Precision test of modern nuclear structure models by collinear laser spectroscopy
The radius is a fundamental property of an atomic nucleus. Amongst others, the charge density distribution
of a nucleus can be characterized by the root-mean-square (rms) nuclear charge radius.
Early electron scattering experiments in the 1930s empirically showed that the nuclear radii increase roughly with A1/3, where A is the number of nucleons (protons and neutrons). Assuming a constant saturation density inside the nucleus, the liquid drop model was proposed by G. Gamow and based on this model a semi-empirical mass formula was formulated by C. F. v. Weizsäcker.
Since the first investigations of nuclei, various precision measurements of charge radii have revealed many facets of nuclear structure and dynamics along chains of isotopes, e.g. the kink at a shell closure or the quantitatively not fully understood odd-even staggering between nuclei with consecutive odd and even neutron numbers.
Modern nuclear structure models are challenged by the rich collection of data across the nuclear chart available today and aim at a global description of nuclear charge radii. The nuclear density functional theory (DFT) allows a microscopic description of nuclei througout the whole mass table and has been particularly successful in the medium and heavy mass region. The charge radii of 40Ca and 48Ca can already be described quite well, but the DFT models fail to explain the detailed isotopic trends as the fast increase of the nuclear charge radius from 48Ca to 52Ca (see our news of 08.02.16) or the intricate behavior of charge radii between 40Ca and 48Ca.
Thus, in DFT, the non-relativistic Fayans pairing functional was developed in order to improve the description of isotopic trends. It particularly significantly improves the description of the odd-even staggering of charge radii, which could not be accommodated by an alternative relativistic density functional approach. New precision data on charge radii along long isotopic chains are essential in order to test the predictions of such new DFT models.
In a recent article published in Physical Review Letters M. Hammen et al. present new results of charge radii of cadmium isotopes,
with Z=48 one proton pair below the Z=50 proton shell closure. The experiments were conducted with the collinear
laser spectroscopy apparatus COLLAPS
at the radioactive ion beam facility
ISOLDE/CERN , Geneva. Transitions in the
neutral Cd atom as well as in the singly-charged Cd ion have been studied with different experiments by high-resolution collinear
For the spectroscopy on neutral cadmium atoms the 5s5p 3P2 -> 5s6s 3S1 transition at 508.7 nm was used (see N. Frömmgen et al., Eur. Phys. J. D 69, 164 (2015) ). It was performed with continuous beams delivered from the ISOLDE general-purpose separator (GPS) and was restricted to 106-124,126Cd.
In order to study the singly charged cadmium ions, they were excited in the 5s 2S1/2 -> 5p 2P3/2 transition using laser light at 214.5 nm copropagating with the ion beam. The experiments were performed with bunched and cooled beams from ISCOOL (ISOLDE's radiofrequency quadrupole cooler–buncher) at the high-resolution separator (HRS). More detailed information in our news of 07.05.13 and 25.01.16 and the related articles of D. T. Yordanov et al..
With the exception of 99Cd, the isotope shifts of Cd isotopes were measured along the complete sdgh shell from 100Cd (N=52) up to the shell closure at 130Cd (N=82). The differences in mean-square nuclear charge radii of the measured cadmium isotopes with respect to the reference isotope 114Cd were extracted from the isotope shifts. The charge radii show a smooth parabolic behavior on top of a linear trend and a regular odd-even staggering across the almost complete sdgh shell.
The experimental results were compared with predictions from relativistic (FSUGarnet+BNN) and non-relativistic (Skyrme, Fayans)
nuclear DFT models. Except the Fayans pairing functional, all DFT models fail to reproduce the isotopic trend as a whole and the odd-even
staggering of the charge radii in detail. On the one hand, this is due to the two new gradient terms in the Fayans functional,
i.e. the gradient term within the surface term and the gradient term in the pairing functional. On the other hand, the newly proposed
Fayans parametrization - optimized to the change in the mean square charge radii of isotopes of the calcium chain - performs very well
also for the cadmium chain.
