\section{The structure of nuclear matter}\label{sec:nucstruc}% Adam

\subsection{Overview}

The nucleus is one of the most challenging quantum many-body systems to describe. This is largely due to the fact that the primary modes of excitation (single-particle excitation, spherical vibrations, rotations of a deformed shape) all act on a very similar energy scale, meaning that all are observed in nature and become mixed together. The key to describing the diverse features of nuclear structure is to develop a robust and complete understanding of the nuclear force which acts between the constituent nucleons. This is a major challenge because of the enormous computational power required to describe the behaviour of tens or hundreds of nucleons, and the many contributions to the nuclear force which subtly change as a function of neutron and proton number, neutron-proton ratio, and excitation energy. Nonetheless, tremendous progress has been made in recent years in both developing the theoretical tools and frameworks which can make this link from QCD to nuclei, and in the acquirement of pertinent nuclear data that can challenge and drive forward the development of these theoretical calculations. Canadian researchers are at the forefront of this field of research and the many contributions and activities are described in this Chapter. With continued support and strategic investment, Canada is well positioned to make key contributions to the field of nuclear structure research in the coming years.

\subsection{The Canadian program}

\subsubsection{Canadian effort in nuclear structure theory} \label{sec:nucstruc:theory}

Canada has emerged as a world-leading effort over the past 10-15 years in the field developing theoretical descriptions of atomic nuclei from first principles. The goal of these initiatives is to develop a predictive {\it ab-initio} theory of nuclear structure and nuclear reactions for light and medium mass nuclei. Such a theory is needed for understanding of exotic nuclei investigated at rare isotope facilities like ISAC and ARIEL at TRIUMF, for understanding of nuclear reactions important for astrophysics, for understanding of fusion reactions important for the future energy generation as well as for the testing of fundamental symmetries in nuclear processes. At the same time, it provides a feedback on the quality of inter-nucleon interactions used as input to these calculations and ultimately helps to improve our knowledge of the nucleon-nucleon interaction, and in particular of the still-not-completely-understood three-nucleon interaction.

The theoretical efforts in Canada for nuclear structure are mainly focused in the two theory groups located at TRIUMF and the University of Guelph. These groups have been developing the capability to theoretically describe light- and medium-mass nuclei as systems of nucleons interacting by forces rooted in the fundamental theory of strong interactions, QCD. Using a low-energy expansion of QCD, namely chiral effective field theory ($\chi$EFT), one can derive forces among nucleons and their interactions with external probes in a consistent way. The $\chi$EFT interactions are utilized and different frameworks to perform calculations of structure effects. Studies in light- and medium-mass nuclei are crucial to test such a theory and allow cross-fertilization with experiments performed both at TRIUMF and elsewhere. Indeed, an abundance of close collaborations exist between theoretical and experimental nuclear physicists which are essential in driving progress and discoveries. Detailed examples of the specific efforts being pursued by Canadian nuclear structure theorists are provided in Section \ref{sec:Theory} with a few of highlights given here.

The theory group at the University of Guelph employs several {\it ab-initio} many-body methods, most of which can be described as Quantum Monte Carlo (QMC) simulations to produce improved formulations of nuclear forces to understand the physics of neutron star crusts and cores, neutron-rich nuclei, as well as phenomena at the interface of nuclear physics and ultracold atoms. These are non-perturbative simulations which have an excellent track record in quantum chemistry, atomic physics, and solid-state theory. A main strength of this approach is the ability to work at interfaces, whether between different theories ({\it ab-initio} vs phenomenology) or between different physical systems (neutron stars vs cold atoms). Some recent highlights have used local chiral EFT in light nuclei and neutron matter\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevLett.116.062501}{J. Lynn {\it et al}, Phys. Rev. Lett. 116, 062501 (2016)}} and made novel developments in first-principles or mean-field techniques\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.99.014321}{E. Rrapaj {\it et al}, Phys. Rev. C 99, 014321 (2019)}}.

Another theoretical framework being used is the no-core shell model with continuum (NCSMC)\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevLett.110.022505}{S. Baroni, P. Navratil, and S. Quaglioni, Phys. Rev. Lett. 110, 022505 (2013)}}$^,$\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.87.034326}{S. Baroni, P. Navratil, and S. Quaglioni, Phys. Rev. C 87, 034326 (2013)}}$^,$\footnote{\href{https://iopscience.iop.org/article/10.1088/0031-8949/91/5/053002}{P. Navratil {\it et al.}, Physica Scripta 91, 053002 (2016)}}. This approach describes the reacting system using a basis expansion with two key components: one describing all nucleons close together, forming the composite nucleus, and a second one describing the separated clusters. The former part utilizes a square-integrable basis expansion treating all nucleons on the same footing. The latter part factorizes the wave function into products of cluster components and their relative motion with proper bound-state or scattering boundary conditions. The chiral NN and 3N forces served as input for the NCSMC calculations. Some of the calculations, when appropriate, are done with the square-integrable basis expansion part only, i.e., within the no-core shell model (NCSM)\footnote{\href{https://doi.org/10.1016/j.ppnp.2012.10.003}{B. R. Barrett, P. Navratil, and J. P. Vary, Prog. Part. Nucl. Phys. 69, 131 (2013)}}. A recent highlight using this approach is the description of the $^{10}$C nucleus scattering on the proton\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevLett.118.262502}{A. Kumar {\it et al.}, Phys. Rev. Lett. 118, 262502 (2017); Editors Suggestions and Viewpoint in Physics.}} measured at TRIUMF IRIS facility which is discussed in Section~\ref{sec:intro_ns}.

The VS-IMSRG is another framework which has been developed with strong Canadian leadership. This allows us to calculate properties of light to heavy nuclei starting from only input nuclear forces and electroweak currents. A tremendous level of progress has been made in the past few years in the development of the valence-space VS-IMSRG into a world-leading and far-reaching {\it ab-initio} tool. The first major breakthrough allowed Researchers to capture the bulk effects of 3N forces between valence nucleons, and it was found that ground-state energies calculated with the VS-IMSRG from carbon to nickel agree with results of large-space {\it ab-initio} methods, generally to the 1\% level or better, effectively extending the reach of {\it ab-initio} nuclear structure calculations to essentially all light- and medium- mass nuclei. Indeed it has now been shown with new NN+3N forces which reproduce saturation in infinite matter, that results agree well with experiment in nuclei as heavy as the Sn isotopes, published as a Phys. Rev. Lett. Editor's Suggestion\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevLett.120.152503}{T.D. Morris {\it et al.}, Phys. Rev. Lett. 120, 152503 (2018); Editors Suggestion.}}. This new approach has been used to predict both the proton and neutron driplines which define the limits of existence up to the nickel isotopes (See Section \ref{sec:Theory}). Its success in reproducing experimental data has resulted in a large number of joint theoretical and experimental studies in the past few years.

\begin{figure}[ht!]
\centering
  \includegraphics[width=0.75\textwidth]{Figs/GT-quenching.pdf}
  \caption{Comparison of experimental and theoretical Gamow-Teller matrix elements for medium-mass nuclei in the $sd$-shell (top panel) and lower $pf$-shell (bottom panel). The theoretical results were obtained using phenomenological shell-model interactions with an unquenched standard Gamow-Teller operator (orange squares); and using the valence-space IMSRG approach with the NN-N$^4$LO+3N$_{\rm lnl}$ interaction and consistently evolved Gamow-Teller operator plus 2BC (green diamonds). The linear fits show the resulting quenching factor $q$ given in the panels, and shaded bands [P.~Gysbers {\it et al.} Nat. Phys. 15, 428 (2019)].}
  \label{fig:GT-quenching}
\end{figure}

Together, these two theoretical approaches have also been used to address the 50-year-old puzzle of why observed $\beta$-decay rates in nuclei are found to be systematically smaller than for free neutrons. The fundamental coupling constant is quenched by a factor of about 0.75 and this was not understood. As can be seen in Figure \ref{fig:GT-quenching}, it has now been demonstrated with these {\it ab-initio} theories that this quenching arises to a large extent from the coupling of the weak force to two nucleons as well as from strong correlations in the nucleus.

A great opportunity exists to further strengthen and grow these programs with strategic investment into HQP who can accelerate the efforts of these recognized world leaders at the forefront of an exciting and fast-moving discipline which is symbiotic with Canadian experimental efforts in nuclear physics.

\subsubsection{Studies of neutron halos and skins}

Halo nuclei probe some of the most urgent questions in nuclear physics. The classical example of a halo nucleus is $^{11}$Li where the two neutrons nearest the Fermi surface are weakly bound, so that their spatial wave functions are diffuse compared to stable nuclei. These properties are confirmed by a very small two-neutron separation energy and a large inclusive reaction cross section. Many of these details were revealed by experiments led by Canadian researchers and studying the details of halo nuclei remains an insightful pursuit with new experimental results continuing to challenge the most sophisticated {\it ab-initio} theories.

The weakly bound exotic $^{11}$Be nucleus, famous for its ground-state parity inversion and distinct $n+^{10}$Be halo structure, was investigated from first principles using chiral two- and three-nucleon forces within the no-core shell model with continuum framework\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevLett.117.242501}{A. Calci {\it et al.}, Phys. Rev. Lett. 117, 242501 (2016)}}. The explicit treatment of continuum effects was found to be indispensable and revealed that the details of the $^{11}$Be spectrum is sensitive to the specifics of the three-nucleon force. It was found that only certain chiral interactions are capable of reproducing the parity inversion making this a valuable benchmark for them. With such interactions, the extremely large $E1$ transition between the bound states is reproduced. These theoretical calculations predict new features in the spectrum and have highlighted experimental short-comings in our understanding which prompts further studies.

