1 Introduction

Laser spectroscopy techniques used at radioactive ion beam facilities lie at the crossroads of atomic and nuclear physics, where measurements of the atomic hyperfine structure (hfs) are used to extract the electromagnetic properties of the nucleus. Among the many techniques implemented over the past decades, variants of the collinear laser spectroscopy (CLS) method have seen the most widespread application throughout the known nuclei [1, 2]. Courtesy of the inherently high resolution and efficiency, collinear laser spectroscopy provides routine access to changes in the nuclear mean-square charge radii \(\delta \langle r^2 \rangle \), the nuclear spin I, the nuclear magnetic dipole moment \(\mu \), and the electric quadrupole moment Q. The magnetic dipole moment is closely linked to the configuration of the valence particles in nuclei, and can thus be used to investigate e.g., the single-particle character of the nucleus, or the validity of particular configurations assumed or predicted by nuclear models. The electric quadrupole moment on the other hand, is related to nuclear deformation and is generally used to explore the collective properties of nuclei.

Table 1 Information on the collinear laser spectroscopy setups which are operating or are under development at radioactive ion beam facilities. The abbreviation CLSF stands for collinear laser spectroscopy with fluorescence detection, CRIS is collinear resonance ionization and MR-ToF is a multi-reflection time-of-flight device. In the first column CLS is used for setups without a unique name
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The ability to extract these four fundamental nuclear properties from a single measurement, and the complementary sensitivity of these observables to different aspects of nuclear structure, have led to the implementation of collinear laser spectroscopy in many radioactive ion beam (RIB) facilities worldwide [1, 2]. Traditionally, on-line isotope separator (ISOL) facilities were the favored, and almost exclusive, sites for laser spectroscopy of radioactive nuclei. These include CERN-ISOLDE [3], IGISOL at JYFL [4] and ISAC-TRIUMF [5]. Projectile fragmentation (PF) facilities hosting advanced beam stopping and ion manipulation devices have more recently become available for collinear laser spectroscopy experiments e.g., NSCL/MSU [6]. A list of collinear laser spectroscopy setups at online facilities either operational or planned are summarized in Table 1. Since 1976, when the collinear laser spectroscopy technique was first proposed by Kaufman [7], the method has gone through several transformations and technical refinements. It continues to evolve to this day, in order to advance on both the precision and the efficiency frontier. We note, as indicated in Table 1, that laser-radiofrequency (laser-rf) spectroscopy is expected to play an increasingly important role in future experimental setups. However, this method is yet to be used online in a collinear geometry, though online experiments with trapped ions have been performed [8]. The successful deployment of such techniques will drive the field towards higher-precision spectroscopy, offering access to e.g., higher-order nuclear moments.

The purpose of this work is to give an overview of the most commonly used collinear laser spectroscopy techniques and to demonstrate the advantages, versatility, and sensitivity thereof through different examples. The structure of this article is as follows: firstly, following this brief introduction, Sect. 2 discusses the hyperfine interaction and the extraction of the nuclear properties from the measured hyperfine structure spectra. Then, an introduction to the method of collinear laser spectroscopy is given in Sect. 3, in which several different variants of the technique are discussed. In Sect. 4, the nuclear observables which can be obtained using collinear laser spectroscopy are discussed in more detail through the use of recent examples from the literature. Finally, we summarize the article in Sect. 5.

2 Nuclear properties from atomic measurements

When the atomic electrons and the nucleus both have angular momenta greater than zero, there will be a hyperfine interaction between the two systems. The strength of this interaction is proportional to the magnitude of the nuclear electromagnetic moments. For a nucleus with a nuclear spin \(\vec {I}\) and an atomic fine-structure state with total angular momentum \(\vec {J} = \vec {L} + \vec {S}\), we can define the angular momentum of the whole system as \(\vec {F} = \vec {I} + \vec {J}\). It follows from the standard quantum-mechanical angular momentum addition rules that the possible values of F are \(F = I+J, I+J - 1, \ldots , \left| I-J \right| \). The effect of the hyperfine interaction is most readily evaluated using perturbation theory. The first-order perturbation Hamiltonian can be expressed using a multipole expansion, where every term is factorized into a product of a nuclear operator and an electronic one. To first order, the leading contributions to the energy shift due to the hyperfine interaction for a state with total angular momentum F are given by:

$$\begin{aligned} \varDelta E_F = \frac{1}{2}AK+B\frac{(3/4)K(K+1)-J(J+1)I(I+1)}{2I(2I-1)J(2J-1)},\nonumber \\ \end{aligned}$$
(1)

where \(K=F(F+1)-J(J+1)-I(I+1)\). A and B are the magnetic dipole and electric quadrupole hyperfine constants, respectively,

$$\begin{aligned} A = \frac{\mu }{I} \frac{B_0}{J} \quad \text {and} \quad B = eQ V_{zz}, \end{aligned}$$
(2)

with \(\mu \) the magnetic dipole moment and Q the electric quadrupole moment of the nucleus. \(B_0\) is the magnetic field generated by the electrons at the site of the nucleus, and \(V_{zz}\) is the electric field gradient. Note, as a result of the hyperfine interaction, a fine structure level splits into either \(2I+1\) levels, if \(I\le J\), or \(2J+1\) levels, if \(J<I\). When \(I\le 1/2\) or \(J\le 1/2\), the nucleus does not possess a measurable spectroscopic quadrupole moment, and the second term in Eq. 1 is not present.

Only the magnetic dipole and electric quadrupole perturbations are presented in the first-order approximation shown in Eq. 1. Additional terms due to the nuclear magnetic octupole, electric hexadecapole, etc. moments, are also present but their influence is not typically measurable with CLS [30], requiring instead, yet higher precision techniques [31]. The presented expression is obtained with first-order perturbation theory and the energy shifts in second-order have been neglected. When the separation of fine structure levels is small and the hyperfine structure within a level is large, second-order contributions may be present and probed [32]. Additional shifts can also occur due to the Zeeman effect, however, in typical laboratories exposed to the earth’s magnetic field, i.e. a few 10 \(\mu T\), this effect can be neglected relative to the typical precision of CLS.

