Exotic nuclei are characterized by having a number of neutrons (or protons) in excess relative to stable nuclei. Their shell structure, which represents single-particle motion in a nucleus1,2, may vary due to nuclear force and excess neutrons3,4,5,6, in a phenomenon called shell evolution7. This effect could be counterbalanced by collective modes causing deformations of the nuclear surface8. Here, we study the interplay between shell evolution and shape deformation by focusing on the magnetic moment of an isomeric state of the neutron-rich nucleus 75Cu. We measure the magnetic moment using highly spin-controlled rare-isotope beams and achieve large spin alignment via a two-step reaction scheme9 that incorporates an angular-momentum-selecting nucleon removal. By combining our experiments with numerical simulations of many-fermion correlations, we find that the low-lying states in 75Cu are, to a large extent, of single-particle nature on top of a correlated 74Ni core. We elucidate the crucial role of shell evolution even in the presence of the collective mode, and within the same framework we consider whether and how the double magicity of the 78Ni nucleus is restored, which is also of keen interest from the perspective of nucleosynthesis in explosive stellar processes.


The Cu isotopes, which carry 29 protons (that is, the atomic number is Z = 29), play a key role in efforts to understand the structure of exotic nuclei. Figure 1a displays the observed low-lying energy levels of Cu isotopes with even numbers of neutrons, N ≈ 40–48. We start with a naive picture in which the 29 protons consist of one ‘last’ proton on top of the Ni (Z = 28) magic core, and in low-lying states of spin parity Iπ = 5/2 or 3/2, this last proton occupies the f5/2 or p3/2 orbital, respectively, with the rest of the nucleus, including the neutrons, being a spherical Ni core in its Iπ = 0+ ground state.

Fig. 1: Shell evolution in neutron-rich Cu isotopes.
Fig. 1

a, Experimental systematics of energy level and spin parity for odd-A Cu isotopes10,11,28,29. Red and blue bars represent the 5/2 and 3/2 states, respectively. Inset, the low-lying isomeric states of 75Cu, which emit a 61.7 keV γ-ray with a half-life of T1/2 = 310(8) ns and a 66.2 keV γ-ray with T1/2 = 149(6) ns (ref. 13). The spin parity values in red were identified as a result of the present experiment. b, Theoretical energy of the \(5{\mathrm{/}}2_1^ -\) state as measured from the \(3{\mathrm{/}}2_1^ -\) state, calculated in three different ways with the A3DA-m Hamiltonian21. The red squares are obtained from the full calculation with the Monte Carlo shell model (MCSM). The blue solid line represents the single-particle energies in the naive shell evolution scenario, driven by the monopole interaction. The green dashed line represents the effects of the core excitation, when the most relevant monopole interaction between the πf5/2 or πp3/2 orbital and the νg9/2 orbital is deactivated. The vertical pink arrow indicates schematically the effect of core excitation, whereas the horizontal red arrow indicates the shift of the crossing point.

Figure 1a illustrates the energy drop of the 5/2 level10 over 1 MeV from an excited state in 69Cu down to the ground state of 75Cu (ref. 11), implying the possibility of a crossing between the proton f5/2 and p3/2 orbitals. This behaviour is recognized as one of the most ideal examples of shell evolution7,12. Figure 1b further shows the calculated energy differences between the 5/2 and 3/2 states based on the single-particle model (blue solid line), exhibiting a lowering similar to the experimental one. This lowering occurs due to the monopole component of the nuclear forces, particularly the tensor force, as more neutrons are added to the g9/2 orbit12. Figure 1b also displays the results of a full calculation (red squares) beyond the single-particle model. The trends appear to be similar among the two sets of results in Fig. 1b and the corresponding energy difference obtained from Fig. 1a. Although the single-particle picture thus appears well representative, certain collective modes must be admixed, as hinted by the differences between the two calculations. Note that ‘collective modes’ here mean excitations of the Ni core, such as surface oscillations. Therefore, to pin down how the shell evolves and how it competes with the collective modes, it is necessary to consider the wavefunction.