% Figure 
\begin{figure}[ht!]
\centering
\includegraphics[width=0.8\columnwidth]{Figs/29F-Halo.pdf}
\caption{\label{29F-Halo}
%
(a) Isotope identification showing $^{29}$F events separated using the BigRIPS fragments separator at RIKEN. (b) Red symbols show measured reaction cross sections of $^{27;29}$F. (c) Nuclear chart showing the location of $^{29}$F (red square) and a schematic concept of its halo structure discovered from the measurement.}
\end{figure}

Recent studies at RIKEN-RIBF in Japan have unveiled the heaviest two-neutron halo observed till date in the last bound $N$ = 20 isotone\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevLett.124.222504}{J.S. Bagchi {\it et al.}, Phys. Rev. Lett. 124, 222504 (2020)}}, see Figure \ref{29F-Halo}. It is the first Borromean halo observed in the proton sd-shell. The halo is formed because of the $2p_{3/2}$ orbital unexpectedly becoming lower in energy thereby intruding into the $N$ = 20 shell gap and hence making it disappear. The results are explained by state-of-the-art shell model calculations. {\it Ab-initio} predictions in a coupled-cluster framework are challenged in explaining the halo in $^{29}$F pointing to our still limited knowledge on the nuclear force from first principles.

There are also ongoing efforts studying the $^8$He and $^{11}$Li systems with various ISAC experiments. It was found in a one-neutron-removal measurement using the IRIS facility that $^{10}$Li resonances play an important role in the halo structure of $^{11}$Li\footnote{\href{https://doi.org/10.1016/j.physletb.2016.02.060}{A. Sanetullaev {\it et al.}, Phys. Lett. B 755, 481 (2016)}}. Proton inelastic scattering of $^{11}$Li with IRIS also revealed a large enhancement of soft dipole strength originating from the halo\footnote{\href{https://doi.org/10.1016/j.physletb.2017.09.079}{J. Tanaka {\it et al.}, Phys. Lett. B 774, 268 (2017)}}. These examples highlight the importance of studying a system using a variety of methods or reactions as each one probes a different aspect of the structural phenomenon. TRIUMF-ISAC remains the source for some of the highest intensities of these light beams anywhere in the world so is the venue of choice to perform such research.

\subsubsection{Tests of {\it ab-initio} theories in light- to medium-mass systems}

Understanding the strong nuclear force binding the protons and neutrons to form the wide variety of complex nuclei in the Universe has been a century long challenge. The shell model is, in many ways, the standard model of low-energy nuclear structure.  Phenomenological shell models with valence particles (or holes) coupled to an otherwise inert core have been successful at explaining a wide range of nuclear observables such as ground-state spins, parities, binding energies, and charge radii, and excited-state properties such as excitation energies. The desire is to obtain these descriptions from first principles, rather than using phenomenology. The chiral effective field theory enables a link for a description of the nuclear force connected with the theory of quantum chromodynamics but requires certain parameters that are not uniquely defined. Strategic measurements of certain nuclear properties are necessary in order to refine the theory. 

From a measurement of proton elastic scattering on $^{10}$C at TRIUMF using IRIS and {\it ab-initio} nuclear reaction calculations, it was found that the shape and magnitude of the measured differential cross section is strongly sensitive to the nuclear force prescription (Fig. \ref{fig:IRIS-10C-Highlight})\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevLett.118.262502}{A. Kumar {\it et al.}, Phys. Rev. Lett. 118, 262502 (2017); Editors Suggestions and Viewpoint in Physics.}}

Electromagnetic transition rates have been a particular challenge for both phenomenological and {\it ab-initio} shell models, and the complex interaction between valence and core nucleons was traditionally subsumed in highly phenomenological effective electric charges.  Over the past decade, modern treatments of the nucleon-nucleon interaction, many-body techniques, and theoretical uncertainties have offered a means to eliminate the phenomenology of effective charges and provide testable predictions, in many cases with an accuracy exceeding the available measurements.  The Canadian $\gamma$-ray spectroscopy group has focused on measurements of low-lying $B(E2)$ reduced electric quadrupole transition strengths in mirror nuclei in the the $sd$ shell using Coulomb excitation techniques.  In particular, our experiments have capitalized on a particular ISAC strength, production and delivery of intense post-accelerated beams of Mg isotopes.  Measurements on the mirror pairs $^{21}$Mg-$^{21}$F\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.99.051301}{P. Ruotsalainen {\it et al.}, Phys. Rev. C 99, 051301 (2019)}},  $^{22}$Mg-$^{22}$Ne\footnote{\href{https://doi.org/10.1016/j.physletb.2018.05.064}{J. Henderson et al., Phys. Lett. B 782, 468 (2018)}}, and $^{23}$Mg-$^{23}$Na\footnote{J. Henderson {\it et al.}, in preparation} have supported the No-Core Symplectic Shell Model, while the In-Medium Similarity Renormalization Group method was found to underpredict the average (isoscalar) $B(E2)$ strength in the pairs.

The excitation of the proton drip-line nucleus $^{20}$Mg was explored using deuteron inelastic scattering with the IRIS facility and provided the first observation of its lowest resonance state\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.99.021301}{J.S. Randhawa {\it et al.}, Phys. Rev. C 99, 021301(R) (2019)}}. This finding has challenged the existing {\it ab-initio} theory predictions opening new scope to constrain the nuclear force. It was also found that there is a large deformation from excitation to the first 2$^+$ state suggesting a possible weakening of the $N$ = 8 shell at the proton drip-line. During the 2022--2026 period it is planned to make a direct measurement of the lifetime of this sole excited state in the $^{20}$Mg nucleus using TIGRESS and TIP. 

The mass of neutron-deficient Mg isotopes, $^{27,28,29}$Mg were precisely measured with the TITAN system to examine the validity of the isobaric mass multiplet equation and compare to {\it ab-initio} calculations\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.96.034316}{M. Brodeur {\it et al.}, Phys. Rev. C 96, 034316 (2017)}}.

The first direct observation of a $\beta p^{+}$ decay in $^{11}$Be was performed using a radioactive beam of $^{11}$Be provided by TRIUMF-ISAC\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevLett.123.082501}{Y. Ayyad {\it et al.}, Phys. Rev. Lett. 123, 082501 (2019)}} in conjunction with a prototype active target time projection chamber (PAT-TPC)\footnote{\href{https://doi.org/10.1016/j.nima.2012.06.050}{D. Suzuki {\it et al.}, Nucl. Instrum. Methods Phys. Res., Sect. A 691, 39 (2012)}}. 
The branching ratio for the $\beta  p^{+}$ channel was determined to be $1.3(3)\times10^{-5}$, in agreement with a previous indirect measurement. This experiment shows that this decay process is sequential and proceeds through a newly identified narrow resonance with a width of 12.5\,keV located at an energy of $11425 \pm 20$~keV. New theoretical calculations that include this resonance in $^{11}$B can only now reproduce the measured branching ratio which is orders of magnitude larger than previously thought.


\subsubsection{Evolution of nuclear shell structure}

In the last decade, a significant fraction of the research programs at radioactive ion beam facilities has been driven by the observation that the traditional nuclear shell gaps, or ``magic numbers'', are modified in light neutron-rich nuclei and new shell gaps such as $N$=16 and $N$=32 appear with large neutron excess\footnote{\href{https://iopscience.iop.org/article/10.1088/0031-8949/2013/T152/014007}{T. Otsuka, Phys. Scripta T152, 014007 (2013)}}. First indications of this evolution of nuclear shell structure came from anomalies in the masses of neutron-rich Na and Mg isotopes and subsequent data on excitation energies, transition strengths and spectroscopic factors have confirmed the picture of a weakening of the $N$=20 shell gap and the generation of a so-called ``island of inversion'' around $^{32}$Mg in which deformed configurations involving 2p-2h and 4p-4h excitations across the shell gap become the ground state. The evolution of the sub-shell gap at $N$=34 established in neutron-rich $^{54}$Ca\footnote{\href{https://doi.org/10.1038/nature12522}{D. Steppenbeck {\it et al.}, Nature 502, 207 (2013)}} remains the subject of intense study\footnote{\href{https://journals.jps.jp/doi/abs/10.7566/JPSCP.6.010007}{Y. Utsuno {\it et al.}, JPS Conf. Proc. 6, 010007 (2015)}}, while strong deformation of $^{64}$Cr has been interpreted in terms of the disappearance of the harmonic oscillator (sub-)shell gap at $N$ = 40 in neutron-rich nuclei\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.82.054301}{S.M. Lenzi {\it et al.}, Phys. Rev. C 82, 054301 (2010)}}. From the theoretical perspective, the microscopic origins of the evolution of shell structure in light and intermediate mass nuclei has been linked to shifts of the effective single-particle energies associated with the central, tensor, and three-nucleon (3$N$) components of the monopole interaction between valence nucleons e.g.\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevLett.104.012501}{T. Otsuka {\it et al.}, Phys. Rev. Lett. 104, 012501 (2010)}}$^,$\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.90.024312}{J.D. Holt {\it et al.}, Phys. Rev. C 90, 024312 (2014)}}, while modifications of the spin-orbit interaction, pairing correlations, and coupling to continuum states have all been discussed in the context of shell structure evolution in heavy nuclei approaching the neutron dripline\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.85.064329}{I. Hamamoto, Phys. Rev. C 85, 064329 (2012)}}.

