Nuclear Structure and Dynamics

The shape of an atomic nucleus is a result of a delicate interplay between macroscopic, liquid drop-like and microscopic shell structure effects. Nuclei with a closed shell configuration are spherical in their ground states, but away from magic numbers deformed ground states are observed. Small changes in the nucleon number can lead to rapid changes in deformation and states of different deformation can coexist at close excitation energies. In the first ISAC experiment with a post-accelerated heavy beam, recently published in Physics Letters B, the shape coexistence in ⁹⁶Sr was studio with TIGRESS and SHARC by means of the d(⁹⁵Sr,p) transfer reaction. These results suggest coexistence of three different configurations in ⁹⁶Sr and strong shape mixing of two excited 0⁺ states.  

Virtually contamination-free radioactive ion beams can now be provided at ISAC from a new ion-guide laser ion source (IG-LIS) [1]. This IG-LIS allows for experiments on isotopes that for decades have been overwhelmed by contamination from surface-ionized isobars. TRILIS now routinely provides isotopes from 37 different elements. Laser ionization schemes for an additional 24 elements are ready for off-line testing. TRILIS also supports an in-source laser spectroscopy program that investigates fundamental properties of the rarest isotopes such as atomic energy levels and elemental ionization potentials have been determined for the first time [2] or improved significantly [3].

A better view of the strong force: An IRIS experiment discovered that using rare isotopes to scatter protons can reveal subtle, new characteristics of the nuclear strong force which binds protons and neutrons, the building blocks of all matter. The strong force appeared well understood for explaining simple nuclei, such as hydrogen isotopes, but its extension to complex, many body systems has exposed important gaps. Theorists have proposed new models, but many strong force characteristics in these models can only be constrained with experiments. As reported in Physical Review Letters (2017), using the rare isotope carbon-10 (¹⁰C), IRIS's researchers showed that the intensity distribution of scattered protons by rare isotope is highly sensitive to different theoretical models of the strong force, providing a key new way to constrain them.  

Extending first principles of nuclear structure to all open-shell nuclei: The breadth of first-principles nuclear structure calculations in medium- and heavy-mass nuclei has largely been limited to closed-shell and neighboring nuclei or spherical even-even systems. As reported in Physical Review Letters (2017), TRIUMF nuclear theorists developed a new approach for calculating virtually any property of the atomic nucleus. It generalizes the ideas of the nuclear shell model to capture the effects of three-nucleon forces among valence nucleons with a valence-space Hamiltonian specifically targeted to each nucleus of interest. Predicted ground-state energies from carbon through nickel agree with results of other large-space ab initio methods, generally to the 1% level. This approach then effectively extends the reach of ab initio nuclear structure calculations to essentially all medium- and many heavy-mass nuclei.    

Understanding the phenomenon of parity inversion in beryllium-11: It has been known since 1960s that the spectrum of beryllium-11 (¹¹Be) has peculiar features, namely, its weakly bound ground state has positive parity contrary to the standard shell model picture. Yet, a first-principles explanation of this phenomenon has been lacking. As reported in Physical Review Letters (2016), TRIUMF nuclear theorists investigated this nucleus ab initio and demonstrated that the inclusion of continuum effects is crucial for a description of the ¹¹Be system. The results showed that the spectrum is extremely sensitive to the details of the nuclear two- and three-nucleon interactions and constitutes an important benchmark for future forces. In particular, the parity inversion of the bound states could be achieved only by a nuclear force that provides accurate predictions of nuclear radii and matter saturation properties.    

Unified ab initio approach to bound and unbound states: Theoretical understanding of weakly bound and unbound atomic nuclei produced and investigated at TRIUMF and other rare isotope facilities requires quantum mechanical description that includes continuum effects, in other words, the nuclear bound and unbound states must be treated on the same footing. As reported in Physical Review Letters C (2013), TRIUMF nuclear theorists achieved such a description by introducing a novel ab initio approach called no-core shell model with continuum capable of predicting properties of exotic nuclei from basic interactions between nucleons. As the first demonstration of this approach we calculated the properties of resonances of the unbound exotic ⁷He nucleus that was subject of several experimental investigations contradicting each other especially in properties of a low-lying ½- resonance. Our results clearly discriminated among three experiments agreeing with only one of them.       