The nuclear magnetic dipole moment is one of the primary observables by which the nuclear wavefunction can be probed. The present study focuses on the measurement and implications of the magnetic moment of the excited state with Iπ = 3/2 of 75Cu. Two low-lying isomeric states are known for 75Cu at the excitation energies of 61.7 keV and 66.2 keV (ref. 13), as shown in the inset of Fig. 1. Their spin parities are expected to be either 1/2 or 3/2, with the latter being inherited from the ground states of lighter isotopes up to 73Cu. The magnetic moment of the 3/2 isomeric state, in conjunction with that of the 5/2 ground state11, provides a stringent test of the theoretical description of Cu isotopes. The excitation energies are usually used as the first test of any such theory, but they do not directly reflect the structure of the wavefunctions. By contrast, the moments are more directly related to the wavefunctions. Thus, once this moment is verified, we can catch a glimpse of the properties of the wavefunction.

Although the magnetic moments play an important role, those of the excited states in extremely neutron-rich nuclei, such as 75Cu, have not been measured so far. This is because there has been no way to produce spin alignment (rank-two orientation) for such nuclei. To produce high spin alignment in 75Cu, we employed the recently introduced two-step reaction method9, utilizing the close relation between the angular momentum transferred to the fragment and the direction of the removed momentum14 in the second projectile fragmentation (PF) reaction, where high production yields for rare-isotope (RI) beams were ensured by combining a technique of momentum–dispersion matching in the ion optics used for beam transport. In ref. 9, the two-step PF scheme was demonstrated for the production of the excited state with Iπ = 4+ of 32Al from the projectile of 48Ca via one-neutron removal from an intermediate product of 33Al (Iπ = 5/2+), and 8% spin alignment was achieved in spite of the mass difference between the projectile and the final fragment. In the present work, the one-nucleon removal from the Iπ = 0+ state was used as the second PF reaction. When a proton occupying an orbital with angular momentum j is removed from the 0+ state of 76Zn, a state in which spin I(=j) should be preferentially populated in the final fragment of 75Cu, and the relation between the direction of spin and the kinematics is considered to be refined, the spin alignment can be enhanced as compared to ref. 9.

The experiment was conducted using the in-flight superconducting RI separator BigRIPS15 at the RIKEN RIBF facility16 by means of the aforementioned two-step PF scheme. The 75Cu beam was produced via a PF reaction for the removal of one proton from 76Zn, which was a product of the in-flight fission of a primary beam of 238U. The 75Cu beam was then introduced into an experimental apparatus at focal plane F8 for time-differential perturbed angular distribution (TDPAD) measurements. (See Methods for experimental details.)

Figure 2a shows the γ-ray energy spectrum, in which peaks corresponding to the 61.7 keV and 66.2 keV γ-rays are clearly observed. R(t) ratios representing the anisotropy for both γ-rays were evaluated (see Methods) and an oscillatory pattern was observed only for the 66.2 keV γ-ray, as shown in Fig. 2b, where the statistical significance of the oscillation was found to be greater than 5σ. The spin parity of the 66.2 keV level was firmly identified as 3/2 from the clear oscillation observed in the R(t) ratio. On the other hand, the spin parity of the 61.7 keV level, for which no oscillatory pattern was observed, is most probably 1/2, because the rank-two anisotropy parameter (A22 in equation (3) in the Methods) is identically zero for the I = 1/2 system, inducing no oscillation in the TDPAD spectrum. The g factor of the 66.2 keV isomer in 75Cu was determined to be g = 0.93(4), and thus the magnetic moment was found to be μ = 1.40(6)μN in units of the nuclear magneton μN.

Fig. 2: Experimental results.
Fig. 2

a, Observed γ-ray energy spectrum. The two peaks corresponding to the 61.7 keV and 66.2 keV γ-rays are labelled. b, R(t) ratios deduced from N13(t) and N24(t), in accordance with equation (2), for the 66.2 keV γ-rays. Error bars represent standard deviation. The solid line represents the theoretical R(t) function expressed in equation (3) after fitting to the experimental R(t) plot. See Methods for equations.

