High-spin spectroscopy of 140 Nd

The population of the high-spin states in 140 Nd was investigated using the reaction 96 Zr( 48 Ca,4 n ). The results from two experiments, one with the EUROBALL array and one with the JUROGAM II + RITU + GREAT setup employing the recoil decay tagging technique, have been combined to develop a very detailed level scheme for 140 Nd. Twelve bands of quadrupole transitions and eleven bands of dipole transitions were identiﬁed and their connections to low-lying states were established. Calculations using the cranked Nilsson-Strutinsky and the tilted axis cranking models were used to interpret the observed structures. The overall good agreement between the experimental results and the calculations assuming a triaxial shape of the nucleus strongly support the existence of a stable triaxial shape at high spins in this mass region.


I. INTRODUCTION
The nuclei with A ∼ 140 having a few holes in the N = 82 shell closure are spherical or only slightly deformed in the ground state [1]. They can be easily polarized by unpaired nucleons resulting from broken pairs. Depending on the orbitals close to the Fermi surfaces for protons and neutrons, the nucleus can evolve from one shape to another with increasing excitation energy, or can exhibit different coexisting shapes in certain spin ranges: spherical and triaxial at medium spins, and triaxial and highly deformed or superdeformed at high spins. At low spins the presence of isomers based on simple particle-hole excitations helps to establish the active quasiparticle configurations and test the suitability of various nuclear potentials, whereas at high spins the combined contribution of neutron holes in the N = 82 core and neutron particles in the high-j orbitals above the N = 82 gap drive the nuclear shape toward a stable triaxial shape with γ ≈ +30 • [2,3]. At very high spins superdeformation is observed [4]. The analysis of the data coming from large γ arrays is made difficult by the presence of low-energy γ rays and isomeric states that often are not measured in the performed experiments. Such a situation is encountered in the weakly deformed Nd nuclei with neutron numbers close to the N = 82 shell closure, with irregular sequences of transitions and possible yrast traps. In fact, isomeric states were observed in 138 Nd (I π = 10 + , T 1/2 = 410 ns) [5], in 139 Nd (I π = 23/2 + , T 1/2 = 272 ns) [6], and in 140 Nd (I π = 10 + , T 1/2 = 32 ns and I π = 7 − , T 1/2 = 600 μs) [7].
New experimental data were recently published for the 140 Nd nucleus, which has a I π = 20 + isomeric state at E x = 7.43 MeV [8], with T 1/2 = 1.23 μs [9]. This lifetime supports the I π = 20 + spin-parity assignment and the interpretation as a six-quasiparticle spherical configuration that coexists with the surrounding triaxial bands.
The 140 Nd nucleus was also studied in a high-statistics experiment using the EUROBALL array and the results of the experiment have been published in two recent papers [3,4]. Many bands were observed at high spins and some of them were also linked to low-lying states. Theoretical calculations with the cranked Nilsson-Strutinsky (CNS) model were used to interpret the observed bands, and the existence of stable triaxiality at high spin in this mass region was claimed. However, even if the level scheme was developed up to very high spins, no transitions feeding the 20 + isomeric state from higher-lying states were observed. We have therefore performed a dedicated experiment to search for the transitions populating the 20 + isomer. As the lifetime of the isomer of 1.23 μs is long enough to employ the recoil-tagging technique, we used the high efficiency gas-filled recoil mass separator RITU and the two high efficiency setups for γ -ray detection, JUROGAM II and GREAT, placed at the entrance and at the focal plane of the spectrometer, respectively. The results on the population of the 20 + isomer in 140 Nd are published in Ref. [10]. This recoil isomer tagging experiment revealed states which were unobserved in the prompt coincidence experiment with EUROBALL, and induced us to reanalyze the data of the EUROBALL experiment in order to clarify and understand the newly observed transitions. The combined analysis of the two experiments led to the observation of many new bands and weak transitions which enabled the construction of a much more clear and complete high-spin level scheme for 140 Nd. The present level scheme includes 12 bands of only quadrupole transitions, 11 dipole bands, and many interconnecting transitions, which lead to the determination of the excitation energy and spins for most of the observed states. In many cases also the parity was determined.
The configuration assignment to the observed bands is made with the CNS and the tilted axis cranking (TAC) models. For the dipole bands, the new procedure introduced recently in the interpretation of the low-and medium-spin bands in the neighboring 138 Nd nucleus is used [11].
The details of the experimental setups are presented in Sec. II. The results of the data analysis are presented in Sec. III. The configurations of the different bands are discussed in Sec. IV. Finally, the summary is given in Sec. V.

