Abstract
The tin isotope 100Sn is of singular interest for nuclear structure due to its closed-shell proton and neutron configurations. It is also the heaviest nucleus comprising protons and neutrons in equal numbers—a feature that enhances the contribution of the short-range proton–neutron pairing interaction and strongly influences its decay via the weak interaction. Decay studies in the region of 100Sn have attempted to prove its doubly magic character1 but few have studied it from an ab initio theoretical perspective2,3, and none of these has addressed the odd-proton neighbours, which are inherently more difficult to describe but crucial for a complete test of nuclear forces. Here we present direct mass measurements of the exotic odd-proton nuclide 100In, the beta-decay daughter of 100Sn, and of 99In, with one proton less than 100Sn. We use advanced mass spectrometry techniques to measure 99In, which is produced at a rate of only a few ions per second, and to resolve the ground and isomeric states in 101In. The experimental results are compared with ab initio many-body calculations. The 100-fold improvement in precision of the 100In mass value highlights a discrepancy in the atomic-mass values of 100Sn deduced from recent beta-decay results4,5.
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Main
The nuclear landscape is shaped by the underlying strong, weak and electromagnetic forces. The most salient features are the pillars of enhanced differential binding energy associated with closed-shell configurations, the best example of which is Z = 50 (tin), featuring the largest number of
Nuclei in the immediate vicinity of 100Sn offer important insight for understanding the single-neutron and proton states in this region and constitute an excellent proxy for the study of 100Sn itself. However, experiments have so far only been feasible with in-beam gamma-ray spectroscopy at fragmentation facilities4,5,7,8,9,10. By direct determination of the nuclear binding energy, high-precision atomic-mass measurements provide a crucial model-independent probe of the structural evolution of exotic nuclei. Precision mass measurements are traditionally performed at isotope separation online (ISOL) facilities; however, the production of medium-mass, neutron-deficient nuclides at such facilities is prohibitively difficult, explaining the lack of accurate mass values in the region. Measurements performed at the FRS Ion Catcher at GSI11 and the Cooler-Storage experimental Ring (CSRe) in Langzhou12 (both high-energy, heavy-ion fragmentation facilities) recently extended direct mass measurements to the 101In ground and isomeric states. However, the 100In mass value is still constrained 63% indirectly through its beta-decay link to 100Cd (ref. 13).
Thus, the first experimental challenge overcome in this work was the production and separation of the successfully studied 99,100,101g,101mIn states. A detailed schematic of the necessary stages, from radioactive ion beam production to beam purification, preparation and measurement, is shown in Fig. 1. The exotic indium isotopes were produced at the Isotope Separator On Line Device (ISOLDE) located at CERN. A 1.4 GeV proton beam impinged on a thick lanthanum carbide target, producing a swath of neutron-deficient radioactive species of various chemical elements. After diffusion from the heated target, the indium atoms of interest were selectively ionized using a two-step resonance laser ionization scheme provided by the ISOLDE Resonant Ionization Laser Ion Source (RILIS)14. The ion beam was extracted from the source and accelerated to an energy of 40 keV. The mass number (A = Z + N) of interest was selected using ISOLDE’s high-resolution dipole mass separator and delivered to the ISOLTRAP online mass spectrometer15.
The ions were first accumulated in ISOLTRAP’s linear radiofrequency quadrupole cooler and buncher trap16. The extracted bunches were subsequently decelerated by a pulsed drift cavity to an energy of 3.2 keV before being purified by the multireflection time-of-flight mass spectrometer (MR-ToF MS)17, where multiple passages between two electrostatic mirrors rapidly separate the short-lived indium ions from much more abundant molecules of approximately the same mass. For all investigated isotopes, surviving molecular ions 80–82Sr19F+ were predominant in the ISOLDE beam. After a typical trapping time of about 25 ms, a resolving power in excess of m/
The rate of 100In and 101In behind the MR-ToF MS was sufficient to perform Penning-trap mass measurements. For 100In the conventional time-of-flight ion-cyclotron-resonance (ToF-ICR) technique was used (Methods and Extended Data Fig. 1). Even-N neutron-deficient indium isotopes are known to exhibit long-lived isomeric states lying a few hundred kiloelectron-volts above the corresponding ground state, owing to the close energy proximity between the
Table 1 summarizes our experimental results and compares them with the literature. The ISOLTRAP mass values for the ground and isomeric states of 101In agree well with averages obtained from refs. 11,12. The excitation energy is determined to be 668(11) keV, reducing the uncertainty by a factor of four. The ToF-ICR measurement of 101gIn is in excellent agreement with the value measured using PI-ICR. 100In is found to be 130 keV more bound, while the mass uncertainty is improved by almost a factor of 90.