The magnitude of the spin alignment in the 75Cu was found to be 30(5)%. Although the statistical yield tends to be considerably small for exotic nuclei such as 75Cu, 5σ significance is achieved in the TDPAD spectrum even with only 2,000 events of the γ-ray detection owing to the high spin alignment. Indeed, the 30(5)% spin alignment realized shows only a slight reduction from a maximum value, 41%, estimated in a similar way to ref. 17 with a consideration of the momentum acceptance. The alleviated reduction effect on the spin alignment, by virtue of the refined choice of reaction to populate the 3/2 state, demonstrates an advantageous feature of the two-step PF scheme incorporating the j − I correspondence.

The nuclear magnetic moment is evaluated usually in the nuclear structure calculation by the μ operator8,18:

$${\bf{\upmu }} = \left\{ {g_{\mathrm{s}}({\mathrm{p}}){\bf{s}}_{\mathrm{p}} + g_{\mathrm{s}}({\mathrm{n}}){\bf{s}}_{\mathrm{n}} + g_\ell ({\mathrm{p}}){\boldsymbol{\ell }}_{\mathrm{p}} + g_\ell ({\mathrm{n}}){\boldsymbol{\ell }}_{\mathrm{n}}} \right\}\mu _{\mathrm{N}}$$

where sp(n) and \({\boldsymbol{\ell }}_{{\mathrm{p}}({\mathrm{n}})}\) represent contributions from proton (neutron) spin and orbital angular momentum, respectively. The coefficients, gs and \(g_\ell\), called the spin and orbital g factors, respectively, carry not only free-nucleon values but also corrections such as the meson-exchange and in-medium effects. This work uses standard values, gs(p) = 3.91, gs(n) = −2.68, \(g_\ell ({\mathrm{p}}) = 1.1\) and \(g_\ell ({\mathrm{n}}) = - 0.1\). The present Iπ = 3/2 state can be interpreted, in the naive picture, as a system consisting of a single proton in an appropriate orbital around an inert core. The magnetic moment in the single-particle limit (the Schmidt value) can then be calculated for a proton in the p3/2 orbital, resulting in a value of μ(πp3/2) = 3.05μN. Figure 3 depicts the measured and calculated magnetic moments of 69–79Cu. The measured value for 69Cu appears to be not too far from the Schmidt value, suggesting that the picture of a single proton orbiting an inert core makes sense. However, Fig. 3 indicates that the measured value deviates greatly as N increases.

Fig. 3: Systematics of the magnetic moments for odd-A Cu isotopes.
Fig. 3

Filled (open) circles represent experimental data for the 3/2 (5/2) states11,28,30. Error bars correspond to one standard deviation. The filled red circle represents the result obtained in this work. The solid green (blue) lines indicates the present MCSM calculations for the 3/2 (5/2) states. μ(πp3/2) and μ(πf5/2) denote the proton Schmidt values for p3/2 and f5/2, respectively.

To investigate the implications of this growing deviation, theoretical studies were conducted using the Monte Carlo shell model (MCSM)19,20. The same Hamiltonian (A3DA-m) and the same large model space, 20 ≤ N(Z) ≤ 56, that have previously been used in successful calculations for Ni isotopes21 were employed. The magnetic moments were calculated from wavefunctions thus obtained with the g factors in equation (1). The results shown in Fig. 3 demonstrate a remarkably consistent trend compared to the experimental values for all measured magnetic moments of the 5/2 and 3/2 states, including the deviation from the Schmidt value, which appears to be maximal at 75Cu.

By taking the deviation from the Schmidt value, one can extract the effect of the core excitations. It is thus found that this effect is rather sizable, but the calculated magnetic moments still agree well with the experimental values. Let us now investigate whether this effect destroys the shell evolution picture.