Although the electromagnetic moments may be extracted from Eq. 2 using a precise calculation of the relevant electromagnetic fields, see e.g., [33], it is a more common practice to use an empirical approach and to extract the ratio of the nuclear moments and hyperfine constants of a pair of different isotopes of the same element, by using the known nuclear moment and hyperfine parameter of the reference isotope:

$$\begin{aligned} \mu =\frac{A}{A_{\text {ref}}}\frac{I}{I_{\text {ref}} } \mu _{\text {ref}}. \end{aligned}$$
(3)

Similarly, for quadrupole moments,

$$\begin{aligned} Q = \frac{B}{B_{\text {ref}}} Q_{\text {ref}}. \end{aligned}$$
(4)

In the majority of cases, reference isotopes are used that are either naturally occurring or long-lived, with their moments having been measured to high precision via non-optical methods, for example Nuclear Magnetic Resonance (NMR). This scaled extraction however is made under the assumption of an ideal point-like nucleus. For example, Eq. 2 for the A-coefficient assumes that the magnetic field generated by the electrons is constant across the nuclear volume. This is not the case and gives rise to an effect called the hyperfine anomaly (HFA). Although this effect is typically small relative to experimental uncertainties (<1%) it is observed to rise close to 10% for some cases and can be observed in collinear laser spectroscopy. As a result of the HFA, the ratio of the hyperfine parameters of the lower and upper state may not be constant throughout an isotopic chain and trends in this ratio can be used to further explore the magnetic structure of the nucleus [34,35,36].

Figure 1 illustrates an example of an atomic system with two fine-structure levels \(J=3/2\) and 1/2 of a hypothetical nucleus with \(I=3/2\). As discussed above, the fine structure levels are split due to the hyperfine interaction, with additional shifts caused by the electric quadrupole interaction for the F sub-states of the \(J=3/2\) level. The net effect of the hyperfine interaction is thus a shift in the transition energy by an amount \(\varDelta E_{F_U}-\varDelta E_{F_{L}}\). Laser spectroscopy exploits the use of allowed electric dipole transitions between two hyperfine states in different fine-structure levels. In Fig. 1, the peaks observed therefore correspond to transitions from a state with angular momentum \(F_L\) of the lower-lying fine structure level (\(J=3/2\)), to a state with angular momentum \(F_U\) of the excited fine-structure level (\(J=1/2\)). When scanning the frequency of a laser near the center frequency \(\nu \), six resonances are found (two transitions, \(F_L = 0\rightarrow F_U = 2\) and \(F_L = 3\rightarrow F_U = 1\), being dipole-forbidden). The separation of the resonances is directly proportional to the underlying nuclear moments, governed by Eq. 1. One of the key strengths of laser spectroscopy is, in many cases, an unambiguous determination of the nuclear spin. In our example, as \(I\le J\), a spin assignment can be made by simply counting the number of observed peaks in the optical spectrum. We will return to a discussion of the nuclear spin determination in more detail in Sect. 4.4.

Fig. 1
figure 1

Example of an atomic transition for the measurement of the hyperfine structure spectrum. The laser probes the transition from the \(J=3/2\) electronic level to \(J=1/2\). The nuclear spin is \(I=3/2\)

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The relative intensities of the peaks are dependent upon the angular momenta of the constituent hyperfine levels. By calculating the matrix elements of the electric dipole operator, the ratio of the intensities of the hyperfine transitions from the lower states with \(F_{L}\), \(J_{L}\), to the upper states with \(F_{U}\), \(J_{U}\), can be obtained as:

$$\begin{aligned} R(F_{U},F_{L}) = (2F_{U}+1)(2F_{L}+1)\begin{Bmatrix} I&F_{U}&J_{U}\\ 1&J_{L}&F_{L} \end{Bmatrix}^2. \end{aligned}$$
(5)

In this expression, the curly braces indicate a Wigner 6-j symbol. When a transition is forbidden due to the conservation of angular momentum (e.g., when \(\varDelta F \ne 0, \pm 1\), or when \(F_U = F_L = 0\)), this Wigner term will be zero. In principle, the relative intensities of the resonances which are obtained with low laser power (i.e. below saturation), and in the absence of significant optical pumping effects, follow this expression. Under these conditions, a comparison of relative amplitudes with Eq. 5 may assist the determination of the nuclear spin [37].

In addition to the hyperfine splitting of the fine structure levels, and the corresponding shifts in transition frequencies due to the hyperfine interaction, the fine structure energy levels also shift from isotope to isotope due to the monopole interaction between the electron cloud and the (different) nuclear charge distribution. This isotope shift between isotopes with atomic masses A and \(A'\) can be related to the changes in the mean-square charge radii \(\delta \langle r^2 \rangle \):

$$\begin{aligned} \delta \nu ^{A,A'}=M\frac{m_{A'}-m_A}{m_Am_{A'}} + F\delta \langle r^{2}\rangle ^{A,A'}, \end{aligned}$$
(6)

where \(m_A\) are the respective masses and the factors F and M are the atomic field shift and mass shift factors. Determination of these factors is a critical step in the extraction of \(\delta \langle r^2 \rangle \) from the isotope shifts. Atomic structure calculations, for example multi-configuration Dirac-Fock calculations, many-body perturbation theory or coupled-cluster calculations may be used, with typical uncertainties of the order of 10\(\%\) [38, 39]. The mass and field shift factors can also be empirically calibrated using the King plot method [40], whereby isotope shift data is combined with independently measured nuclear charge radii obtained from e.g., electron scattering or muonic X-ray data, or existing laser spectroscopy measurements. In order to extract both F and M, however, this independent radius data needs to be available for at least three different isotopes, which is not always the case. It should be noted that the extracted value of \(\delta \langle r^2 \rangle \) using laser spectroscopy, either via the King plot method or with the support of atomic structure calculations, is nuclear model independent. This is another key feature of the optical approach, critically differing from the majority of non-optical measures of the nuclear charge distribution. In Eq. 6, higher-order nuclear radial moments have been neglected as these are not accessible for laser spectroscopy measurement. In principle, this approximation is only valid for light isotopes. Higher-order radial moments have to be considered when heavy isotopes are studied as follows:

$$\begin{aligned} \varLambda ^{A,A'}= & {} \delta \langle r^{2}\rangle ^{AA'}+\frac{C_{2}}{C_{1}}\delta \langle r^{4}\rangle ^{AA'}+\frac{C_{3}}{C_{1}}\nonumber \\ {}{} & {} +\delta \langle r^{6}\rangle ^{AA'}+\cdots , \end{aligned}$$
(7)

where \(\varLambda ^{A,A'}\), which remains proportional to \(\delta \langle r^2 \rangle ^{A,A'}\), is the so-called nuclear parameter and \(C_2/C_1\), \(C_3/C_1\) are the Seltzer coefficients, tabulated in [41].