A. JUROGAM II + RITU + GREAT experiment
In the JUROGAM II experiment, high-spin states in 140 Nd have been populated via the 96 Zr( 48 Ca,4n) reaction, with a 180 MeV 48 Ca beam provided by the K130 cyclotron at the University of Jyväskylä, Finland. The target consisted of a selfsupporting 96 Zr foil of 735 μg/cm 2 thickness. The experimental setup was composed of JUROGAM II + RITU + GREAT. The JUROGAM II array [12] placed at the entrance of the RITU spectrometer [13] is composed of 39 Comptonsuppressed Ge detectors: 24 clover detectors and 15 coaxial tapered detectors. The clovers are placed on two rings at 75.5 • (12 clovers) and 104.5 • (12 clovers) symmetric with respect to 90 • , while the tapered detectors are placed on two rings at backward angles of 133.6 • (10 detectors) and 157.6 • (5 detectors). The GREAT spectrometer [14] around the focal plane of RITU was composed of several types of detectors. A multi-wire proportional counter (MWPC) was used to measure the position of the recoils and to give the time reference for the delayed γ -γ coincidences and for the measurement of the time of flight of the recoils between the MWPC and a silicon DSSD detector placed downstream of the MWPC. Behind the DSSD was placed a segmented planar Ge detector of 12 cm × 6 cm corresponding to 24 × 12 segments with a thickness of 1.5 cm, used for the measurement of x rays and low-energy γ rays. For the measurement of high-energy γ rays, a large volume clover having each crystal segmented into four was placed just above the focal plane reaction chamber and two clovers were placed on the right and left sides of the reaction chamber. The JUROGAM II array has been used for a standard coincidence measurement of γ rays, while the time correlated events in JUROGAM II and GREAT were used to measure delayed γ -γ coincidences.
The trigerless total data readout (TDR) [15] time stamped the events, which were then sorted using the GRAIN code [16]. Events were created in GRAIN using the signal from the MWPC as a "trigger," with the energies of any gamma rays detected within a time window of [−5 μs, +10 μs] with respect to the time reference given by the MWPC being collected into an event. Given the lifetime of the 20 + isomer in 140 Nd of 1.23 μs and the flight time through RITU of around 650 ns, this time window allowed us to measure the major part of the isomer decay and the delayed γ -γ coincidences. The event rate in the MWPC was around 13 kHz, which was low enough to avoid the overlap between successive events separated in average by 80 μs. The analysis was performed with the GAMMAWARE [17] and RADWARE [18,19] programs.

014323-3
A total of 5 × 10 9 events has been collected. Thanks to the high efficiency of the various γ -ray arrays, we produced γ -γ matrices for each array, i.e., one for JUROGAM II at the target position, and two for the Ge detectors at the focal plane: one for the clovers and one segmented planar Ge detector. The lifetime of the isomeric states in the nuclei implanted in the DSSD detector at the focal plane has been measured using γ -time matrices.
The transition multipolarities of the newly observed prompt transitions above the isomers have been extracted from the anisotropies using asymmetric γ -γ matrices constructed for the JUROGAM II array.

B. EUROBALL experiment
In the EUROBALL experiment, high-spin states in 140 Nd have been populated via the 96 Zr( 48 Ca,4n) reaction induced by a 195 MeV 48 Ca beam delivered by the Vivitron tandem accelerator at the Institut de Recherches Subatomiques, Strasbourg. A self-supporting 96 Zr foil of 735 μg/cm 2 thickness was used as a target. Gamma-ray coincidences were measured with the EUROBALL spectrometer [20], consisting of 30 single, tapered Ge detectors, and 15 cluster and 26 clover composite Ge detectors, each surrounded by a BGO Comptonsuppression shield. Out of the total number of 239 Ge crystals, 230 could be used in our analysis. Multiplicity information was obtained from the inner ball of 210 BGO detectors. Events were written to tape with the requirement that at least 11 BGO detectors of the inner ball and four Ge crystals before Compton suppression were in prompt coincidence. Presorting of the data, which included Compton suppression and add-back for the composite detectors, resulted in a total of 1.5 × 10 9 events with a γ -ray coincidence fold 3. The γ -ray coincidences were sorted into three-and four-dimensional coincidence arrays (cube and hypercube, respectively), and the analysis was carried out with the RADWARE software package [18,19].
To determine the multipolarity of transitions, several gated matrices (with gates set on all detectors on specific transitions with known quadrupole and dipole character of 140 Nd) were sorted with all detectors on one axis and detectors at 90 • and at forward/backward (f,b) angles, respectively, on the other axis. Gates were set on the axis with all detectors, and the anisotropy defined by the intensity ratio W (f,b)/W (90 • ), was determined for the transitions in the resulting spectra. The multipolarity of the new transitions identified in 140 Nd were assigned based on the comparison of the deduced anisotropies with the average anisotropies extracted for known pure E2 and E1 transitions in nuclei populated in the reaction, which have the values of 0.61 ± 0.03 and 0.28 ± 0.05, respectively.