Figure 4b–d presents T-plots, which visualize major components of MCSM wavefunctions with white circles (see Methods)21,22. For N = 40, a magic number, the T-plots for 68Ni and 69Cu, shown in Fig. 4d(i),b(i), respectively, show many similarities, including a concentration around a spherical shape. Thus, the 3/2 state in 69Cu is considered to be a proton in the p3/2 orbital on top of a spherical core of 68Ni, as illustrated in Fig. 4a(i). Figure 4b(ii),c(i) presents plots for the 3/2 and 5/2 states of 75Cu, respectively; the T-plots are spread more widely than for the N = 40 case because the excess neutrons produce more shape oscillations. This characteristic feature is further shared by 74Ni, as shown in Fig. 4d(ii). Thus, the 3/2 and 5/2 states of 75Cu are considered to correspond, to a large extent, to a proton orbiting around a 74Ni core that exhibits certain excitations or shape oscillations from a perfect sphere, as illustrated intuitively in Fig. 4a(ii).

Fig. 4: Theoretical interpretations.
Fig. 4

a, Illustrations of a Cu isotope as a proton orbiting around a spherical Ni core (i), a Ni core with excitations (surface oscillations) (ii) and a Ni core with weak excitations (iii). b, T-plots for the 3/2 states in Cu isotopes 69Cu (i) and 75Cu (ii). c, The 5/2 states in Cu isotopes 75Cu (i) and 79Cu (ii). d, Ground states in Ni isotopes 68Ni (i), 74Ni (ii) and 78Ni (iii), where the potential energy surface relative to the minimum is represented by a 3D contour with two independent coordinates of quadrupole moments, as drawn in the inset.

Now that this background has been elucidated, we shall return to the interplay between the shell evolution and the collective mode, or the core excitation. The effect of the core excitation varies as N increases, as shown in Fig. 3, mainly due to the growing occupancy of neutrons in the g9/2 orbital, and it differs between the 3/2 and 5/2 states because of alternating couplings. The deviation from the Schmidt value is maximal at 75Cu; however, the picture of a proton orbiting around a correlated Ni core still appears to be reasonable for this nucleus.

Returning to Fig. 1b, the MCSM full calculation shows a distinct decrease in energy until the inversion near 75Cu. The slope of the ‘shell evolution’ curve resembles that of the full calculation, and the energy gain from the former to the latter is mainly a result of core-excitation effects (the vertical arrow). We also calculated the energy expectation values for the same wavefunctions by setting the πf5/2νg9/2 and πp3/2νg9/2 monopole interactions to be equal, thereby eliminating most of the shell-evolution effects. This is labelled as ‘core excitation’, which is remarkably close to constant with no symptom of inversion. Thus, the shell evolution indeed arises even in the presence of core excitations, whereas the core excitation is not a major driving force in the present case. The nearly constant energy shift due to the core excitation moves the inversion point on the N axis to the left (the horizontal arrow). This feature reinforces the concept of shell evolution rather than destroying it. Present and past measurements of the magnetic moment verify this structural evolution. In particular, the simultaneous agreement for the two states in 75Cu is crucial, leading to the conclusion that the shell evolves even in the presence of the collective modes. (See Methods for related uncertainties.)

The present structural evolution scenario yields an intriguing prediction of the closed-shell properties of the doubly magic nucleus 78Ni and its neighbour 79Cu (refs. 23,24). Their T-plots, shown in Fig. 4c(ii),d(iii), depict the profound minima of the potential energy surface at the spherical shape. T-plot points are clustered around the spherical shape in both 78Ni and 79Cu; however, more spreading or fluctuation is evident than in 68Ni or 69Cu. This is because the magic number N = 40 lies between major shells with opposite parities, whereas the magic number N = 50 is due to spin–orbit splitting, and excitation can occur by one particle. The present study thus foresees the existence of a spherical doubly magic 78Ni nucleus, while fluctuations may be stronger. Therefore, 78Ni can be the first jj-coupled doubly magic nucleus with significant sphericity25,26. The implications of such properties for nucleosynthesis are of considerable interest, for instance, through β-decay rates27.


