# Mass measurements of As, Se and Br nuclei and their implication on the
proton-neutron interaction strength towards the N=Z line

I. Mardor1,2, S. Ayet San Andrés3, T. Dickel3,4, D. Amanbayev4, S. Beck3,4, J.
Bergmann4, H. Geissel3,4, L. Gröf4, E. Haettner3, C. Hornung4, N. Kalantar-
Nayestanaki5, G. Kripko-Koncz4, I. Miskun4, A. Mollaebrahimi4,5, W. R.
Plaß3,4, C. Scheidenberger3,4, H. Weick3, S. Bagchi6,3,4,‡, D. L. Balabanski7,
A. A. Bezbakh8,9, Z. Brencic10, O. Charviakova11, V. Chudoba8,9, P.
Constantin7, M. Dehghan3, A. S. Fomichev8, L. V. Grigorenko8,12,13, O. Hall14,
M. N. Harakeh5, J.-P. Hucka3,15, A. Kankainen16, O. Kiselev3, R. Knöbel3, D.
A. Kostyleva3,4, S. A. Krupko8, N. Kurkova8, N. Kuzminchuk3, I. Mukha3, I. A.
Muzalevskii8,9, D. Nichita7,17, C. Nociforo3, Z. Patyk11, M. Pfützner18, S.
Pietri3, S. Purushothaman3, M. P. Reiter14, H. Roesch3,15, F. Schirru3, P. G.
Sharov8,9, A. Spătaru7,17, G. Stanic19, A. State7,17, Y. K. Tanaka20, M.
Vencelj10, M. I. Yavor21, J. Zhao3, for the Super-FRS Experiment Collaboration
1Soreq Nuclear Research Center, 81800 Yavne, Israel  2Tel Aviv University,
6997801 Tel Aviv, Israel  3GSI Helmholtzzentrum für Schwerionenforschung GmbH,
64291 Darmstadt, Germany  4II. Physikalisches Institut, Justus-Liebig-
Universität Gießen, 35392 Gießen, Germany  5Nuclear Energy Group, ESRIG,
University of Groningen, 9747 AA Groningen, The Netherlands  6Saint Mary’s
University, NS B3H 3C3 Halifax, Canada  Extreme Light Infrastructure-Nuclear
Physics (ELI-NP), Horia Hulubei National Institute for R&D in Physics and
Nuclear Engineering, Str. Reactorului 30, 077125 Bucharest-M$\breve{a}$gurele,
Romania  8Flerov Laboratory of Nuclear Reactions, JINR, 141980 Dubna, Russia
9Institute of Physics, Silesian University in Opava, 74601 Opava, Czech
Republic  10Jozef Stefan Institute, SI-1000 Ljubljana, Slovenia  11National
Centre for Nuclear Research, Hoża 69, 00-681 Warszawa, Poland  12National
Research Centre “Kurchatov Institute”, 123182 Moscow, Russia  13National
Research Nuclear University “MEPhI”, 115409 Moscow, Russia  14University of
Edinburgh, EH8 9AB Edinburgh, United Kingdom  15Technische Universität
Darmstadt, D-64289 Darmstadt, Germany  16University of Jyväskylä, 40014
Jyväskylä, Finland  17Doctoral School in Engineering and Applications of
Lasers and Accelerators, University Polytechnica of Bucharest, 060811
Bucharest, Romania  18Faculty of Physics, University of Warsaw, 02-093
Warszawa, Poland  19Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany
20High Energy Nuclear Physics Laboratory, RIKEN, 2-1 Hirosawa, Wako, 351-0198
Saitama, Japan  21Institute for Analytical Instrumentation, RAS, 190103 St.
Petersburg, Russia<EMAIL_ADDRESS>
###### Abstract