Fig. 2
figure 2

Collinear laser spectroscopy techniques at RIB facilities. a After the radioactive isotopes are produced and extracted from the target, the mass-separated ion beam is cooled and bunched in a gas-filled linear Paul trap. The bunched beam is transported to the collinear beamline where it can be neutralized in a charge-exchange cell, typically filled with an alkaline vapor of K or Na. The interaction region is located in part of the setup. b The interaction region of CLSF. The photons emitted during the de-excitation from hyperfine levels are detected using photomultipler tube (PMT) detectors. c The interaction region of the CRIS technique. Several laser beams are used for excitation and step-wise laser ionization of the atoms. Ions rather than photons are detected in this method

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3 Collinear laser spectroscopy

Laser spectroscopy techniques involve the use of at least one laser, which is used to excite a transition between two atomic fine structure states. Over the years, various schemes to detect whether this transition has taken place (as the frequency is scanned over a specified range) have been developed [1, 2]. Here, we restrict our attention to collinear laser spectroscopy techniques. Throughout the years, CLS has been used to study the nuclear structure properties of nuclides throughout the nuclear chart, from very light isotopes such as Li (\(Z=3\)) [42], all the way to heavy isotopes, e.g., Pu (\(Z=94\)) [43]. Even though the highest experimental efficiency can be achieved in systems with a simple atomic structure, measurements have been performed on complex atoms as well, such as iron [44]. The main steps involved in CLS experiments are presented in Fig. 2 and will be discussed in more detail in the sections below. In general, the radioactive ion beam has to be suitably prepared prior to the optical experiment to improve the properties of the ion beam and to ensure the beam is in the charge state most suitable for the element of interest. As shown in Fig. 2a, this typically requires a cooling and bunching of the ion beam in an RFQ device [45], and neutralization in a charge exchange cell in case the ions of the specific element are not suitable for the measurement. Finally, the laser-atom (ion) interaction takes place in the so-called interaction region. The two main approaches for the hfs measurements, fluorescence detection (CLSF) and CRIS are shown in Fig. 2b, c respectively.

3.1 Accelerated beams in a collinear geometry

When studying an ensemble of atoms inside of a hot cavity atomizer or in the high-pressure environment of gas-stopping cells, both in common use at RIB facilities, the width of the optical resonance can be significantly broadened due to Doppler and pressure broadening, respectively. This is detrimental to the precision of the spectroscopy, and often prevents extraction of the nuclear observables of interest. The advantage of collinear laser spectroscopy is that it is largely insensitive to the energy spread imparted to the ensemble during the production or thermalization process. This is because, upon electrostatic acceleration to a few 10 keV beam energy, the velocity spread \(\delta v\) of the ensemble is reduced kinematically [7]. Indeed, during the acceleration, the energy spread of the beam remains unchanged due to the conservation of energy, but the spread in velocity is reduced:

$$\begin{aligned} \delta E = \delta \left( \frac{mv^2}{2}\right) =mv \ \delta v = \text {const.} \end{aligned}$$
(8)

and therefore

$$\begin{aligned} \delta v \propto \frac{1}{v}. \end{aligned}$$
(9)

As a consequence, the width of optical resonances obtained with collinear laser spectroscopy is typically not limited by Doppler broadening. The frequency of the light observed by an ion of mass m and charge q accelerated to a kinetic energy of qV which travels collinearly in the direction of the laser beam can be related to the rest-frame frequency \(\nu _{R}\) using:

$$\begin{aligned} \nu _{R} = \nu \sqrt{\frac{1+\beta }{1-\beta }}, \quad \beta = \sqrt{1-{\biggr ( \frac{mc^2}{mc^2+qV}\biggr )^2}}, \end{aligned}$$
(10)

with c being the speed of light. Note that the mass of the electron(s) and their binding energy may have to be taken into account when calculating the mass m, in particular for lighter isotopes. The relationship presented in Eq. 10 can be exploited to scan over an optical transition as well: accelerating or decelerating the ions leads to a corresponding change in the wavelength as observed in their frame of reference. This velocity tuning can be done by applying a potential to the light collection system or the charge exchange cell. Since such potential changes can be rapidly and accurately applied, fast and reproducible scans can be performed. However, some experiments rely on changing the laser frequency to measure the hyperfine structure spectrum. The limitation of this technique is the speed at which the laser frequency can be accurately changed.

In Fig. 3 (top), the calculated contribution of the Doppler effect to the total width of the optical resonance for a transition wavelength \(\lambda = 328~\text {nm}\) and an ion of mass \(A = 75\) is shown, assuming an initial temperature of 2000 K. As the beam is accelerated, the velocity spread is compressed, and the Doppler broadening is reduced. The remaining Doppler contribution to the total resonance width is of the order of a few MHz, or less. The limiting factor is thus often the bandwidth of the laser, and/or the intrinsic width of the optical transition. Most commonly, electric dipole-allowed transitions are employed, in which the excited state has a lifetime of the order of a few ns to a few 100 ns. Thus, typical resonance widths are of the order of 10–100 MHz.

Fig. 3
figure 3

Top panel: reduction in the observed linewidth as function of the energy of the ion beam (see text for details). The horizontal dashed line is placed at 50 MHz. Below this, a comparison of optical data obtained on \(^{75}\)Cu with in-source laser spectroscopy, and two collinear laser spectroscopy methods. Note that the two collinear datasets were obtained using a different optical transition. Data are adapted from [46,47,48,49] and overlaid for illustrative purposes. The collinear geometry offers a considerable improvement in resolution; as shown in the bottom panels, the substructure which cannot be resolved in-source becomes apparent

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The middle panel of Fig. 3 provides an illustration of the improved resolution of collinear laser spectroscopy as compared to measurements performed on thermal atoms inside of a standard hot cavity ion source in use at the ISOLDE facility in CERN. This is illustrated with data obtained on \(^{75}\)Cu in three different experiments. A Doppler-broadened in-source laser spectroscopy measurement is shown [46], whose resolution is improved upon by two subsequent collinear laser spectroscopy measurements. One spectrum was obtained using a fluorescence detection scheme [47], while the second was obtained several years later using collinear resonance ionization spectroscopy [48, 49]. The bottom two panels illustrate the CLS and CRIS measurements in more detail. The differences between these latter two measurements will be discussed further in Sects. 3.4.1 and 3.4.2.