Two-step PF scheme

In the present experiment the two-step PF scheme was employed in the production of spin-aligned 75Cu beams. In the reaction at the primary target position F0, 76Zn (with one proton added to 75Cu) was produced by the in-flight fission of a 345-MeV/nucleon 238U beam on a 9Be target with thickness of 1.29 g cm−2 in thickness. This thickness was chosen to provide the maximal production yield for the secondary 76Zn beam. A wedge-shaped aluminium degrader with mean thickness of 1.65 g cm−2 was placed at the first momentum-dispersive focal plane F1, where the momentum acceptance was ±3%. The secondary 76Zn beam was transmitted to a second wedge-shaped aluminium plate with a mean thickness of 0.81 g cm−2 placed at the second momentum-dispersive focal plane F5. Thus, 75Cu nuclei (including those in the isomeric state 75mCu) were produced through a PF reaction involving the removal of one neutron from 76Zn. The target had a thickness of 3 mm: consequently, the spread of the momentum due to the dispersal of the reaction positions in the secondary target is comparable to the width of the momentum distribution31, σG = 90 MeV/c for one-nucleon removal. The 75Cu beam was subsequently transported to the double-achromatic focal plane F7 under conditions such that the momentum dispersion generated at the site of the first reaction was effectively cancelled out. The momentum selection to produce the spin alignment was performed using information obtained from two parallel-plate avalanche counters placed at F7. Only events in which beam particles were detected within a horizontal region of ±12 mm were recorded and analysed offline.

TDPAD measurement

The TDPAD apparatus consisted of an annealed Cu metal stopper, a dipole magnet, Ge detectors, a plastic scintillator and a collimator. The Cu stopper was 3.0 mm thick with an area of 30 × 30 mm2, and the dipole magnet provided a static magnetic field of B0 = 0.200 T. De-excitation γ-rays were detected by four Ge detectors perpendicular to the magnetic field at angles of ±45° and ±135° with respect to the beam axis. Three of the four Ge detectors were of the planar type (low-energy photon spectrometer) and the remaining one was of the coaxial type. The plastic scintillator (0.1 mm thick) was placed upstream of the stopper, and the signal from the scintillator served as a time zero for the TDPAD spectrum.

TDPAD measurements enable us to determine the g factor by observing the time-dependent anisotropy of the de-excitation γ-rays emitted from nuclei during spin precession under an external magnetic field. From the experimental findings, a ratio R(t), defined as

$$R(t) = \frac{{N_{13}(t) - \epsilon N_{24}(t)}}{{N_{13}(t) + \epsilon N_{24}(t)}}$$

is evaluated, where N13(t) and N24(t) are the respective sums of the photo-peak counting rates at two pairs of Ge detectors placed diagonally with respect to each other and ϵ is a correction factor for the detection efficiency. Theoretically, R(t) is also given by

$$R(t) = - \frac{{3A_{22}}}{{4 + A_{22}}}{\mathrm{sin}}\left( {2\omega _{\mathrm{L}}t} \right)$$

Here, the Larmor frequency ωL is given by ωL = NB0/ħ, where g is the g factor for 75Cu, and has a relation to the magnetic moment μ and the nuclear spin I as μ = gIμN. Parameter A22 is the rank-two anisotropy parameter, defined as A22 = AB2F2, where A denotes the degree of spin alignment, B2 is the statistical tensor for complete alignment and F2 is the radiation parameter32.

In the present experiment, the R(t) ratio was evaluated in accordance with equation (2). The statistical significance of the oscillation for the 66.2 keV γ-ray was found to be greater than 5σ, with A22 = −0.17(3), which was obtained from a least-χ2 fit of the theoretical function given in equation (3) to the experimental one by equation (2).