Mass measurements often provide the first glimpses of changes to the expected shell-model orbitals, reflected in the binding energies along chains of isotopes. Indeed as the on-line commissioning experiment of the TITAN MR-TOF, mass measurements of neutron-rich titanium isotopes\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevLett.120.062503}{E. Leistenschneider {\it et al}, Phys. Rev. Lett. 120, 062503 (2018)}} illuminated the emergence of the a subshell closure at $N$=32 and benchmarked state-of-the-art calculations performed within the VS-IMSRG framework. Additional mass measurements in the neighbouring vanadium isotopes clearly showed the $N=32$ subshell closure is quenched with the addition of this extra proton\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.98.024310}{M. P. Reiter {\it et al}, Phys. Rev. C 98, 024310 (2018)}}. The VS-IMSRG calculations successfully describe the occurrence of the $N$=32 subshell closure, but are found to over-predict its strength and extent in the titanium and vanadium chains.

The state-of-the-art GRIFFIN and TIGRESS spectrometers, together with their auxiliary detection systems, provide ideal opportunities to gain new insights into the evolution of nuclear shell structure in light and medium mass nuclei. With the GRIFFIN spectrometer at ISAC-I, the evolution of shell structure in the island of inversion surrounding the neutron-rich $N$=20 nucleus $^{32}$Mg has been investigated through $\beta$ decay studies of $^{32}$Na (experiment S1507) and $^{32,33,34,35}$Mg (S1367). These experiments, which included high-efficiency $\gamma-\gamma$ angular correlation measurements to establish spin and parity assignments for excited states in the daughter nuclei, are currently in the analysis phase. Mass measurements in this region from the TITAN group revealed\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.92.061301}{A.A. Kwiatkowski {\it et al}, Phys. Rev. C 92, 061301 (2015)}}, and then confirmed\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.96.024325}{A.T. Gallant {\it et al}, Phys. Rev. C 96, 024325 (2017)}}, an unusual cross-over of the in the two-neutron separation energies of $^{33}$Mg and $^{34}$Al.

A high-statistics GRIFFIN data set for the $\beta$ decay of $^{47}$K studying hole states and the role of three nucleon forces in doubly-magic $^{48}$Ca has recently been submitted for publication\footnote{J.K. Smith, {\it et al.}, submitted to Phys. Rev. C (2020)}, while a detailed study with GRIFFIN of $^{46}$K $\beta$ decay to $^{46}$Ca was published in\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.100.054327}{J.L. Pore {\it et al.}, Phys. Rev. C 100, 054327 (2019)}}. The suggested sub-shell closure at $N=34$ in the neutron-rich Ca isotopes has recently been studied in experiment S1602 through $\beta$ decay studies of $^{52,53,54}$K $\rightarrow$ $^{52,53,54}$Ca with the DESCANT neutron detector array coupled with GRIFFIN to provide a high-efficiency $\beta$-delayed n-$\gamma$ coincidence detection capability. 

Complementary information on shell structure evolution is obtained from experiments with accelerated radioactive beams from ISAC-II, as demonstrated by the recent measurement of spectroscopic factors in the d($^{25}$Na, p$\gamma$) reaction with TIGRESS that revealed a reduction in the $N$=20 shell gap already in $^{26}$Na\footnote{\href{https://doi.org/10.1016/j.physletb.2016.05.093}{G.L. Wilson {\it et al.}, Phys. Lett. B 759, 417 (2016)}}. This program will be extended to the associated appearance of $N$=16 as a new magic number in neutron-rich nuclei through simultaneous spectroscopic factor and excited state lifetime measurements in $^{26}$Ne populated via the $^{25}$Ne(d,p)$^{26}$Ne reaction in high-priority TIGRESS experiment S1702.

Canadian Researchers have also led a complementary experiment IS651 at the new HIE-ISOLDE facility at CERN. A radioactive beam of $^{28}$Mg was scattered off a radioactive tritium target to populate states in $^{30}$Mg after two-neutron transfer. For the first time, the full HIE-ISOLDE beam energy of 9.5 AMeV was used for a transfer experiment with the MINIBALL $\gamma$ ray spectrometer. The high beam energy allowed a more straightforward interpretation of spectroscopic factors compared to previous transfer experiments performed at ISOLDE. As the two-neutron transfer into the intruder 2p$_{3/2}$ orbital is highly favoured, the experiment determined the amount of intruder configurations in the ground state and excited states in $^{30}$Mg. These results, currently under analysis, will determine whether the transition into the island of inversion is following the surprising recent predictions\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.95.021304}{N. Tsunoda {\it et al.}, Phys. Rev. C 95, 021304(R) (2017)}} of the EKK-theory. 

Opportunities at facilities employing high-energy fragmentation reactions to produce rare-isotope beams have also been utilized in the study of shell evolution. A recent example is the determination of the proton radii in neutron-rich N isotopes via charge changing cross section measurements at GSI in Germany\footnote{\href{https://doi.org/10.1016/j.physletb.2019.01.024}{S. Bagchi {\it et al.}, Phys. Lett. B 790, 251 (2019)}}. Contrary to the conventional expectation that radii increase with mass number ($A^{1/3}$), the proton radii show a decreasing trend exhibiting a local minimum at $^{21}$N. This signals a neutron sub-shell closure at $N$=14 because of which the $1d_{5/2}$ orbital is fully occupied. The attractive proton-neutron interaction between the $1d_{5/2}$ neutrons (with $j = l+1/2$) and the $1p_{1/2}$ protons ($j = l - 1/2$) is therefore strongest for $^{21}$N. This causes both the $1d_{5/2}$ neutron orbital and the $1p_{1/2}$ proton orbital to become more bound causing the decrease of the proton radius.

There has been a focused effort to explore the structure of isotopes around the doubly-magic $^{132}$Sn nucleus. These investigations have important implications for nuclear astrophysics in respect to the significance of these isotopes in the rapid neutron-capture ($r$) process. A better understanding of the nuclear structure in this region will strengthen theoretical calculations and predictions which will lead to a more precise modelling of the $r$ process. Mass measurements of the ground states and isomers in $^{125-127}$Cd isotopes\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.96.044323}{D. Lascar {\it et al.}, Phys. Rev. C 96, 044323 (2017)}} are reported from TITAN along with the $^{125-130}$In isotopes\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.97.024312}{C. Babcock {\it et al.}, Phys. Rev. C 97, 024312 (2018)}}. This is accompanied by detailed $\gamma$-ray spectroscopy using the GRIFFIN spectrometer. Results from are reported for the decay of beams of $^{129}$In\footnote{F.H. Garcia {\it et al.}, submitted to Phys. Rev. C (2020)}, $^{131}$In\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.99.045805}{R. Dunlop {\it et al.}, Phys. Rev. C 99, 045805 (2019)}} and $^{132}$In\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.102.024327}{K. Whitmore {\it et al.}, Phys. Rev. C 102, 024327 (2020)}} as well as the half-lives of $^{128-130}$Cd\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.93.062801}{R. Dunlop {\it et al.}, Phys. Rev. C 93, 062801(R) (2016)}}. These studies of the daughter $^{129-132}$Sn nuclei reveal a very complex set of structures but on different single-particle structure existing in these nuclei. In general the results are in good agreement with the latest {\it ab-initio} calculations.

\subsubsection{Studies of nuclear collectivity, shape coexistence, and shape transitions}

A key question in nuclear physics is how simple patterns emerge in complex nuclei. To put this another way, how do macroscopic behaviours manifest themselves from the microscopic proton and neutron interactions. In reality, it is a complex combination of excitation modes that is typically observed in nuclei and, with very similar excitation energy scales, it is often difficult to disentangle the coupled excitation modes. Many collective phenomena cannot yet be predicted from the microscopic interactions of the individual nucleons, but theoretical developments towards this ultimate goal are advancing quickly. Experimental studies are essential to elucidate the nature of excitation modes and drive theoretical advancements. A number of important contributions have been made from experiments performed at TRIUMF-ISAC.

A major focus over the past 5 years has been to develop the techniques necessary to perform experiments with high-mass ($A \geq 30$) accelerated radioactive beams from ISAC-II.  These efforts culminated in the successful completion of the flagship experiments to investigate the evolution of single-particle structure and shape coexistence in the neutron-rich Sr isotopes through a series of $(d,p)$ transfer experiments with TIGRESS and SHARC.  The $^{94}$Sr$(d,p)^{95}$Sr and $^{96}$Sr$(d,p)^{97}$Sr experiments have probed the single-particle nature of the low-lying states in the odd-$A$ Sr isotopes as the sudden shape transition at $N = 60$ is approached, while the $^{95}$Sr$(d,p)^{96}$Sr experiment has probed the neutron $s_{1/2}$ component of the shape coexisting $0^{+}$ states in $^{96}$Sr\footnote{\href{https://doi.org/10.1016/j.physletb.2018.09.031}{S.~Cruz {\it et al.}, Phys. Lett. B 786, 94 (2018)}}$^,$\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.100.054321}{S.~Cruz {\it et al.}, Phys. Rev. C 100, 054321 (2019)}}. Additional analysis of the $^{95}$Sr$(d,t)^{94}$Sr reaction channel has identified the previously unobserved, but expected, 0$^+$ states in $^{94}$Sr\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.102.024335}{S. Cruz {\it et al.} Phys. Rev. C 102, 024335 (2020)}} to lie very close to the predicted energies and result from a strong mixing of different shapes. In contrast, co-linear laser spectroscopy performed at the TRUMF-ISAC polarizer beamline with the neighbouring Rb isotopes identified the spin (and existence) of a low-lying isomeric state in $^{98}$Rb which rules out the idea of shape co-existence in the rubidium isotope chain around $N$=60\footnote{\href{https://doi.org/10.1140/epja/i2015-15023-2}{T. Procter et al. Eur. Phys. J. A, 51, 23 (2015)}}.
The success of these first high-mass accelerated radioactive beam experiments at ISAC-II, coupled with the other established facilities in ISAC-I, sets the stage for a broad program of nuclear collectivity and shape-coexistence studies that will be performed with TIGRESS and its auxiliary detector systems during the 2022--2026 period using the high-purity charge-bred beams of high-mass isotopes that will be provided by the new CANREB component of ARIEL beginning in 2021. 