Since the 100Sn 2016 Atomic-Mass Evaluation (AME2016) mass excess value of −57,280(300) keV (ref. 20) is derived from that of 100In and the
Because the binding energy is a large quantity, finite differences are commonly used for assessing changes in nuclear structure from the mass surface. Shown in Fig. 2 (open grey symbols) is the two-neutron empirical shell gap defined as
Since the lack of mass data for the N = 48 isotopes of In (Z = 49), Cd (Z = 48) and Ag (Z = 47) prevents derivation of this quantity out to 100Sn, we adapt an approach proposed in ref. 22 using
In recent years, there has been great progress advancing ab initio calculations in medium-mass nuclei23,24 up to the tin isotopes2 based on modern nuclear forces derived from chiral effective field theory of the strong interaction. Most ab initio approaches are benchmarked on even–even nuclei, which are considerably simpler to compute, but this excludes from the benchmark effects that are only visible in odd nuclei. Among these are the single-particle states accessible to the unpaired nucleon and their interaction with the states of the even–even core, the blocking effect on pairing correlations and, in the case of odd–odd nuclei, the residual interaction between the unpaired proton and neutron. The latter two give rise to an odd–even staggering (OES) of binding energies, which can be quantified by a three-point estimator. Odd systems thus provide a complementary and stringent testing ground for state-of-the-art theoretical approaches. Among ab initio approaches, the valence-space formulation of the in-medium similarity renormalization group (VS-IMSRG)25 is able to access a broad range of closed- and open-shell nuclei in the nuclear chart26. In addition, we will explore the shell-model coupled-cluster (SMCC) method27 in this region. Both the VS-IMSRG and coupled-cluster calculations provide access to a broad range of observables, such as ab initio calculations of beta decays—up to 100Sn (ref. 3). The VS-IMSRG was also recently shown to adequately describe both OES of nuclear masses and charge radii in neutron-rich odd-Z copper (Z = 29) isotopes28. Here we present VS-IMSRG and SMCC results that allow direct comparisons with the odd-Z nuclides adjacent to the iconic 100Sn nucleus.
We have performed cross-shell VS-IMSRG29 and SMCC calculations using the 1.8/2.0(EM) two-nucleon (NN) and three-nucleon (3N) interactions of ref. 30. This interaction is fitted to the properties of nuclear systems with only A = 2, 3 and 4 nucleons (with 3N couplings adjusted to reproduce the triton binding energy and the 4He charge radius), and gives accurate results for ground-state energies of light and medium-mass nuclei26,31. To further explore the sensitivity to chiral effective field theory interactions, we also consider the NN + 3N(lnl) interaction32 that has proven to constitute a valuable addition to existing chiral Hamiltonians in medium-mass nuclei33 but has yet to be tested in heavier systems. Finally, we show results for the 100Sn region with the
Figure 3a presents the experimental three-point empirical formula of the OES,
Figure 3b shows the experimental trend of
Methods
MR-ToF MS mass measurement and analysis
The relation between the time of flight t of a singly charged ion of interest and its mass mion is given by t = a(mion)1/2 + b where a and b are device-specific calibration parameters. These can be determined from the measured flight times t1,2 of two reference ions with well known masses mion,1 and mion,2. From the time-of-flight information of all the singly charged species, the mass of an ion is then calculated from the relation mion1/2 = CToF
Principle of Penning-trap mass spectrometry
Penning-trap mass spectrometry relies upon the determination of the free cyclotron frequency
ToF-ICR mass measurements and analysis
The mass of 100In was measured using the well established ToF-ICR technique using both one-pulse excitation42 and two-pulse, Ramsey-type excitation43. In this method, the free cyclotron frequency of an ion is directly determined. From one experimental cycle to the next, the frequency of an excitation pulse is varied. Following this excitation, the ions are ejected from the trap and their time of flight to a downstream microchannel plate detector is measured. The response of the ions to the applied excitation is a resonant process whose resonance frequency is
PI-ICR mass measurements and analysis
To separate the A = 101 isomers, the recently introduced PI-ICR technique was used18. With this method, the radial frequency of ions prepared on a pure cyclotron or magnetron orbit is determined through the measurement of the phase they accumulate in a time tacc using the projection of their motion onto a position-sensitive multichannel plate detector. The PI-ICR technique offers several advantages over the regular ToF-ICR technique. First, it is a non-scanning technique, which greatly reduces the number of ions required to perform a measurement; that is, only five to ten ions are required, where a minimum of 50–100 are required for ToF-ICR. While the resolving power of the ToF-ICR method is entirely limited by the excitation time, the resolving power of PI-ICR depends on the observation time and the ion-distribution spot size projected on the detector.
