\,466(14)$ | AME20 | $6(20)$
${}^{115}{\rm Rh}$${}^{40}{\rm Ar}^{2+}$ | 0.999706804(50) | $5.0\times 10^{-8}$ | $-109\,252(16)$ | $-109\,269.1(73)$ | AME20 | $17(18)$
${}^{127}{\rm Sb}$${}^{14}{\rm N}_{2}^{2+}$ | 0.999902999(83) | $8.3\times 10^{-8}$ | $-80\,939(19)$ | $-80\,971.5(51)$ | AME20 | $33(19)$
${}^{127}{\rm Sn}^{\rm m}$${}^{14}{\rm N}_{2}^{2+}$11footnotemark: 1 | 0.999925199(31) | $3.1\times 10^{-8}$ | $-77\,735(15)$ | $-77\,742.7(92)$ | AME20 | $3(18)$
${}^{155}{\rm Sm}^{2+}$ | 0.999977444(16) | $1.6\times 10^{-8}$ | $-70\,195(14)$ | $-70\,191.2(13)$ | AME20 | $-4(14)$
${}^{155}{\rm Pm}^{2+}$ | 1 |  |  |  $-66\hskip 1.99997pt940.0(47\rightarrow 71)$ | AME20 |
${}^{155}{\rm Nd}^{2+}$ | 1.000032340(15) | $1.5\times 10^{-8}$ | $-62\,273(14)$ |  $-62\,283.8(9)$.2) | AME20 | $11(17)$
${}^{155}{\rm Pr}^{2+}$ | 1.000079748(18) | $1.8\times 10^{-8}$ | $-55\,431(14)$ | $-55\,415(17)$ | AME20 | $-16(22)$
${}^{154}{\rm Pr}$${}^{1}{\rm H}^{2+}$ | 1.000112383(71) | $7.1\times 10^{-8}$ | $-50\,722(18)$ |  $-50\,711.7(2)$.5) | CPT | $-10(18)$
${}^{155}{\rm Ce}^{2+}$ | 1.00013418(19) | $1.9\times 10^{-7}$ | $-47\,576(31)$ |  $-47\,780(300)$# | AME20 |  $204(302)$#
${}^{154}{\rm Ce}$${}^{1}{\rm H}^{2+}$ | 1.000153507(80) | $8.0\times 10^{-8}$ | $-44\,787(18)$ |  $-44\,779.9(2)$.4) | CPT | $-7(19)$
Table 3: Weighted average of the measured mass excess. The observed chi-square values of the weighted averages are indicated in column “$\chi^{2}$.” The literature mass excess values are shown in column “MElit” and their reference are indicated in the next column; AME20 [11, 12] and CPT [9]. The differences between mass excess values, $\Delta{\rm ME}\equiv{\rm ME}_{\rm Weight.~{}Ave.}-{\rm ME}_{\rm lit}$, are given in the last column.  Species | Weight. Ave. (keV) | $\chi^{2}$ | MElit (keV) | Reference of MElit |  $\Delta{\rm ME}$ (keV)
---|---|---|---|---|---
${}^{151}{\rm La}$ | $-53\,542(17)$ | 0.07 | $-53\,310(435)$ | AME20 | $-231(436)$
${}^{151}{\rm Ce}$111Admixture of the ground state and the isomeric state | $-61\,230(15)$ | 0.14 | $-61\,225(18)$ | AME20 | $-5(23)$
${}^{152}{\rm Ce}$ | $-58\,891(17)$ | 0.00 | $-58\,878.3(23)$ | CPT | $-13(17)$
${}^{153}{\rm Ce}$ | $-54\,710(21)$ | 0.10 | $-54\,711.5(24)$ | CPT | $2(21)$
${}^{154}{\rm Ce}$ | $-52\,082(15)$ | 0.40 | $-52\,068.9(24)$ | CPT | $-13(15)$
${}^{153}{\rm Pr}$ | $-61\,564(22)$ | 0.12 | $-61\,547.5(24)$ | CPT | $-17(22)$
${}^{154}{\rm Pr}$ | $-58\,009(15)$ | 0.03 | $-58\,000.7(25)$ | CPT | $-8(15)$
${}^{151}{\rm Nd}$ | $-70\,945(20)$ | 0.00 | $-70\,943.2(11)$ | AME20 | $-2(20)$
Figure 5: Neutron-number dependence of Ce-isotope mass excess. Each line
indicates a theoretical prediction. See the text for their details. For $N\geq
98$, the 0 line corresponds to the extrapolation of AME20.  Figure 6: Two
neutron separation energy $S_{\rm 2n}$. The prediction of FRDM12, the dotted
line, is given for Ce isotopes.  Figure 7: Hafl-lives and $R_{\rm 2n}$-values
(see Eq. 14) of the Ce and Nd isotopes. The red point is the calculated value
based on the ${}^{155}{\rm Ce}$ mass in the present measurement.