Neutron-skin as a portal to neutron star properties: With the new era opened up by the LIGO and VIRGO observation of neutron-star mergers, multi-messenger astronomy will provide us with new ways to constrain the equation of states of neutron-rich matter. Stronger constraints will be obtained by combining such future data with observations on finite nuclei. Indeed, neutron-rich nuclei provide a portal to study neutron-rich matter, in that they form a neutron-skin around their surface which is directly related to the equation of state of nuclear matter. As reported in Nature (2016), TRIUMF theorists and international collaborators provided the first ab initio computation of calcium-48 (⁴⁸Ca), a nucleus with 20 protons and 28 neutrons. It was predicted that a neutron-skin is formed, though much smaller than previously thought, calling for new experimental investigations.  

Measurement of the most exotic neutron emitters at BRIKEN: The BRIKEN (Beta-delayed neutron measurements at RIKEN for nuclear structure, astrophysics, and applications) project started in 2016 at the RIKEN Nishina Center in Japan. As reported in the Journal of Instrumentation (2017) the ambitious goal of the collaboration is to design the most efficient neutron detector array for the measurement of the most exotic nuclei that can be produced today. With TRIUMF research collaboration, so far 268 nuclei have been measured, and for 180 of them the neutron branching ratio and for 60 the decay half-life has been measured for the first time. The neutron-branching ratio of the doubly-magic isotope nickel-78 has been measured for the first time, and will help to pinpoint theoretical predictions of neutron-magic nuclei.

Role of the continuum in Beryllium-11: The exotic nucleus beryllium-11 (¹¹Be) is a one-neutron halo nucleus, one in which the last proton or neutron appears to be in a large, extended orbit around an otherwise normal core. The extent to which ¹¹Be truly behaves as a lone neutron in a large orbit around a ¹⁰Be core has been the subject of two important TIGRESS experiments, both of which employed scattering of ¹¹Be off of heavy metal thin foil targets. The first, also using TRIUMF's Bambino, as measured the ratio of elastic scattering to Coulomb excitation, the process in which energy is transferred to a nucleus from the electric field of another, and (in most cases) re-emitted as a gamma ray. As reported in Physical Review Letters (2017), this high-precision measurement revealed the influence of coupling to the continuum, the role of virtual states corresponding to unbound, free neutrons interacting with ¹⁰Be. A second experiment with TIGRESS, published in Physics Letters B (2014), also identified breakup reactions, those in which enough energy is transferred to break ¹¹Be into ¹⁰Be and a free neutron, a “continuum” state.  The first measurement was accurate enough to validate a first-principles calculation of the gamma-decay rate, which revealed the influence of the coupling of virtual, continuum states to the overall structure of the bound states of ¹¹Be.  The second showed that the overall reaction dynamics depended not just on the continuum but also on highly excited states in the ¹⁰Be core itself.  

How magic are the magic numbers?: Tracking single-particle levels in sodium-26: The standard shell model explains tightly bound nuclei in terms of magic numbers associated with large energy gaps between quantum mechanical single-particle levels. These magic numbers are well understood in nearly stable nuclei, but the magic numbers change in nuclei with a large neutron excess. As published in Physics Letters B (2014), a TIGRESS-SHARC experiment measured reactions of radioactive sodium-25 (²⁵Na) beams on targets containing deuterium (one proton, one neutron). In particular, reactions where one neutron was taken out of the deuterium, measured the single-particle wave function composition of ²⁶Na. The results showed that the neutron single-particle levels are already starting to be squeezed together by a complicated feature of the neutron-proton interaction, an effect which ultimately leads to the breakdown of the neutron magic number 20 in the so-called “island of inversion” around magnesium-32 (³²Mg).

First measurement and ab initio calculation of rare excited nucleus' energy loss Using GRIFFIN, researchers confirmed the existence of a very rare case of energy loss from excited scandium-50 (⁵⁰Sc) nuclei and the TRIUMF theory group produced the first ab initio calculation of this transition rate. Nuclei in hot excited states become more stable by emitting radiation in the form of gamma (γ) rays, high energy photons, that carry away both energy and angular momentum. Usually, the gamma rays carry away one or two units of angular momentum and do not change the parity. As reported in Physical Review C (2017), scientists used the GRIFFIN spectrometer to identify the angular momentum of states in ⁵⁰Sc using γ-γ angular correlations. The existence was of a transition magnetic octupole was confirmed which carries away three units of angular momentum at once. This decay is so rare that the parent state lives for a full half a second instead of the typical one- trillionth of a second.    