Mass measurements of the 69As, 70,71Se and 71Br isotopes, produced via
fragmentation of a 124Xe primary beam at the FRS at GSI, have been performed
with the multiple-reflection time-of-flight mass spectrometer (MR-TOF-MS) of
the FRS Ion Catcher with an unprecedented mass resolving power of almost
1,000,000. For the 69As isotope, this is the first direct mass measurement. A
mass uncertainty of 22 keV was achieved with only 10 events. For the 70Se
isotope, a mass uncertainty of 2.6 keV was obtained, corresponding to a
relative accuracy of $\delta$m/m = 4.0$\times 10^{-8}$, with less than 500
events. The masses of the 71Se and 71Br isotopes have been measured with an
uncertainty of 23 and 16 keV, respectively. Our results for the 70,71Se and
71Br isotopes are in good agreement with the 2016 Atomic Mass Evaluation, and
our result for the 69As isotope resolves the discrepancy between the previous
indirect measurements. We measured also the mass of the molecule 14N15N40Ar
(A=69) with a relative accuracy of $\delta$m/m = 1.7$\times 10^{-8}$, the
highest yet achieved with a MR-TOF-MS. Our results show that the measured
restrengthening of the proton-neutron interaction ($\delta$Vpn) for odd-odd
nuclei along the N=Z line above Z=29 (recently extended to Z=37) is hardly
evident at the N-Z=2 line, and not evident at the N-Z=4 line. Nevertheless,
detailed structure of $\delta$Vpn along the N-Z=2 and N-Z=4 lines, confirmed
by our mass measurements, may provide a hint regarding the ongoing
$\approx$500 keV discrepancy in the mass value of the 70Br isotope, which
prevents including it in the world average of ${Ft}$-value for superallowed
0${}^{+}\rightarrow$ 0+ $\beta$ decays. The reported work sets the stage for
mass measurements with the FRS Ion Catcher of nuclei at and beyond the N=Z
line in the same region of the nuclear chart, including the 70Br isotope.

  * $\ddagger$Present address: Indian Institute of Technology (Indian School of Mines), Dhanbad, Jharkhand 826004, India

  * November 2020

##  1 Introduction

Nuclear masses are key properties of atomic nuclei, as they are a measure of
the nuclear binding energy, which reflects the details of nuclear structure
and forces between the nucleons. The extension of nuclear mass measurements
towards rare short-lived nuclei far from the stability valley is important for
widening nuclear structure models to all regions of the nuclear chart [1, 2]
and for astrophysical nucleosynthesis calculations [3].

Nuclear masses of nuclei around the N=Z line provide crucial input for
determining the rapid proton-capture (rp-) process path that takes place in
Type-I X-ray bursts and steady-state nuclear burning in rapidly accreting
neutron stars [4, 5].

Experimental masses of numerous odd-odd N=Z nuclei, which decay via super-
allowed $0^{+}\rightarrow 0^{+}$ $\beta^{+}$-transitions, determine $Q_{EC}$
values for these transitions. These values, together with the half-lives and
decay branching ratios, formulate the ${Ft}$-values that in turn verify the
unitarity of the CKM matrix, a crucial test of the Standard Model [6, 7].

However, the ${Ft}$-value of 70Br that is derived from its precise half-life
and decay branching ratio [8] and only direct mass measurement (Penning trap
[9]) deviates by approximately 12$\sigma$ from the world average. Since the
measurements of ref. [8] are accurate enough and not under dispute, the source
of this discrepancy is its mass value. The mass measurement of ref. [9]
differs by approximately 500 keV from that obtained via positron end-point
energy [10], which gives a consistent ${Ft}$-value, but with a large
uncertainty.

Actually, the Penning trap result was derived from measuring the 70mBr isomer
($t_{1/2}$ = 2.2 s) and subtracting its known excitation energy, because the
cycle time employed in the measurement [9] was much longer compared to the
half-life of the 70Br isotope ((78.42 $\pm$ 0.51) ms [8]). Therefore, the
Penning trap measurement of ref. [9] is not included in the current ${Ft}$
value world average, and a new direct mass measurement of the 70Br isotope is
called for in ref. [6, 7].

In this article, we focus on insights that can be derived from accurate mass
measurements on the interaction strength between the last proton and the last
neutron of intermediate-mass nuclei towards the N=Z line. By ’last’ we refer
to the nucleons that occupy the highest energy orbitals in the nucleus. This
interaction strength, denoted as $\delta$Vpn, can be deduced from the double
difference of binding energies (obtained directly from mass measurements) of
the nucleus of interest and its neighbors. For odd-odd nuclei with N neutrons
and Z protons, whose binding energy is $B(N,Z)$, the expression is [11]:

$\delta V_{pn}(N,Z)=[B(N,Z)-B(N-1,Z)]-[B(N,Z-1)-B(N-1,Z-1)].$ (1)

Assuming that the nuclear core remains essentially unchanged in the four
nuclei of Eq. 1, such a double difference largely cancels out the p-p and n-n
pairing interactions and the mean field component of the binding energy,
isolating the empirical p-n interaction strength [12, 13, 14, 15]. Moreover,
$\delta$Vpn can be used as a sensitive filter to study anomalies on the mass
surface [16]

It has been predicted that $\delta$Vpn depends on the spatial overlap of wave
functions of the last neutron and proton [17]. This prediction seems to be
corroborated by experimental data around doubly-magic nuclei [18, 19], and
especially by the dramatic increase of $\delta$Vpn at N=Z nuclei, which is
attributed to the manifestation of Wigner’s SU(4) isospin and spin symmetry
[11].