This first successful test of the new elaborated Fayans pairing functional shows the importance of precision data on rms nuclear charge radii for the further development of pairing within nuclear density functional theory.
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Precise exploration of the neutron-deficient isotopes 101-109Cd
In recent years, numerous nuclear-structure studies were performed on isotopes of the cadmium isotopic chain, highlighting the importance of precision measurements in this region of the nuclear chart. Precision mass measurements of 129-131Cd with ISOLTRAP at ISOLDE/CERN adressed stellar nucleosynthesis (see our news of 04.12.15). Collinear laser spectroscopy on neutron-rich cadmium isotopes with COLLAPS confirmed the applicability of the simple nuclear shell model for complex nuclei (see our news of 07.05.13). In 2016, the simple nuclear structure in 111-129Cd was revealed (see our news of 25.01.16).
In a recent article published in Physical Review C (Rapid Communication), D. T. Yordanov et al. report on the laser spectroscopic investigation of neutron-deficient cadmium isotopes from 109Cd down to 101Cd. The precision measurements were carried out with the collinear laser spectroscopy setup COLLAPS at ISOLDE-CERN, Geneva. The cadmium ions were excited in the transition 5s 2S1/2 -> 5p 2P3/2 at 214.5 nm and superimposed with a continuous wave laser beam to scan the hyperfine structure. For the first time, frequency quadrupling for collinear laser spectroscopy was used. To this end, the cw laser beam was produced by sequential second-harmonic generation from the output of a titanium-sapphire laser.
The experiment yielded accurate ground-state electromagnetic moments for 101-105Cd. The electromagnetic moment of 101Cd was determined for the first time. Furthermore, the precison of the quadrupole moment of 103Cd could be vastly improved. The 5/2+ electromagnetic moments in 101-107Cd show similar behavior to the linear trends associated with the 11/2− states in neutron-rich 111-129Cd measured in 2016. Thus, the data were initially discussed in the context of simple structure in complex nuclei. However, a more realistic view on the underlined nuclear structure was obtained by large-scale shell-model calculations using the SR88MHJM Hamiltonian. They reveal a prominent role of the two proton holes of Cd (Z=48) relative to the magic number Z=50.
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Monitoring the temperature of smallest particles
The stability of molecules, clusters, and nanoparticles in free space depends significantly on their heating and cooling through thermal radiation. These processes become manifest among other things in the interstellar continuum emission. The investigation of the radiation behavior of smallest particles is part of the experimental laboratory astrophysics. This became possible due to the development of cryogenic ion traps and storage rings, in which molecular and cluster ions at ambient temperatures of some Kelvin are stored for minutes. For the first time the inner energy of stored ions is continuously monitored with time resolution allowing for a better understanding of the thermal radiation behavior. Employing the electrostatic Cryogenic Trap for Fast ion beams (CTF) at the Max-Planck-Institut für Kernohysik (MPIK) in Heidelberg a proof-of-principle experiment was performed determining continuously the energy distribution of Co4− anions using a pulsed, tunable laser. The new method, which is based on measuring delayed electron emission after photon absorption, was published by C. Breitenfeldt et al. in Physical Review Letters. It is currently applied and further developed in experiments at the Cryogenic Storage Ring (CSR) at the MPIK.
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Exploration of the island of inversion at neutron number N=40
The simple nuclear shell model successfully describes the ordering of the energy levels of the nucleons (protons and neutrons)
near the "valley of stability". It allows to explain the exceptional stability of nuclei with "magic" proton or neutron numbers
(completely filled proton or neutron shells). In 1975 mass measurements of neutron-rich nuclei showed that the N=20 shell
closure vanishes near 32Mg. The region with this unexpected change in nuclear structure was called "island of inversion".