III. RESULTS AND LEVEL SCHEME
The relevant part of the level scheme of 140 Nd is shown in Fig. 1. We do not draw all states and transitions, but only those which are relevant for the development of the level scheme at high spins. The information about the observed bands and their decays out, given in Table I, was obtained from the EUROBALL experiment. The highest transitions of bands Q11 and Q12 and the states in the ground-state band up to I π = 7 − were not drawn in the present level scheme to avoid shrinking it any further. However, the related information is given in Table I. Four bands published previously in Ref. [3], bands 8-11, are not linked to the low-lying states and will not be discussed in the present paper.
The large majority of the previously observed states are confirmed, but the combined results of the two experiments induce some important changes with respect to the previously published level schemes [3,8]. The most important one is the positive-parity assignment to the 16 + state at 6153 keV, which is opposite to that assigned in Ref. [3]. The positive-parity assignment was considered and discussed as possible alternative in our previous paper [8], but the available information at that time was not sufficient to disentangle between positive and negative parity. The observation of many new transitions in the JUROGAM II experiment and the careful analysis of the data of the EUROBALL experiment lead to the identification of several new transitions which connect the different observed bands both at low and high spins. The anisotropies of the newly observed transitions allowed an unambiguous positive-parity assignment to the 16 + state at 6153 keV, which has as a consequence the change of the parity of several high-spin bands with respect to the previous publication [3].
The task to establish the parity of the states at high spins is not easy. In our case, the existence of the long-lived 20 + isomer [8] allowed us to assign the parity to some states on the basis of the expected weak strength of the transitions from the isomer to the states in question. In addition, we also observed three transitions of 1008, 1084, and 1274 keV connecting high-spin states of the bands Q11 and Q10, Q8 and D9, and D11 and Q8, respectively, whose anisotropies constrained the relative spin-parity of the bands. The most populated band at high spins is Q1. Its decay is very fragmented and proceeds towards states of both positive and negative parity. This is an indication of a drastic shape change from nearly spherical to a triaxial shape induced by the occupation of the h 9/2 neutron intruder orbital from above the N = 82 shell closure (see the discussion in Sec. IV). We confirm all previously observed transitions deexciting the two 18 + states populated by the 624 and 612 keV transitions, with the exception of the 859 keV transition which appears in the spectrum gated by 612 keV only because it is a member of the Q1 band. We identified four new transitions of 325, 952, 1042, and 1665 keV deexciting the 18 + states. In our previous paper [3] we have clearly identified the bands Q1 and Q3. In the published level scheme there were also several irregular structures around the bands Q1 and Q3, which were not grouped into bands since no clear decay pattern was identified. The transitions of those structures are now assigned to bands Q2, Q4, and D9. With the additional information from the JUROGAM II experiment, which indicates that band Q9 has a delayed decay [10], we could clearly identify the TABLE I. Energies, intensities, anisotropies, multipolarities, and spin-parity assignments of γ -ray transitions of 140 Nd from the EUROBALL experiment. The transitions are grouped in bands and the transitions connecting a given band to low-lying states are listed at the end of each band separated by a blank line.
The error on the transition energies is 0.2 keV for transitions below 1000 keV and intensities larger than 5% of the 140 Nd reaction channel, 0.5 keV for transitions above 1000 keV and intensities lower than 5%, and 1 keV for transitions above 1200 keV and/or weaker than 1%. b Relative intensities corrected for efficiency. The transition intensities were obtained from a combination of total projection and gated spectra. c The anisotropy has been deduced from two asymmetric γ -γ coincidence matrices sorted with all detectors on one axis and detectors at 90 • and at forward/backward angles, respectively, on the other axis. The tentative spin-parity of the states are given in parenthesis.
two new bands Q2 and Q4 which decay towards Q1 and Q3, respectively. We confirm all previously identified transitions of bands Q1, Q2, and Q3. The new weakly populated band Q4 decays only towards Q3. The transitions populating higher-lying states of band Q9 which were previously drawn as non-yrast sequences are now ordered and placed in the newly identified dipole band D11. Band Q10 has been identified previously and it was clear that it decays through a structure like a dipole band with crossover transitions. The JUROGAM II experiment was again very helpful in understanding the structure of this band and its decay. In fact, we observed the transitions of bands Q10 and D10 in the spectra gated by low-lying transitions of 140 Nd observed at the focal plane of RITU, which indicates that the bands have a delayed decay component. We have accurately searched for the transitions linking D10 to the 20 + isomer, but we could not find any.
