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The properties of exotic nuclei on the verge of existence play a fundamental part in our understanding of nuclear interactions. Exceedingly neutron-rich nuclei become sensitive to new aspects of nuclear forces. Calcium, with its doubly magic isotopes (40)Ca and (48)Ca, is an ideal test for nuclear shell evolution, from the valley of stability to the limits of existence. With a closed proton shell, the calcium isotopes mark the frontier for calculations with three-nucleon forces from chiral effective field theory. Whereas predictions for the masses of (51)Ca and (52)Ca have been validated by direct measurements, it is an open question as to how nuclear masses evolve for heavier calcium isotopes. Here we report the mass determination of the exotic calcium isotopes (53)Ca and (54)Ca, using the multi-reflection time-of-flight mass spectrometer of ISOLTRAP at CERN. The measured masses unambiguously establish a prominent shell closure at neutron number N = 32, in excellent agreement with our theoretical calculations. These results increase our understanding of neutron-rich matter and pin down the subtle components of nuclear forces that are at the forefront of theoretical developments constrained by quantum chromodynamics.

The quest for the value of the electron's atomic mass has been subject of continuing efforts over the last decades [1,2,3,4]. [5] and which are thus responsible for its predictive power, the electron mass me plays a prominent role, as it is responsible for the structure and properties of atoms and molecules. This manifests in the close link with other fundamental constants, such as the Rydberg constant R∞ and the fine-structure constant α [6]. However, the low mass of the electron considerably complicates its precise determination. In this work we present a substantial improvement by combining a very accurate measurement of the magnetic moment of a single electron bound to a carbon nucleus with a state-of-the-art calculation in the framework of bound-state Quantum Electrodynamics. The achieved precision of the atomic mass of the electron surpasses the current CODATA [6] value by a factor of 13. Accordingly, the result presented in this letter lays the foundation for future fundamental physics experiments [7,8] and precision tests of the SM [9,10,11] Throughout the last decades, the determination of the atomic mass of the electron has been subject to several Penning-trap experiments, as continuing experimental efforts try to further explore the scope of validity of the SM and require an exceedingly precise knowledge of me. The uniform magnetic field of these traps gives the possibility to compare the cyclotron frequency of the electron with that of another ion of known atomic mass, typically carbon ions or protons. The first such direct determination dates back to 1980, when Gräff et al. made use of a Penning trap to compare the cyclotron frequencies of a cloud of electrons with that of protons, which were alternately confined in the same magnetic field, yielding a relative precision of about 0.2 ppm [2]. Since then, a number of experiments have pushed the precision by about 3 orders of magnitude [1,12,13,4]. The latest version of the CODATA compilation of fundamental constants of 2010 lists a relative uncertainty of 4•10 -10 , resulting from the weighted average of the most precise measurements (Fig. 2). Since the cyclotron frequency of the extremely light electron is subjected to troublesome relativistic mass shifts if not held at the lowest possible energy, direct ultra-high precision mass measurements are particularly delicate. To circumvent this problem, the currently most precise measurements, including this work, pursue an indirect method which allows achieving a previously unprecedented accuracy. Among the seemingly fundamental constants which parameterize the Standard Model (SM) of physicsA single electron is bound directly to the reference ion, in this case a bare carbon nucleus (Fig. 1). In this way, it becomes possible to calibrate the magnetic field B at the very place of the electron through a measurement of the cyclotron frequency

Despite being a complex many-body system, the atomic nucleus exhibits simple structures for certain ‘magic’ numbers of protons and neutrons. The calcium chain in particular is both unique and puzzling: evidence of doubly magic features are known in ^40,48Ca, and recently suggested in two radioactive isotopes, ^52,54Ca. Although many properties of experimentally known calcium isotopes have been successfully described by nuclear theory, it is still a challenge to predict the evolution of their charge radii. Here we present the first measurements of the charge radii of ^49,51,52Ca, obtained from laser spectroscopy experiments at ISOLDE, CERN. The experimental results are complemented by state-of-the-art theoretical calculations. The large and unexpected increase of the size of the neutron-rich calcium isotopes beyond N = 28 challenges the doubly magic nature of 52Ca and opens new intriguing questions on the evolution of nuclear sizes away from stability, which are of importance for our understanding of neutron-rich atomic nuclei