Due to the relation to the overlap of the wave functions, it is expected that
for N=Z nuclei (and in general), $\delta$Vpn will decrease with increasing Z.
This is because of three cumulative reasons. First, as Z increases, the
nuclear radii increase, the average distance between the last proton and
neutron increases, and their mutual interaction strength decreases even for
nucleons occupying the same orbitals. Second, as Z increases, the Coulomb
force causes the proton and neutron single-particle energies to differ even
when they are in the same orbital [17]. Third, the spin-orbit term in the
nuclear mean-field potential increases with mass, gradually breaking the spin
part of Wigner’s SU(4) symmetry [11]. The decrease with Z has been observed
experimentally for all measured even-even nuclei [17] and odd-odd nuclei up to
Z=29 [20].

The authors of ref. [20] note that from Z=29 and on, ’there is an indication
of a trend toward the restrengthening of $\delta$Vpn’. We submit that based on
a newer direct mass measurement of 65As [21] and a very recent indirect mass
measurement of 73Rb [22], this restrengthening trend may be confirmed, as
shown in figure 1, which depicts the experimental data for N=Z odd-odd nuclei
from Z=29 to Z=37.

Figure 1: Proton-neutron interaction strength as a function of Z for odd-odd
N=Z nuclei from the 58Cu isotope to the 74Rb isotope. Black points are
experimental data or AME16 [23] evaluations based on experimental data. The
red point for the 74Rb isotope is the AME16 evaluation based on systematics.
Hoff$\\_$20 refers to [22] and Davids$\\_$80 refers to [10].

For the 74Rb isotope, we included in figure 1 both the $\delta$Vpn that is
extracted from the AME16 [23] mass value of 73Rb and that from [22], to show
how the 2020 measurement emphasizes the restrengthening trend. For the 70Br
isotope , we included in figure 1 both the AME16 value that is based on the
Penning trap measurement of [9], and the older indirect measurement based on
positron endpoint energy [10], due to the approximate 500 keV discrepancy
described above.

The different values for the 70Br isotope give systematically different local
trends of $\delta$Vpn, either peaking at this isotope [10] or flattening out
[9] before continuing to increase towards the 74Rb isotope. A new mass
measurement of the 70Br isotope and heavier isotopes in the N$\leq$Z region
should resolve the question which is the correct trend.

For the mass measurement of such nuclei, which are mostly very short-lived
(10’s of ms) and with low production cross sections, an optimal device is the
multiple-reflection time-of-flight mass spectrometer (MR-TOF-MS) [24], which
is sensitive even to nuclei that are produced at rates as low as a few events
per hour or day [25, 26]. The MR-TOF-MS has a unique combination of
performance parameters: fast (cycle times of a few milliseconds), accurate
(relative mass-measurement uncertainty down to the 10-8 level), sensitive
(only a few detected ions per nucleus are required for accurate mass
determination), non-scanning (simultaneous measurement of many different
nuclei) and can be used to spatially resolve isobars and even isomers [27, 28,
26].

In this work, we present accurate MR-TOF-MS mass measurements of the 69As,
70,71Se and 71Br isotopes, all near the N=Z line. These results help to
confirm trends of $\delta$Vpn as a function of Z for odd-odd N-Z=2 and N-Z=4
isotopes in the region Z=29-37, which may provide hints on the expected N=Z
$\delta$Vpn behavior around the 70Br isotope.

##  2 Experimental Setup

The nuclei presented in this work were produced and spatially separated at
relativistic energies via projectile fragmentation at the Fragment Separator
(FRS) at GSI [29], and delivered to the FRS Ion Catcher [30] where the ions
were slowed down and thermalized in a gas-filled Cryogenic Stopping Cell (CSC)
[31, 32, 33]. Subsequently, the ions were extracted and transported via a
Radio Frequency Quadrupole (RFQ) beam-line [34, 35] to a MR-TOF-MS [36, 37],
to perform mass measurements and ion counting [28] with mass resolving powers
at full width at half maximum (FWHM) of almost 1,000,000.

The production mechanism was fragmentation of a 124Xe primary beam impinging
on a Be target of 4009 mg/cm2 thickness at 982 MeV/u, with intensities up to
3$\times 10^{9}$ ions per spill and a typical spill length of 2.5 seconds. The
FRS was set up in achromatic mode from the target to the mid focal plane by
using a wedge shaped aluminum degrader (141 mrad, 4005 mg/cm2) at the focal
plane F1. At the mid focal plane a secondary reaction target was installed.
From the mid to the final focus the FRS was set to a dispersive mode. A new
degrader system, including a variable angle degrader, was used at the final
focal plane to range-bunch the ions. The measured range distribution after
range bunching was about 50 mg/cm2 [38]. All isotopes in this work were
measured with the same FRS setting, and only the degrader thickness in the
final focal plane was changed. In addition to their accurate mass measurement
in the MR-TOF-MS, the ions were also identified by the FRS particle ID system.