3.2 Beam preparation and atomic state manipulation

Prior to performing collinear laser spectroscopy, nowadays the mass-selected ion beam is first injected into a gas-filled linear Paul trap [45], often referred to as an RFQ, as shown in Fig. 2a. Through long-range, viscous interactions with the gas inside the trap, usually helium, the ions are cooled to the temperature of the gas (room temperature), reducing the energy spread of the ensemble. The ions can be released from the trap in bunches by pulsing the voltage of the axial confining field. This gives a time structure to the beam which is advantageous for background reduction when a continuous laser beam is used in CLSF, or avoiding duty cycle losses when pulsed laser systems are employed in CRIS. The time period for accumulating the beam in the Paul trap is typically between 10 ms and 500 ms. The produced bunches are 1–10 \(\mu \)s long.

The cooler-buncher devices can also be used to prepare the ions in a certain state for laser spectroscopy measurements. For example, if the ionic ground state has low sensitivity to the nuclear properties of interest, the population can be transferred into a metastable state using an optical pumping technique. This is achieved by illuminating the axis of the cooler-buncher device with (pulsed) laser light to obtain a redistribution of population following the excitation of ground states [50, 51]. Given the long dwell time of the ions, several laser pulses are available to enhance the efficiency of the optical pumping, which is particularly important for spectroscopically weak transitions. If the population of the initial state is sufficiently high, and optical pumping mainly shelves the electrons in the metastable state of interest, this method significantly increases the sensitivity and the efficiency of the CLS measurements downstream.

The electronic structure of the ion may not be conducive to optical spectroscopy. This could be for example because the wavelengths required to excite the ion from its ground state are not accessible with current laser technology, i.e., if the wavelengths lie in the vacuum ultra-violet (below 200 nm) region. In this case, the ion beam is first neutralized in-flight through the use of a charge exchange cell as shown in Fig. 2. These devices contain a sample of an element with a low vapour point, typically an alkali element like potassium or sodium. By heating this cell, a vapour is produced. When the fast ion beam travels through the vapour, it is neutralized in a charge-exchange reaction with the alkali atoms. Thus, a fast atom beam is produced. Depending on the atomic structure of the element, the beam energy, and the choice of neutralizer, the atoms may not be produced in their atomic ground state, but also in atomic metastable states [52]. This can be advantageous, as it enables the use of these metastable states for the spectroscopy, but can also be a hindrance, lowering the efficiency of the measurements due to a redistribution of the population among several states. Many designs have been developed over the years for neutralization (see e.g. Ref. [53] for a comparison of two common designs).

3.3 Accuracy and systematic effects

Precise and accurate measurements in a collinear geometry rely on the accurate knowledge of both the laser frequency \(\nu \) and the acceleration voltage V in Eq. (10), as these are required to calculate the frequency observed in the rest frame of the fast atoms or ions. The measurement of the laser frequency (or, equivalently, the laser wavelength) is most often performed using wavelength meter devices based on interferometers, which are commercially available. The relative accuracy of the top-end devices are in the 1 MHz range. The considerably more complicated challenge of obtaining high absolute accuracy is in principle not required, as the extraction of nuclear observables relies only on relative resonance frequencies. For the measurements which require the highest experiment precision, for example in the case of very light isotopes, more sophisticated wavelength measurement devices have to be used, such as frequency combs [54].

Accurate measurements of the acceleration voltage in the 30 kV–60 kV range are challenging. It is typically done by the use of accurately calibrated voltage dividers and voltmeters. Inaccurate measurements have significant effects on both the accuracy of the extracted isotope shifts and hyperfine constants. Conversely, the measurement of the spectra of isotopes with precisely known constants can also be used to calibrate the voltage [55, 56]. Again, when the highest precision is required, as in the case of CLS studies of the lightest isotopes, Doppler-shifted resonance frequencies can be measured in a collinear and anti-collinear geometry. In such experiments the rest-frame frequency can be measured (with a frequency comb) independently of inaccuracies in calibrating the ion beam velocity [57].

3.4 Detection methods

Collinear laser spectroscopy setups can be divided into two main groups based on the detection method used to reconstruct the hyperfine structure of the measured isotopes: photon detection and particle detection. The detected particles can be ions, atoms or products of radioactive decay. In the following, a short description is given for collinear laser spectroscopy methods which have been successfully applied over the years to perform measurements on radioactive ion beams.

3.4.1 Collinear laser spectroscopy with fluorescence detection (CLSF)

In conventional CLSF, the laser excitation of the atoms or ions is followed by the detection of the photons emitted when the atom decays back to a lower-lying atomic state. This technique is schematically shown in Fig. 2b. Here, the interaction region and the photon detection take place in the same chamber or in a close vicinity to each other. The highest photon count per atom or ion is achieved for closed optical systems, where the atom relaxes back into the same state from where the laser excitation took place. Stronger optical transitions, which correspond to excited states with a short half-life, are preferable as they will yield more photons within a given distance (constrained by the length of the detection region). The fluorescence light emitted by the atoms or ions is collected by light collection optics, and focused on a Photo-Multiplier Tube (PMT). The solid angle coverage of this light collection system and the quantum efficiency of the PMT(s) constitute the main limitation to the efficiency of conventional CLSF. Typically, about one photon per several thousand atoms can be collected, though in some cases efficiencies as high as one photon per a few hundred atoms have been reported [58]. The main source of background counts is the scattered laser light, and the spontaneous de-excitations occurring in front of the PMTs. The former can in some cases be avoided if the wavelength of the laser light does not coincide with that of the detected photons. The latter is significant when the measurements are performed on atoms, emitting so-called beam-light. This refers to the phenomena when highly excited states are populated in the CEC during the neutralization process, which rapidly decay at the site of the photon detection setup. The versatility and relative simplicity of conventional CLSF have led to its implementation in many RIB laboratories worldwide, as listed in Table 1. These setups consist of a charge-exchange cell, in case the experiment requires atoms rather than ions, and a light collection region, where the laser-atom interaction and photon detection take place.

Over the past years, a wealth of data was obtained using collinear laser spectroscopy experiments with fluorescence detection. These measurements have been used to explore the nuclear structure in the vicinity of \(Z=50\) near the \(N=82\) shell closure in neutron-rich isotopes [17, 59, 60] and near \(N = 50\) on the neutron-deficient side [23]. Also in the mid-mass range near \(Z = 28\) [61,62,63,64,65,66] and lighter isotopes close to the \(N = Z\) = 20 shell closures [67,68,69,70,71], crucial data has been gathered over the past decade. Additional information in these regions was gathered using the collinear resonance ionization spectroscopy method [20, 49, 72], discussed next.

