ISOLTRAP measures cadmium isotope masses for the first time, probing a key nuclear shell gap
Christoph Schweiger, Daniel Lange and Vladimir Manea for the ISOLTRAP collaboration
General view from above of the ISOLDE facility showing clearly the different beamlines being led to the experiments. Source:
Τhe mass of a particle is one of its fundamental properties, which not only allows its identification but, in the case of a composite particle, provides insight into its structure and the global strength of the interaction that binds its constituents together. Atomic nuclei are one example of such a composite particle, consisting of Z protons and N neutrons.
The mass of the nucleus MN (Z, N ) is then given by the sum of its constituent masses and the mass equivalent of their binding energy, EB,nuc(Z, N ):
Mass measurements of radioactive isotopes usually study the nucleus surrounded by its atomic electrons, hence, the experimentally determined value is the full atomic mass, containing in addition the Z electron masses and the effect of the
electron binding energy, EB,e(Z, N ):
In nuclear physics one however studies differences of atomic masses, called mass filters, which cancel in many cases completely the contribution from the electron binding energy. They are essential tools for tracing the fingerprints of nuclear
structure along isotopic chains and for performing sensitive tests of nuclear models.
Experimental efforts to determine the atomic masses of radioactive isotopes focus on regions of the nuclear chart with interesting features linked to nuclear-structure phenomena. These can be found, for example, around nuclear shell closures, where mass filters usually exhibit discontinuities. In particular, the empirical shell gap is a filter which allows quantifying the shell-closure strength [1]. It has been used across the chart to quantify the evolution of nuclear shells with neutron-proton imbalance, one of the main topics in nuclear-structure research. A region which has, in recent years, garnered a lot of interest is found around the doubly magic, self-conjugate nucleus 100Sn, which is the heaviest bound nucleus with an equal number of protons and neutrons [2, 3]. Apart from its appeal for nuclear-structure studies, it is located close to the path of the astrophysical rapid proton-capture process [4] making the region central for studies at different radioactive ion beam facilities
worldwide using techniques like mass spectrometry [5, 6, 7, 8, 9, 10], decay spectroscopy [11, 12] and laser spectroscopy [13].
Figure 1: Two-neutron separation energies as a function of the neutron number for different isotopic chains in the region of 100Sn. The black open circles are data from the Atomic Mass Evaluation [14], prior to the Isoltrap measurements, which are shown in solid red circles. The blue circle marks a data point relying partially on a recent measurement by the LEBIT mass spectrometer at FRIB [10]. Green circles are extrapolations using the systematics of Coulomb Displacement Energies (CDE).
In recent years, the Isoltrap mass spectrometer [15] has joined the efforts to expand knowledge in this region, with several successful measurement campaigns [5, 6, 9] during the last years. The global impact of the Isoltrap mass measurements in this region is illustrated in Fig. 1, which plots for different isotopic chains the two-neutron separation energy, a mass filter given by:
where M(Z, N ) is the mass of the nuclide with Z protons and N neutrons, and mn is the neutron mass. The smooth trends of S2n along isotopic chains are interrupted by the discontinuities in the vicinity of N = 50, which mark the shell-closure effect.
ISOLTRAP [17, 15] is a multi-ion-trap apparatus located at the ISOLDE facility at CERN. Figure 2 shows a schematic overview of the apparatus. Its experimental efforts concentrate on precision mass measurements of radionuclides produced at ISOLDE using multi-reflection time-of-flight (MR-ToF) [18].
Figure 2: Schematic overview of the Isoltrap experimental apparatus. For details, see the text. Figure taken from [16].
and Penning-trap (PT) mass spectrometers (MS). In a typical experimental cycle, the quasi-continuous radioactive ion beam from ISOLDE is captured in a radio-frequency quadrupole cooler and buncher (RFQ-CB), where helium buffer gas cools and bunches the ions. Subsequently, the ion bunches are extracted, slowed down and injected into the MR-ToF MS for a mass measurement or mass separation. If higher precision is required, a tandem-PT MS is available, in which ions are first injected into a preparation PT, where they are mass-selectively cooled in a buffer gas [19], and then injected into the precision PT for the actual mass measurement using time-of-flight or phase-imaging ion-cyclotron-resonance techniques [20, 21].
An MR-ToF MS relies on the time-of-flight separation of ions with a well-defined kinetic energy of about 2 keV at Isoltrap. The device consists of two electrostatic mirrors in a coaxial arrangement that store ions axially. The potentials applied to the mirror electrodes are critical and are set to operate the device isochronously, i.e., so that ions of the same mass have the same time- of-flight irrespective of the initial energy spread. Typically, the ions can be reflected back and forth between the electrostatic mirrors for a few thousand reflections, enabling effective flight path lengths in the range of kilometers. With this technique, mass resolving powers m/∆m ∼ 2.5 · 105 [22] can be reached within tens of milliseconds and single-ion sensitivity, allowing the study of exotic and short-lived radionuclides.