We have instead identified a new E2 transition of 1008 keV which links band Q11 to Q10, which fixes the excitation energy and spin-parity of bands Q10 and D10, since Q11 is linked to band Q3 and therefore its excitation energy and spins are known. The existence of the 1008 keV transition can be understood through the mixing of the 35 + states of the bands Q10 and Q11, which are separated by only 51 keV.  However, the decay of band D10 remains unknown. It can be that due to the high excitation energy of the band the decay is fragmented. Moreover, one cannot exclude the possible existence of another unidentified isomeric state to which band D10 decays.
The band Q5 was observed previously and linked to lowlying states. We confirm all previously identified transitions and extend it at the bottom by two more states populated and deexcited by the 868 and 1566 keV transitions, respectively. Four new transitions with energies of 415, 533, 543, and 932 keV link band Q5 to bands D8, D7, Q1, and D5, respectively.
Band Q6 is new. It consists of only two states linked by the 803 keV transition and decays towards band Q5 through the 287, 326, and 1026 keV transitions.
Band Q7 was observed previously and its transitions and decay-out are confirmed. The 1274 keV transition linking band D11 to the 31 + state of band Q7 is also confirmed, giving     additional confidence in the spin-parity assignment to the highspin bands.
Band Q8 is new. It decays to band Q7 through the 826 and 953 keV transitions.

The dipole bands (D1-D11)
Spectra obtained by doubly gating on selected transitions of the different D bands are shown in Figs. 5-7. Most of the transitions in these spectra were observed in prompt coincidence with both the EUROBALL and JU-ROGAM II arrays. The use of the recoil tagging technique in the JUROGAM II experiment allowed the observation of very weak transitions populating the 20 + isomer. The results of this experiment have been published in a separate paper [10].
Band D1 is new. It is weakly populated and decays through the 1283 keV I = 2 transition to the 13 − state. We chose the E2 character for the 1283 keV transition which leads to a negative-parity assignment for the states of band D1, since in   Band D5 is new, in the sense that previously observed transitions which were placed in the level scheme without emphasizing a band structure are now grouped in a sequence of dipole transitions with energies ranging from 161 to 523 keV. Several new transitions were placed at the bottom of the band (215, 325, 418, 456, 509, 540, 548, 867, 1156). The decay of the band is fragmented and occurs from the four lowest-lying states to the negative-parity states below the 20 + isomer.
Band D6 has been observed previously. We add one more transition of 599 keV at the top and one of 1024 keV deexciting it towards band D5.
Band D7 is also new, in the sense that previously observed transitions were grouped to form a band of dipole transitions. In addition to the previously observed transition we identified one transition of 154 keV at the bottom of the band and several decay transitions towards bands D5 and D6 (486, 660, 1035 keV).
Band D8 was observed previously and is confirmed. We identified one new decay transition of 545 keV towards band D6.
Band D9 is new. It is composed of transitions previously observed and placed on top of band Q1. We have now draw the observed states differently and add two new transitions of 592 and 792 keV on top of the band and one crossover transition of 877 keV.
Band D10 is new. It consists of the transitions which were previously placed at the bottom of band Q10, to which we add many newly identified transitions: 245, 287, 522, 578, 599, 653, 680, 992, 1100, 1232 keV. However, as discussed in the previous subsection, the decay of band D10 to low-lying states is not established. It is clear that it decays to one or more isomeric states since we see the transitions of band D10 in coincidence with the low-lying transitions of 140 Nd observed at the focal plane of RITU, but the band can also have prompt decay branches.
Band D11 is the highest excited dipole band and is composed of transitions that were not grouped in bands previously (see the discussion of band Q9). Many new transitions have been identified and put together to form a dipole band with crossover transitions, which decays towards Q9. Band D11 is also connected to band Q7 by the 1274 keV transition.

IV. DISCUSSION
The level structure of 140 Nd with 60 protons and 80 neutrons can be considered to arise from an interaction between 10 proton particles on top of the Z = 50 major shell and 2 neutron holes in the N = 82 major shell. In the low-energy regime, the nucleus is expected to have a small deformation, 2 ∼ 0.1-0.2. Thus it is convenient to express the single-particle states in terms of j -shell quantum numbers. The lowest proton configuration has four protons holes in the πg 7/2 , πd 5/2 orbitals which interact and are strongly mixed. Higher angular momenta from proton configurations can be obtained by exciting one or two protons from πg 7/2 , πd 5/2 to πh 11/2 . The lowest neutron configuration has two holes in the νd 3/2 , νs 1/2 orbitals which interact and are strongly mixed. Higher angular momenta from neutron configurations can be obtained by exciting one or two neutrons from the νh 11/2 orbital into the νd 3/2 , νs 1/2 orbitals, all lying below the N = 82 shell gap. Higher excited states and angular momenta can be obtained from neutron excitations above the N = 82 shell gap into the νf 7/2 , νh 9/2 , and νi 13/2 orbitals.