Background: Microscopic calculations of heavy nuclei face considerable difficulties due to the sizes of the matrices that need to be solved. Various approximation schemes have been invoked, for example by truncating the spaces, imposing seniority limits, or appealing to various symmetry schemes such as pseudo-SU(3). This paper proposes a new symmetry scheme also based on SU(3). This proxy-SU(3) can be applied to well-deformed nuclei, is simple to use, and can yield analytic predictions. Purpose: To present the new scheme and its microscopic motivation, and to test it using a Nilsson model calculation with the original shell model orbits and with the new proxy set. Method: We invoke an approximate, analytic, treatment of the Nilsson model, that allows the above vetting and yet is also transparent in understanding the approximations involved in the new proxy-SU(3). Results: It is found that the new scheme yields a Nilsson diagram for well-deformed nuclei that is very close to the original Nilsson diagram. The specific levels of approximation in the new scheme are also shown, for each major shell. Conclusions:The new proxy-SU(3) scheme is a good approximation to the full set of orbits in a major shell. Being able to replace a complex shell model calculation with a symmetry-based description now opens up the possibility to predict many properties of nuclei analytically and often in a parameter-free way. The new scheme works best for heavier nuclei, precisely where full microscopic calculations are most challenged. Some cases in which the new scheme can be used, often analytically, to make specific predictions, are shown in a subsequent paper.

We determined the experimental value of the g factor of the electron bound in hydrogenlike ²⁸Si¹³⁺ by using a single ion confined in a cylindrical Penning trap. From the ratio of the ion's cyclotron frequency and the induced spin flip frequency, we obtain g = 1.995 348 958 7(5)(3)(8). It is in excellent agreement with the state-of-the-art theoretical value of 1.995 348 958 0(17), which includes QED contributions up to the two-loop level of the order of (Zα)² and (Zα)⁴ and represents a stringent test of bound-state quantum electrodynamics calculations.

Atomic physics techniques for the determination of ground-state properties of radioactive isotopes are very sensitive and provide accurate masses, binding energies, Q-values, charge radii, spins, and electromagnetic moments. Many fields in nuclear physics benefit from these highly accurate numbers. They give insight into details of the nuclear structure for a better understanding of the underlying effective interactions, provide important input for studies of fundamental symmetries in physics, and help to understand the nucleosynthesis processes that are responsible for the observed chemical abundances in the Universe. Penning-trap and and storage-ring mass spectrometry as well as laser spectroscopy of radioactive nuclei have now been used for a long time but significant progress has been achieved in these fields within the last decade. The basic principles of laser spectroscopic investigations, Penning-trap and storage-ring mass measurements of short-lived nuclei are summarized and selected physics results are discussed. † going to cryogenic temperatures, or enhancing the induced signal by using higher charge states and/or longer accumulation times. Ideal applications for this method are mass measurements of super-heavy element (SHE) isotopes for nuclear structure studies as they are performed at SHIPTRAP [25,26]. SHE are produced in minuscule quantities, and typically have half-lives of hundreds of milliseconds to a few seconds. A proof-ofprinciple experiment is planned at the TRIGA reactor facility TRIGA-TRAP at Mainz University [27] and applications for HITRAP with highly charged ions are foreseen [28]. Requirements for Mass Measurements of Radioactive IonsThe specific requirements for the mass measurements of radioactive ions stem from the parameters of the ions themselves. For example the required sensitivity (depending on the production yield) and measurement speed (depending on the half-life) as well as the envisaged application which dictates the required precision. In order to be meaningful, all measurements should deliver reliable data, hence precise and accurate. The physics requirements can be categorized with the corresponding relative precision as follows:• nuclear structure, δm/m ≈ 1 × 10 −7• nuclear astrophysics, δm/m ≈ 1 × 10 −7/−8 • test of fundamental symmetries, neutrino physics, δm/m ≈ 1 × 10 −8/−9