This enabled the parallel operation of two independent experiments with the
same secondary beam - proton decaying nuclei were investigated with the EXPERT
setup (see, e.g., [39]) installed after the secondary reaction target at the
mid focal plane, and the longer-living nuclei that are described in this work
were studied at the FRS Ion Catcher at the final focus of the FRS.

The CSC temperature during the experiment was 130 K, higher than the standard
working temperature ($\sim$85 K). The CSC was operated with an areal density
of 3.3 mg/cm2 and extraction times of about 80 ms.

##  3 Data Analysis

We analyzed the data according to the procedure presented in [28]. Here we
emphasize the parts that were particularly important for this work. The drifts
of the time-of-flight data during the experiment were corrected performing a
time-resolved calibration using a well-known mass. The peak shape was obtained
from a high-count reference and used for fitting the ion-of-interest. The
analytical function describing the peaks is the Hyper-EMG [40], and a weighted
maximum likelihood estimate (wMLE) was used to fit this function to the un-
binned data. All measured nuclei in this work were measured as singly-charged
positive ions.

The relationship between time-of-flight and mass-to-charge is defined in
equation 2,

$\frac{m}{q}=\frac{c(t_{exp}-t_{0})^{2}}{(1+N_{it}b)^{2}}$ (2)

where $b=l_{it}/l_{tfs}$ ($l_{it}$ is the path length for one turn in the
analyzer and $l_{tfs}$ is the path length from the injection trap to the
detector), $c=2U_{eff}/l_{tfs}^{2}$ ($U_{eff}$ is the effective voltage),
$t_{exp}$ is the total measured time-of-flight that takes into account a time
delay between the start signal and the real start of the ions ($t_{0}$), and
$N_{it}$ is the number of turns in the analyzer (see [28] for a more detailed
description). The parameter $t_{0}$ was common for all the data analyzed in
the context of this work and was determined to be 274 $\pm$ 2 ns.

Mass values were obtained using calibrant ions that made the same and
different turn number with respect to the ion-of-interest. We used four stable
molecules that were present in the spectrum and underwent three different turn
numbers in the analyzer, and whose relative mass accuracy $\delta$m/m is in
the $10^{-11}$ level (much better than the accuracy that we expect for the
unstable nuclei of interest): 12C${}_{5}\\!^{1}$H10 (A=70) performing 847
turns, 12C${}_{5}\\!^{1}$H9 (A=69) performing 853 turns, and 14N15N40Ar (A=69)
and 12C19F3 (A=69) each performing 854 turns. We always used 12C19F3 (the most
abundant peak in the spectrum) together with two other molecules to perform
the calibration for the mass measurement of the fourth molecule.

In practice, we used 12C19F3 (A=69) together with a) 12C${}_{5}\\!^{1}$H10
(A=70) and 12C${}_{5}\\!^{1}$H9 to measure 14N15N40Ar (A=69) for the same-turn
accuracy test, with b) 12C${}_{5}\\!^{1}$H10 and 14N15N40Ar (A=69) to measure
12C${}_{5}\\!^{1}$H9, and with c) 12C${}_{5}\\!^{1}$H9 and 14N15N40Ar (A=69)
to measure 12C${}_{5}\\!^{1}$H10.

The measurement with the same-turn calibration of 14N15N40Ar (A=69) showed a
deviation from literature of (0.6 $\pm$ 1.1) keV, which represents a relative
mass uncertainty 1.7$\times 10^{-8}$. For the multi-turn calibration, the
measurement of 12C${}_{5}\\!^{1}$H10 and 12C${}_{5}\\!^{1}$H9 resulted in a
deviation from literature of (-1.2 $\pm$ 2.9) keV ($\delta$m/m of 4.4$\times
10^{-8}$) and (0.9 $\pm$ 2.9) keV ($\delta$m/m of 4.5 $\times 10^{-8}$),
respectively, with only about 300 events for each molecule.

The above analyses of the molecular masses show that both of our calibration
procedures (same-turn and multi-turn) provide accuracy in the low $10^{-8}$
level. We have reached in the past relative uncertainties of 6.0$\times
10^{-8}$ with our system, but then it was achieved with approximately 6000
events [28]. The relative mass uncertainty of 1.7 $\times 10^{-8}$ achieved
for 14N15N40Ar (A=69) in this work is the most accurate measurement yet
performed with a MR-TOF-MS, due to our unprecedented mass resolving power of
almost 1,000,000 FWHM. The uncertainty evaluation of the molecules and
unstable isotopes of this work include all the systematic contributions that
were presented in ref. [28].