In particular, a series of multi-step safe Coulomb excitation experiments with re-accelerated $N\approx Z$ beams ranging from the doubly-magic $^{56}$Ni to $^{100}$Sn and along the chain of the Sn isotopes will be possible with TIGRESS in combination with SHARC or TIP for measuring transition probabilities and lifetimes of nuclear levels. Neutron-proton correlations, shape coexistence, and the evolution of shapes will be investigated in odd-odd $^{62}$Ga and $^{74}$Rb nuclei, while mirror symmetry and shape changes in $^{70}$Br and $^{70}$Se will be investigated by measuring transition probabilities. To explore whether the $N=Z=50$ shell gap remains valid at the proton-drip line, the evolution of shell structure will be investigated in the even-even $^{100-112}$Sn isotopes by extracting the transition probabilities of the low-lying states.

The SPICE detector, optimized for in-beam conversion electron spectroscopy with radioactive ion beams, was  commissioned at ISAC-II in the past 5 years\footnote{\href{https://doi.org/10.1016/j.nima.2018.07.064}{M. Moukaddam {\it et al.}, Nucl. Inst. And Meths. A 905, 180 (2018)}} and the first physics results have been published\footnote{\href{https://doi.org/10.1140/epja/i2018-12604-5}{J. Smallcombe {\it et al.}, Eur. Phys. J. A 54, 165 (2018)}}. This experiment, using SPICE+TIGRESS, found that the $E0$ transition strengths in $^{110}$Pd are consistent with the expectations from the axial rotor model. Detailed spectroscopic studies following $\beta$ decay have been performed using the 8$\pi$ spectrometer and PACES in the Sn and Cd isotopes\footnote{\href{https://doi.org/10.1140/epja/i2017-12213-x}{J.L. Pore {\it et al.}, Eur. Phys. J. A 53, 27 (2017)}}$^,$\footnote{\href{https://doi.org/10.1140/epja/i2017-12412-5}{D.C. Cross {\it et al.}, Eur. Phys. J. A 53, 216 (2017)}}$^,$\footnote{\href{https://doi.org/10.1140/epja/i2016-16036-y}{B. Jiggmedorj {\it et al.}, Eur. Phys. J. A {\bf 52}, 36 (2016)}} which reevaluated the nature of low-spin states and provided evidence for strong $E0$ transition branches. High-quality data sets have been acquired with the powerful GRIFFIN+PACES+LaBr$_3$(Ce) setup for the Hg, Er, Ce and Ge isotopes for which the data is now under analysis and the first results have been published\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.100.024301}{B. Olaizola, {\it et al.}, Phys. Rev. C 100, 024301 (2019)}}.  Work is also underway to couple the high-efficiency SPICE detector with the GRIFFIN spectrometer for use in $\beta$-decay studies. The upgrade from PACES to SPICE will greatly enhance the detection efficiency and spectral quality for internal conversion electron spectroscopy. This will extend the possibilities for studies of shape coexistence in exotic nuclei not possible with the current facility. The first experiments, investigating the neutron-rich Ni isotopes around $N=40$ with SPICE at GRIFFIN, will be performed in the next 5 years.

In a set of complementary measurements on the stable Ni isotopes led by Canadian Scientists at the Australian National University (ANU), enhanced $E0$ transitions were identified between low-lying $2^+$ states\footnote{\href{https://doi.org/10.1016/j.physletb.2018.01.076}{L.J. Evitts {\it et al.}, Phys. Letts. B, 779, 396 (2018)}}$^,$\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.99.024306}{L.J. Evitts {\it et al.}, Phys. Rev. C 99, 024306 (2019)}} which presently cannot be explained with existing theories. In parallel with these experimental efforts, the same group have worked with theorist Alex Brown of Michigan State University (MSU) to develop a microscopic approach to theoretical $E0$ transition strengths that dramatically improves the accuracy of calculations by capturing the polarizing effect of valence nucleons on the core\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.95.011301}{B.A. Brown {\it et al.}, Phys. Rev. C 95, 011301(R) (2017)}}.

TIP studies in the past 5 years have employed safe and unsafe Coulomb excitations as well as fusion-evaporation reactions using stable and radioactive beams from ISAC-II.  A high precision lifetime measurement for the 2$^+_1$ state in $^{94}$Sr near the shape transition region around $A$ = 100 and $N$ = 60 was performed using unsafe projectile Coulomb excitation\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.96.011302}{A. Chester {\it et al.,} Phys. Rev. C 96, 011302(R) (2017)}},  providing a value approximately 25\% larger than previously reported while the relative error was reduced by a factor of approximately 8. As a result, a baseline deformation has been established for Sr isotopes with $N \le$58, which is a necessary condition for the quantum phase transition interpretation of the onset of deformation in this region.  Subsequently the CsI(Tl) ball detectors have been successfully used for evaporated light charged-particle identification via pulse-shape analysis in several experiments. The data from the two proton evaporation channel in the $^{18}$O+$^{12}$C fusion reaction provided the spectroscopic and DSAM lifetime measurements in $^{28}$Mg\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.100.014322}{J. Williams {\it et al.,} Phys. Rev. C 100, 014322 (2019)}} needed to map the influence of the $fp$ neutron orbitals on the structure of nuclei near the ``island of inversion'' centred on $^{32}$Mg. This development enabled stringent testing of state-of-the-art phenomenological and {\it ab-initio} Shell Model calculations.  Reaction channel selectivity following pulse-shape analysis of digitized waveforms has been employed using the silicon diode wall in a DSAM measurement of the first excited state reduced transition probability in the ``standard candle'' $^{36}$Ar\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.96.024305}{P. Voss {\it et al.,} Phys. Rev. C 96, 024305 (2017)}}, resolving discrepancies between previous measurements and yielding good agreement with Shell Model calculations.  Finally, high-precision RDM/DSAM measurements from unsafe Coulex in $^{84,86}$Kr nuclei\footnote{\href{https://doi.org/10.1016/j.nima.2017.11.029}{A. Chester {\it et al.,} Nucl. Instr. and Meth. A 882, 69 (2018)}}$^,$\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.97.044311}{J. Henderson {\it et al.,} Phys. Rev. C 97, 044311 (2018)}} indicated  a more precipitous than anticipated reduction in the strength of the transition from the first excited to the ground state in the $N$=50 isotones approaching the $Z$=40 subshell, resulting in a more pronounced minimum at $^{90}$Zr.

% Figure 
\begin{figure}[ht!]
\centering
\includegraphics[width=0.8\columnwidth]{Figs/8pi-Cd_PRL_Ed_Sug.pdf}
\caption{\label{8pi-Cd_PRL_Ed_Sug}
%
An illustration of the multiple co-existing nuclear shapes discovered in $^{112}$Cd through high-precision decay spectroscopy with rare isotope beams provided by the TRIUMF-ISAC facility.}
\end{figure}

A major re-interpretation of the Cd isotopes has been put forward based on measurements performed with the $8\pi$ spectrometer of the $\beta$ decays of $^{110}$In and $^{112}$In/Ag
\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevLett.123.142502}{P.E. Garrett {\it et al.}, Phys. Rev. Lett. 123, 142502 (2019)}}$^,$\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.101.044302}{P.E. Garrett {\it et al.}, Phys. Rev. C 101, 044302 (2020)}}.
This work assigned rotational-like bands and, with the aid of beyond-mean-field calculations, suggested that the structures of $^{110,112}$Cd exhibited multiple-shape coexistence. This new interpretation is illustrated in Figure \ref{8pi-Cd_PRL_Ed_Sug}. This opens a significant opportunity for study into multiple shape coexistence since these Cd isotopes are stable and thus amenable to study with a wide variety of techniques. This work has led to new experimental programs at other facilities using a variety of experimental probes, and it is intended to revisit these $\beta$-decays to seek additional decay branches with the increased sensitivity provided by the GRIFFIN spectrometer that may permit the extension of the assigned rotational bands. Building on the previous successful experiments performed with the 8$\pi$ spectrometer, shape coexistence phenomena in the semi-magic $^{118}$Sn isotope\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.102.024323}{K. Ortner {\it et al.}, Phys. Rev. C 102, 024327 (2020)}} has been investigated.

