Collinear laser spectroscopy at ISOLDE: new methods and highlights

For some light short-lived isotopes the problem of sensitivity can be addressed by optically polarising the nuclei and detecting the polarisation in the angular distribution of β-decay electrons or positrons, which is asymmetric with respect to the nuclear spin direction. With implantation of the beam into a suitable host crystal lattice this has the further advantage of offering an alternative access to the nuclear moments, which is based on NMR detected by the influence of radiofrequency on the β-decay asymmetry (β-NMR). The magnetic moments of nuclei interact with a static magnetic field, while the quadrupole moments interact with an electric field gradient produced at their lattice site in a non-cubic crystal. The latter is particularly important for light atomic systems where the quadrupole interaction is too small to be resolved in the hyperfine structure of spectral lines.

Polarisation occurs by optical pumping between the m_F states of the coupled atomic system of electronic and nuclear spin. The spins are decoupled in the strong magnetic field before entering the host crystal where the nuclear spin polarisation relaxes within typically a few seconds. Resonant interaction of the atoms with the circularly polarised laser light produces atomic and nuclear spin polarisation. After implantation of the polarised radioactive beam in a suitable crystal, a NMR signal is observed as a change in the β-decay asymmetry.

Optical pumping and β-NMR experiments were initiated already at ISOLDE-2 with the goal of measuring the spin and the magnetic moment of the famous two-neutron halo nucleus ¹¹Li [21]. The result of $I=3/2$ ruled out strong deformation as a possibility to explain the exceptionally large matter radius obtained from break-up cross-sections [22] in high-energy reactions. Later on, with refined NMR techniques, even the quadrupole moment could be determined by measuring the interaction with the electric field gradient at the Li lattice site in a LiNbO₃ crystal [23]. In the comparison of ⁹Li and ¹¹Li it turned out that the two additional (halo) neutrons have little effect on the quadrupole moment.

${}^{11}$Li revisited. Based on these achievements a new effort was made after 2000 towards a considerable improvement of the quadrupole moment measurement on ¹¹Li, with the primary goal of detecting an influence of the halo neutrons on the ⁹Li core which is responsible for the electrical properties. Compared to the previous approach, a new NMR magnet offered a more homogeneous magnetic field and from a systematic study of implantation crystals it became possible to gain an order of magnitude in resolution by replacing the LiNbO₃ ionic crystal by a metallic Zn crystal [24]. The multiple-rf resonance technique employed already previously, uses a set of radio frequencies depending on the quadrupole moment Q as a parameter and requires the exact knowledge of the Larmor frequency which is determined by the magnetic moment. For this purpose a new precise measurement of the g-factor ratio between ¹¹Li and ⁸Li was performed in an auxiliary experiment using a cubic Si crystal. The result of $\mu {(}^{11}\mathrm{Li})=3.6712(3){\mu }_{N}$ is an order of magnitude more accurate than the previous value [21], due to the narrow resonance linewidth in the Si crystal as compared to Au or LiF hosts [24].

The quadrupole splitting of the NMR signal of ¹¹Li was measured with reference to ⁹Li which both have the same spin and similar magnetic and electric moments. In this way systematic uncertainties related to resonance shapes and rf-field broadening could largely be avoided. The result is $Q{(}^{11}\mathrm{Li})/Q{(}^{9}\mathrm{Li})=1.088(15)$, meaning that the quadrupole moment of ¹¹Li is nearly 10% larger than that of ⁹Li. We can try to interpret this observation [11] assuming the simple picture of a ⁹Li core surrounded by two halo neutrons in spherical orbits. From experiment [25, 26] we know that the rms charge radius $\langle {r}^{2}{\rangle }^{1/2}$ increases by 10.2(2.8)%, from 2.25(5) fm for ⁹Li to 2.48(4) fm for ¹¹Li, while we find that the quadrupole moment increases by 8.8(1.5)%. For identical deformation of ⁹Li and ¹¹Li one should expect an increase of the quadrupole moment proportional to the mean square radius $\langle {r}^{2}\rangle$. However, if we ascribe the increase of the radius to a recoil effect caused by the spherical halo, the centre-of-mass (CM) movement produces an isotropic expansion of the (non-spherical) charge distribution and the quadrupole moment increases just with $\langle {r}^{2}{\rangle }^{1/2}$. This explains the striking analogy between the quadrupole moments and the rms charge radii without any additional influence of the halo neutrons on the ⁹Li-core structure.