3.4.2 Collinear resonance ionization spectroscopy (CRIS)

While CLSF has been used for many decades, the CRIS approach in its current form is relatively new. Pioneering experiments were performed in the early 90s [73]. A dedicated beamline for CRIS measurements was installed at ISOLDE only after the introduction of a cooler-buncher, which yielded the first high-resolution results in 2015 [19]. In the CRIS method, after the resonance excitation, further laser excitation takes place, eventually promoting an electron to the continuum and thus ionizing the atoms. The subsequent laser excitations benefit from using a broadband laser, covering several GHz range in the frequency space to promote electrons from all hyperfine levels of the excited state. For the final laser ionization, a high-power laser can be used to achieve efficient non-resonant ionization. Alternatively, transitions to auto-ionizing states can be used, requiring less laser power. The use of field ionization [73, 74], whereby a high-lying Rydberg level is ionized by an electric field, can also be used, yet has not seen widespread use with radioactive isotopes.

A typical CRIS setup, shown in Fig. 2a, c, receives bunched ion beams and consists of: a charge-exchange cell; deflector plates that remove the remaining ions; a differential pumping region; an interaction region with ultrahigh-vacuum requirements; and finally a chamber for the particle detectors. The length of the interaction region should be sufficiently long to accommodate the full length of the ion bunch; for example, at ISOLDE, this translates to a required minimum length of 1.5 m and the interaction time of around 2 \(\mu \)s. An advantage of CRIS is that it relies on the detection of ions rather than photons. Furthermore, the laser-induced ions can be electrostatically guided to a decay spectroscopy station for the delivery of isomerically purified beams [21], or to have an enhanced selectivity [20].

Achieving high spectral resolution while using high-energy laser systems is facilitated by the use of delayed ionization [19, 75,76,77], with the best performance so far of 20 MHz resolution, achieved for Fr (\(Z = 87\)). The high efficiency of laser ionization and single-ion detectors serves to boost the signal. As compared to photon detectors, which also detect e.g., stray laser light and other light emitted by the atom or ion beam, the use of ion detectors also reduces the background significantly. The background counts using the CRIS technique come from detecting ions created in the interaction region which are not related to the frequency of the laser used for the measurement of the hfs. These ionization processes can be non-resonant laser ionization, collisional ionization or field ionization of highly-exited atoms.

Comparisons of the results obtained with conventional CLS and CRIS have been performed throughout the nuclear chart, e.g. francium [19, 78], gallium [66, 79], and potassium [20, 71]. The bottom panel of Fig. 3 places results from both techniques obtained for \(^{75}\)Cu side-by-side. Note that different atomic transitions are used for the CRIS and CLS measurements, as the former technique requires weak, while the latter relies on strong atomic transitions. More and more facilities house both of these methods, however, the CRIS at ISOLDE is the only setup which has so far produced results using radioactive beams. The other beamlines presented in Table 1 are still under development or in the commissioning phase. In some cases the two techniques are combined in one experimental setup, in other cases separate experiments exist. The strengths and weaknesses of these techniques have to be considered to determine the optimal method for the study of an element.

The CRIS approach has so far only been used to ionize atoms to a singly-charged state. This is mainly due to the fact that the ionization of singly-charged ions requires the use of deep ultraviolet light for several transitions until the final ionization step can take place. This exemplifies some of the drawbacks of the technique: typically, multi-step laser resonance ionization of atoms requires a comparatively more complex suite of laser systems. Furthermore, producing narrowband, pulsed laser light comes with additional complexity and constitutes an area of active development. In addition, the study of complex atoms with dense metastable level structures, many of which are populated during the charge exchange process, can impose an efficiency loss to the CRIS method, as is the case for all CLS methods. In specific cases, other techniques which can circumvent the charge-exchange process may thus be preferable.

3.4.3 In-flight optical pumping and polarization

The collinear geometry enables a long interaction time between the laser and ion (atom) beam (\(\approx \mu \)s). Thus, collinear experiments can also be used for inducing nuclear polarization [80,81,82,83] or to manipulate the atomic population in preparation for the hyperfine structure measurement [15, 16, 84].

Optical polarisation in a collinear geometry combined with \(\beta \)-detected nuclear magnetic resonance (\(\beta \)-NMR) is an established method, with a long history and diverse scientific program, not only for nuclear structure research, but for materials research and life sciences as well [14, 85]. The beam of atoms or ions is optically polarized using circularly polarized laser light. The polarization of the laser light, \(\sigma ^{+}\) or \(\sigma ^{-}\), imposes restrictions on the possible excitations into the levels of the Zeeman splitting, which are \(\varDelta m_{F}=-1\) or \(\varDelta m_{F}=+1\), for the two polarizations, respectively. In this manner, the population of electrons is transferred into a magnetic substate (\(m_{F}\) state) with a maximum or minimum value. The induced atomic polarization is partially transferred to the nucleus via the adiabatic decoupling and hyperfine interaction. A weak magnetic guiding field is used to maintain the polarization of the beam along the distance it travels. At the end of the beamline, an implantation point is installed in a transverse magnetic field, B. The most commonly used hosts are crystals, however recently liquid samples have also been tested [82]. The final stage of this experiment is the detection of the \(\beta \)-decay and the observation of the asymmetries in the emitted \(\beta \)-particles along and opposite to the magnetic field. One possibility is to correlate the laser frequency used for nuclear polarisation with the detected asymmetry and thus obtain the hyperfine structure spectrum. Another possibility is to make sure the laser frequency is optimal for nuclear polarisation and then use a radiofrequency signal for the destruction of the nuclear polarization. In this case, as a function of the radio frequency \(\nu \), an asymmetry is observed in the \(\beta \)-decay spectrum. This gives access to the Larmor frequency: \(\nu = g \mu _{N} B/h\), and thus directly to the nuclear g-factor. Note however that this method is limited to isotopes with non-zero nuclear spin and short half-lives and which undergo \(\beta \)-decay.

Another method that exploits the collinear geometry for optical pumping is often referred to as the state-selective collisional ionization technique [16, 84]. Here, the incoming beam is first neutralized. In the next step, laser light is used to resonantly pump the atom from one state to another (meta-)stable state, which has a significantly different cross section for collisional ionization. The fast beam then passes through a collisional re-ionization cell, after which both the atoms and the ions are detected. Thus, when the laser light is on resonance with an atomic transition, either the atom beam increases and the ion beam decreases, or vice versa, enabling a measurement of the hyperfine structure. Another variant of this method utilizes an optical pumping stage prior to a neutralization stage. The spectroscopy is then performed by also detecting both atom and ion beams, and relying on a difference in charge-exchange cross section between two (meta-)stable ionic levels [15, 86].