The level structure of 140 Nd at low spins has been well described within the CNS model as built on spherical configurations up to the 20 + isomer [8], which was interpreted as a maximum aligned configuration with four proton holes in the π (dg) subshell and two neutron holes in the νh 11/2 subshell, i.e., a π (dg) 4 ⊗ νh 2 configuration. The new bands observed at medium and high spins are sequences of either quadrupole or dipole transitions, which we labeled as Q and D bands, and will be discussed separately using the CNS and the TAC models, respectively.

A. The cranked Nilsson-Strutinsky (CNS) formalism
The Q bands will be analyzed using the cranked Nilsson-Strutinsky (CNS) formalism [21][22][23]. This formalism is based on the Nilsson or modified oscillator potential, where the total energy is obtained as a sum of the rotating liquid drop energy and the shell energy [23,24]. This energy is calculated in a mesh of deformations ε 2 , γ , and ε 4 , and the minimum is searched as a function of these parameters. In the calculations of the single-particle energies, we have used the so-called A = 150 parameters [25], which are known to give a good description of the low-deformation configurations of nuclei with a few particles outside the 146 Gd core; see, e.g., [26] and references therein. By introducing some minor approximations which are essentially negligible at the small deformations of the triaxial 140 Nd bands, it becomes possible to label the orbitals as belonging to a specific N shell and as being of high-j (intruder) or low-j character. These labels are applicable in the full deformation space, which makes it possible to specify the configurations of the triaxial bands in Nd nuclei with N ≈ 78-80 relative to a 132 Sn core as π (d 5/2 g 7/2 ) p 1 α 1 (h 11/2 ) p 2 α 2 , (1) ν (d 3/2 s 1/2 ) −n 1 α 3 (h 11/2 ) −n 2 α 4 (h 9/2 f 7/2 ) n 3 α 5 (i 13/2 ) n 4 α 6 , defining the number of particles and holes in the different groups of orbitals. In addition, signature α is a preserved quantum number which can be specified for each orbital and thus also for the different groups in Eq. (1). For an odd number of particles or holes, α takes the values +1/2 or −1/2, while for the low-lying configurations α = 0 for an even number of particles. With no loss of information we can use the condensed configuration labels (p 1 ) α 1 (p 2 ) α 2 , (n 1 ) α 3 (n 2 ) α 4 (n 3 ) α 5 (n 4 ) α 6 . ( In these labels, the signature α will be written as ± for an odd number of particles while α = 0 for an even number of particles will not be specified. Furthermore, if α is not specified for a small number of odd particles in a high-j shell, it is assumed that it takes the favored value, α = 1/2 for even N and α = −1/2 for odd N . In order to distinguish the large number of calculated bands in 140 Nd, we will use the labeling in Eq. (2), which is more complete than [p 2 , n 2 (n 3 n 4 )] which has been used in previous studies of the triaxial bands in 138-140 Nd [2,3,6]. The new feature to specify the signature in the CNS labels has been introduced in a less systematic way previously; see, e.g., [27][28][29][30].

B. CNS analysis of high-spin bands in 140 Nd
Calculated potential energy surfaces in the spin range I = 24-48 are shown in Fig. 8. There are essentially three different structures which are seen as different minima. The configurations close to spherical shape with no particles excited across the N = 82 gap are lowest in energy up to I ≈ 40. For example the favored termination predicted for I = 32 [8] is seen as a well developed minimum at ε 2 ≈ 0.2 and γ ≈ 30 • . The triaxial minimum at ε 2 = 0.20-0.25, γ = 30 • -35 • starts to develop around I = 20 and becomes yrast around I = 40. Finally, the superdeformed minimum [4] at ε 2 ≈ 0.45, γ ≈ 0 • is seen for essentially all spin values but it becomes lowest in energy first for spin values close to 60h. The calculated deformation of the different triaxial high-spin configurations are rather stable, with ε 2 ≈ 0.20, γ ≈ 32 • , and ε 4 ≈ 0.01 in the I = 20-30 spin range. In Fig. 9 we show two energy surfaces for the [82,22 (20)] configuration assigned to band Q1 for spins I = 18 and I = 24, which shows a minimum at the same deformation as the minimum calculated for (π = +, α = 0) for I = 24 shown in Fig. 8.