The trend of experimental quadrupole moments from ⁷Li to ¹¹Li (figure 2) is perfectly reproduced by a no-core shell model (NCSM) using an effective interaction derived microscopically from a nucleon–nucleon potential fitted to nucleon scattering data [27]. Only the absolute values of all quadrupole moments are about 30% smaller than the experimental values. This may be explained by a limited model space and could be adjusted by using effective charges.

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Magnesium. The neutron-rich magnesium isotopes cover the upper sd-shell and range into the so-called island of inversion which is characterised by a disappearance of the N = 20 shell gap. For the prominent N = 20 nucleus ³²Mg strong deformation was postulated from the large $B({\rm{E}}2;{2}^{+}\to {0}^{+})$ value [28] and this is consistent with the behaviour of other observables as, e.g., the nuclear masses and excitation energies in this region. Measuring nuclear moments and radii of the magnesium isotopes remained a challenge for sensitivity reasons.

At ISOLDE laser ionisation with RILIS offers favourable production conditions for the short-lived odd-A isotopes around ³²Mg. Optical pumping with sufficient laser power of a few mW can be performed in one of the UV resonance lines of Mg⁺ ions at 280 nm and used for β-NMR experiments. For the longer-lived isotopes closer to stability further interesting information on the radii and moments can be obtained from conventional collinear laser spectroscopy measurements.

The series of experiments covering all these aspects started with a great surprise about the spin and the magnetic moment of ³¹Mg. This nucleus appeared to be an ideal β-NMR candidate because of the short half-life of 250 ms and a still abundant production of more than 10⁵ ions per second. Beta-decay asymmetries up to 10% were reached by excitation in the transition $3{\rm{s}}{}^{2}{{\rm{S}}}_{1/2}\to 3{\rm{p}}{}^{2}{{\rm{P}}}_{3/2}$ (D2 line). The spin and magnetic moment were measured by combining the results from two experimental techniques, based on the atomic hyperfine structure and on the nuclear interaction with external magnetic fields. With the nuclear g-factor obtained from the NMR Larmor frequency, the spin I was directly deduced from the atomic (ground state) hyperfine structure splitting being proportional to the parameter $g(I+1/2)$.

Contrary to all expectations from systematics and from shell-model calculations the N = 19 nucleus ³¹Mg turned out to have the spin $I=1/2$ with a positive parity [29]. This puzzling result initiated some theoretical effort [30] that succeeded to reproduce the level assignments based on the measured ground state spin and confirmed a ground state wave function being dominated by 2p–2h intruder configurations as inferred already from the magnetic moment [29]. Further controversy with conclusions from nuclear spectroscopy and shell-model theory came up with the measurements on ³³Mg yielding $I=3/2$ combined with a magnetic moment that was consistent only with a negative parity [31, 32]. The ³³Mg ground state could again be shown to have a nearly pure 2p–2h intruder nature, contrary to the earlier suggested 1p–1h configuration and in agreement with the structure of other isotopes in the 'island'.

Although the β-decay asymmetry served as a very sensitive method of detecting optical resonance in short-lived isotopes, it remained of limited use for the accurate measurement of isotope shifts. This is a consequence of the complicated line shapes caused by the optical pumping process in a magnetic field varying along the beam path. However, a realistic description of the resonance line shapes is possible if optical pumping is performed in ions for which the interaction with the light can be switched on and off by the Doppler effect and the resonance condition is established only in a well-defined low-magnetic-field region.