Shape coexistence in the region above doubly-magic $^{78}$Ni has been investigated in the $^{80}$Ge nucleus in a high-statistics decay spectroscopy experiment with GRIFFIN.  The results show that shape coexistence is not present at low energies as previously reported and prompted a detailed theoretical investigation using state-of-the-art shell model calculations\footnote{\href{https://doi.org/10.1103/PhysRevLett.125.172501}{F.H. Garcia {\it et al.}, Phys. Rev. Lett. 125,172501 (2020)}}.  These studies will continue with the study of shape coexistence in $^{114}$Sn [TRIUMF experiment S1916] and $^{82}$Ge [S1683]. A new direction of research will be to exploit the $\beta$-decay of $^{92}$Rb to probe the Pygmy Dipole Resonance that is not fully understood. The GRIFFIN spectrometer is ideally suited to performing such studies given its very high detection efficiency for $\gamma - \gamma$ coincidences combined with the ability to perform $\gamma - \gamma$ angular correlation measurements.

\subsection{Experimental facilities}

\subsubsection{Experiments at the ISAC and ARIEL facilities of TRIUMF}

The Isotope Separator and Accelerator (ISAC) and the future ARIEL facility are some of the world's most powerful sources of rare-isotope beams. These facilities are essential to the nuclear structure research and the various experimental setups described in this section. The details of these facilities are discussed in Sec.~\ref{sec:triumf}.

\paragraph{GRIFFIN}\label{sec:nucstruc:griffin}

(TRIUMF) Guelph, SFU, Regina, Queen's; {\intl USA}

\begin{figure}[ht!]
\centering
\includegraphics[width=0.6\columnwidth]{Figs/GRIFFIN-Babu.jpg}
\caption{\label{GRIFFIN}
%
The GRIFFIN Spectrometer with its 16 Compton-suppressed high-purity germanium clover detectors arranged in a rhombicuboctahedral geometry. Undergraduate student Aditya Babu is calibrating the equipment for future measurements. Photo courtesy of TRIUMF.}
\end{figure}

GRIFFIN is a new high-efficiency $\gamma$-ray spectrometer comprised of 16 Compton-suppressed high-purity germanium (HPGe) clover detectors arranged in a rhombicuboctahedral geometry that has been optimized for $\gamma$-ray detection following the $\beta$ decay of low-energy radioactive beams provided by the ISAC-I facility at TRIUMF.  The first phase of the GRIFFIN project, with a total project cost of \$8.98M, was funded jointly by CFI , TRIUMF, and the University of Guelph over the 4-year period from 2011 to 2015, while the addition of the GRIFFIN Compton-suppression shields was completed through a second phase of the project funded by an additional \$3.57M award from CFI, the Ontario Ministry of Research and Innovation and the British Columbia Knowledge Development Fund over the 2016--2019 period.  GRIFFIN incorporates a powerful suite of auxiliary detection systems that have also been developed by our group. Eight cylindrical Compton-suppressed lanthanum bromide crystals with a 5\% doping of cerium (LaBr$_3$(Ce)) placed in the ancillary triangular positions of the array are used for fast-timing lifetime measurements of nuclear levels. In the middle of the array, around the beam’s implantation point, covering the upstream half of the chamber, a set of five LN$_2$ - cooled lithium-drifted silicon detectors (PACES) is used for conversion electron measurements. A fast 1 mm thin plastic called Zero Degree Scintillator (ZDS) can be placed just a few millimeters behind the ion-deposition point in the tape for $\beta$ particle tagging. These detectors can also be replaced by another plastic scintillator detector called SCEPTAR, which consists of two sets of 10 plastic scintillators for superior $\beta$ detection efficiency. GRIFFIN can also be coupled with DESCANT  - 70 liquid scintillator neutron detectors that cover a 1.08$\pi$  solid angle, for $\beta$-delayed neutron emission studies.  The combination of this versatile suite of auxiliary detection systems and the very high $\gamma$-ray detection efficiency of GRIFFIN forms a highly-sensitive facility for nuclear decay spectroscopy research with low-energy radioactive ion beams that is unique in the world.  A comprehensive description of GRIFFIN and its ancillary detectors can be found in Nucl. Inst. Meths. A 918, 9 (2019)\footnote{\href{https://doi.org/10.1016/j.nima.2018.11.115}{A.B. Garnsworthy {\it et al.}, Nucl. Inst. Meths. A 918, 9 (2019)}}. The full suite of detectors is operated with a custom-built digital data acquisition system with a 100 MHz sampling frequency\footnote{\href{https://doi.org/10.1016/j.nima.2017.02.040}{A.B. Garnsworthy {\it et al.}, Nucl. Inst. Meths. A 853, 85 (2017)}}.

A series of new and upgraded ancillary detectors are under development for GRIFFIN which will enhance the experimental capabilities. A major upgrade of SCEPTAR to the Ancillary detector for Rare-Isotope Event Selection (ARIES) detector is under development at TRIUMF and will be optimized for use with GRIFFIN. The ARIES detector will come online in 2022 offering high efficiency for beta-tagging and coincidence fast-timing for LaBr$_{3}$ detectors, as well as enable $\beta-\gamma$ angular correlation measurements.
The Regina Cube for Multiple Particles (RCMP) is a compact array of double-sided silicon strip detectors that is being designed by researchers at the University of Regina to surround the central implantation position of GRIFFIN. Anticipating first experiments in 2022, RCMP will extend the reach of the present GRIFFIN program towards extremely neutron-deficient nuclei by detecting charged particles ($\alpha$-particles and protons) emitted from exotic nuclear decays.  Of particular interest are studies of multiple-particle decay channels such as $\beta$-delayed two-proton ($\beta$2p) and $\alpha$-proton ($\beta\alpha$p) emissions that are relevant for nuclear astrophysics and give insight into the importance of particle-particle correlations in the parent nuclei.

\paragraph{General Purpose Station Gas Proportional $\beta$ Counter and Tape System}\label{sec:nucstruc:gps}

(TRIUMF) Guelph, SFU, Regina, Queen's

A 4$\pi$ continuous-flow gas proportional $\beta$ counter, tape transport system, and stand-alone HPGe $\gamma$-ray detector for high-precision $\beta$ decay half-life measurements is operated on a separate ISAC-I low-energy beam line referred to as the General Purpose Station (GPS)\footnote{\href{https://doi.org/10.1007/s10751-013-0890-x}{G.C. Ball, Hyperfine Interact 225, 133 (2014)}}.  At GPS, the low-energy radioactive beam from ISAC-I is implanted into a 25 mm wide, 25 $\mu$m thick aluminized mylar tape of a fast tape transport system.  After a collection period of $\sim 4$ half-lives, the ISAC beam is interrupted and the sample is moved out of the vacuum chamber through two stages of differential pumping and into the 4$\pi$ gas counter.  After multiscaling the signals from the counter for approximately 25 half-lives, the data are stored and the cycle repeated.  Sample purity is monitored with a HPGe detector located just outside the 4$\pi$ counter, or by delivering the beam to GRIFFIN, and great care is taken to investigate, and eliminate, systematic effects in order to achieve the $0.01\% - 0.02\%$ precision required for the superallowed Fermi $\beta$ decay half-life measurements described in Section~\ref{sec:funsym} below.

\paragraph{TITAN}\label{sec:nucstruc:titan}

(TRIUMF) Calgary, Manitoba, McGill, SFU; {\intl France, Germany, Netherlands, South Korea, UK, USA}

TITAN (TRIUMF's Ion Trap for Atomic and Nuclear science) is a unique ion trap experiment, currently consisting of five individual ion traps coupled together: an RFQ cooler and buncher, a Multi-Reflection TOF isobar separator and spectrometer, an Electron Beam Ion Trap, an Electron Plasma Cooler trap, and a precision Penning trap. Figure \ref{fig:TITAN-MPET} shows a photograph of graduate student, Eleanor Dunling, holding the inner electrode assembly of the TITAN precision Penning trap. This one-of-a-kind setup has the fastest beam preparation and measurement cycle for on-line precision mass measurements (by an order of magnitude, with a duty cycle time of 5~ms, hence providing access to isotopes with $T_{1/2} \gtrsim 5$ ms), it is the only system in the world to provide highly-charged radioactive ions, which boost the precision by one to two orders of magnitude (depending on the charge state and $Z$ of the isotope). TITAN started in 2003 originally funded for equipment and project through an NSERC RTI, and later augmented with additional equipment from CFI and NSERC SAP RTI. The operation of the system is supported in Canada through NSERC SAP project grants. International partners have contributed as well and the estimated total capital investment in TITAN to date is \$4.5M.

%==================================================
\begin{figure}[ht]
\begin{center}
%\vskip 0.5cm
\includegraphics[angle=0,width=0.5\textwidth]{Figs/TITAN-MPET.jpg}
\end{center}
\caption{Photograph of graduate student, Eleanor Dunling, holding the inner electrode assembly of the TITAN precision Penning trap.
\label{fig:TITAN-MPET}
}
\end{figure} 
%==================================================

The core piece of the TITAN setup is the Penning trap mass spectrometer. Mass spectrometry can now be performed in two ion traps, relying either on kinematics (time of flight or MR-TOF) or on a cyclotron-frequency determination (Penning trap). The former is preferred for its high sensitivity and non-scanning technique. The latter is preferred for higher precision and resolving power (at least one order of magnitude). TITAN was the first on-line system to implement charge-breeding which can improve the precision of Penning trap mass spectrometry, be used for tertiary beam production and beam purification. The EBIT itself can also be used for in-trap $\gamma$-ray spectroscopy and in the near future the setup will be augmented with a suite of high-purity germanium detectors.