4 Nuclear structure observables

4.1 Changes in the nuclear mean-square charge radius

At the level of precision achieved by collinear laser spectroscopy experiments, subtle details of nucleon-nucleon interactions can be examined by measuring the changes in the mean-square charge radii along an isotopic chain. Among other phenomena, charge radii have been used to unveil a signature of shape coexistence [64, 87], map the border of the island of inversion [88], study the proton superfluidity in proton-rich isotopes [69], investigate the nature of newly proposed shell closures [20] and the rigidity of traditional shell closures in isotopes far away from stability [63]. More information on different techniques to measure nuclear charge radii and their role in nuclear structure research can be found in [89].

The extraction of the changes in the nuclear mean-square charge radius requires a measurement of the hyperfine structure of two isotopes, one being the reference for the measured changes. The equation for the extraction of the \(\delta \langle r^2 \rangle \) is defined in Eq. 6. Until very recently, for short-lived radioactive isotopes this nuclear property has only been extracted using laser spectroscopy techniques. However, electron scattering has recently demonstrated the required sensitivity for online use [90], which will soon enable comparison with laser spectroscopy data, and charge-exchange reactions have also been exploited for nuclear radius determination (albeit in nuclear-model dependent fashion) [91]. The sensitivity of the used atomic transition to the nuclear size is contained in the atomic field shift factor F. The highest sensitivity is expected when probing an atomic transition in which a significant change in s- electron content occurs between the states. The wave function of s-electrons have a non-zero probability density over the volume of the atomic nucleus and are the most perturbed by the nuclear field. For s to p transitions, mass shifts dominate the perturbation for low-Z elements. The field and mass shift then become comparable around \(Z\sim 30\) and, finally, field shifts dominate in heavier atoms.

Besides the isotope shift, an isomer shift can also be extracted, in case both nuclear states have sufficiently long half-lives for laser spectroscopy studies. In practice, in such measurements, the contribution of the difference in masses of these two states is often negligible, and the isotope shift is determined by the field shift factor. Finally, the nuclear charge radius is calculated using:

$$\begin{aligned} R = \sqrt{\delta \langle r^{2} \rangle + R_{A}^{2}}, \end{aligned}$$
(11)

where \(R_{A}^{2}\) is the charge radius of a reference isotope, often obtained from electron scattering or muonic X-ray experiments.

The study of the nuclear structure often only relies on the changes in the mean-square charge radii and nuclear structure phenomena are observed as a change in the trend of the \(\delta \langle r^{2} \rangle \) [89]. A classic example of this is the appearance of a characteristic increase in the \(\delta \langle r^{2} \rangle \) when a magic neutron number is crossed. This signature of nuclear magicity persists in the neutron-rich Sn isotopes at \(N=82\) [92] and proton-rich Ni and Ag isotopes at \(N=28\) and \(N=50\), respectively [63, 93]. On the other hand, it is for example absent at \(N=20\) in the region of stable Ca [69, 70] and K [94], and also at the \(N=32\) sub-shell closure in neutron-rich K [20].

4.2 Nuclear magnetic dipole moment \(\mu \)

The magnetic dipole moment of a nucleus arises as the net sum of the angular and intrinsic dipole moments of the nucleons inside the nucleus, and is expressed as \(\mu = I \mu _{N} g\), with \(\mu _{N}\) the nuclear magneton (\(\mu _N = 3.1524512550(15)\times 10^{-8}\) eV/T) and g the nuclear g-factor. The magnetic moment of an odd-mass nucleus can be approximately calculated by assuming that only the valence nucleon contributes to the magnetic moment, with all other nucleons coupling to spin zero. In this strict single-particle approximation, the magnetic moment of a nucleus with the unpaired nucleon placed in an orbit with \(j = l \pm s\) can be calculated according to the following expressions:

$$\begin{aligned} \mu&= jg_{l}+\frac{g_{s}-g_{l}}{2} \quad \text {for} \quad j=l+1/2 \end{aligned}$$
(12)
$$\begin{aligned} \mu&= jg_{l}-\frac{g_{s}-g_{l}}{2} \frac{j}{j+1} \quad \text {for} \quad j=l-1/2, \end{aligned}$$
(13)

where \(g_{l}\) and \(g_{s}\) are the orbital and spin g-factors of the odd nucleon, proton \((\pi )\) or neutron \((\nu )\), which are

$$\begin{aligned} g_l^{(\pi )} = 1&\qquad g_s^{(\pi )} = +5.585694702(17) \end{aligned}$$
(14)
$$\begin{aligned} g_l^{(\nu )} = 0&\qquad g_s^{(\nu )} = -3.82608545(90). \end{aligned}$$
(15)

These expressions define the so-called Schmidt limits for the \(j=l\pm 1/2\) nuclei. Although simple in nature, these equations are remarkably successful in reproducing the general trends, in particular close to magic numbers. It is experimentally observed that the measured magnetic moments nearly always fall between these Schmidt limits. Deviations from the Schmidt estimates, in spherical nuclei, are commonly attributed to the simplicity of the model; effects such as core polarization and meson exchange currents, beyond a simple single-particle description, must be considered. To account for these effects, the g-factors \(g_{l,s}^{(\pi , \nu )}\), which we refer to as the free-nucleon g-factors, are typically replaced by effective g-factors. These are found to be slightly different for different regions of the nuclear chart. As an example, for the medium-mass region, the most commonly used values are \(g_{l}^{\pi , \text {eff}}=1.1\), \(g_{l}^{\nu , \text {eff}}=-0.1\) and, \(g_{s}^{\text {eff}}=0.7 g_{s}^{\text {free}}\).

Laser spectroscopy experiments can be used to extract the nuclear magnetic moment. This can be done using both the lower and the upper atomic state, though often one is more precise than the other. For example, for the structure given in Fig. 1, the hyperfine dipole splitting of the excited state is larger, and can thus be more accurately determined. Once the magnetic moment is obtained, its value can be compared to the simple Schmidt moments, which can aid in assigning a valence particle configuration to the nucleus. Deviations from the effective Schmidt lines may indicate that the configuration of the nucleus is rather mixed. More insight into the nuclear wavefunction can nowadays be obtained from more sophisticated models and calculations. For example, large-scale configuration interaction calculations (often referred to as shell-model calculations) can be used to further investigate the dominant configuration of the valence particles which determine the nuclear properties. For a detailed discussion on how nuclear magnetic moments and g-factors can be used to explore nuclear structure, we refer the reader to Ref. [95].