The quantitative simulation of the resonance line shapes of a β-asymmetry spectrum is shown in figure 3 for the example of ³¹Mg. It is the result of optical pumping in a weak magnetic field and subsequent decoupling of the electronic and nuclear spins with detection of nuclear spin polarisation [12]. For measuring the isotope shifts within the chain of magnesium isotopes [33] this feature was exploited for the neutron-rich ²⁹Mg and ³¹Mg and the neutron-deficient ²¹Mg. The conventional method of optical resonance detection was used for odd-A isotopes close to stability and on doubly-even isotopes including the special case of ³²Mg for which the weak signal had to be brought out from the background by counting photons in coincidence with ions.

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The mean square charge radii extracted from these isotope shifts exhibit a minimum around stable ²⁶Mg. This corresponds to a minimum of deformation in the middle of the sd shell around N = 14. From the steep increase beyond ³⁰Mg the borderline of the island of inversion is localised between ³⁰Mg and ³¹Mg, in accordance with the conclusions from spins and magnetic moments.

Isotope shift measurements on light elements with $Z\lt 10$ have not been possible at COLLAPS until recently, due to the limitations caused by voltage measurements and the limited knowledge of the exact starting potential of the ions. The acceleration voltage is known to about 10⁻⁴ relative uncertainty and has even been calibrated to somewhat higher accuracy using a high-precision high-voltage divider [34]. However, this still leads to an uncertainty of about 15 MHz for the isotope shift between ⁹Be⁺ and ¹¹Be⁺ in the $2{\rm{s}}\to 2{\rm{p}}$ resonance lines, which has to be compared to the expected field-shift contribution of approximately 5 MHz. In order to address this chain of isotopes, a technique that combines collinear laser spectroscopy using counter-propagating and co-propagating laser beams with frequency-comb technology was developed. The beam line setup and the frequency-comb locked laser system are described in detail in [35]. This allowed the measurement of absolute transition frequencies in the laboratory frame for both directions (${\nu }_{\pm }$), which are related to the rest-frame frequency ${\nu }_{0}$ according to

$$\begin{eqnarray}&&{\nu }_{\pm }={\nu }_{0}\gamma (1\pm \beta ).\end{eqnarray} \tag{ 1 }$$

The velocity of the ions $\beta =\upsilon /c$ as well as the time dilation factor $\gamma ={(1-{\beta }^{2})}^{-1/2}$ depend on the acceleration voltage, but with both absolute transition frequencies measured precisely in the laboratory frame, these variables can be eliminated:

$$\begin{eqnarray}&&{\nu }_{+}\cdot {\nu }_{-}={\nu }_{0}^{2}{\gamma }^{2}(1+\beta )(1-\beta )={\nu }_{0}^{2}.\end{eqnarray} \tag{ 2 }$$

Hence, the rest-frame transition frequency ${\nu }_{0}=\sqrt{{\nu }_{+}\cdot {\nu }_{-}}$ can be extracted without additional knowledge of the ion velocity or acceleration voltage. Spectra taken with co- and counter-propagating laser beams look like mirror images. This is an additional asset since small inaccuracies from the modelling of the line shape shift the peak centre into opposite directions. Consequently, the respective shift largely cancel each other when taking the geometric average.

Isotope shifts $\delta {\nu }_{\mathrm{IS},\exp }^{9,A}={\nu }^{A}-{\nu }^{9}$ were measured for ${}^{7-12}$Be. To extract differences in the mean square nuclear charge radii, these were combined with state-of-the-art ab initio atomic structure calculations for the three-electron system [36–38], providing the mass shift $\delta {\nu }_{\mathrm{MS},\mathrm{theory}}^{A,{A}^{\prime }}$ and the field shift factor F with very high accuracy. The radii changes are related to the isotope shifts by

$$\begin{eqnarray}&&\delta \langle {r}_{c}^{2}{\rangle }^{9,A}=\displaystyle \frac{\delta {\nu }_{\mathrm{IS},\exp }^{9,A}-\delta {\nu }_{\mathrm{MS},\mathrm{theory}}^{9,A}}{F}.\end{eqnarray} \tag{ 3 }$$