Shell-model calculations in nuclear physics are quite similar to configuration interaction calculations in other fields of science. The major differences are that (1) the two ingredients are protons and neutrons instead of electrons and (2) nuclear forces are considered instead of Coulomb or other forces. Conventionally, the matrix of the Hamiltonian with respect to many Slater determinants is diagonalized. Because many configurations are needed in large systems, the dimensions of the matrix can be enormous, making the calculation infeasible: however, many interesting and important problems lie beyond this limit. MCSM represents a breakthrough in this regard. A set of Slater determinants, called MCSM basis vectors, is introduced, and the diagonalization is performed in the Hilbert space spanned by the MCSM basis vectors. Each MCSM basis vector is a Slater determinant composed of single-particle states that are superpositions of the original single-particle states, and the amplitudes of these superpositions are determined through a combination of stochastic and variational methods. Even when the dimensions are on the order of 1023 in the conventional shell model, the problem can be solved, to a good approximation, with up to approximately 100 MCSM basis vectors. This method has seen many applications up to Zr isotopes.

The present MCSM calculations were performed with the A3DA-m interaction. This interaction was fixed, before this work, based on the microscopic G-matrix with certain empirical modifications so as to describe experimental energy levels of Ni isotopes21. The validity of this interaction has been confirmed independently in recent studies on different topics33,34. The MCSM calculation with a large model space such as that employed in this work can describe both the excited state and the ground state appropriately, involving various cross-shell excitations.

The magnetic moment is calculated by equation (1) with four coefficients, gs(p, n) and \(g_\ell ({\mathrm{p}},{\mathrm{n}})\), for which some uncertainties exist. Following the usual prescription35,36, the spin g factors gs(p) and gs(n) are reduced from their free-space values, represented by the so-called spin quenching factor qs. The empirically obtained appropriate value of qs is in or around the range 0.70–0.75 for calculations in an incomplete LS (or harmonic oscillator) shell37,38, to which the present work belongs. The value 0.70 is used in the main text, as in ref. 37. The orbital g factors \(g_\ell ({\mathrm{p}})\) and \(g_\ell ({\mathrm{n}})\) take values \(g_\ell ^{{\mathrm{free}}}({\mathrm{p}}) = 1\) and \(g_\ell ^{{\mathrm{free}}}({\mathrm{n}}) = 0\) in free space, respectively. In nuclear medium, the isovector correction based on the meson-exchange picture is made usually as \(g_\ell ({\mathrm{p}}) = g_\ell ^{{\mathrm{free}}}({\mathrm{p}}) + \delta g_\ell\) and \(g_\ell ({\mathrm{n}}) = g_\ell ^{{\mathrm{free}}}({\mathrm{n}}) - \delta g_\ell\) (refs. 35,36), with the empirical value of \(\updelta g_\ell\) being between 0 (ref. 37) and 0.1 (ref. 39).

The measured magnetic moments of 75Cu are 1.40(6)μN for the first 3/2 state, as obtained by the present work, and 1.0062(13)μN for the first 5/2 state11. We can evaluate the values of qs and \(\updelta g_\ell\) from these. Because of the small error of the 5/2-state moment, it is treated as a single value, 1.0062. By moving within the error bar of the 3/2-state moment, the values of qs and \(\updelta g_\ell\) move from \((q_{\mathrm{s}},\updelta g_\ell ) = (0.67,\sim 0)\) to (0.78, 0.13). This range is essentially within the uncertainties of qs and \(\updelta g_\ell\). The two measured magnetic moments can thus be nicely reproduced with the present eigen wavefunctions of the first 3/2 and 5/2 states, and the main conclusion is insensitive to the uncertainties associated with qs and \(\updelta g_\ell\). We note that the simultaneous determination of the values of qs and \(\updelta g_\ell\) can provide a precious insight, as shown here, spotlighting the advantage of the measurement of more than one magnetic moment for a single nucleus.

We can further investigate another uncertainty arising from the shell-evolution strength. In Fig. 1b, a certain relevant monopole interaction is removed to obtain the ‘core excitation’ result. Instead of removing it fully, we now weaken this particular monopole interaction, and see how the magnetic moments are changed. The actual MCSM calculations indicate that if the 10% weakening (90% remaining) of this monopole interaction is made, the \(\left( {q_{\mathrm{s}},\updelta g_\ell } \right)\) values obtained similarly appear to be between (0.62, −0.05) and (0.71, 0.07). The situation is shifted to or beyond the edge of the uncertainties of qs and \(\updelta g_\ell\), and a further reduction will kick us out almost completely. The uncertainty of the monopole interaction strength is now deduced, based on the magnetic moments, to be about 10% of its strength. This uncertainty is so small that the shell evolution is quite robust in the present case.