Since then, the intensive examination of neutron-rich exotic nuclei revealed other islands of inversion at neutron numbers N=8, 28, and 40. Such regions with deformed nuclear structure caused by nuclear collectivity (bulk motion of many nucleons) leading to intruder configurations, i.e. configurations outside the sd-shell, can't be explained by the simple nuclear shell model. The properties of excited nuclear states along the N=40 isotones suggest a rapid development of collectivity from a doubly magic 68Ni (Z=28, N=40), to a transitional 66Fe (Z=26, N=40) and finally a strongly deformed 64Cr (Z=24, N=40). Additionally, dominant collective behavior appears to persist past N=40 possibly merging the N=40 island of inversion with a region of deformation in the vicinity of doubly magic 78Ni (Z=28, N=50).
More precise mass values of neutron-rich chromium isotopes are needed to further investigate the sudden onset of deformation towards N=40 in the chromium isotopic chain suggested by AME2016 and they are also of interest in the field of astrophysics.
In a recently in Physical Review Letters published article M. Mougeot et al. report on the first precision measurements of the ground-state binding
energies of short-lived neutron-rich chromium isotopes 58-63Cr. The measurements were performed using
multi-reflection time-of-flight mass spectrometer/separator (MR-ToF MS) at ISOLDE/CERN, Geneva. For the first time, chromium ion
beams were produced by a resonance ionization laser ion source (RILIS) at the
ISOLDE facility . The purified ion beam was cooled
inside a preparation Penning trap and then injected into ISOLTRAP's precision Penning trap. Here, the high-precision mass measurements
of chromium ions 58-62Cr were carried out by the time-of-flight ion-cyclotron resonance (ToF-ICR) technique.
The ToF-ICR yields the atomic masses of the chromium ions by determination of the ratio between the cyclotron frequency νc,ref of reference 85Rb+ ions and the cyclotron frequency νc of the chromium ions.
In the case of 63Cr, the production yield was so low that the mass determination could only be performed using ISOLTRAP's MR-ToF MS as a mass spectrometer. Thus, the masses of 59-63Cr were determined using the time-of-flight ratios with isobaric CaF+ ions and 85Rb+ ions as reference.
The new determined mass values are up to 300 times more precise than the literature values thus greatly refining our
knowledge of the mass surface in the vicinity of the island of inversion around N=40.
From the determined mass excesses the two-neutron separation energies S2n of the chromium isotopes were deduced. The S2n trend allows to probe the evolution of nuclear structure with neutron number. In contrast to a sudden onset of deformation suggested by the AME2012 the new precise S2n trend appears very smooth with an upward curvature when approaching N=40, resembling the S2n trend of Mg in the original island of inversion from N=14 to 20. This trend shows a gradual enhancement of ground-state collectivity and thus gradual onset of deformation in the chromium chain.
The experimentally determined S2n trend for the chromium isotopes was compared to predictions from various nuclear models. The evolution of the S2n trend is well reproduced by both the UNEDF0 energy-density functional and the LNPS' phenomenological shell model interaction. Moreover, first ab initio calculations were applied to open-shell chromium isotopes. The new precise data provide important constraints to guide the ongoing development of such theoretical ab initio approaches to nuclear structure.
Please read more in the article ... >
Further information also in the press release of the MPIK .
Further press releases:
Review article on Penning-Trap Mass Measurements
Atomic masses are unique like fingerprints and provide insight into the structure of the atomic nucleus,
because the atomic mass is directly related to the nuclear binding energy, which is the sum of the
interactions holding the nucleons (protons and neutrons) together.
In the early days after the discovery of the existence of neon isotopes in 1913, atomic mass spectrometry was used to identify isotopes as parts of the same chemical element with different numbers of neutrons. Since then, the mass spectrometry methods have been increasingly improved. Today, advanced Penning-trap systems are used for the application of the most modern mass spectrometry method that provides the highest mass precision and mass-resolving power. Penning-trap mass spectrometry currently offers relative mass uncertainties down to 10-10 for radionuclides and even below 10-11 for stable species.
In a recent review article published in Annual Review of Nuclear and Particle Science, J. Dilling, K. Blaum, M. Brodeur, and S. Eliseev provide a comprehensive overview of the techniques and applications of Penning-trap mass spectrometry in nuclear and atomic physics. In the article, the fundamental principles of Penning traps, including novel ion manipulation, cooling, and detection techniques, are reviewed.