The MR-TOF, which was commissioned in 2017, has emerged as an important tool for beam development, which often hinders the timely realization of experiments. Yields can be measured simultaneously with executing the nuclear-structure and -astrophysical objectives. Thus, in the future the MR-TOF will perform the majority of the TITAN mass measurements, continue in its role of beam development, and will serve as a high-resolution beam purifier for the subsequent ion traps. The Measurement Penning Trap (MPET) was de-commissioned in 2018 and will be re-commissioned as cryogenic one with two detection techniques: the Time-Of-Flight\footnote{\href{https://doi.org/10.1063/1.346185}{G. Bollen, Journal of Applied Physics 68, 4355 (1990)}} and Phase-Imaging Ion-Cyclotron-Resonance\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevLett.110.082501}{S. Eliseev {\it et al.}, Phys. Rev. Lett. 110, 082501 (2013)}}  techniques. The latter can improve the precision, resolving power, and sensitivity of the former; and, both benefit from higher charge states, in particular the precision. As this will remain a unique advantage among Penning-trap mass spectrometers dedicated to nuclear physics, this feature will be leveraged to pursue studies of fundamental interactions and cases requiring exceptional precision or resolving power.

\paragraph{Collinear laser spectroscopy}\label{sec:nucstruc:laser}

(TRIUMF) McGill; {\intl UK, Japan, Jordan, USA}

Fast beam, collinear laser spectroscopy has long been seen as a highly sensitive method with which to probe nuclear structure of ground and long lived isomeric states. When coupled to radioactive beam facilities that are capable of producing long chains of isotopes of many chemical elements these techniques provide invaluable information on the evolution of nuclear structure from stability out to the drip lines (see for example\footnote{\href{https://doi.org/10.1016/j.ppnp.2015.09.003}{P. Campbell, I.D. Moore, M.R. Pearson. Progress in Particle and Nuclear Physics 86, 127 (2016)}}). The use of high resolution laser spectroscopy of the atomic electrons, which in turn directly probe the nucleus, leads to a non-destructive, highly sensitive probe that can extract subtle nuclear effects in a largely nuclear spin independent way. These properties include the ground state nuclear spin, magnetic dipole and electric quadrupole moments along with the changes in the root mean squared charge radii. In certain cases it is also possible to extract higher order affects such as the nuclear magnetisation distribution, magnetic octupole moments and the absolute charge radii. As such the results from this work have far reaching impact across many areas of nuclear physics ranging from nuclear structure through weak nucleon-nucleon interactions to fundamental symmetry tests of the standard model. through to initial measurements required in order to pursue both biomedical and material science research.

Since the implementation of the last long range plan, this collaboration has had a successful experimental program that has led to the identification and characterisation of two isomeric states in each of $^{204,206}$Fr\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevC.91.044307}{Voss {\it et al.}, Phys. Rev. C, 91 044307, (2015)}}. This found the shortcomings of the single particle model in this region of the nuclear chart as well as providing the local Francium trapping group with the information required for high precision measurements in some of these isomers.  In addition to this the spin (and existence) of a low lying isomeric state in $^{98}$Rb was determined, ruling out the idea of shape co-existence in the rubidium isotope chain in this region\footnote{\href{https://doi.org/10.1140/epja/i2015-15023-2}{Procter {\it et al.}, The European physical Journal A, 51, 23 (2015)}}. This work was all made possible by a collaboration with the \textsc{TITAN} group at \textsc{TRIUMF} as the use of their radio frequency buncher was invaluable. Significant technical development was also undertaken, most notably utilising the time domain within both the data-acquisition system as well as time correlated temporal manipulation of the narrow line width laser systems. This achieved unprecedented precision and is summarised in Ref.\footnote{\href{https://doi.org/10.1016/j.nima.2015.11.145}{A. Voss {\it et al.}, Nucl. Instr. Meth. A 811, 57 (2016)}}.

In the near future, it is expected that the \textsc{CANREB} facility at \textsc{TRIUMF} will become available. The use of the radio-frequency quadrupole buncher from this facility, as opposed to utilising the \textsc{Titan} buncher, should dramatically increase the regions of the nuclear chart that are available. In general, laser spectroscopic techniques are blind to contaminants within a beam with the exception of the space charge limit of the buncher that is used. Utilising the newly developed \textsc{CANREB} RFQ with a significantly higher space charge limit will greatly expand the regions of the nuclear chart that are accessible without the need for complex target development. 

\paragraph{DESCANT}\label{sec:nucstruc:descant}

(TRIUMF)    Guelph

\begin{figure}[ht!]
\centering
\includegraphics[width=0.7\columnwidth]{Figs/DESCANT.jpg}
\caption{\label{fig:DESCANT}
%
A photograph of the 70-element DESCANT neutron detector array coupled with the GRIFFIN spectrometer at ISAC-I.}
\end{figure}

DESCANT, the DEuterated SCintillator Array for Neutron Tagging, is a 70-element array of deuterated liquid-scintillator detectors that can be used with both the TIGRESS and GRIFFIN $\gamma$-ray spectrometers\footnote{\href{https://doi.org/10.1007/s10751-013-0891-9}{P.E. Garrett, Hyperfine Interact 225, 137 (2014)}}.  DESCANT currently resides at the ISAC-I facility and is used in studies of $\beta$-delayed neutron emitters with the GRIFFIN spectrometer \footnote{\href{https://doi.org/10.1016/j.phpro.2015.05.059}{V. Bildstein {\it et al.}, Phys. Procedia, 66, 465 (2015)}}. DESCANT forms a close-packed array that replaces the forward ``lampshade" of 4 HPGe clover  detectors in each of the GRIFFIN and TIGRESS $\gamma$-ray spectrometers, providing high detection efficiency for neutrons in the range of $\approx 100$~keV to 10~MeV.  A recent experiment to study the decay of the neutron-rich K isotopes  performed in 2019 measured $\gtrsim 50$\% intrinsic efficiency for some $\beta-n$ decays, although the efficiency is dependent on the shape of the neutron spectrum. The DESCANT detectors have a 15 cm depth. With a 50 cm flight path from the source, DESCANT thus does not provide a high-resolution measurement of neutron energies via the time of flight (TOF) technique.  In order to address this, a new device DAEMON (Detector Array for Energy Measurements Of Neutrons), based on thin plastic scintillator detectors, is currently being designed for use in conjunction with DESCANT. As it is presently envisioned, DAEMON would be composed of plastic scintillator bars that could be positioned directly on the front faces of the DESCANT detectors and provide energy measurements via TOF with a resolution better than 100~keV at 1~MeV. 

\paragraph{IRIS}\label{sec:nucstruc:iris}

(TRIUMF) Guelph, McMaster, Regina, Saint Mary's, SFU; {\intl Japan, UK, USA, France}

\begin{figure}[ht!]
\centering
\includegraphics[width=0.7\columnwidth]{Figs/IRIS-Target.pdf}
\caption{\label{fig:IRIS-Target}
%
Views of the solid hydrogen or deuterium target assembly of the IRIS detector at TRIUMF-ISAC-II.}
\end{figure}

The ISAC Reaction Induced Spectroscopy station, IRIS, is a facility for studying direct reactions by charged particle spectroscopy using the reaccelerated beams of rare isotopes with energies from 5-12 $A$ MeV provided by the ISAC-II facility at TRIUMF. Construction of the facility was funded by CFI and was developed in partnership with Japan by a Canada-wide collaboration involving Saint Mary's University, University of Guelph, Simon Fraser University, McMaster University and TRIUMF. This collaboration pioneered techniques in developing thin solid hydrogen and deuterium targets (see Fig. \ref{fig:IRIS-Target}) to boost the reaction yield, thereby allowing reaction studies of very neutron-rich nuclei possible, since they can only be produced with rather small intensity. Such a target is also necessary to eliminate backgrounds arising from the carbon content of polyethylene foils that are typically used elsewhere. A low-pressure ionization chamber is another unique feature of the facility that makes it possible to identify beam contaminants before reaction with the target. Arrays of segmented silicon strip detectors register the reaction products. These powerful, innovative features make IRIS a major world-class facility in Canada.

Furthermore, the solid H$_2$ or D$_2$ target at IRIS is currently uniquely bringing a high degree of competitive advantage. There are several active targets in facilities around the world. The project plans for the EXACT-TPC will have some similarities to existing active targets in the world but has its advantageous feature particularly for improved gas amplification using thick GEMs and MICRO-Mesh-Gaseous Structure (Micromegas) that will allow use of pure H$_2$ and D$_2$ gases. The EXACT-TPC project is a world-wide collaboration aimed at a program that is optimally suited for TRIUMF.