A T-plot is a method of analysing an MCSM wavefunction. The intrinsic quadrupole moments are calculated for each MCSM basis vector, and the corresponding vector is identified by a circle on the potential energy surface with those quadrupole moments as coordinates. The overlap probability of each MCSM basis vector with the eigenstate being considered is represented by the size of the circle as an indicator of its importance. Angular momentum/parity projection is performed in this process. Thus, with a T-plot, one can visualize the shape characteristics of an MCSM basis vector and its importance for a given eigenstate. The main area indicates the shape and the spreading represents the extent of quantum fluctuations.

Detailed theoretical outputs

The MCSM calculation indicates that in the 3/2 state of 75Cu the occupation number of the proton p3/2 orbital is 0.86, somewhat smaller than unity, whereas that of the proton f5/2 orbital is 0.35. Likewise, in the 5/2 state, the p3/2 orbital is occupied with a similarly small probability. Thus, the single-particle nature remains to a certain extent.

This argument of the T-plot for 75Cu can be theoretically quantified in terms of the so-called spectroscopic factor, 0.50 for πp3/2 and 0.46 for πf5/2, from 74Ni to 75Cu. These values represent the probabilities that the Iπ = 3/2 and 5/2 states of 75Cu are created by adding one proton to the ground state of 74Ni without any disturbance. Although these probabilities are rather large, other states of the core, such as various surface oscillations, must account for most of the remaining probability. Figure 4a(ii) schematically illustrates such a situation of single-particle motion on top of a core exhibiting various excitations.

Behavior of the 1/2 state

In the present experiment the spin parity of the 61.7 keV level was assigned to be Iπ = 1/2 based on the non-observation of the oscillation signal. At a glance, the level energies of the 1/2 (including (1/2)) states of the Cu isotopes seem to be connected with the lowering of the 5/2 states, as shown in Fig. 1a. The nature of the 1/2 state of 75Cu is discussed in terms of the transition probability, which was first measured and discussed for assumed level schemes in ref. 13. Based on the level scheme fixed by the present study, the reduced transition probability from the 1/2 state to the 5/2 ground state was determined to be B(E2) = 22.5(8) in Weisskopf units, which was well reproduced by the MCSM output B(E2) = 23.5 (in Weisskopf units). Referring to the wavefunction by the MCSM output with a notice that the magnetic moment of the 5/2 state is well reproduced, it could be supposed that the core of the 1/2 state is rather similar to those of the 3/2 and 5/2 states, whereas the valence proton occupies the f5/2, p3/2 and p1/2 orbitals with considerable admixtures. As for 69,71,73Cu, the B(E2) values from the 1/2 states (including those in brackets) to the 3/2 ground state have been reported40, and an increasing trend of B(E2) over N = 40, combined with the lowering of the level energies of the 1/2 states, might indicate the rather collective nature of those states.

Data availability

The data used in the present study are available from the corresponding author upon reasonable request.

Additional information

Journal peer review information: Nature Physics thanks Thomas Papenbrock and other anonymous reviewers for their contribution to the peer review of this work.

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The experiment was performed under programme no. NP1412-RIBF124R1 at RIBF, operated by RIKEN Nishina Center for Accelerator-Based Science and CNS, The University of Tokyo. The authors thank the RIKEN accelerator staff for their cooperation during the experiment. This work was supported in part by a JSPS KAKENHI grant (16K05390), and also in part by JSPS and CNRS under the Japan-France Research Cooperative Program. The MCSM calculations were performed on the K computer at RIKEN AICS (hp140210, hp150224, hp160211, hp170230). This work was also supported in part by the HPCI Strategic Program (‘The Origin of Matter and the Universe’) and ‘Priority Issue on Post-K computer’ (Elucidation of the Fundamental Laws and Evolution of the Universe). D.L.B., and A.K. acknowledge support by the Extreme Light Infrastructure Nuclear Physics (ELI-NP) Phase II, a project co-financed by the Romanian Government and the European Union through the European Regional Development Fund – the Competitiveness Operational Programme(1/07.07.2016, COP, ID 1334). D.R. was supported by the P2IO Excellence Center.