The determination of the mass m of an ion with electric charge q in a Penning trap is based on
the measurement of its cyclotron frequency νc. The different types of Penning-trap facilities employ very
different techniques to measure the cyclotron frequency. At online facilities, high-precision Penning traps are
applied for mass measurements on short-lived nuclides. Here, the novel phase-image ion cyclotron resonance (PI-ICR)
technique is intended to replace the established time-of-flight ion cyclotron resonance (ToF-ICR) technique.
At cryogenic offline setups, mass ratios of long-lived or stable nuclides are measured by the fast Fourier ion cyclotron resonance (FT-ICR) technique.
The authors provide a detailed overview of all high-precision Penning-trap mass spectrometers for unstable
isotopes installed at radioactive ion beam (RIB) facilities. Offline installations for stable and long-lived
species are described in detail as well.
Finally, the applications of high-precision mass data in nuclear physics as well as fundamental physics research are discussed in the review article. The applications in atomic and nuclear physics range from nuclear structure studies and related precision tests of theoretical approaches to the description of the strong interaction to tests of the electroweak Standard Model, quantum electrodynamics and neutrino physics, and applications in nuclear astrophysics.
Today, the Penning-trap spectroscopy method is fully accepted by the atomic and nuclear physics community for high-precision mass measurements. In the future, specialized and highly developed Penning-trap systems will be more and more widely used at ever-increasing precision and resolution.
Please read more in the review article ... >
High-precision test of Einstein's energy-mass equivalence
The energy-mass equivalence expressed by the famous formula E=mc2 was the most important new finding of Einstein's special theory of relativity and is crucial for its validity. Since direct validations via precision annihilation experiments are limited to precisions of a few parts per million, less direct but more precise approaches are considered. A good candidate is the neutron capture reaction in which the newly formed isotope releases the gained binding energy as gamma rays. By comparing the precisely measured gamma-ray energy with the precisely determined mass defect of the formed isotope using Einstein's equation, the energy-mass equivalence can be tested with high accuracy.
In a recent article published in Nature Physics M. Jentschel and K. Blaum explain the verification of Einstein's simple equation by two completely independent experimental techniques. The gamma-ray wavelengths and thus the gamma ray energies can be determined by diffraction angle measurements with a double perfect-crystal spectrometer. The lattice spacing is known with eight-digit accuracy and the diffraction angle measurements can be done with seven-digit accuracy. To match this precision, the mass defect has to be determined with 11-digit accuracy by high-precision Penning-trap mass measurements.
For the combination of both experimental techniques only the three isotope pairs 1,2H, 32,33S and 28,29Si have so far been suitable. With the existing data, it has been possible to demonstrate the equality of mass and energy at the level of 1.4(4.4)·10–7. An isotope pair for an improved test of the energy-mass equivalence is proposed.
Please read more in the Nature Physics article ... >
Investigation of nucleosynthesis processes of light p-nuclei
The stellar nucleosynthesis of heavy chemical elements beyond iron is of special interest in nuclear astrophysics. Stable proton-rich nuclei, the so-called p-nuclei, can't be created by the s- or p-process. Heavy p-nuclei are usually produced by the γ-process (photo-dissociation) in supernova explosions. However, the "light p-nuclei" in the medium mass region cannot be understood in the framework of standard nucleosynthesis. For the production of such light p-nuclei, the astrophysical rp-process (rapid proton capture) and νp-process (neutrino-driven nucleosynthesis) have been suggested.
In a recent article published in Physics Letters B, Y. M. Xing et al. report on precision mass measurements of five neutron-deficient nuclei, 79Y, 81,82Zr, and 83,84Nb. The measurements were performed by isochronous mass spectrometry with the experimental storage ring CSRe at the Heavy Ion Research Facility in Lanzhou (HIRFL), China. The masses of 82Zr and 84Nb were measured for the first time with an uncertainty of ~10keV, and the masses of 79Y, 81Zr, and 83Nb were re-determined with a higher precision.