\paragraph{TIGRESS and ancillary detectors}\label{sec:nucstruc:tigress}

(TRIUMF) Guelph, Saint Mary's, SFU; {\intl France, Spain, UK, USA}

TIGRESS is an array of 16 Compton-suppressed 32-fold segmented clover-type HPGe $\gamma$-ray detectors optimized for in-beam $\gamma$-ray spectroscopy with the accelerated radioactive ion beams provided by the ISAC-II superconducting heavy ion linear accelerator at energies approaching or beyond the Coulomb barrier.  The 32-fold segmentation of the TIGRESS HPGe detectors enables precise translation of the $\gamma$-ray energies measured in the laboratory to the rest frame of the nucleus.

\begin{figure}[ht!]
\centering
\includegraphics[width=0.7\columnwidth]{Figs/TIGRESS-AlexK.jpg}
\caption{\label{fig:TIGRESS}
%
Undergraduate student, Alex Kurkjian, helping install a 32-fold segmented high-purity germanium clover detector into the TIGRESS spectrometer in the TRIUMF-ISAC-II facility.}
\end{figure}

TIGRESS\footnote{\href{https://doi.org/10.1007/s10751-013-0905-7}{G. Hackman and C.E. Svensson, Hyperfine Interact 225, 241 (2014)}} was funded by an \$8.06M NSERC RTI-3 grant over the 6-year period from 2003--2009, and has been augmented by more than \$2.5M of associated detectors funded through NSERC RTI and CFI awards.  As in the case of GRIFFIN, the sensitivity of TIGRESS is dramatically enhanced through its coupling with a suite of specialized charged-particle and neutron detector systems that can be tailored, for each experiment, to the reaction of interest.  These include: i) the Bambino detector, comprised of two $24\times32$-fold segmented annular “CD-type” Si detectors, optimized for Coulomb excitation experiments with TIGRESS; ii) the Silicon Highly-segmented Array for Reactions and Coulex (SHARC)\footnote{\href{http://dx.doi.org/10.1088/1748-0221/6/02/P02005}{C.Aa. Diget {\it et al.}, JINST 6, P02005 (2011)}} comprised of up to 2000 channels of double-sided silicon strip detectors (DSSDs) with nearly 4$\pi$ solid angle coverage around the reaction target at the centre of the TIGRESS array, optimized for light charged particle detection in single- and two-nucleon transfer reactions with accelerated radioactive ion beams in inverse kinematics; iii) The SPectrometer for Internal Conversion Electrons (SPICE) ancillary detector\footnote{\href{https://doi.org/10.1016/j.nima.2018.07.064}{M. Moukaddam {\it et al.}, Nucl. Inst. And Meths. A 905, 180 (2018)}}, a large-volume, highly-segmented lithium-drifted silicon (Si(Li)) detector located in vacuum that is shielded from direct sight of the target by a photon shield, for in-beam internal-conversion-electron spectroscopy that allows detailed investigations of shape coexistence in exotic nuclei far from stability;  iv) the TIGRESS Integrated Plunger (TIP), a ``plunger" device surrounded by an array of radiation-hard CsI detectors\footnote{\href{https://doi.org/10.1016/j.nima.2017.11.029}{A. Chester, {\it et al.}, Nucl. Inst. Meths. A 882, 69 (2018)}}$^,$\footnote{\href{https://doi.org/10.1016/j.nima.2019.05.069}{J. Williams {\it et al.}, Nucl. Inst. And Meths. A 939, 1 (2019)}}, the latter for identification of weak reaction products or scattered particles amongst strong backgrounds, the former for measuring lifetimes of long-lived ($\tau > 1$~ps) states; v) the TRIumf Fast Ionization Chamber (TRIFIC)\footnote{\href{https://doi.org/10.1016/j.nima.2019.03.075}{A. Chester {\it et al.}, Nucl. Inst. And Meths. A 930, 1 (2019)}}, a tilted-plane heavy-ion gas counter for counting and identifying the nuclear charge of beam particles and beam-like reaction products and designed for rates approaching $10^6$~particles per second; and, vi) DESCANT, described in Section \ref{sec:nucstruc:descant}. TIGRESS can also be coupled with the EMMA spectrometer as discussed in the next section.

\paragraph{EMMA and focal plane detectors}\label{sec:nucstruc:emma}

(TRIUMF) Guelph, McGill, McMaster, SFU, St. Mary's; {\intl UK}

\begin{figure}[ht!]
\centering
\includegraphics[width=0.6\columnwidth]{Figs/EMMA-TIGRESS.pdf}
\caption{\label{fig:EMMA-TIGRESS}
%
A photograph of the TIGRESS and EMMA spectrometers taken during their first experiment together in September 2019. Here the two halves of the TIGRESS support structure have been separated to allow access to the EMMA target chamber. }
\end{figure}

The Electromagnetic Mass Analyser (EMMA) is a recently-commissioned vacuum-mode recoil mass spectrometer located in the ISAC-II experimental hall.  EMMA employs a symmetric configuration of electrostatic and magnetic deflectors to separate the products of nuclear reactions from the beam, focus them in both energy and angle, and disperse them in a focal plane according to their mass/charge ratios. The spectrometer was designed to couple with TIGRESS around the target position in order to provide $\gamma$-ray spectroscopic information in coincidence with the detection of heavy-ion reaction products. EMMA's design enables the measurement of fusion evaporation, radiative capture, and transfer reactions for nuclear structure and astrophysics and all of these types of reactions have been studied during its commissioning and first experiments with stable and radioactive ion beams from ISAC-II. Its complement of focal plane detectors enables the identification of recoiling nuclei and facilitates subsequent recoil decay spectroscopy. The commissioning of and initial operating experience with the spectrometer are described in\footnote{\href{https://doi.org/10.1016/j.nima.2019.03.070}{B. Davids {\it et al.}, Nucl. Instrum. Meth. Phys. Res. A 930, 191 (2019)}}.  Currently, approximately half of all approved TIGRESS experiments involve heavy-ion detection in EMMA, and all EMMA experiments except for one require TIGRESS.  TIGRESS is thus presently situated at the EMMA target location, as shown in Fig.~\ref{fig:EMMA-TIGRESS}.  In anticipation of these TIGRESS+EMMA experimental campaigns, the TIGRESS and EMMA data acquisition systems have been integrated to allow the EMMA focal plane data acquisition system to either run as a fully standalone system or as a second data stream sharing the same clocks and time-stamps as TIGRESS with the data time-correlated offline.  This new data acquisition scheme was validated in 2018 and used for first experiments in 2019.  Future developments include SHARC-II, a charged particle detector specifically designed for TIGRESS+EMMA experiments, and associated data acquisition upgrades leveraging technologies initially designed for GRIFFIN but also used in ALPHA-g and to be used with RCMP (described in Section \ref{sec:nucstruc:griffin}).

\paragraph{The 8$\pi$ Spectrometer}

(SFU) TRIUMF

\begin{figure}[ht!]
\centering
\includegraphics[width=0.5\columnwidth]{Figs/8pi-SFU.jpg}
\caption{\label{fig:8pi}
%
The 8$\pi$ spectrometer in the Nuclear Science Laboratory at SFU.}
\end{figure}

The possibility of studying the structures of nuclei far from stability via spontaneous fission was recognized when large arrays of $\gamma$-ray detectors became effective in disentangling the complex and rich spectra from fragments emitted in the fission of $^{252}$Cf and $^{248}$Cm\footnote{\href{https://iopscience.iop.org/article/10.1088/0034-4885/58/11/002}{I. Ahmad and W.R. Phillips, Rep. Prog. Phys. 58, 1415 (1995)}}. The operation of a 14.1~MeV deuterium/tritium neutron generator at the SFU Nuclear Science Laboratory\footnote{\href{https://doi.org/10.1093/rpd/ncv402}{J. Williams {\it et al.}, Radiat. Prot. Dosimetry 171, 313 (2016)}}, combined with the $8\pi$ $\gamma$-ray spectrometer\footnote{\href{https://doi.org/10.1007/s10751-013-0888-4}{A. B. Garnsworthy and P. E. Garrett, Hyp. Int. 225, 121 (2014)}} relocated from TRIUMF, offers many opportunities for studies of the products of nuclear reactions induced by fast neutrons. The goal for the upcoming LRP cycle is to deploy the $8\pi$ spectrometer, including the BGO calorimeter and all 20 Compton-Suppressed HPGe detectors as a powerful combination for the study of fission fragments produced in thick-sources (Shown in Figure \ref{fig:8pi}).  High-fold $\gamma$-ray gating on HPGe data will be used for fission fragment identification while the total $\gamma$-ray energy and multiplicity data from the BGO calorimeter will provide information on energy and angular momenta distributions for a given mass split. These measurements will be unique as previous arrays could not match the sensitivity of the $8\pi$ BGO calorimeter. 

\subsubsection{International collaborations and Canadian-driven programs at
  offshore laboratories}\label{sec:nucstruc:intcoll}
  
\paragraph{PREX and CREX}\label{sec:nucstruc:prex}

(JLab) Manitoba, Winnipeg; {\intl Croatia, Italy, Slovenia, Ukraine, USA}

PREX II proposes to measure the neutron radius of lead to a precision of 1\% and will provide crucial information about the neutron matter equation of state (EOS) at nuclear densities, anchoring nuclear structure theories and potentially providing evidence for nuclear matter phase transitions\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevLett.120.172702}{F.J. Fattoyez J. Piekarewicz, and C.J. Horowitz, Phys. Rev. Lett. 120, 172702 (2018)}}.  The CREX experiment proposes to make a 0.9\% measurement, and will connect the regions of the nuclear landscape that can be calculated using {\it ab-initio} techniques that are not computationally feasible for lead.  They both have implications for neutron star structure, heavy ion collisions and atomic parity violation (APV).  

The capability of JLab to produce highly polarized, high current, stable electron beams makes it the only existing laboratory to carry out such an experiment at the required energies and statistical precision.  Advances in experimental techniques have made it feasible to use parity violation in the weak interaction to measure various nuclear and nucleon properties.  By measuring the parity-violating asymmetry $A_{PV}$ in elastic scattering of longitudinally polarized electrons from an unpolarized nucleus, it is possible to measure the weak form factor $F_{W}(Q^2)$\footnote{\href{https://doi.org/10.1016/0375-9474(89)90432-6}{T.W. Donnelly, J. Dubach and I. Sick, Nucl. Phys. A 503, 589 (1989)}}.  Because the $Z$ boson couples mainly to neutrons, the weak charge density distribution can be related to the neutron density.  The ``neutron skin'' is defined as the difference in the RMS neutron and proton distributions, $R_n-R_p$, of a nucleus. 