### $\bm{A/q=75.5}$

All observed peaks in the half-integer $A/q$ series belong to the $2+$ ions.
We can reject the possibility of the $4+$ ions because no chemical element has
a 4th ionization potential below the helium 1st ionization potential of 25 eV.
In addition to atomic ions, the ions with adducts of 40Ar and 1H were
identified.

For ${}^{111}{\rm Pd}$, we determine a mass excess of ${\rm ME}({}^{111}{\rm
Pd})=-85866(30)~{}{\rm keV}$, which deviates from the AME value by
$120(30)~{}{\rm keV}$, consistent with an admixture of the ground and the
isomeric state of $E_{\rm X}=172~{}{\rm keV}$. ${}^{151}{\rm Ce}$ also has a
long-lived isomeric state, but its energy is still not determined. Any
candidate of the isomeric state’s peak cannot be found, and the peaks of
${}^{151}{\rm Ce}$ are treated as a single component in the fit process; the
measured value includes the ambiguity that comes from this issue.

### $\bm{A/q=76.0}$

In this $A/q$ series, ${}^{40}{\rm Ar}_{2}$-attached $3+$ ions were observed
in addition to the previous, $A/q=75.5$ case. The long-lived isomeric state
exists in 112Rh; its energy is still unknown. Two long-lived isomeric states
of $E_{\rm X}=150~{}{\rm keV}$ and unknown excitation energy have been
reported for ${}^{152}{\rm Pm}$. The measured mass excess of ${}^{152}{\rm
Ce}$ is consistent with our previous value, ${\rm ME}({}^{152}{\rm
Ce})=-58845(61)~{}{\rm keV}$ [23].

### $\bm{A/q=76.5}$

Three nuclides of ${}^{113}{\rm Ru}$, ${}^{125}{\rm Sn}$, and ${}^{125}{\rm
In}$ have long-lived isomeric states in this $A/q$ series. The excitation
energies of the latter two are $E_{\rm X}({}^{125}{\rm Sn}^{\rm
m})=27.5~{}{\rm keV}$ and $E_{\rm X}({}^{125}{\rm In}^{\rm m})=360~{}{\rm
keV}$, respectively, and for ${}^{113}{\rm Ru}^{\rm m}$, its excitation energy
is unknown yet. Thus, they are not taken into consideration for the
modification of the mass reference error.

### $\bm{A/q=77.0}$

The ${}^{40}{\rm Ar}$-attached $2+$ ions were not observed in this $A/q$
series because there was an intense contaminant peak close to their predicted
positions, and the IMD eliminated both. The isomeric state is reported for
${}^{154}{\rm Pm}$, but the excitation energy is unknown yet. The measured
mass excess value shows lighter mass compared with the literature value
evaluated based on the $\beta$-endpoint measurement of ${}^{154}{\rm
Nd}(\beta^{-}){}^{154}{\rm Pm}$ [24].

### $\bm{A/q=77.5}$

The long-lived isomeric states of $E_{\rm X}=181~{}{\rm keV}$ and $E_{\rm
X}=41~{}{\rm keV}$ are known for ${}^{115}{\rm Cd}$ and ${}^{115}{\rm Pd}$,
respectively. Therefore, they are not included in the mass correlation, but
their measured mass values indicate that the contribution from the isomeric
states is dominant in their peaks. ${}^{127}{\rm Sn}$ also has a long-lived
isomeric state. However, its energy is as low as $5~{}{\rm keV}$, and
${}^{127}{\rm Sn}$ is not removed from the mass correlation for the
reexamination of $\delta m_{\rm ref}({}^{155}{\rm Pm})$. ${}^{127}{\rm Sb}$ is
not included in the mass correlation due to the reason discussed below.

The mass of ${}^{127}{\rm Sb}$ has been evaluated by using the mass of
${}^{127}{\rm Te}$ via the $\beta$-endpoint measurement [25] and is determined
to be ${\rm ME}({}^{127}{\rm Sb})=-86665(19)~{}{\rm keV}$ by the direct
measurement for the first time. We find the small peaks close to the predicted
positions of ${}^{155}{\rm Ce}$. The fit results presented in Fig. 3 show a
similar intensity ratio to the others and also return similar values; the
observed chi-square value of two measurements, $\rho^{2}_{602}({}^{155}{\rm
Ce})=1.00013423(28)$ and $\rho^{2}_{604}({}^{155}{\rm Ce})=1.00013413(26)$, is
$\chi^{2}({}^{155}{\rm Ce})=0.061$ and is sufficiently small to the 95%
confidence level of $\chi^{2}_{95\%}=3.84$. Thus, we conclude these peaks are
${}^{155}{\rm Ce}$ and experimentally determine its mass for the first time;
${\rm ME}({}^{155}{\rm Ce})=-47576(31)~{}{\rm keV}$.

