Breakthrough in the experimental and computational investigation of shape coexistence in mercury isotopes
In atomic nuclei, the complex many-body systems consisting of protons and neutrons obey the Pauli exclusion principle.
Thus, the nucleons occupy quantum levels that are separated by energy gaps leading to the simple nuclear shell model which
is comparable to Bohr's model of the atom. Atomic nuclei exhibit single-particle nature in the vicinity of closed shells
at the so called magic proton and neutron numbers (Z,N=8,20,28,50,82 and N=126). Away from the closed shells the nucleons
show collective behaviour. Consequently, nuclear size and shape are changing when protons and neutrons are added or removed.
High-resolution optical spectroscopy is suited to directly probe the valence particle configuration and changes in nuclear size or deformation by measuring the hyperfine splitting as well as the isotope shift. The understanding of nuclear deformation can be significantly improved by studying radionuclides where dramatic changes in shape occur with the removal of only a single nucleon.
A unique example is the change of the charge radius along the mercury (Hg, Z=80) isotopic chain, a "shape staggering" which was observed in the 1970s by laser spectroscopy. Whilst the even-mass mercury isotopes steadily shrink with decreasing N as seen for lead (closed proton shell Z=82), the odd-mass isotopes 181,183,185Hg exhibit a striking increase in charge radius. This astonishing discovery led to the still theoretically challenging phenomenon of "shape coexistence", where normal near-spherical and deformed structures coexist in the atomic nucleus at low excitation energy.
Although a vast number of studies on the isotopes of the mercury chain has already been carried out, two challenges remain that are cruical for understanding the nature of "shape staggering":
In order to precisely locate its occurance, previously experimentally inaccessible neutron-deficient mercury isotopes have to be investigated and for further theoretical progress microscopic many-body calculations of such heavy nuclei like Hg are required.
In a recent article published in Nature Physics Bruce A. Marsh et al. report breakthroughs on the experimental and the theoretical/computational front of mercury "shape coexistence" studies.
The experiment was performed at the CERN-ISOLDE isotope separator facility using in-source resonance ionization spectroscopy with unprecedented sensitivity for the study of the isotope shift and the hyperfine structure of radiogenic mercury isotopes. To this end, the 254 nm first-step transition laser wavelength of the 3-step ionization scheme for Hg+ ion production was scanned. For the first time, the laser spectroscopy measurements were extended to four lighter mercury isotopes below 181Hg (177-180Hg) and laser spectra of 181-185Hg were remeasured. The measured hyperfine parameters gave access to the nuclear spins, the magnetic dipole and the electric quadrupole moments. The isotope shifts were measured relative to the reference isotope 198Hg. They were used to calculate the changes in mean-square charge radii with respect to N=126 along the isotopic chain 177-185Hg. The new experimental data confirm previous results and the extended results for 177-180Hg firmly prove that the shape staggering is a local phenomenon. They show that the odd-mass mercury isotopes return to sphericity at A=179 (N=99) and thus establish 181Hg as the shape-staggering endpoint.
In order to mathematically describe the energy levels of the nucleons in the context of the nuclear shell model, the
many-particle system is separated into an inert nucleus with closed shells and a valence space. While light nuclei
can be calculated with conventional configuration interaction calculations for protons and neutrons, the calculation of heavy
nuclei requires the application of advanced computational methods. Thus, in order to theoretically study the unique shape staggering
in the mercury isotopes, the researchers exploited recent advances in computational physics. They performed Monte Carlo Shell
Model (MCSM) calculations incorporating the largest valence space ever used. The calculations were performed for the ground and the
lowest excited states in 177-186Hg. The MCSM results are in remarkable agreement with the experimental observations. They reveal the
underlying microscopic origin of the shape staggering between N=101 and N=105 as an abrupt and significant reconfiguration of the
the proton 1h9/2 and neutron 1i13/2 orbital occupancies.
This new insight describes the duality of single-particle and collective degrees of freedom in atomic nuclei and thus provides a deeper understanding of the structure of atomic nuclei in general.
Please read more in the Nature Physics article ... >
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.
Please read more in the article ... >