The Case of the Missing Neutrinos: After 15 years of solar-neutrino measurements, 13% of the theoretically expected flux, or number, of neutrinos is unobserved. This is leading physicists to explore a variety of possible reasons, from the underlying nuclear physics to detector design. One proposed reason is the energetic cost of the detector material to capture a neutrino. To explore this, TITAN deployed its high-accuracy, high-precision Penning trap, the only one in the world coupled to a charge breeder. The charge breeder's removal of electrons boosted the precision of the measurements with gallium and germanium isotopes and allowed for a novel radioactive-beam purification. As reported in Physical Letters B (2013), TITAN measurements validate the final piece of the nuclear physics underpinning the predicted neutrino flux, and thus the cause of the missing neutrinos remains an open case.

Mass cartography of the island of inversion points to strong correlation energy: Analogous to electron shells in chemistry, neutrons and protons occupy similar, exceptionally stable configurations, which are seen as sharp ridges in mass cartography. As the ratio of protons to neutrons changes, this stability can disappear, for example around sodium-31 (³¹Na). The neighbourhood is difficult to examine due to low production rates and half-lives, too short for a typical Penning-trap mass spectrometer. TITAN, however, routinely measures isotopes with half-lives below 50 ms, or thousands of a second. TITAN's ongoing survey reveals a singularity: The energy, or mass cost, of two neutrons is higher for magnesium-33 (³³Mg) than for aluminum-34 (³⁴Al). As reported in Physical Review C (2015) investigating with premier shell-model calculations points to gains in correlation energy as the cause.    

Isomeric states in light francium nuclei: Francium is the heaviest alkali element. In addition to its simple atomic structure, it also possesses a fairly simple nuclear structure based on what has been observed to be an inert lead core with 5 additional protons. This combination makes francium one of the leading candidates upon which to perform high precision experiments to test both nuclear and atomic theories as well as to perform fundamental tests of the standard model. A precursory experiment to investigate the nuclear structure of very light francium isotopes confirmed for the first time that several isotopes contain long-lived isomeric states. The nuclear structure of these states has been determined via laser spectroscopy, providing invaluable input and tests of both nuclear and atomic theories.    

Lithium moments: ¹¹Li is one of the most extreme cases of nuclear structure that can be produced at ISAC. With a nuclear containing 8 neutrons and only 3 protons, it has long been known that the final 2 neutrons form a halo outside of a nuclear core. A collaboration between nuclear and condensed matter scientists at TRIUMF has developed a unique method with which to probe the distribution of charge within the nucleus with hitherto unachievable precision. This measurement, combining nuclear detection methods within a zero magnetic field nuclear quadrupole resonance spectrometer, showed that the 2 outer neutrons have very little influence on the shape of the nucleus’ core, instead causing it to oscillate around a common centre of mass.  

Seeing francium nuclei as tiny magnets: The ratio of the hyperfine splittings of s and p states is not constant across isotopes due to the isotope-dependent distribution of nuclear magnetization, a phenomenon called the hyperfine anomaly. By carrying out measurements of the hyperfine splitting of the excited electronic 7p_1/2 state at the 100-ppm level, and comparing to previously known ground state 7s splittings, the hyperfine anomaly in six isotopes of francium (Fr) was experimentally determined. As reported in Physical Review Letters (2015) the measured magnetic distributions behave regularly from ²¹³Fr through ²⁰⁷Fr, but ²⁰⁶Fr stops behaving like a spherical nucleus with valence nucleons. The results are valuable input for future calculations of both the anapole moments and the neutron radii needed for small corrections to Francium Trapping Facility measurements of atomic-parity violation for ^207−213Fr.  

Electron jumps reveal subtle changes in shape of francium nuclei: As part of the commissioning process for the Francium Trapping Facility, precise measurements were carried out on the isotopic dependence of the 7s − 7p_1/2 electronic transition in a chain of different francium isotopes. As reported in Physical Review A (2014) these data were combined with previously measured isotope shifts in the 7s - 7p_3/2 transition. Isotope shifts are a sensitive measure of changes in the nuclear charge radius, or size of the nucleus, between isotopes of the same atom. Comparison of the two data sets provides insights into the change of electron behaviour as the number of neutrons in the nucleus varies. The results provide a sensitive gauge of the ability of the atomic many-body calculation to describe the francium atom at a level necessary for the interpretation of the Facility's future atomic-parity violation measurements with francium.    