##  4 Results

###  4.1 Mass Measurement of the 69As isotope

The mass of the 69As isotope has been previously measured only indirectly, via
the endpoint energy of its $\beta^{+}$ decay [41, 42] and the endpoint energy
of its mother nucleus (the 69Se isotope) $\beta^{+}$ decay [42]. The values
from these three measurements (with uncertainties of 50 keV) present some
inconsistency with each other, but nevertheless the value at AME16 is a
weighted average of them, with a minor weight from the $\beta^{+}$ decay of
the 69Se isotope [43], and an overall uncertainty of 30 keV [23].

In this work, we performed the first direct mass measurement of the 69As
isotope. The acquired data with the MR-TOF-MS contained only 10 events,
highlighting the sensitivity of our system, as can be seen in the left side of
figure 2. The total time-of-flight for this measurement was about 23.1 ms and
the 69As ions performed 901 turns inside the analyzer. In this case, the
calibration was obtained with the molecular isobar 12C19F3 (A=69), which
performed the same number of turns as the 69As ion. Some of these molecules
are produced by ionization in the CSC and others from the electron impact
source of the MR-TOF-MS (fragment of the molecule C3F8). Due to the low number
of events, the mass uncertainty is dominated by statistics and possible
unknown contamination and is 22 keV, corresponding to a relative accuracy of
$\delta$m/m = 2.8$\times 10^{-7}$.

The mass-excess value and uncertainty of the 69As isotope from this work are
given in table 1 and are compared to the AME16 value and previous indirect
measurements in figure 3. It can be seen in figure 3 that our result resolves
the discrepancy between the previous indirect mass measurements of the 69As
isotope.

Figure 2: Left panel: Measured mass-to-charge ratio spectrum of singly charged
69As isotopes. The square points represent the histogram of the un-binned
data, which is shown as well in the lower part of the plot. A Hyper-EMG
function with two exponentials on the left side and one exponential on the
right side (Hyper-EMG(2,1)) with a FWHM of 74 keV (mass resolving power of
870,000 FWHM) was used for fitting the un-binned data (’rug’ graph below the
histogram), the shape parameters of which were obtained from the calibrant
data (red line). Right panel: Same as on the left, for the 70Se isotope,
showing the results after the wMLE fit of a Hyper-EMG(2,1) with a FWHM of 67
keV (mass resolving power of 970,000 FWHM) to a set of data containing 256
counts of the 70Se isotope.

###  4.2 Mass Measurement of the 70Se isotope

The mass of the 70Se isotope has been previously measured both indirectly and
directly. The direct measurements have been performed with time-of-flight
(GANIL [44, 45]), Penning traps (ISOLTRAP at ISOLDE/CERN [46] and LEBIT at
NSCL [9]) and isochronous mass measurements (ESR at GSI [47]). The AME16 [23]
mass value and uncertainty (1.6 keV) are based mainly on the results from ref.
[9]. The more recent Penning trap result is consistent with [9] but with a
larger uncertainty (17 keV) [46]. The isochronous measurement result [47] has
a large uncertainty (70 keV) and deviates by 2$\sigma$ from the measurements
with the Penning traps. The direct time-of-flight results are with even larger
uncertainties, 130 keV [44] and 460 keV [45], and both are consistent with the
Penning trap measurements.

In this work we performed the first mass measurement of the 70Se isotope with
a MR-TOF-MS. The total number of accumulated events is 485 with 2 different
turn numbers (848 and 895) with a total TOF of about 21.9 and 23.1 ms,
respectively.

In the data sets where the 70Se ion underwent 848 turns, an isobaric molecule
13C19F3 (A=70) undergoing also 848 turns (produced partially in the CSC and
partially from the electron impact source in the MR-TOF-MS) was used as a
calibrant. In the measurement with 895 turns the ion of interest performed a
different number of turns than the calibrant. Therefore, an accurate multi-
turn calibration was performed by the determination of the parameter $c$ (see
Eq. 2) using other singly charged species performing different turn numbers,
namely: 12C${}_{5}\\!^{1}$H10 (A=70) performing 847 turns,
12C${}_{5}\\!^{1}$H9 (A=69) performing 853 turns and 14N15N40Ar (A=69) and
12C19F3 (A=69) performing 854 turns.

The parameter $b$ (see Eq. 2) was determined in the different measurements
from 12C19F3 (A=69) or 14N15N40Ar (A=69) performing 854 turns. Following the
procedure described in [28], an uncertainty of 2.6 keV was obtained, which
corresponds to a relative accuracy $\delta$m/m of 4.0$\times 10^{-8}$. A
sample spectrum containing 256 counts is shown in figure 2.