Total charge radii were then obtained by combining $\delta \langle {r}_{c}^{2}{\rangle }^{9,A}$ with the known charge radius of the stable isotope ⁹Be determined using elastic electron scattering [39]. The results, shown in figure 4, reveal a characteristic trend that can be explained by the cluster structure of these light nuclei. This is visualised in a very simplified picture in the small panels below the graph. The lightest isotope ⁷Be can be regarded as a two-body cluster $\alpha +{}^{3}\mathrm{He}$. CM motion blurs the proton distribution and leads to a rather large charge radius. The stable ⁹Be has an $\alpha +\alpha +n$ structure and is less extended than ⁷Be due to the compactness of the α particles and the binding strength of the additional neutron. This effect is even enhanced with the second neutron added in ¹⁰Be. The sudden upward trend to ¹¹Be is attributed to the one-neutron halo character of ¹¹Be which can be disentangled into a ¹⁰Be core and a loosely bound neutron. This halo character increases the matter radius and also affects the charge radius due to the CM motion of the core. The further increase towards ¹²Be is attributed to a strongly mixed sd character of the two outermost neutrons, indicating the disappearance of the N = 8 shell closure for beryllium. A more detailed discussion of the nuclear charge radii in comparison with ab initio microscopic nuclear structure calculations and conclusions about the shell closure can be found in [40–42]. The investigation of both lines of the $2{\rm{s}}{}^{2}{{\rm{S}}}_{1/2}\to 2{\rm{p}}{}^{2}{{\rm{P}}}_{1/\mathrm{2,3}/2}$ fine structure doublet also yielded information on the fine-structure splittings for all isotopes [43]. These are in reasonable agreement with advanced calculations by Puchalski and Pachucki [44] and provided an important test of many-body non-relativistic bound-state quantum electrodynamics theory.

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In the odd-A K ($Z=20-1$) and Cu ($Z=28+1$) isotopes it had been observed that the first-excited-state energy decreases dramatically with an increasing number of neutrons between N = 20 and 28 in potassium and beyond N = 40 in copper. In the K isotopes the energy of the 1/2⁺ level (due to a hole in the πs${}_{1/2}$ orbital) decreases gradually as the νf${}_{7/2}$ level is being filled and this level becomes the ground state in ⁴⁷K [73]. In the Cu isotopes the 5/2⁻ level energy (due to a proton in the πf${}_{5/2}$ level) was seen to decrease between ⁶⁹Cu and ⁷³Cu [74], as the νg${}_{9/2}$ is being filled.

In 2005 Otsuka et al explained this monopole migration of single-particle levels as due to the tensor part of the nucleon–nucleon monopole interaction, and they provided an intuitive explanation as to where and how this monopole migration would occur in the nuclear chart [75]. The interaction is strongest between protons and neutrons, and between nucleons having the same radial quantum number. The interaction is attractive for orbits that have opposite intrinsic and orbital spin, and repulsive between orbits that have their intrinsic and orbital spins in the same direction. The strength of the interaction increases as the orbits are being filled.

Thus in the K isotopes, it is the increase of the attractive force between the ${{\rm{d}}}_{3/2}$ protons and the neutrons filling the ${{\rm{f}}}_{7/2}$ level that induces a stronger binding of the proton level, thus reducing the gap with the π1s${}_{1/2}$ level and even reversing these effective single-particle levels at N = 28. An open question was how this level inversion would change when the next neutron orbit, ${{\rm{p}}}_{3/2}$ would be filled. That question was answered by hyperfine structure measurements on the K isotopes between N = 18 and 32. The ground state spin remains 1/2⁺ in ⁴⁹K but re-inverts back to 3/2⁺ in ⁵¹K [51]. The composition of the ground state wave functions could be confirmed by the large scale shell model calculations which reproduced the measured magnetic moments very well [52].