A new tool to explore exotic nuclear structure: Forty years of after the discovery of magnesium- 31 (³¹Mg), TRIUMF's ability to produce the world's highest spin-polarization for rare nuclei has successfully enabled Japanese and Canadian researchers to clarify this rare isotope's exotic structure. High spin polarization makes it possible to efficiently measure a rare nuclei's basic, but hard-to-know, quantum numbers–the spins and parities of the ground and excited states of a resulting nucleus from the b-decay of the polarized nucleus. As reported in Physics Letters B (2017), one of the highlights from this new method is the finding of “shape coexistence” in ³¹Mg. Here, states with various types of shape coexist in a narrow and low excitation energy region. Shape coexistence can be seen as a result of subtle competition between a persistent spherical shape due to the neutron magic number 20, and prevalence of deformation due to nuclear correlations.

An isomeric state in rubidium-98: Several elements around rubidium undergo a dramatic change in the nuclear shape when they cross 60 neutrons within the nucleus. ⁹⁸RB is the first isotope in the Rb chain above this number and had been postulated to contain a long-lived isomeric state. This was confirmed for the first time using laser spectroscopy measurements at ISAC, where not only was the state confirmed but also the shape, size and spin of both nuclear states were determined. Using this information it could be shown that both states were built on the same on the same basic structure and the isomer was not, as was previously thought, based on the shape of the light nuclei.    

TITAN reveals shell model breakdown at the extreme: Certain combinations of protons and neutrons form exceptionally stable nuclei. While these closed-shell configurations are well understood in stable nuclei, they change in exotic nuclei. Previous mass determinations with TITAN found a closed shell for calcium (Ca) with 32 neutrons. Now, as reported in Physical Review Letters (2018), TITAN’s measurements of neighbouring titanium isotopes shows that the shell weakens more quickly than predicted by state-of-the-art nuclear theory. The results are also noteworthy as TITAN’s first measurements with its Multi-Reflection Time-Of-Flight mass separator (MR-TOF). The MR-TOF has a remarkable sensitivity, able to make precise measurements with just a single radioactive nucleus.      

Clarifying a key step in the origin of the elements: As reported in Physical Review C (2016) researchers using GRIFFIN have produced the highest-precision measurement ever of the half-life of cadmium-130  (¹³⁰Cd), a rare isotope that's a cornerstone for understanding cosmic element formation. Astrophysical observations are providing mounting evidence that heavy elements are forged in the merger of neutron stars. However, to understand and accurately simulate this element formation process (r-process), it's necessary to experimentally characterize the key rare isotopes involved. This is especially the case for the half-lives of isotopes with masses of about 130 since theoretical models have been tuned to reproduce the half-life of ¹³⁰Cd and then predict half-lives in the entire region. Thus, scientists used GRIFFIN to produce a ¹³⁰Cd half-life measurement three-times more precise than the previously adopted world average, a result which will help astrophysicists more clearly see our stardust origins.    

Testing modern nuclear structure theories: As published in Physics Letters B (2018), this recent TIGRESS result measured the gamma-ray excitation transition rate in magnesium-22 (²²Mg) and its mirror sodium-22 (²²Ne). Mirror nuclei are pairs of nuclei where there are as many protons in one as neutrons in the other and vice versa. Based on “isospin symmetry”, the relative transition rates in mirror pairs ought to be well understood. However, in selected nuclei around atomic mass 21 to 24, there appears to be a much higher transition rate in the proton-rich pair compared to the neutron-rich mirror partner. This discrepancy cannot be explained within the phenomenological shell model, the standard model for nuclear structure, but for gamma-ray transition rates, it invokes an empirical “effective charge” parameter. The ²²Mg experiment was two-fold: 1) measure the transition rate in ²²Mg with high enough precision to determine if the anomalous proton-rich transition rate was an anomaly in selected nuclei or a trend across the whole mass region; and, 2) compare results to modern calculations that do not use effective charges but that calculate transition rates from first principles. The results clearly showed that, indeed, ²²Mg’s transition rate is anomalously high compared to ²²Ne, and furthermore, the first principles also were also unable to reproduce it.        

A clearer view of the structure of exotic lithium: The study of the transfer of a single neutron during a nuclear reaction from the target to a rare isotope from a beam provides crucial information on the structure of the nucleus created in the reaction. While most of the nuclei studied in this way are bound, some, such as lithium-10 (¹⁰Li), are not; when formed via the d(⁹Li,p) reaction, ¹⁰Li breaks up promptly into ⁹Li and a neutron. As reported in Physical Review Letters (2017), detecting the protons and ⁹Li breakup products of this reaction in coincidence, TUDA experimenters have provided important new information on the much debated structure of ¹⁰Li.  