The mass-excess value and uncertainty of the 70Se isotope from this work are
given in table 1 and are compared together with previous measurements to the
value given in AME16 [23] in figure 3. It can be seen in figure 3 that our
result is consistent with previous high accuracy measurements and has an
accuracy similar to the best one.

Our relative uncertainty for the 70Se isotope is similar to the best relative
uncertainty recorded so far for an unstable nucleus by a MR-TOF-MS,
$\delta$m/m = 3.5$\times 10^{-8}$ for 65Ga in GARIS-II at RIKEN [48]. Notice
that our level of uncertainty was obtained with almost a factor of 40 less
events due to the much higher mass resolving power in our MR-TOF-MS.

###  4.3 Mass Measurement of the 71Se isotope

The mass of the 71Se isotope has been previously measured both indirectly and
directly. The direct measurements have been performed with time-of-flight
(GANIL [44, 45]), Penning trap (ISOLTRAP at ISOLDE/CERN [46]) and isochronous
mass measurements (ESR at GSI [47]). The AME16 [23] mass value and uncertainty
(2.8 keV) are based mainly on the results from ref. [46]. The isochronous
measurement result [47] has a large uncertainty (70 keV) and deviates by
1.3$\sigma$ from the Penning trap measurements. The direct time-of-flight
results have even larger uncertainties, 112 keV [44] and 317 keV [45], and
both are consistent with the Penning trap measurements (see figure 3 for a
comparison with AME16).

The mass of the 71Se isotope was measured with only 7 counts. The ions
underwent 895 turns in about 23.1 ms. There was no same-turn calibration
possible and the measurement was performed calculating the parameter $c$ (see
Eq. 2) from the multi-turn calibration used with 70Se and using 13C19F3 (A=70)
as a precision calibrant, which performed 6 turns more than 71Se (901 turns).
The uncertainty achieved was 23 keV or a relative mass accuracy $\delta$m/m of
3.4$\times 10^{-7}$, where the main contributions are statistical error and a
non-perfect correction of the TOF drifts.

###  4.4 Mass Measurement of the 71Br isotope

Due to its closest location to the N=Z line, the mass of the 71Br isotope has
been previously measured only twice, by time-of-flight (GANIL [44]) and a
Penning trap (LEBIT at NSCL [9]). The AME16 mass value and uncertainty (5.4
keV) are based solely on the results of ref. [9]. The time-of-flight result
has a much larger uncertainty, 570 keV [44], which is consistent with the
value from ref. [9]. The comparison can be seen in figure 3.

The measurement of the 71Br isotope included a total of 19 counts. The ions
underwent 895 turns in about 23.1 ms. This isotope was measured together with
the 71Se isotope and the same calibration procedure was performed. The mass is
in good agreement with the one presented in AME16 and presents an uncertainty
of 16 keV or a relative mass accuracy $\delta$m/m of 2.5$\times 10^{-7}$.

Figure 3: Deviation of the measured mass-excess of this work (see table 1), denoted by ’FRS-IC’, and previous ones from the values given in AME16 [23]. [70Bo19] refers to [41], [77Ma22_1] and [77Ma22_2] refer to [42], which includes the published endpoint energies of the decays 69As($\beta$+)69Ge and 69Se($\beta$+)69As, respectively, [98CH20] refers to [45], [01HA66] refers to [47], [02LI24] refers to [44], [09SA12] refers to [9] and [11HE10] refers to [46]. The gray band around the horizontal axis represents the AME16 uncertainty. Breaks in the Y axis with different scale widths are included in order to be able to see high-accuracy data as well as low-accuracy data. Note that if one of the borders of the error bar is out of the displayed region, then it is not shown. Table 1: Results table of the different isotopes measured in this work and their comparison with AME16 [23]. Half-lives were extracted from [49]. The symbol $\dagger$ denotes a literature value based on indirect mass measurements. See section 4 for information about the mass references used in the measurement of each isotope. Nuclei | Half-Life |  MEFRS-IC |  MEAME16 |  MEFRS-IC \- MEAME16 | Number
---|---|---|---|---|---
|  | / keV | / keV | / keV | of Events
69As |  (15.2 $\pm$ 0.2) min |  -63116 $\pm$ 22 |  $\dagger$ -63110 $\pm$ 30 |  -6 $\pm$ 37 | 10
70Se |  (41.1 $\pm$ 0.3) min |  -61926.0 $\pm$ 2.6 |  -61929.9 $\pm$ 1.6 |  3.9 $\pm$ 3.0 | 485
71Se |  (4.74 $\pm$ 0.05) min |  -63147 $\pm$ 23 |  -63146.5 $\pm$ 2.8 |  0 $\pm$ 23 | 7
71Br |  (21.4 $\pm$ 0.6) s |  -56481 $\pm$ 16 |  -56502 $\pm$ 5 |  21 $\pm$ 17 | 19

##  5 Discussion

The proton-neutron interaction strength for N=Z nuclei, $\delta$Vpn(N=Z), is
expected to decrease with increasing mass (see Section 1 [11, 17]) whereas
recent mass measurements show a restrengthening of this parameter in the range
Z=29-37, as depicted in figure 1. This could be explained by various physical
phenomena, including the amount of overlap between wave functions of valence
protons and neutrons [17, 18, 19], the growth of deformation in nuclei [14,
50], and the manifestation of Wigner’s SU(4) symmetry at N=Z nuclei [11].