In the Cu isotopes, it was predicted that in ⁷⁵Cu the 5/2⁻ level would become the ground state because of the increasing attraction between the π0f${}_{5/2}$ and the ν0g${}_{9/2}$ orbits, leading to an inversion of the ${{\rm{p}}}_{3/2}$ and ${{\rm{f}}}_{5/2}$ proton effective single-particle levels at N = 46. High-resolution experiments on Cu isotopes using optical detection could be performed up to ⁷⁵Cu, establishing experimentally the spin inversion [49]. Low-resolution in-source resonance ionisation spectroscopy proposed a ground state spin/parity 5/2⁻ for ⁷⁷Cu as well [76], and this was recently confirmed by high-resolution studies up to ⁷⁸Cu, using the high-resolution CRIS technique (see section 3.3 for details on the method). Data are currently being analysed and details on spins, radii and moments will be extracted [77]. In the Ga isotopes (Z = 31) the inversion of the single-particle proton orbitals is not as clear-cut and a very rich ground state structure has been observed between N = 40 and N = 50 [50]. Up to ⁷⁹Ga the ground state spin is 3/2⁻, except for ⁷³Ga (N = 42) where the ground state was measured to be 1/2⁻, contrary to the earlier reported 3/2⁻. From the measured magnetic and quadrupole moments it could be inferred that the ground state wave functions gradually change from three protons in the πp${}_{3/2}$ orbit for the stable ${}^{\mathrm{69,71}}$Ga to a very mixed wave function for the 1/2⁻ ground state in ⁷³Ga. The moments of ${}^{\mathrm{75,77}}$Ga are consistent with two protons in πf${}_{5/2}$ and one proton in πp${}_{3/2}$, while the full inversion of the proton ${{\rm{f}}}_{5/2}$ and ${{\rm{p}}}_{3/2}$ level occupations occurs in ⁷⁹Ga (N = 48) which has a leading πf${}_{5/2}{}^{3}$ configuration, coupled to spin 3/2. Only at ⁸¹Ga, at N = 50, does the ground state actually become 5/2⁻. Also, a new isomeric state was observed in ⁸⁰Ga [66] and its beta-decay properties were recently measured at ISOLDE [78]. Laser spectroscopy was also well-placed to confirm the existence of and firmly assign spins to long-lived isomeric states in the Zn isotopes. In particular an intruder isomeric state was established in ${}^{79{\rm{m}}}$Zn [65], which notably displayed a signature of shape coexistence.

No evidence for an N = 32 shell gap. A variety of spectroscopy experiments on neutron-rich isotopes with $Z\geqslant 20$ suggested the appearance of a new magic number at N = 32 towards ⁵²Ca [79–82]. Recent mass measurements up to ⁵⁴Ca confirmed that result and 'unambiguously establishes a prominent shell closure at neutron number N = 32' [83]. Furthermore, mass measurements up to ⁵³K confirmed the local 'doubly-magic' nature of ⁵²Ca [84].

However, in the mean square charge radii of the K isotopes, no clear evidence for a sub-shell closure at N = 32 is observed [54]. We also measured the mean square charge radii of the Ca isotopes from N = 20 up to 32, and also in these isotopes no signature of a shell effect at N = 32 is seen [48]. In figure 5(a), all recently measured (and published) charge radii from K up to Ga are shown. A clear increase is observed in the radii when crossing N = 28. For K and Ca, no flattening towards N = 32 is seen, which would be expected for a magic shell gap. Additionally, also from the magnetic moments of the odd-A Ca isotopes no signature for a shell closure at N = 32 is observed [55]. Indeed, the observed magnetic moment of ⁵¹Ca, with 31 neutrons, requires excitations of neutrons across N = 32 in the higher pf-orbits, to reproduce the observed value. These results illustrate that more experimental studies on the single-particle nature of the ground state wave functions of Ca isotopes, such as transfer reaction experiments, are needed to further investigate this ambiguity.

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Weak localised sub-shell effect at N = 40. In the neutron-rich Ni region, the presence of a magic number at N = 40 has been debated for several years in literature. By now it is commonly accepted that the signatures for the sub-shell gap (large $E({2}^{+})$ and low B(E2)) could also be induced by the fact that this is a gap between orbits with opposite parity, thus requiring at least two neutron excitations to mix into the normal wave function and thus leading to a more pure ⁶⁸Ni configuration (it has $E({2}_{1}^{+})\gt 2$ MeV). The magnetic and quadrupole moments of the Cu isotopes around ⁶⁹Cu suggest also a 'magic' behaviour for ⁶⁹Cu, but as for the excitation energies and transition probabilities this can also be understood as mostly due to the parity change [47, 63].