EMMA set to help reveal the hearts of stars and atoms: In 2018, the coupling of the EMMA and TIGRESS spectrometers will mark the beginning of EMMA’s scientific program to probe the deep nature of nuclear reactions in stars and the subtleties of extreme nuclear structure. EMMA's arrival is the culmination of a multi-year series of commissioning steps successfully demonstrating the spectrometer’s enormous potential for TRIUMF's rare isotope beam program. In December 2016, commissioning of the spectrometer as a whole began with a test beam of argon-36 (³⁶Ar) bombarding a very thick gold (Au) foil. The spectrometer was initially tuned for elastically scattered Ar ions and its first mass/charge spectrum was collected. As shown in figure A, both the 13⁺ and 14⁺ charge states were detected simultaneously, the dispersion–the key ability to distinguish between states–agreed exactly with calculations. In September 2017 an argon-40 (⁴⁰Ar) beam bombarded a very thin Au target and elastically back-scattered Au ions were detected in two charge states simultaneously and used to measure the energy, angular, and mass/charge acceptances; substantially improved resolving power was observed. In November 2017, EMMA accepted its first radioactive beam, sodium-24 (²⁴Na) which was used to induce fusion evaporation reactions on a copper target. Various fusion products with atomic masses from 80 to 85 were clearly detected and resolved in a single spectrometer setting. EMMA will use of both the light, neutron-deficient beams from ISAC and the future heavy, neutron-rich beams from ARIEL to explore radiative capture and transfer reactions that are central to astrophysical research, and fusion reactions important to the study of nuclear structure.

Rare isotope sheds light on how dead stars re-ignite: Novae are stellar element-making explosions caused when a white dwarf, the carbon-cinder of a once giant star, accretes hydrogen-rich material onto its surface from a companion star. A key to help astrophysicists better understand novae is through determining the rates of reactions that create and destroy the key rare isotopes they're observed to produce, including sodium-22 (²²Na). As reported in Physical Review C (2016) scientists used DSL to determine, for the first time using the Doppler-shift attenuation method, the lifetimes of several energetic states magnesium-23 (²³Mg) the rare isotope that dominates the destruction of ²²Na. The researchers' more precise lifetime measurements of related states help explain the structure and behaviour of these rare isotopes and thus the underlying nuclear physics driving novae.  

A new path to element formation: IRIS’ first results give astrophysicists and nuclear physicists a deeper understanding of the nuclear states and pathways involved in element formation. As reported in Physical Review Letters (2015), the results provide the experimental evidence for a new kind of nuclear excitation, soft dipole resonance. IRIS researchers identified this resonance in neutron-rich lithium-11 (¹¹Li), the heaviest bound lithium isotope, with three protons and eight neutrons, two of which orbit, barely held, in a halo, far from the nuclear core. Oscillation of the halo neutrons, the experiment revealed, leads to an extremely brief, quasi-bound nuclear resonance state, significantly changing the potential for neutron capture, as occurs in stars during element formation. The results confirm theoretical predictions and provide an important path for developing new nuclear models to predict the properties of neutron-rich isotopes.                                

Tin-100: A gateway to ab initio calculations in heavy nuclei: For many years Tin-100 (¹⁰⁰Sn) has stood as a distant milestone of first-principles calculations of atomic nuclei, a gateway to modeling nuclei in the heavy-mass region above atomic mass 100. ¹⁰⁰Sn is the heaviest self-conjugate nucleus, it exhibits the largest known β-decay strength, and is close to the proton dripline. As reported in Physical Review Letters (2017), TRIUMF nuclear theorists linked the structure of nuclei around ¹⁰⁰Sn, the heaviest doubly magic nucleus with equal neutron and proton numbers, to nucleon-nucleon and three-nucleon forces constrained only by data of few-nucleon systems. The results provide the first ab initio prediction that ¹⁰⁰Sn is indeed doubly magic, paving the way for ab initio calculations to the heaviest nuclei.            

TRIUMF helps provide IAEA with evaluation of beta-delayed neutron emitters In a coordinated research project under the auspices of the International Atomic Energy Agency (IAEA), Canadian researchers from TRIUMF and McMaster University have evaluated all existing beta-delayed neutron emitters and provided recommended values for their decay half-lives and neutron-branching ratios. These new recommendations, released as an IAEA report, together with the new data from ongoing experiments, will be integral part of a newly created database. Among a variety of applications, the data will be a key input in astrophysical studies for a better understanding of the heavy element production in explosive stellar events including core-collapse supernovae and binary neutron star mergers. Such a reliable and regularly updated database is essential for a better understanding of these important physical properties, especially for benchmarking theoretical predictions of yet unmeasured nuclei.