Fig. 4
figure 4

The hyperfine structure of the ground state and isomer in \(^{129}\)In (top) and \(^{131}\)In (bottom), first reported in [72]. The resonances associated with the isomer are shaded in blue. The difference in the nuclear structure at \(N=80\) and \(N=82\) is evident from the hfs, even without performing detailed analysis: the structure of the ground-state becomes wider since \(\mu _{\text {gs}}\) increases, and the structure of the isomer collapses, since \(\mu _{\text {iso}}\) becomes smaller

Full size image

As an example, recently, the nuclear magnetic moment of In (\(Z=49\)) isotopes was measured using collinear laser spectroscopy, using the CRIS technique, up to N = 82 [72]. This serves as a prime example to demonstrate the sensitivity of the collinear laser spectroscopy techniques to the evolution of the nuclear structure. In Ref. [72], a sudden change in the magnetic dipole moments of both the \(I = 9/2^-\) ground state and long-lived isomeric \(I = 1/2^-\) states was found at \(N=82\), indicating the abrupt onset of single-particle behavior close to this nuclear magic number. This sudden change in the moments is in contrast to the magnetic moments of all previously measured In isotopes, which displayed a remarkably flat trend across more than 20 mass units. To demonstrate the sensitivity of the collinear laser spectroscopy to such structural changes, and how these changes can be inferred in a nuclear-model independent fashion, we show the hyperfine spectra of \(^{129}\)In and \(^{131}\)In in Fig.4. While \(^{129}\)In with \(N=80\) has a very similar structure to lighter isotopes in the chain, the change of the nuclear structure at \(N=82\) is evident from the obtained spectrum of \(^{131}\)In. To aid in interpreting the spectrum, the resonances corresponding to the isomer are shaded in blue. For the ground state with \(I=9/2\), the magnetic moment becomes larger, and the resonances spread further apart. For the \(I=1/2\) isomer, the magnetic moment decreases in magnitude, and the three clearly resolved lines in \(^{129}\)In merge into one for \(^{131}\)In. Since the spin of these states remains the same in both isotopes, the ratio of their magnetic moments is equal to the ratio of the hyperfine A parameters, according to Eq. 3. For the \(I=9/2\) states this results in \(A_{129}/A_{131}=0.881(4)\) while for \(I=1/2\), \(A_{129}/A_{131}=7.8(27)\).

4.3 Nuclear electric quadrupole moment Q

Collinear laser spectroscopy, due to its excellent resolution, can be used to measure the spectroscopic quadrupole moment from the hyperfine B constant, provided the nuclear spin \(I>1/2\). For isotopes with an odd number of protons, a single-particle estimate of the quadrupole moment can be evaluated as:

$$\begin{aligned} Q_{s.p.}=-e \frac{2j-1}{2j+2}\langle r^2 \rangle _{s.p.}, \end{aligned}$$
(16)

where \(\langle r^2 \rangle _{s.p.}\) is the mean-squared charge radius of the valence proton. It is also possible to predict the quadrupole moment of nuclei with n valence protons outside the inert core in a seniority-\(\nu \) configuration:

$$\begin{aligned} Q= Q_{s.p.} \frac{2j+1-2n}{2j-1-2\nu }. \end{aligned}$$
(17)

This equation predicts that, as a shell is filled, the quadrupole moments will increase linearly, crossing zero when the shell is half-full. Such trends have been explored in the Ca region, for both odd-proton Ca [96] and odd-neutron Sc [97] isotopes, the heavy mass region in Ref. [98] and recently in the mass region of Sn in [26]. While these simple relations are useful to understand the structure of isotopes with only one or a few nucleons outside of closed shells, their applicability is limited. For instance, odd-neutron nuclei are also found to have non-zero quadrupole moments, which cannot be explained using Eq. 16, and again core polarization effects should be introduced.

Fig. 5
figure 5

Study of the nuclear deformation in Y (\(Z=39\)) isotopic chain around N=60 [87]. a The hfs spectra of \(^{96-101}\)Y, shown with the mass number on the y-axis, display a clear jump towards lower centroid frequencies at \(N=59\) due to the sudden change in nuclear size. b This change is evident from the extracted change in the mean-squared charge radii with respect to the \(N=50\) isotope. The dashed line connects the ground-state datapoints. c The extracted spectroscopic quadrupole moments display the same abrupt change in the trend at \(N=59\). The dashed line here is only to guide the eye. Note that \(Q_{s}\) can only be measured for isotopes with \(I>1/2\)

Full size image

Deformed nuclei can possess quadrupole moments which are much larger in magnitude than (and usually of opposite sign to) the single-particle values obtained using Eq. 16. This reflects the fact that the quadrupole moment provides a measure of the collectivity of the nuclear wavefunction. When the quadrupole moment is smaller than zero, the nucleus is said to be oblate deformed, and when it is larger than zero, the nucleus is said to be prolate deformed. In addition, we can distinguish between static and dynamic deformation. Assuming that the studied nucleus can be treated as an axially symmetric deformed system, the following expressions link the static deformation parameter to the intrinsic quadrupole moment:

$$\begin{aligned} Q_{0}&\approx \frac{5 Z \langle r^2 \rangle _{\text {sph}}}{\sqrt{5\pi }} \langle \beta _{2} \rangle (1+0.36 \langle \beta _{2} \rangle ), \end{aligned}$$
(18)
$$\begin{aligned} Q_{0}&= Q_{s} \frac{(I+1)(2I+3)}{I(2I-1)} \end{aligned}$$
(19)

where \(\langle r^2\rangle _{\text {sph}}\) is the mean-square charge radius of a spherical nucleus with the same volume, \(Q_{0}\) is the intrinsic quadrupole moment and \(Q_s\) is the spectroscopic quadrupole moment. The dynamic quadrupole deformation parameter \(\langle \beta ^2_{2} \rangle \) can be obtained from the mean-squared charge radius using:

$$\begin{aligned} \delta \langle r^2 \rangle = \delta \langle r^2 \rangle _{\text {sph}}+ \langle r^2 \rangle _{\text {sph}} \frac{5}{4\pi } \sum _{i}{\delta \langle \beta _{i}^{2} \rangle }. \end{aligned}$$
(20)

Changes in \(\langle r^2 \rangle \) due to the change in the collective shape are typically dominated by the quadrupole term, \(i=2\) in Eq. 20. More information on the role of electric quadrupole moments in the study of nuclear structure can be found in [95].