The nuclear charge radii could provide evidence of the existence of a shell gap at N = 40. A distinct upward kink in the course of charge radii as a function of neutron number is seen at all the major neutron-shell closures above N = 20 (i.e. 28, 50, 82, 126). We have measured the changes in nuclear mean square charge radii across the Cu [64] and Ga [68] isotope chains and the new data for Zn and Ni are under analysis. A cursory look at the Cu radii shows nothing remarkable but a close analysis [64], where the main volume-change contribution to radii is subtracted, does show a dip around N = 40 in both the odd-N and even-N systematics. A similar analysis of the Ga isotopes is less convincing, although there is a reversal of the normal odd–even staggering at N = 40 giving ⁷¹Ga a smaller radius than the average trend would predict. The $E({2}_{1}^{+})$ systematics for Zn (Z = 30) isotopes, where the state is below 1 MeV in ⁷⁰Zn and actually lower than $E({2}_{1}^{+})$ in the lighter ${}^{60-68}$Zn isotopes, does not suggest to expect a signature in the radii for a N = 40 shell gap. It may only be evident in the Ni isotopes where the Z = 28 shell closure strengthens the doubly-magic effect.

In the region between Z = 20 and 28, the πf${}_{7/2}$ orbital is gradually filled and an onset of deformation is expected around proton mid-shell. Therefore we have investigated the Mn (Z = 25) isotopes from N = 26 to 39. As the quadrupole moment is the most sensitive observable to static deformation, a hyperfine level with a sufficiently large electric field gradient has to be studied, which requires the population of a metastable state in the ion. This was achieved through optical pumping from the ionic ground state by laser excitation in ISCOOL [61]. We established firmly the ground state spin of all Mn isotopes and long-lived isomers up to ⁶⁴Mn [58, 59]. All odd-A Mn isotopes, except for ⁵³Mn at N = 28, have a ground state spin/parity 5/2⁻, that deviates from the expected 7/2⁻: this is a first signature for the non-spherical nature of these isotopes. A comparison of the magnetic and quadrupole moments with large scale shell model calculations in different model spaces shows that proton excitation across Z = 28 as well as neutron excitation across N = 40 and N = 50 (into the ${{\rm{g}}}_{9/2}$ and ${{\rm{d}}}_{5/2}$ orbits) are needed to reproduce the observed values from N = 36 onwards [58, 61]. The slope in the charge radii of the Mn isotopes clearly increases from N = 36 onwards, confirming the increase in deformation that was observed also in the quadrupole moments [60]. This is best seen in figure 5(b) where the charge radii of all isotopic chains are plotted relative to the value at N = 30. A remarkable similarity is seen in the trend of the radii beyond N = 28, contrary to e.g. the Pb region where the slope of the radii beyond N = 126 increases with proton number [85]. In the odd–odd ${}^{58-64}$Mn isotopes a long-lived isomeric state coexists with the ground state. We firmly established a spin 1 and a spin 4 to the two levels in each of these isotopes [59] and their magnetic moments are well reproduced by shell model calculations in the pf-space up to N = 35, while proton and neutron excitations outside this model spaces are needed from N = 37 onwards.

Spectroscopy of cadmium at COLLAPS was originally motivated by nuclear astrophysics: the neutron-rich isotopes were expected to shed light on a shell-quenching hypothesis at N = 82 and its consequences for the duration of the r-process along the waiting-point nuclei below ¹³⁰Cd, whereas the neutron-deficient ones should elucidate the role of the cadmium isotopes in the rp-process for rapidly accreting neutron stars [86]. Surprisingly, the properties of the $11/{2}^{-}$ isomers in the range of ${}^{111-129}$Cd turned out to be of utmost interest since they are found to behave in an extremely predictable manner. While this can be partially understood in the conventional interpretation of the nuclear shell model, a full description must clearly go beyond this picture. Laser spectroscopy studies were performed on atomic Cd in the $5{\rm{s}}5{\rm{p}}\,{}^{3}{{\rm{P}}}_{2}\to 5{\rm{s}}6{\rm{s}}{}^{3}{{\rm{S}}}_{1}$ transition as well as on Cd⁺ in the $5{\rm{s}}{}^{2}{{\rm{S}}}_{1/2}\to 5{\rm{p}}{}^{2}{{\rm{P}}}_{3/2}$ transition. The latter required cw laser light at 214.5 nm, produced by fourth-harmonic generation of 860 nm light output of a titanium-sapphire laser.