With the precise mass measurements, especially the region of low α-separation energies (Sα) predicted by
FRDM'92 (finite range droplet mass model 1992) in neutron-deficient Mo and Tc isotopes was addressed.
From the determined mass excess values the two-proton (S2p) and two-neutron (S2n) separation energies and thus
the α-separation energies could be deduced.
The new mass values do not support the existence of a pronounced low-Sα island in Mo isotopes. As a consequence, the predicted Zr–Nb cycle in the rp-process of type I X-ray bursts does not exist or at least is much weaker than previously expected.
Furthermore, the new precise mass values allowed to address the overproduction of 84Sr found in previous νp-process calculations. The new masses lead to a reduction of the 84Sr abundance. This reduces the overproduction of 84Sr relative to 92,94Mo.
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The high-precision comparison of basic properties of matter/antimatter counterparts provides stringent tests of charge-parity-time
(CPT) invariance of the Standard Model. The experiments of the
target comparisons of the fundamental properties
of protons and antiprotons by determining and comparing their charge-to-mass ratios and magnetic moments in Penning traps.
In 2014 the collaboration directly measured the magnetic moment of the proton with 3.3 parts per billion (p.p.b.) precision at the Johannes Gutenberg University Mainz using a challenging double Penning-trap technique (see our news of 28.05.14). In a recent experiment at Mainz the collaboration improved the precision of the proton magnetic moment by a factor of eleven using an optimized double Penning-trap technique (see our news of 24.11.17). Last year the BASE collaboration also measured the antiproton magnetic moment with an unprecedented fractional precision of 1.5 p.p.b. (see our news of 18.10.17).
The precision of these experiments is, however, largely limited by the particle mode energy in the Penning trap. A reduction of the particle preparation times using sympathetically cooled protons/antiprotons is expected to significantly further improve the measurement precision.
In a recent article published in the Journal of Modern Optics, M. Bohman et al. present an upcoming experiment
to sympathetically cool single protons and antiprotons in a Penning trap by resonantly coupling the particles to laser-cooled
beryllium ions using a common endcap technique.
The measurement of the magnetic moment of a single proton or antiproton in a Penning trap is based on the measurement of the frequency ratio of the Larmor frequency and the cyclotron frequency (νL/νc). The Larmor frequency νL is determined by detection of spin transitions, which can only be observed at very low temperatures (cyclotron energies E+/kB < 0.6 K), where the axial frequency νz is stable enough.
In the previous proton/antiproton experiments time consuming selective resistive cooling techniques have been used to prepare the
particles below a threshold E+/kB < 1 K. The successful application of sympathetic cooling of protons and antiprotons to
deterministically low temperatures by coupling the particles to laser-cooled beryllium ions drastically reduces the cycle time of
An analysis of the energy exchange in the complete system leads to cyclotron energies below 30 mK/kB. Thus, a reduction of the ion preparation time from nearly an hour or more to just a few minutes can be expected.
To apply sympathetic cooling not only to protons but also to the negatively charged antiprotons, the BASE collaboration decided to use one trap for the proton (or antiproton) and a second trap for the beryllium ion cloud and connect the two with a common endcap. Each Penning trap has an outer endcap electrode, two inner correction electrodes, a central ring electrode and one shared endcap.
To realize the new sympathetic cooling scheme a heavily modified version of the double Penning-trap setup used for the proton measurements in 2014 at Mainz has been built. The new apparatus for an improved upcoming proton g-factor measurement consists of five traps: the new source trap (ST) for particle preparation, the analysis trap (AT) for spin state analysis, the precision trap (PT) for high precision frequency measurements, the coupling trap (CT) for common endcap coupling, and the beryllium trap (BT) for storage of laser cooled beryllium ions.
The upcoming application of sympathetic cooling with the common endcap technique on protons and antiprotons using the improved five Penning trap system will provide a direct CPT test at more than an order of magnitude improved precision and allow the most precise direct CPT comparison of single baryons.
Please read more in the article ... >