As an example for the investigation of nuclear deformation from collinear laser spectroscopy, results obtained for the Y (\(Z=39\)) isotopic chain [87] are presented in Fig. 5. In this region of the nuclear chart, a sudden change in the nuclear structure occurs at \(N=60\). This is apparent from the measured hfs spectra presented in Fig. 5a by looking at the position of the measured structures with respect to each other. The spectrum of \(^{96}\)Y and \(^{97}\)Y contain 2 and 3 states, respectively. While the spectra of \(^{96,97,98}\)Y are well aligned with each other, the hfs of \(^{99,100,101}\)Y are significantly shifted towards lower frequencies, due to the sudden change in the size of the nuclear charge radius of these isotopes. The extracted quadrupole moments and changes in the mean-squared charge radii allow for a more detailed investigation of the underlying structural changes, as shown in Fig. 5b, c. The same abrupt change is observed at \(N=60\) in both of the measured observables. Whereas the quadrupole moment depends on the mean of the quadrupole deformation parameter, \(\langle \beta _2\rangle \), and is sensitive also to the sign of the deformation, the mean-square charge radius depends on the mean-square quadrupole deformation, \(\langle \beta _2^2\rangle \), and differential changes are obtainable for all nuclei including those with \(I<1\). For nuclei where both are obtainable, these complementary probes of deformation reveal also the level of “\(\beta \)-softness”. In the yttrium chain, the transition occurs from weakly deformed oblate nuclei (\(A<98\)) to strongly deformed prolate nuclei (\(A>98\)). This is accompanied by an increase in the rigidity of the deformation. For the lighter nuclei \(\langle \beta _2\rangle ^2<\langle \beta _2^2\rangle \), suggesting a dynamic component, but after the shape change, a static deformation is seen where \(\langle \beta _2\rangle ^2\sim \langle \beta _2^2\rangle \).

4.4 Nuclear spin

In many cases the nuclear spin, I, can be unambiguously assigned using laser spectroscopic data. This constitutes a direct measurement, since the spin is established without reference to nuclear models or systematics, and alternative assignments can be excluded.

There are several ways to extract the nuclear spin from the measured hyperfine structure spectrum. Firstly, the number of observed peaks in the spectrum depends on the nuclear spin I and the total angular momentum of the excited electron J: the allowed values of the total angular momentum F are \(|I+J|\), \(|I+J|-1,\ldots , |I-J|\). When \(I<J\), the number of peaks is thus determined by I, and therefore also the number of allowed transitions between the two hfs manifolds. This is clear from the spectra of the two nuclear states of \(^{129}\)In and \(^{131}\)In, obtained with a J = 3/2 to J = 1/2 transition, shown in Fig. 4. As another example, we discuss the spin determination of \(^{31}\)Mg [80]. For this measurement, the collinear geometry was used to induce spin-polarisation by optical pumping. The data obtained in this measurement is reproduced in Fig. 6, adapted from [80]. In this figure, the \(\beta \) asymmetry is shown as function of the Doppler tuning voltage for \(^{31}\)Mg. The laser was tuned close to the \(S_{1/2} \rightarrow P_{1/2}\) line. The x-axis can therefore be taken as proportional to the laser wavelength observed in the frame of reference of the fast Mg ions. The arrows underneath the spectrum show that for a nuclear spin of \(I=1/2\), only three resonances are expected based on the atomic selection rules. For a spin \(I\ge 3/2\), six resonances are expected. Experimentally, only three resonances are observed, thus clearly establishing that \(I=1/2\). Further evidence is found from the separation between the simulated resonance locations, which are based on the g-factor obtained from a subsequent \(\beta \)-NMR measurement. Only \(I=1/2\) yields consistent splittings in this hyperfine spectrum.

Fig. 6
figure 6

Observed \(\beta \) asymmetry as function of the Doppler tuning voltage for \(^{31}\)Mg, with the laser tuned across the \(S_{1/2} \rightarrow P_{1/2}\) line (adapted from [80]). The arrows underneath the spectrum indicate predicted resonance locations, assuming different values of I, from which a confident assignment of \(I=1/2\) can be made (see text for more details)

Full size image

The nuclear spin can also be obtained from the ratio of the hyperfine A parameters along an isotopic chain. This ratio is constant, under the assumption that the hyperfine anomaly or second-order hyperfine interaction can be neglected (as is often the case). As an example, this approach was applied to measure the spin of \(^{72,74,76}\)Cu [99, 100].

The intensity of the hyperfine transitions is dependent on the nuclear spin as shown in Eq. 5. However, in a measurement the intensity of the measured peaks can also be affected by other factors such as optical pumping and saturation effects. Thus, spin assignments using these peak ratios must be applied with great care. If the intensity ratios of peaks in the measured spectra of isotopes with known I are identical to those defined in Eq. 5, it may be possible to assign the nuclear spin of the nucleus with an unknown I. This approach was followed to assign the spin of \(^{51}\)K [71].

In a few cases where the methods above do not succeed in discriminating between alternative spin assignments definitively, explicit values for the nuclear properties may be extracted for each possible value of nuclear spin. Often, the incorrect spin will result in unrealistically large or small charge radii [20]. Similar arguments can also be made using the nuclear electromagnetic moments [101].

5 Conclusions

This work discussed how collinear laser spectroscopy is a versatile and sensitive tool for the study of nuclear properties. The technique has a rich history, yet is continuously being further developed, especially the sensitivity and versatility. Over the years, many different implementations of the method have been used for the study of radioactive isotopes. Courtesy of the collinear geometry and relatively long interaction times, the ion (atom) beams can be manipulated using collisions in vapor cells, using (potentially several) laser(s) for state manipulation, polarisation or ionization, all in pursuit of achieving the best sensitivity, selectivity and precision.

As demonstrated in this work, the nuclear electromagnetic moments and changes in the mean-square charge radii can be extracted from collinear laser spectroscopy measurements. This extraction depends on a correct assignment of the nuclear spin and a definitive assignment is often obtainable from the hyperfine structure analysis. These observables allow for gaining a comprehensive understanding of the nuclear structure of the measured nuclear states. The examples presented and discussed above demonstrate the nuclear model-independent way that information about the evolution of the nuclear structure can be extracted from the hyperfine spectra. It is also worth mentioning that new long-lived isomeric states were discovered using CLS [64, 66, 102].

Similar to other experimental techniques in RIB facilities, the main force driving the experimental developments is the measurement of isotopes close to the proton drip-line, and very neutron-rich systems. The implementation of high-precision measurement techniques is an emerging frontier and will play a significant role in exploring higher order nuclear moments and other unexplored phenomena. The potential of collinear laser spectroscopy techniques has been recognized in the nuclear physics community, which is demonstrated by the commitment to the installation of these techniques in future radioactive ion beam facilities.