Overall, the isotopes from ¹⁰⁰Cd up to the shell-closure at ¹³⁰Cd were studied and nuclear magnetic moments and electric quadrupole moments were extracted from the spectra using reference dipole moments and calculated electric field gradients, respectively. The electric quadrupole moments of the $11/{2}^{-}$ isomers extracted from the spectra are shown in figure 6 [70]. They exhibit an extremely linear behaviour along a chain of 10 isomers. According to the naive shell-model picture and assuming an effective charge for the (identical) neutrons filling the ${{\rm{h}}}_{11/2}$ shell, a linear increase starting from an oblate nucleus, crossing zero at mid-shell and having maximum prolate deformation just before the shell-closure is expected. While this simple structure is at first sight reflected by the quadrupole moments, a second look reveals considerable differences from this model: the number of 10 odd-mass isomers is 4 more than the expected number for solely filling the ${{\rm{h}}}_{11/2}$ shell and the zero-crossing is not exactly at mid-shell. In [70], a degeneracy of the ${{\rm{h}}}_{11/2}$ and some of the neighbouring ${{\rm{s}}}_{1/2},{{\rm{d}}}_{3/2}$, and ${{\rm{d}}}_{5/2}$ orbitals has been suggested to explain these observations, giving rise to a kind of a 'super-shell' that is shared by the I = 0 neutron pairs. With this assumption, a single-particle quadrupole moment of ${Q}_{\mathrm{sp}}=-667(31)$ mbarn and a constant core deformation with ${Q}_{\mathrm{const}}=-85(8)$ mbarn can be extracted. This implies a rather large effective neutron charge of ${q}_{\mathrm{eff},n}=2.5e$. Later it was shown that these assumptions can indeed be used to explain also the isomer shifts between the respective ground state and the isomer, which were found to follow a distinct parabolic dependence as a function of the atomic mass number [72]. Even though the nuclear shape is very close to spherical all along the isotopic chain and never exceeds a deformation parameter of 0.07, this unique regularity in the isomeric shift can be understood as a manifestation of nuclear deformation. Finally, the hyperfine structure anomaly for isotopes and isomers with ${{\rm{s}}}_{1/2}$, ${{\rm{d}}}_{5/2}$, and ${{\rm{h}}}_{11/2}$ states was evaluated and a linear relationship observed for all nuclear states except ${{\rm{s}}}_{1/2}$. This is in accordance with the Moskowitz–Lombardi rule, being established in the mercury region of the nuclear chart, and was observed in all four atomic and ionic levels that were investigated [71].

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The measurements on the francium isotope chain formed part of the commissioning phase of the CRIS experiment. This work was motivated by evidence for the phenomenon of shape coexistence in the neutron-deficient isotopes and isomers [96]. Towards the neutron-rich the aim was an extension of knowledge around the region of reflection asymmetry. Previously, measurements had been performed on ${}^{207-213}$Fr and ${}^{220-228}$Fr using laser spectroscopy on thermal atomic beams [97, 98]. To date the measurements cover 20 ground and isomeric states spanning the chain from ²⁰¹Fr to ²³³Fr. The high selectivity and high resolution of the CRIS technique presented an opportunity to separate low energy nuclear isomers and subsequently perform nuclear decay spectroscopy in quasi-background-free conditions.