The single-particle Routhians at this deformation are drawn in Fig. 10 as functions of the rotational frequency ω. Then in Fig. 11 we illustrate how the spin is built in the [82,22 (20)] configuration which is assigned to the Q1 band; see below.
There are four high-j particles which are almost fully aligned at ω = 0, namely two h 11/2 protons and two h 9/2 f 7/2 neutrons. The spin contribution from these particles at ω = 0 is ∼ 16.3h which comes rather close to the maximum value of 18h. These values are consistent with the fact that the Q1 band has not been observed below I = 18h. With increasing rotational frequencies, the (dg) protons and h 11/2 neutrons contribute about equally to the spin while the contribution from the holes in the (sd) 3 neutron orbital at the top of the N = 4 shell is negligible. In the N = 4 proton orbitals, a crossing is formed at ω/ω 0 ≈ 0.07 between the α = 1/2 branches of the (dg) 4 and (dg) 5 orbitals. In Fig. 11 we have followed the (dg) 4 orbital through the crossing, which leads to a smooth development of the spin contribution for the (dg) particles. In the CNS calculations, for configurations with four α = 1/2 (dg) protons, the lowest four orbitals of this type are occupied, i.e., the (dg) 4 orbital is occupied at low frequencies and the (dg) 5 orbital at high frequencies. This leads to a discontinuity in the spin contribution and then also in the E-vs-I curves. Such discontinuities are seen in some of the calculated bands discussed below. From the single-particle orbitals in Fig. 10 we can get a good idea about which are the important configurations for the building of triaxial bands. There are only three important proton configurations which have two or three h 11/2 particles. They can be combined with a large number of neutron configurations. We have thus mainly considered the favored configurations with one, two, or three neutrons in the three high-j orbitals which come in the region of the N = 80 Fermi level around ω/ω 0 = 0.04. The bands with negative parity and odd spin (α = 1) resulting from these proton and neutron configurations are shown in Fig. 12. Such figures have also been produced for the other spin-parity combinations and examined in the process of configuration assignment. A typical feature of the triaxial bands is a parabola-like behavior of the E − E rld curves with a well defined minimum at some value of I . These are the bands of main interest here. Besides these bands, one notes that, for example, the bands with one N = 4 neutron hole and one high-j neutron have a rather different behavior with terminating states which are not too far above yrast. For example, the [7 + 3, 1 + 2(01)] configuration terminates at I = 43 − in the state π (d 5/2 g 7/2 ) 7 12.5 (h 11/2 ) 3 13.5 , ν (d 3/2 s 1/2 ) −1 0.5 (h 11/2 ) −2 10 (i 13/2 ) 1 6.5 , where the total spin in the different groups is specified as a subscript. Some bands in Fig. 12 show band crossings, as most clearly seen at I ≈ 39 in the [82, 23 + (21)] configuration. This is caused by the unpaired band crossing between the (dg) 4 and (dg) 5 orbitals discussed above. The E − E rld curves of the Q bands, which are observed in an extended spin range, are compared with the configurations assigned to them in Fig. 13. In general, the difference between experiment and calculations follows the expected trend. It is rather constant and close to zero above I = 30, while it increases towards lower spin values, suggesting that pairing starts to play a role. The Q11 and Q12 bands show the strange feature that the differences increase at the highest spin values, especially for Q11. It is also somewhat strange that the [7 − 3, 3 − 2(21)] configuration is calculated to be so low in energy when compared with its experimental counterpart, Q11. An alternative assignment for the Q11 band is [82, 3 − 3 − (22)], i.e., a configuration with four high-j neutron particles. With  22(20)] configuration drawn as functions of the rotational frequency. The gaps corresponding to this configuration are labeled by rectangles while some other particle numbers are given within circles. The orbitals are labeled by the subshells with the dominating amplitudes and by the ordering within the different groups. The proton d 5/2 g 7/2 orbitals are labeled (dg) and the neutron d 3/2 s 1/2 and h 9/2 f 7/2 orbitals (sd) and (hf ), respectively. this assignment, the energy agrees better with experiment but it is calculated to be too high for I < 40. Furthermore, such an assignment is not preferred because it would mean that the expected yrast band would not be observed, and that a band calculated to lie ∼1 MeV above the yrast line would be observed instead.