In order to discern which interpretation may be behind the surprising trend in
$\delta$Vpn(N=Z), we applied the measured masses of this work and
corresponding data from AME16 [23] and primary literature [41, 42] to
calculate the quantity $\delta$Vpn for N-Z=2 and N-Z=4 isotopes in the proton
number range Z=29-37. The results are shown in figure 4.

Figure 4: Proton-neutron interaction strength as a function of Z for odd-odd
N-Z=2 and N-Z=4 nuclei from Cu isotopes to Rb isotopes. Solid symbols are
experimental data or AME16 evaluations [23] based on experimental data. The
open symbols for $\delta$Vpn(N-Z=4) of the As isotope are values based on the
previous indirect mass measurements of the 69As isotope. [70Bo19] refers to
[41], [77Ma22_1] and [77Ma22_2] refer to [42] that includes the published
endpoint energies of the decays 69As($\beta^{+}$)69Ge and
69Se($\beta^{+}$)69As, respectively. Isotope symbols near the points show the
values which the measurement of this work have an impact on (the 69As isotope)
or confirmed (the 70,71Se, 71Br isotopes). Dotted lines are shown to guide the
eye between $\delta$Vpn points of the same N-Z value.

From comparing figure 4 to figure 1, it is observed that $\delta$Vpn(N=Z) is
much higher (up to a factor of almost 3) than the values for N-Z=2 and N-Z=4,
as expected [11]. Our new direct measurement of the 69As isotope confirms an
essentially monotonic increase of $\delta$Vpn staggering as a function of Z,
as one moves away from N=Z towards N-Z=2 and N-Z=4. It is thus evident that
the significant restrengthening of $\delta$Vpn (approximately 1200 keV, see
figure 1) is a sole characteristic of the N=Z nuclei. The N-Z=2 net increase
is only about 200 keV in the same range, and at N-Z=4 there is staggering that
ends with a net decrease of approximately 100 keV in the overall range.

This may imply that the restrengthening of $\delta$Vpn(N=Z) is related to
partial restoration of a symmetry that is unique to these nuclei. As explained
in Section 1, Wigner’s spin-isospin SU(4) symmetry is known to be broken in
heavier nuclei [11, 17]. Nevertheless, it has been proposed that protons and
neutrons occupying the pf-shell above the magic number 28 exhibit a pseudo-
SU(4) symmetry [51], which follows from the combined invariance in pseudospin
and isospin. Pseudospin is defined for the pf-shell orbitals as a reduction by
one unit of angular momentum, so they behave as pseudo sd-shell orbitals.
Therefore, their pseudospin-orbit interaction is reduced accordingly, pseudo-
SU(4) symmetry is restored, and one may conclude that this causes the increase
of the $\delta$Vpn(N=Z) values.

The pseudo-SU(4) scheme has been used for a qualitative understanding of the
observed Gamow-Teller $\beta$-decay of pf-shell nuclei [51]. The authors of
ref. [51] stated that pseudo-SU(4) could be tested via the trend of
$\delta$Vpn(N=Z) values in the pf-shell. However, the needed mass measurements
were lacking at that time. The experimental information that is presented here
emphasizes the unique behavior of the N=Z nuclei in the pf-shell and can
contribute to the test of the pseudo-SU(4) concept.

It is interesting to study also the detailed structure of $\delta$Vpn as a
function of Z for the N-Z=2 and N-Z=4 nuclei. The accurate measurements reveal
the staggering and overall increase in $\delta$Vpn from the Cu (Z=29) isotopes
to the Br (Z=35) isotopes, and show the beginning of a decrease at the Rb
(Z=37) isotopes. Since the $\delta$Vpn values beyond the closed shell 28 seem
to be influenced by the shell correction and by deformation changes in the
four neighboring nuclei, these results may provide input to detailed
calculations of nuclear deformation [16].