A three-step measurement scheme allows for the direct determination of
VS-IMSRG calculations
The VS-IMSRG calculations25,46 were performed in a spherical harmonic-oscillator basis including up to 15 major shells in the single-particle basis with an oscillator frequency ħ
SMCC calculations
The SMCC approach generates effective interactions and operators through the decoupling of a core from a valence space. We start from a single Hartree–Fock 100Sn reference state, computed in a harmonic-oscillator basis comprising up to 11 major oscillator shells and ħ
Data availability
Source data are provided with this paper.
Code availability
The analysis codes used for the ToF-ICR and MR-ToF MS data are available from the corresponding author upon reasonable request. A second MR-ToF MS analysis code used in this study is available at https://github.com/jonas-ka/mr-tof-analysis. The PI-ICR analysis code45 used in this study is available at https://github.com/jonas-ka/pi-icr-analysis. The code used for the VS-IMSRG calculations is available at https://github.com/ragnarstroberg/imsrg. The source code of KSHELL is available in ref. 48.
Change history
21 February 2022
In the version of this Letter initially published, the following metadata was omitted and has now been included: Open access funding provided by Max Planck Institute of Nuclear Physics (MPIK) (2).
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Acknowledgements
We thank the ISOLDE technical group and the ISOLDE Collaboration for their support. We acknowledge the support of the Max Planck Society, the French Institut National de Physique Nucléaire et de Physique des Particules (IN2P3), the European Research Council (ERC) through the European Union’s Horizon 2020 research and innovation programme (grant agreement 682841 ‘ASTRUm’ and 654002 ‘ENSAR2’) and the Bundesministerium für Bildung und Forschung (BMBF; grants 05P15ODCIA, 05P15HGCIA, 05P18HGCIA and 05P18RDFN1). J.K. acknowledges the support of a Wolfgang Gentner PhD scholarship from the BMBF (05E12CHA). This work was supported by the US Department of Energy, Office of Science, Office of Nuclear Physics, under awards DE-FG02-96ER40963 and DE-FG02-97ER41014. This material is based upon work supported by the US Department of Energy, Office of Science, Office of Advanced Scientific Computing Research and Office of Nuclear Physics, Scientific Discovery through Advanced Computing (SciDAC) programme under award DE-SC0018223. TRIUMF receives funding via a contribution through the National Research Council of Canada, with additional support from NSERC. Computer time was provided by the Innovative and Novel Computational Impact on Theory and Experiment (INCITE) Program. This research used resources of the Oak Ridge Leadership Computing Facility located at Oak Ridge National Laboratory, which is supported by the Office of Science of the Department of Energy under contract DE-AC05-00OR22725. The VS-IMSRG computations were performed with an allocation of computing resources on Cedar at WestGrid and Compute Canada, and on the Oak Cluster at TRIUMF managed by the University of British Columbia department of Advanced Research Computing (ARC). R.N.W. acknowledges support by the Australian Research Council under the Discovery Early Career Researcher Award scheme (DE190101137).
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M.M., D.A., J.K., P.A., I.K., Y.A.L., V.M., T.S., A.W. and F.W. performed the experiment. M.M., D.A., J.K. and R.N.W. performed the data analysis. K.C. and S.G.W. set up the resonant laser ionization scheme. W.J.H. performed the update of the Atomic-Mass Evaluation with the latest experimental results. G.H., J.D.H., G.R.J., T.M., T.P., S.R.S. and Z.H.S. performed the theoretical calculations. K.B., V.M., D.L., A.S., L.S., K.Z. and M.M. prepared the manuscript. All authors discussed the results and contributed to the manuscript at all stages.
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Extended data
Extended Data Fig. 1 Overview of experimental results (continued).
(a), Ramsey ToF-ICR resonance of 100In+ containing about 160 ions. A Ramsey pattern of TRFon-TRFoff-TRFon = 50 ms – 500 ms – 50 ms was used for this measurement. The solid red line corresponds to the least-square adjustment of the theoretical line shape to the data. (b), PI-ICR ion-projection image of 101In+. (0,0) marks the center of the position sensitive detector. In a phase-accumulation of about 62 ms a mass resolving power in excess of 5.105 was reached allowing for the ground (blue) and isomeric (red) states to be separated by the angle
Source data
Source Data Fig. 2
CSV file providing the data to reproduce Fig. 2c.
Source Data Fig. 3
CSV file providing the data to reproduce Fig. 3.
Source Data Extended Data Fig. 1
CSV file providing the data to reproduce Extended Data Fig. 1.
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Mougeot, M., Atanasov, D., Karthein, J. et al. Mass measurements of 99–101In challenge ab initio nuclear theory of the nuclide 100Sn. Nat. Phys. 17, 1099–1103 (2021). https://doi.org/10.1038/s41567-021-01326-9
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DOI: https://doi.org/10.1038/s41567-021-01326-9