One of the criteria used to choose between the various possible configurations for a specific Q band was that the configurations of the band itself and the band towards which it decays are related by simple excitations. We have found that this criterium is in general fulfilled and understand the various connections between the bands as follows:  22(20)] configuration from the different groups of orbitals drawn vs rotational frequency, ω. The total spin contribution from protons is labeled I p and that from the neutrons I n . The frequencies corresponding to the lowest and highest observed spin values in the [82, 22(20)] configuration, 18h and 26h, respectively, are indicated while the value of I/2 with I = I p + I n is shown in both the proton and the neutron panels. The contribution from the h 11/2 neutrons, which is labeled (h 11/2 ) −2 is actually calculated as the contribution from the ten h 11/2 orbitals which are occupied. Note that the contributions from the proton and neutron cores and from the (sd) neutrons, which are drawn at the bottom of the respective diagrams, are essentially negligible.
[82, 22(20)]; simple deexcitation of one neutron from i 13/2 to (h 9/2 f 7/2 ).      The fact that the most favored configurations are active will also mean that the bands which are calculated lowest in energy for I ≈ 30-35 have an experimental counterpart as illustrated for the (π, α) = (−, 1) bands in Fig. 12. Also the (π, α) = (+, 0) bands which are calculated to be lowest in energy are assigned to observed bands. For the other paritysignature combinations there are fewer low-lying calculated bands, which is consistent with the fact that fewer such bands are seen according to the tentative (π, I ) assignments of the observed high-spin bands.

C. The I = 1 bands interpreted by CSM and TAC calculations
The TAC calculations use the same Hamiltonian as the CNS one. The restriction of CNS that the rotational axis must agree with one of the principal axes is lifted. In order to simplify the calculations, the deformations of the various configurations is kept the same. We use ε 2 = 0.17 and γ = 30 • as a compromise. Clearly the deviations of the calculations from experiment are expected to be larger than those for the CNS, which optimizes the deformation parameter for each configuration.
The bands that we discuss in the present paper have at least two protons and two neutrons excited, which reduces strongly the pair correlations, allowing thus their qualitative interpretation in terms of single-particle configurations in the rotating potential. Figures 14 and 15 show the single-particle Routhians calculated by means of the TAC code [32] for a deformation of ε 2 = 0.17 and γ = 30 • , which is a typical value for this mass region [2,3,6,33,34]. The TAC model considers rotation about an axis that is tilted by the angles θ and φ from the principal axes. The long, short, and medium principal axes correspond to (θ, φ) equal to (0, 0), (90 • , 0), and (90 • , 90 • ), respectively. The different configurations are labeled by the four proton and four neutron orbitals which are occupied outside a "core" with Z = 56 and N = 76. In the proton core, the six lowest (dg) orbitals outside Z = 50 are occupied, while there are four h 11/2 holes and two (sd) holes below N = 82 in the neutron core. From the labels on the orbitals in Figs. 14 and 15, it is then straightforward to see which orbitals are occupied in a specific configuration. Because these labels are defined at a fixed deformation, it becomes possible to specify exactly which orbitals are occupied, contrary to the CNS labels where it is assumed that the lowest orbitals within a specific group are occupied (however, in specific cases, excitations within CNS configurations have been considered; see, e.g., [35,36]).
In this section we apply the unpaired version of the cranked shell model (CSM) [31], which classifies the bands as particlehole configurations in the rotating potential. The underlying independent particle approximation of the CSM applies only to relative energies and angular momenta.
In contrast to the standard version of CSM we will adopt band Q1 as reference, which is πABEF ⊗ νAĀCD in CSM notation or [82,22(20)] in the CNS notation used in the previous section. The composition of the angular momentum is illustrated in Fig. 11. The spins of the two proton particles in h 11/2 and two neutron particles in h 9/2 /f 7/2 are fully aligned, adding to the total angular momentum of 18h at the bandhead of Q1.
The experimental Routhian e and alignment i x for each band have been extracted following the standard procedure as described, e.g., in Ref. [31], assuming a reference with variable  The configurations of the dipole bands in 140 N can be understood using TAC calculations similar to those recently performed for the dipole bands in 138 Nd [11]. There are one to three h 11/2 protons and one h 9/2 /f 7/2 neutron, which align their angular momentum with the short axis, because this orientation corresponds to maximal overlap of their doughnut-like density distribution with the triaxial core. As a consequence, the h 11/2 protons and h 9/2 /f 7/2 neutrons favor rotation about the short axis. As seen in the middle panels of Fig. 14, the Routhians A and B have a pronounced minimum at θ = 90 • . There are also one or two h 11/2 neutron holes which align their angular momentum with the long axis, because this orientation minimizes the overlap with the triaxial core. As a consequence, the h 11/2 neutron holes favor rotation about the long axis. As seen in the middle panel of Fig. 15, the RouthiansĀ andB have pronounced maxima at θ = 0 • , which means that holes in these two orbitals drive the rotational axis to θ = 0 • . Alternatively one may say that neutrons in A and B orbitals favor the long axis. The h 11/2 neutrons in the lower orbitals do not drive the rotational axis significantly, because to each Routhian there is a conjugate one (barred) that nearly compensates the drive. The collective angular momentum originating from the rest of the nucleons is maximal for the medium axis, for which the deviation from axial symmetry is maximal.