PREX II (E12-11-101) ran successfully in summer and early Fall of 2019. CREX (E12-12-004) began in fall 2019 and was scheduled to complete data-taking in spring 2020.  The experimental run was paused due to COVID-19, and as of the writing of this brief, is planned to resume data-taking during the summer of 2020.  PREX II has presented preliminary results at the October 2020 APS DNP meeting which agree with the large central value found in the PREX I result, but with a smaller uncertainty. The analysis of the CREX data should be complete by the end of 2022, and some students will need to complete their theses.  There is a future experiment, MREX, which has been proposed to run at the new Mainz accelerator, which would further improve the uncertainty on the neutron skin of heavy nuclei, but there are no plans within our group to apply for NSERC funding related to this experiment at this time.

\paragraph{Studies using reactions of relativistic rare-isotope beams}\label{sec:nucstruc:relatavistic}
(GSI/FAIR (Germany), RIBF (Japan), NSCL/FAIR(USA)) Saint Mary's, TRIUMF; {\intl China, Germany, Japan, the Netherlands, Slovakia, Spain, UK, USA}

This impactful research program uses the reactions of high-energy beams of exotic nuclei on various targets to determine the neutron skin thickness and discover nuclear halos through measurement of their nuclear radii. This research seeks to unveil exotic nuclear forms, neutron halos, neutron skin and new arrangements of nuclear shells in nuclei approaching the edges of the bound nuclear landscape. The thick neutron-dominated surface emerging in these nuclei provides laboratory access to gain knowledge on the equation-of-state of asymmetric nuclear matter that describes the characteristics of neutron-rich cosmic environments such as neutron stars and supernovae. The rare isotopes produced at the in-flight facilities with relativistic energies are crucial to enable these discoveries through direct reactions.

The technique used is measurements of the interaction cross section and charge-changing cross section. These cross sections analyzed using the Glauber model reaction theory are used for determining the matter radius and proton radius. Nuclear orbitals are investigated through nucleon knockout reactions measuring nucleon momentum distributions. The nuclear radii also reflect on nuclear orbitals.

This program exploring reactions with relativistic rare isotope beams is carried out at the world's foremost in-flight rare isotope facilities at GSI-FAIR in Germany, RIBF-RIKEN in Japan and NSCL/FRIB in USA. These facilities have been the discovery frontiers unearthing new isotopes with their novel characteristics and expanding our knowledge of the nuclear landscape. Rare isotope science is at the international frontline of nuclear physics research. Its impactful discoveries led to a Nobel Symposium on the physics with radioactive beams being held in 2012.

\paragraph{Measurements of $\beta$-delayed neutron emitters at the RIBF, RIKEN, Japan}\label{sec:nucstruc:briken} (RIKEN) TRIUMF, McMaster; {\intl Chile, Hong Kong, Japan, Poland, Spain, UK, USA, Vietnam}

The BRIKEN collaboration has the goal to measure half-lives and neutron-branching ratios of $\approx$600 $\beta$-delayed neutron-emitters until 2021, for direct input into astrophysical models for a better understanding of the nucleosynthesis of heavy elements in the $r$-process. This new experimental data will also drive the development of nuclear structure models to reproduce these results and predict the properties of additional nuclei which cannot be accessed experimentally. See Section~\ref{sec:NA:briken} for further details.

%\paragraph{Stable beam experiments at offshore institutions}\label{sec:nucstruc:off-shore-SIB}

\paragraph{International involvement in ISAC}\label{sec:nucstruc:intisac}

Another aspect of the international involvement of the ISAC and Canadian nuclear structure community in the world-wide effort should not be overlooked; this is the presence of foreign researchers and students driving science programs at TRIUMF. The vast majority of experiments performed at ISAC include collaborators from foreign institutions, often as the principal investigators of the study. Most of the major pieces of experimental equipment at ISAC have international participation, both financial and specialist expertise, in their construction and in their operation.

As a recent example, the first direct observation of a $\beta p^{+}$ decay in $^{11}$Be was performed using a radioactive beam of $^{11}$Be provided by TRIUMF-ISAC\footnote{\href{https://link.aps.org/doi/10.1103/PhysRevLett.123.082501}{Y. Ayyad {\it et al.}, Phys. Rev. Lett. 123, 082501 (2019)}} in conjunction with a prototype active target time projection chamber (PAT-TPC)\footnote{\href{https://doi.org/10.1016/j.nima.2012.06.050}{D. Suzuki {\it et al.}, Nucl. Instrum. Methods Phys. Res., Sect. A 691, 39 (2012)}} built in the USA. The branching ratio for the $\beta  p^{+}$ channel was determined to be $1.3(3) \times 10^{-5}$, in agreement with a previous indirect measurement. This experiment shows that this decay process is sequential and proceeds through a newly identified narrow resonance with a width of 12.5~keV located at an energy of $11425 \pm 20$~keV. New theoretical calculations that include this resonance in $^{11}$B can only now reproduce the measured branching ratio which is orders of magnitude larger than previously thought.

\subsection{Beyond the next five years }\label{sec:beyond-structure}

There are many exciting developments planned for the next five to fifteen year period which will position Canadian scientists to make important contributions and discoveries in subatomic physics. With appropriate funding and investment in this field, Canadians will remain in a world-leading position for the foreseeable future.

On the theoretical side, global {\it ab initio} calculations of all nuclei may well become possible in the next five to fifteen years, making statistical analyses of properties and the limits of nuclei from first principles calculations a reality. One particular challenge to overcome for this to be possible is the development of {\it ab initio} theory which accurately describes nuclear deformation. Such achievements will give us the capability to provide first principles input for nucleosynthesis codes well into the r-process region, or nuclear structure predictions of heavy and super-heavy systems. Of course advances in quantum computing could tremendously speed up all these initiatives, and Canadian researchers are currently exploring these directions.

ARIEL will be a next-generation rare-isotope beam facility utilizing the Isotope-Separation-OnLine (ISOL) method for beam production. The ISAC facility first brought rare-isotope beam science to TRIUMF over twenty years ago and continues to be the world's highest-power ISOL facility. While the next-generation Fragmentation facilities such as RIKEN, FRIB and FAIR offer exciting research prospects, ISOL produced rare-isotope beams are ideally suited for world-leading research in nuclear structure, nuclear astrophysics and fundamental symmetries. ARIEL will ultimately triple the number of beam hours available for science with the addition of two new target stations; one for photo-fission using electrons from the eLINAC, and one served by a new proton beamline, plus a symbiotic target dedicated to medical isotope production. There are so many exciting opportunities for the development of new rare-isotope beam species, higher intensities, cleaner beams and longer experiment running periods which will enable a whole host of new discoveries. ARIEL will be the world's most powerful ISOL complex and the only purpose-built multi-user rare-isotope facility in the world. Completion of ARIEL positions Canadian researchers in a very strong position for subatomic physics research over the next decades.

A number of new detector systems, such as the EXACT-TPC and the RCMP detectors, will be commissioned at ISAC in the next few years and will begin their science programs. Many other existing detectors at ISAC will undergo upgrades and revitalization in the next five to ten years to maintain competitiveness or to expand their capabilities as new opportunities present themselves.

These exciting developments will allow new directions of research to be pursued. At this moment it is not possible to predict what these will be. There will be a number of self-selection and peer-review processes in order to identify the most promising research programs to pursue. To give one example, the nuclear structure features related to the stability of the super-heavy elements may be explored. This is a subject not actively being pursued by Canadian researchers at this time, but new capabilities enabled by ARIEL may allow reactions with accelerated beams of very neutron-rich nuclei to access such physics.

Nuclear structure investigations relevant to neutrinoless double beta decay may also gain momentum as a future direction. Presently a handful of initial such studies have been completed or are proposed. However, at this time a number of neutrinoless double beta decay experiments are now operating in Canada or are in the planning stage. The nEXO collaboration are pursuing a $^{136}$Xe-based double-beta decay experiment located at SNOLab.
The LEGEND Collaboration, which has formed primarily from the GERDA and MAJORANA collaborations, aims to develop a phased, $^{76}$Ge-based double-beta decay experimental program with discovery potential at a half-life beyond 10$^{28}$~years. SNOLab is one location under consideration for the LEGEND detector. With these experiments located in Canada there would be good opportunity for collaboration with nuclear structure experts because accurate nuclear structure calculations are essential for producing the final results of these large-scale experiments.

\subsection{Summary}\label{sec:nucstruc:sum}
Nuclear structure research in Canada addresses a range of topics which are of interest in the field today. The research efforts are primarily focused on experiments performed at the TRIUMF-ISAC facility but are also complemented by experiments performed at other laboratories worldwide. There has been significant Canadian capital investment into the ISAC and ARIEL facilities as well as the individual experimental facilities that have been described in this section.  In fact several major pieces of equipment at ISAC have recently been commissioned or have undergone major upgrades. Therefore, in the 2016 to 2026 time period, Canadian researchers are in an excellent position to reap the benefits of these investments by making scientific discoveries in nuclear structure. The timely completion of the ARIEL-II project will be a major enhancement to the rare-isotope beam physics opportunities available at TRIUMF and will ensure Canadian leadership in this exciting research field.