Author information


  1. RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama, Japan

    • Y. Ichikawa
    • , H. Nishibata
    • , A. Takamine
    • , K. Imamura
    • , T. Fujita
    • , T. Sato
    • , Y. Shimizu
    • , D. S. Ahn
    • , K. Asahi
    • , H. Baba
    • , D. L. Balabanski
    • , F. Boulay
    • , J. M. Daugas
    • , N. Fukuda
    • , A. Gladkov
    • , N. Inabe
    • , Y. Ishibashi
    • , Y. Ohtomo
    • , T. Otsuka
    • , T. Sumikama
    • , H. Suzuki
    • , H. Takeda
    • , L. C. Tao
    • , H. Ueno
    •  & H. Yamazaki
  2. Department of Physics, Osaka University, Toyonaka, Osaka, Japan

    • H. Nishibata
    • , T. Fujita
    • , T. Kawamura
    •  & A. Odahara
  3. Center for Nuclear Study, University of Tokyo, Bunkyo, Tokyo, Japan

    • Y. Tsunoda
    •  & T. Otsuka
  4. Department of Physics, Meiji University, Kawasaki, Kanagawa, Japan

    • K. Imamura
  5. Department of Physics, Tokyo Institute of Technology, Meguro, Tokyo, Japan

    • T. Sato
    • , K. Asahi
    • , C. Funayama
    • , S. Kojima
    • , Y. Ohtomo
    •  & Y. Togano
  6. Department of Physics, University of Tokyo, Bunkyo, Tokyo, Japan

    • S. Momiyama
    • , M. Niikura
    •  & T. Otsuka
  7. ELI-NP, Horia Hulubei National Institute of Physics and Nuclear Engineering, Măgurele, Romania

    • D. L. Balabanski
    •  & A. Kusoglu
  8. CEA, DAM, DIF, Arpajon, France

    • F. Boulay
    •  & J. M. Daugas
  9. GANIL, CEA/DSM-CNRS/IN2P3, Bvd Henri Becquerel, Caen, France

    • F. Boulay
  10. Department of Advanced Sciences, Hosei University, Koganei, Tokyo, Japan

    • T. Egami
    • , T. Kawaguchi
    • , T. Nishizaka
    •  & D. Tominaga
  11. Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo, Japan

    • T. Furukawa
  12. CSNSM, CNRS-IN2P3, Université Paris-sud, UMR8609, Orsay-Campus, France

    • G. Georgiev
    • , A. Kusoglu
    •  & D. Ralet
  13. Department of Physics, Kyungpook National University, Buk-gu, Daegu, South Korea

    • A. Gladkov
  14. Department of Physics, University of Tsukuba, Tsukuba, Ibaraki, Japan

    • Y. Ishibashi
  15. Department of Informatics and Engineering, University of Electro-Communication, Chofu, Tokyo, Japan

    • Y. Kobayashi
  16. Department of Physics, Faculty of Science, Istanbul University, Istanbul, Turkey

    • A. Kusoglu
  17. Department of Particle Physics, Weizmann Institute of Science, Rehovot, Israel

    • I. Mukul
  18. Instituut voor Kern- en Stralingsfysica, K. U. Leuven, Leuven, Belgium

    • T. Otsuka
    •  & X. F. Yang
  19. LPSC, CNRS/IN2P3, Univerisité Grenoble Alpes, CNRS/IN2P3, INPG, Grenoble, France

    • G. S. Simpson
  20. State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing, China

    • L. C. Tao


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Y.I. designed the experiment, analysed the data and was chiefly responsible for writing the paper. Y.T. and T.O. worked on the theoretical studies, and T.O. helped with writing the paper. The other authors are collaborators on the experiment.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to Y. Ichikawa.

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