The large number of dipole bands originates from the combination of h 11/2 protons and h 9/2 /f 7/2 neutrons which align with the short axis, and h 11/2 neutrons which align with the long axis. The rotational axis lies therefore in the short-long principal plane being tilted away from the principal axes by a large angle. The tilt breaks the R x (π ) symmetry that induces the signature quantum number, and one observes a I = 1 sequence of rotational states, i.e., a dipole band [37]. The rotational mode is predominantly of magnetic nature, because the mutually perpendicular angular momenta of the proton and neutron h 11/2 orbitals combine to a large transverse magnetic moment, which generates strong M1 transitions.
Most of the dipole bands have configurations which contain two h 11/2 neutron holes that align their angular momentum with the long axis, except the lowest-lying bands D1, D2, and D5 which involve only one h 11/2 neutron hole. Table IV lists the configurations that originate from these combinations and suggests how to interpret the observed dipole bands. The B(M1)/B(E2) ratios of the dipole bands larger than 20 μ 2 N /(eb) 2 characterize the dipole bands as magnetic rotation.
Band D3 is a short sequence of two transitions, which decays to states of band D4 and to the 20 + isomer. We assign a πh 2 (dg) 2 ⊗ νh −2 11/2 (sd) −1 (h 9/2 f 7/2 ) 1 (πABEH ⊗ νABCG) configuration to this band, which has therefore one additional broken pair relative to the 20 + isomer, which contribute to the configuration of band D3 with two neutrons in the h 11/2 and (sd) orbitals, while the two unpaired protons are raised from the (dg) to the h 11/2 orbital.
Band D5 is more excited than bands D1 and D2 and has a very fragmented decay towards states below the 20 + isomer. It is therefore natural to assign a configuration with one more neutron in h 11/2 relative to the configurations of bands D1 and D2. The parity of band D5 is positive, being well established by the 1366 keV E2 transition towards the 16 + state. The configuration that we assign to band D5 is the lowest-lying positive-parity configuration involving 2 h 11/2 neutrons and 2 h 11/2 protons, that is πh 2 (dg) 2 ⊗ νh −2 11/2 (πABEF ⊗ νABGH ).
Band D6 decays to band D5 and has a larger alignment. In order to account for the higher excitation energy of band D6 relative to D5, we can excite one proton from the F to the G positive-parity orbital, leading to the πh 2 (dg) 2 ⊗ νh −2 11/2 (πABEG ⊗ νABGH ) configuration. However, the calculated difference in spin alignment between the bands D5 and D6 does not agree with the experimental value. This effect can be induced by the difference between the deformation used in the calculations and the real deformation of the configurations of bands D5 and D6.
Band D7 has an excitation very similar to band D6 and possibly a positive parity. We can then assign a configuration similar to that of band D6, with one proton moved from the G to the H orbital, that is the πh 2 (dg) 2 ⊗ νh −2 11/2 (πABEH ⊗ νABGH ) configuration.
Band D8 is more excited and has a larger alignment than the bands D6 and D7 to which it decays. A configuration which would account for that is obtained by rising one more proton in h 11/2 . We assign the πh 3 (dg) 1 ⊗ νh −2 11/2 (πABCE ⊗ νABGH ) configuration to band D8.

V. SUMMARY
High-spin states in 140 Nd have been populated using the reaction 96 Zr( 48 Ca,4n) and two powerful setups: EUROBALL and JUROGAM II + RITU + GREAT. The prompt γ -γ coincidences measured with EUROBALL and JUROGAM II and the prompt-delayed coincidences between the γ rays measured at the target position and at the focal plane of the RITU spectrometer allowed the identification of many new transitions, among which are also those populating the 20 + isomer. A very rich and complete level scheme was developed and most of the existing information was confirmed. New bands of quadruple and dipole transitions were identified up to very high spin. The observed bands were discussed using the TAC and CNS models. Possible configurations for the different bands are discussed, showing that rotations can occur in 140 Nd either around a principal or a tilted axis of the intrinsic reference system, depending on the presence in the configurations of protons and neutrons in the h 11/2 orbitals. The global understanding of the observed bands brings a strong support to the existence of a stable triaxial deformation at high spin in this mass region.