The initial experiments used a frequency-doubled pulsed Ti:Sa laser from RILIS [99] to produce the 422 nm light with a linewidth of 1.5 GHz to excite the $7{\rm{s}}{}^{2}{{\rm{S}}}_{1/2}\to 8{\rm{p}}{}^{2}{{\rm{P}}}_{3/2}$ transition. This laser can scan across more than 100 GHz, which is essential for francium which has hyperfine structures that exceed 60 GHz. These experiments measured the isotope shift and magnetic moments of ${}^{202-206}$Fr, with a total experimental efficiency of 1% [100, 101], allowing the study of isotopes with yields as low a 100 ions s⁻¹. This work observed a small departure in the $\delta \langle {r}^{2}\rangle$ from the lead and polonium trend [102, 103] at ${}^{\mathrm{202,203}}$Fr but found no evidence in the measured g-factors for an onset of static deformation [101]. A UHV compatible alpha-decay spectroscopy station [93] was used to study ²⁰⁴Fr, allowing unambiguous identification of the two isomeric states and also to identify overlapping hyperfine components [101]. Beyond N = 126, hyperfine spectra and isotope shifts were measured for ${}^{218{\rm{m}},\mathrm{219,229,231}}$Fr. The $\delta \langle {r}^{2}\rangle$ and associated trend in odd–even staggering was found to be consistent with a deformed configuration for ${}^{218{\rm{m}},219}$Fr and ²²⁰Fr marks the border of the region of reflection asymmetry [104]. The g-factor of ²¹⁹Fr further supported this interpretation as it closely matched those of ${}^{\mathrm{221,223,225}}$Fr, which are known to be well-deformed nuclei [104]. The 1.5 GHz linewidth laser system has proved an ideal method for rapidly locating resonances, which has been recently demonstrated by the measurement of the hyperfine structure and isotope shift of ²¹⁴Fr. With a half-life of 5(1) ms, this is the shortest-lived nuclear ground state to be measured with laser spectroscopy [85, 105], where ISOL production is the limiting factor.

A much higher resolution is required to fully resolve each hyperfine component from which spectroscopic quadrupole moments and spin assignments can be deduced. This was achieved by chopping cw laser light into 100 ns long pulses using a Pockels cell, and then delaying the 1064 nm light from a high power Nd:YAG laser until the cw light had just been extinguished. This method eliminated effects associated with the strong light field and allowed a linewidth of 20(1) MHz to be achieved, while saturating both transitions [94, 106]. With this method the spectroscopic quadrupole moment of ²¹⁹Fr could be determined from the observed hyperfine structure shown in figure 7(a). The quadrupole moment confirmed that the structure of ²¹⁹Fr is quite different from the shell-model description of a nucleus with a half-filled πh${}_{9/2}$ orbital, where an almost zero quadrupole moment is expected (and observed for $A\lt 215$) (figure 7(b)). The measured quadrupole moment confirms a static deformed shape, and its negative value results from Coriolis mixing of the prolate structure that leads to a decoupling of the odd-particle spin from the deformation axis ($K\lt I$). The rapid change in sign of the ground state quadrupole moments in the odd-A isotopes ${}^{219-225}$Fr is consistent with the change in bands from $K=1/{2}^{-}$ in ${}^{\mathrm{219,221}}$Fr to $K=3/{2}^{-}$ in ${}^{\mathrm{223,225}}$Fr, and the associated change in coupling strength to the deformation axis.

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The combination of high-resolution CRIS and α-decay spectroscopy was able to unambiguously assign all hyperfine structure components for the ground and two isomeric states in ²⁰⁶Fr [108]. The branching ratios of the isomeric states could be studied in complete isolation from one another for the first time. Thus the hindrance factors could be determined for each decay chain, allowing a firm assignment of the spins and configurations of the states in ²⁰²At and ¹⁹⁸Bi.

In the last two years, high-resolution CRIS measurements have been performed successfully on the Ga and Cu isotopes, extending our earlier studies towards more neutron-rich isotopes. The data are being analysed and example spectra for ${}^{\mathrm{75,77}}$Cu are shown in figure 8. For copper the sensitivity of the CRIS method has been pushed now to a few 10 ions s⁻¹, allowing the study of ⁷⁸Cu. Further improvements should be possible in ionisation efficiency as well as background reduction, giving hope for a study of ⁷⁹Cu with less than 10 ions s⁻¹.

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