The most recent experimental campaign in the 100Sn region targeted the cadmium isotopic chain and in particular the isotopes 96−98Cd. The main motivation was to determine the strength of the N = 50 shell closure at Z = 48 and to infer its evolution towards 100Sn.
During the previously mentioned work in this region of the nuclear chart [5, 6, 9], the first studies of possible yields for more neutron-deficient isotopes were reported. Meticulous preparations and tests were performed in close collaboration with the target and ion source development (TISD) team at ISOLDE, and design improvements enhanced temperature homogeneity across the LaCx target material, boosting the yield by about a factor of five. During a test run, the improved performance enabled the first measurement of the ground- and isomeric-state masses of 97Cd, in addition to the planned successful yield and beam-composition study of the even more exotic 96Cd. Due to the very low yield of 96Cd on the order of 10−2 1/μC of proton current, not only was consistent target performance crucial, but also the sensitivity and stability of the ISOLTRAP apparatus.
Figure 3: (a) Time-of-flight spectrum at mass A = 96 (top) and A = 97 (bottom), with the ⁹⁶Cd peak visible on the right-hand side of the A = 96 spectrum. For details, see the text. Figure taken from [25]. (b) One-neutron empirical shell gap using AME data [14], the cadmium masses measured by ISOLTRAP (Z = 48) [25] and, for Z = 50, experimental masses from recent ISOLTRAP [26] and LEBIT work [10], together with an extrapolation based on the systematics of Coulomb displacement energies (CDE). Figure taken from [25].
For this, the MR-ToF MS was upgraded with two dedicated temperature stabilisation setups: one to complement the active voltage stabilisation [22, 23] and a second for the MR-ToF MS itself, which can elongate or shrink with changes in the surrounding temperature within the ISOLDE experimental hall [24]. On the RFQ-CB, improvements of the radiofrequency coupling significantly improved efficiency, contributing to improved sensitivity. In the final preparation steps, the mirror-electrode voltages of the MR-ToF MS were optimised to reduce the scattering of contaminants in the expected ToF window of 96Cd in order to accomplish a background-free, clean signature in the final measurement.
The significant improvements in the sensitivity and stability of the mass spectrometer, combined with developments to the ISOLDE target and the exceptional stability of the resonance ionisation laser ion source (RILIS), enabled a measurement of the mass of ⁹⁶Cd. As the observed yield increases with higher proton current from CERN’s Proton Synchrotron Booster (PSB), we are grateful for the exceptional increase in proton current from 2 to 2.5 μA for a significant part of the experimental run.
In total, about 40 counts of ⁹⁶Cd were observed during the week-long experiment, as shown in the time-of-flight spectrum in Figure 3(a). The figure also compares spectra with the RILIS lasers on (grey) and off (red). No counts of ⁹⁶Cd were observed when one of the laser ionisation steps was switched off, confirming that the observed peak corresponds to cadmium. Additionally, we refined and consolidated the previous measurements of the ground and isomeric states of ⁹⁷Cd. The ⁹⁶Cd measurement marks the lowest yield explored so far at ISOLTRAP.
From the measured masses in the cadmium chain, a mass filter called the one-neutron empirical shell gap could be extracted:
where S1n(Z, N ) is the one-neutron separation energy. Figure 3(b) shows its values. The trend of this filter with proton number is a measure of the strength of the N = 50 shell closure as it evolves between different isotopic chains. We compared several theoretical approaches from ab-initio and density functional theory (DFT) with the experimental results, and they agree qualitatively very well. Towards the N = 50 shell closure, we clearly observe an enhancement of ∆1n(Z, N ), which is consistent with the expected doubly magic nature of 100Sn.
These results provide the first direct experimental constraint on the N = 50 empirical shell gap in the cadmium isotopic chain and show that it increases as one approaches 100Sn. The measurement of 96Cd, achieved with only about 40 detected ions, also demonstrates the exceptional sensitivity of the Isoltrap apparatus and the importance of the combined developments in the ISOLDE target, the RILIS resonance laser-ionisation system and the mass spectrometer. Together with the improved mass values for 97Cd and 98Cd, these results provide more stringent benchmarks for nuclear-theory calculations in one of the most challenging regions of the nuclear chart. Future measurements of nuclei even closer to 100Sn will further elucidate how nuclear shell structure evolves at the limits of experimental accessibility and deepen our understanding of the processes involved in the synthesis of proton-rich nuclei.
Acknowledgements: We would like to thank all ISOLDE technical teams for their excellent collaboration. Specifically, we acknowledge the support from the RILIS team, the target and ion source team, the radioprotection team and the ISOLDE operations team. Furthermore, we would like to acknowledge the support of the Proton Synchrotron Booster (PSB) team for maintaining stable conditions and increasing the proton current during the experimental run. This experiment has received funding from the European Union’s Horizon Europe research and innovation programme under grant agreement no. 101057511. We furthermore acknowledge the support of the German Max-Planck-Society for financing the experiment and personnel, and the mechanical engineering office and mechanical and electronic workshops at the Max-Planck-Institute for Nuclear Physics in Heidelberg.
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