For several isotopes, two chemical forms were measured independently. The
results are summarized in Table 3. For ${}^{152-154}{\rm Pr}$, ${}^{1}{\rm
H}$-attached $2+$ ions are observed, but ${}^{150,151}{\rm Pr}{}^{1}{\rm
H}^{2+}$ ions are not and should exist in the TOF spectra of $A/q=75.5$ and
76.5, respectively, by considering their expected yield at ${}^{252}{\rm Cf}$
spontaneous fission. The predicted positions of ${}^{150,151}{\rm
Pr}{}^{1}{\rm H}^{2+}$ are close to ${}^{151,152}{\rm Ce}$’s ones and are
overlapped with them. Based on the evaluated fission yields [1] and the
intensity ratios of ${}^{152}{\rm Pr}{}^{1}{\rm H}^{2+}$/${}^{153}{\rm
Pr}^{2+}$ and ${}^{153}{\rm Ce}$/${}^{153}{}\rm Pr$, the ratio of
${}^{150}{\rm Pr}{}^{1}{\rm H}^{2+}$/${}^{151}{\rm Ce}^{2+}$ (${}^{150}{\rm
Pr}{}^{1}{\rm H}^{2+}$/${}^{151}{\rm Ce}^{2+}$) can be estimated to be
$9.1\times 10^{-3}$ ($2.4\times 10^{-2}$) and would not affect the fit
results. As shown in Table 3, both results for atomic ions and molecules,
which have no contaminants from ${}^{1}{\rm H}$-attached Pr, are consistent
with each other.

The measured mass excesses of ${}^{151-155}{\rm Ce}$ are plotted in Fig. 5 as
a function of neutron number with several theoretical predictions: the
extrapolation of AME20, the finite-range liquid-drop model (FRDM12) [26], the
model of Koura-Tachibana-Uno-Yamada (KTUY05) [27], the Skyrme-Hartree-Fock-
Bogoliubov mass formula with BSk24 parameter set (HFB24) [28], the
macroscopic-microscopic model with surface diffuseness correction (WS4) [29],
and the Bayesian machine learning mass model (BML) [30]. The variance of the
predictions becomes more expansive in the region of $N>90$, and the mass
excesses of ${}^{152-155}{\rm Ce}$ locate the edge of this variance. No model
can reproduce both values and trend of the ${}^{152-155}{\rm Ce}$ mass
excesses, but FRDM12, AME20, and BML seem to be consistent with the result by
considering only the trend. Two-neutron separation energies ($S_{\rm 2n}$) are
plotted in Fig 6, and the FRDM12 can reproduce the trend of Ce isotopes at
$N\geq 94$. This means that the predicted neutron-capture reaction $Q$-values
with several models agree with the new data, and the influence on the
$r$-process calculations themselves should not be a point.

The half-lives of neutron-rich lanthanoid isotopes were measured at RIKEN RIBF
[31]. The measured half-lives of the Ce and Nd isotopes are plotted in Fig. 7,
and the drops in the half-life trends at $N=97$ are observed for both
elements. The authors conclude that the influence of the $\beta$-strength
function would be dominant in the drop in the Nd case compared with the
contribution of the $Q_{\beta}$-value: $T_{1/2}\propto Q_{\beta}^{-5}$. To see
the evolution of the $\beta$-strength function, we newly introduce the ratio,
$R_{\rm 2n}$, defined by

$R_{\rm
2n}(N)\equiv\frac{Q_{\beta}^{5}(N)T_{1/2}(N)}{Q_{\beta}^{5}(N-2)T_{1/2}(N-2)}.$
(14)

The obtained $R_{\rm 2n}$ of both isotope chains are also shown in Fig. 7,
and, for the Nd case, its trend changes at $N=97$. The drops of the half-lives
of Ce isotopes are observed at $N=93$ and $97$. The drop at $N=93$ would be
explained by the $Q_{\beta}$-value systematic because there is no remarkable
behavior in the $R_{\rm 2n}$ trend. In contrast, the new mass value of
${}^{155}{\rm Ce}_{97}$ leads the change of $R_{\rm 2n}$ trend at $N=97$, and
we conclude the half-life drop at this point would be explained via the same
way as the Nd case.

##  V Summary and Conclusions

The masses of neutron-rich isotopes produced via spontaneous fission of
${}^{252}{\rm Cf}$ were measured using MRTOF-MS. For ${}^{155}{\rm Ce}$, the
mass was experimentally determined for the first time with an error of $\delta
m=31~{}{\rm keV}$. A discrepancy between the experimental and literature
values was found for the mass of ${}^{127}{\rm Sb}$, which was previously
deduced through indirect measurements, and we propose new mass excess values
for them. When comparing with the theoretical predictions, there is no
theoretical prediction that can explain both the values and trend of the
${}^{152-155}{\rm Ce}$’s mass excesses consistently. The wide-range and
simultaneous mass measurement of the MRTOF-MS enables us to check the
consistency of the existing mass data. We found a necessity of reexamining the
mass data even if evaluated with the PT-MS measurements.

###### Acknowledgements.

This study was supported by the Japan Society for the Promotion of Science
KAKENHI, Grant Number 17H06090 and 19K14750.

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