Some detailed aspects of the $\delta$Vpn trends of N-Z=4, N-Z=2 and N=Z nuclei
may be similar. The most striking feature in the N-Z=4 and N-Z=2 trends may be
the maximal value of $\delta$Vpn at the Br isotopes. If one assumes that this
structure is maintained also at N=Z, then figure 1 indicates that the
’correct’ value for the mass of the ${}^{70}Br$ isotope is closer to the
indirect mass measurement [10] rather than the more recent Penning trap
measurement [9]. Such a suggested ’peak’ at the 70Br isotope may be connected
to the observed transition from spherical to deformed nuclear shapes along the
N=Z line at Z=35 [52]. Recall that the indirect mass result of 70Br [10] also
leads to a ${Ft}$-value that is consistent with the world average [6].

##  6 Summary and Conclusions

In this work we present the mass measurement of four very-neutron-deficient
isotopes with the MR-TOF-MS at the FRS Ion Catcher at GSI, with an
unprecedented mass resolving power of almost 1,000,000. This is a very
important milestone for mass measurements of rare short-lived isotopes, since
high resolving power is the only way to achieve the required uncertainties and
resolve overlapping peaks when the number of accumulated events is inherently
limited. We performed the first direct mass measurement of the 69As isotope,
and the first MR-TOF-MS mass measurements of the 70,71Se and 71Br isotopes.

We carried out these measurements simultaneously with another experiment that
used the same secondary beam to study proton decaying nuclei at the mid-focal
plane of the FRS. This is an important demonstration of efficient use of rare
ion beams that are currently in great demand at large accelerator facilities.

For the 70Se isotope, we reached a relative mass uncertainty of $\delta$m/m =
4.0$\times 10^{-8}$ with less than 500 events, similar to the best ever
measurement of an unstable nucleus with a MR-TOF-MS [48]. For the other three
isotopes, we reached a relative mass uncertainty of about $2\times 10^{-7}$
with less than 20 events. All our results are in good agreement with the AME16
values.

We measured the mass of the molecule 14N15N40Ar (A=69) with a relative
accuracy of $\delta$m/m = 1.7$\times 10^{-8}$, the highest yet achieved with a
MR-TOF-MS.

Our first direct measurement of the 69As isotope has a better uncertainty than
both previous indirect measurements and the AME16 evaluation. Therefore, our
results significantly increase the confidence in all four AME16 values, and
the consequential conclusions of the nuclear structure and astrophysics models
that rely on them.

Our results impact (the 69As isotope) and confirm (the 70,71Se, 71Br isotopes)
interesting trends in the proton-neutron interaction strength $\delta$Vpn for
N-Z=2 and N-Z=4 in the Z=29-37 range, which singled out the N=Z nuclei in this
region as exhibiting the restrengthening of $\delta$Vpn with increasing Z, in
contrast with the expected behavior. Further, the maximal $\delta$Vpn value at
the Br isotopes with N-Z=2 and N-Z=4 may indicate that the indirect mass
measurement [10] of the 70Br isotope may be more consistent with the regional
$\delta$Vpn trend than the Penning trap measurement [9]. This gives another
important incentive to re-measure the mass of this isotope, in addition to the
apparent deviation of its QEC from the value that is consistent with the
${Ft}$ world average [6, 7].

From the technical point of view, the high accuracy achieved in the
measurements of this work with a small number of events ensure that the MR-
TOF-MS at the FRS Ion Catcher at GSI is ready for accurate measurements of the
masses of rare N$\leq$Z isotopes in the A$\approx$70 region. In particular,
our mass measurement of the 71Br isotope shows that our system is able to
extract the specially reactive element bromine, and thus our path to measure
the 70Br isotope and heavier N=Z isotopes is open and will be realized.

The results presented here were obtained at experiment S459+, which was
performed at the FRS at the GSI Helmholtzzentrum für Schwerionenforschung,
Darmstadt (Germany) in the framework of FAIR Phase-0. This work was supported
by the German Federal Ministry for Education and Research (BMBF) under
contracts no. 05P12RGFN8, 05P16RGFN1 and 05P19RGFN1, Justus-Liebig-Universität
Gießen and GSI under the JLU-GSI strategic Helmholtz partnership agreement,
HGS-HIRe, the Hessian Ministry for Science and Art (HMWK) through the LOEWE
Center HICforFAIR, Polish National Science Centre (2016/21/B/ST2/01227), and
by the Israel Ministry of Energy, Research Grant No. 217-11-023. This project
has received funding from the European Union’s Horizon 2020 research and
innovation programme under grant agreement No 654002. The ELI-NP team
acknowledges the support from the Extreme Light Infrastructure Nuclear Physics
(ELI-NP) Phase II, a project co-financed by the Romanian Government and the
European Union through the European Regional Development Fund - the
Competitiveness Operational Programme (1/07.07.2016, COP, ID 1334).

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