There has been a lot of interest in the study of nuclei around mass number A ≈ 60 in recent years. For nuclei in this mass region, the protons and neutrons both lie in the f p shell, near the doubly magic, spherical nucleus 56 Ni which can act as a natural core for understanding excitations. 56 Ni has proton number and neutron number equal to 28 and therefore the nucleons ll up the f 7 2 shell. Any addition or subtraction of nucleons to this spherical nucleus can have an e ect on its shape at higher excitation. Nuclei with valence nucleons in the upper f p shell region, above the f 7 2 orbital, have the possibility of getting excited into the g 9 2 orbital which has been known to bring about collectivity. Therefore, nuclei in this region are perfect for the study of structural changes from spherical to deformed con gurations. Several studies have been performed to investigate these structural changes in nuclei in this upper f p shell region. The excited high spin states of 59 Cu and 61 Cu nuclei have elucidated the evolution of nuclear shapes from spherical to deformed [1,2]. Similar studies were made on 57 60 Mn, and 58 Ni about the onset of collectivity with the inclusion of the g 9 2 orbital [3,4].
The collective excitations that have been observed in this mass region consist of both the magnetic rotation and the rotation due to a deformed nucleus. Magnetic rotation bands were rst observed in the near-spherical Pb isotopes with A ≈ 200 [5,6], but they have also been observed in lighter nuclei like 58 Fe, 60 Ni, and 61 Ni [7 9]. This phenomenon is usually characterized by bands of strong M1 transitions as opposed to the E2 transitions which indicate rotation due to deformation. Magnetic dipole rotation can be explained using the shears mechanism, where there is a coupling and gradual alignment of the spin of the protons and neutrons making up the total angular momentum of the levels, with the proton and neutron spin vectors as two blades of a shear [10 12]. The cross-over E2 transitions in these bands are generally weak or sometimes not observed as documented in the previous studies on magnetic rotation [12,13]. Magnetic transition probability, B(M1) is expected to decrease with an increase in the total angular momentum vector as the magnetic moment reduces with the closing of the shear blades.
The isotopes, 59 61 Co and 59 Ni all have protons occupying the f 7 2 orbitals, which is completely lled for 59 Ni.
The neutrons on the other hand fill in the f p orbitals above f 7/2 . The experimental results from the high spin excitation will be compared to the large-scale shell model calculation for the three nuclei in consideration. The high-spin excitations give the perfect opportunity to investigate the structural changes from spherical to nearly deformed or deformed nucleus because their valence nucleons lie between the spherical closed shell nuclei and the deformation driving g 9/2 orbital. Prior investigations of 59 Co have not particularly focused on studying such structural changes [14][15][16]. Previous studies of 59 Ni and 61 Co have however focused on rotational bands and the role of the g 9/2 orbital in the development of collectivity [17,18]. This article will focus on the single-particle and collective excitations in these three nuclei.
Two fusion-evaporation reaction experiments were performed at the John D Fox Laboratory, Florida State University (FSU) to populate and study the nuclei of interest. The beam used for both experiments is a long lived radioactive 14 C beam which was accelerated to an energy of 43 MeV using the 9 MV tandem accelerator. The targets were thin unbacked foils of 48 Ti and 50 Ti with thickness around 500μg/cm 2 , and highly enriched up to over 90% for the particular isotope. The reaction 48 Ti( 14 C, p2n) 59 Co populated the high spin states of 59 Co by the evaporation of a proton and two neutrons (p2n channel). High spin states of 59 Ni were also populated using the same target in the reaction 48 Ti( 14 C, 3n) 59 Ni by the evaporation of three neutrons from the compound nucleus (3n channel). The reaction 50 Ti( 14 C, p2n) 61 Co on the other hand, populated the high spin states of 61 Co by the evaporation of a proton and two neutrons from the compound nucleus formed (p2n channel).
The FSU γ-detector array consisting of six High Purity Germanium (HPGe) clover detectors, and three single crystal Germanium detectors was used for detecting the γ rays from the excited states of the three nuclei. Three HPGe clover detectors were coupled to Bismuth Germanium Oxide (BGO) shields, an inorganic scintillator detector, which allows for Compton suppression. The detectors in the array were placed at 90 • , 45 • , and 135 • with respect to the beam axis. This made the calculation for the Directional Correlation of Oriented States (DCO Ratio) possible. The energy and efficiency calibrations of the germanium detector array were performed using known calibrated 152 Eu, 133 Ba, and short-lived 56 Co sources. The 56 Co source was made at FSU using a proton beam. The spectra from the non 90 • detectors were corrected for Doppler shift using the β (v/c) value of recoiling nuclei and the detection angle. The PIXIE digital data acquisition system was used to record the signals from the detectors and digitize for further analysis. For this experiment, the data was collected with a 2-fold γ coincidence.
The event mode data was built into γγ matrices using the Gnuscope software developed at FSU [19]. This was used for γγ coincidence analysis to identify new γ rays in coincidence with previously known transitions, which was then used to build up the level scheme as will be discussed. Angle-dependent asymmetric matrices were also made for Directional Correlation of Oriented States (DCO Ratio) analysis. The DCO ratio (R DCO ) technique was used to infer the spin change between transitions from one energy level to another. This spin change by extension was used to assign the spin of the higher energy level between levels joined by the transition. This assumes that the spin of the lower energy level is already known.
Given that γ 1 , γ 2 are two γ peaks in coincidence, and θ 1 , θ 2 are the angles of their detection, 90 • and 135 • in our case, the R DCO is given by [20]
where
) is the intensity of γ 2 determined from a spectrum in detectors at θ 1 gated on γ 1 detected by detectors at θ 2 .
For gates that were made on pure dipole transitions, if the R DCO is around 1 ± 0.3, then the transition is dipole and if R DCO is around 1.85 ± 0.35, then it is a quadrupole transition. For gates that were made on pure quadrupole transitions, if R DCO is around 0.55 ± 0.15, then the transition is dipole and if R DCO is around 1.05± 0.25, then the transition is quadrupole. The Figure 1 shows the plot of R DCO with energy of γ transitions in 59 Co, 61 Co, and 59 Ni. The γ transitions with known multipolarities were in good agreement with our analysis giving us the confidence to make predictions for the new transitions.
Measuring the polarization asymmetry of the emitted γ rays helps in determining whether the γ ray transitions are magnetic or electric in nature. With this information, we can assign parity to the new states identified by the γγ coincidence analysis, having assigned spin values using the DCO ratio technique. The four crystals in the clover detectors located at 90 • to the beam axis served as Compton Scattering polarimeter which makes polarization asymmetry measurements possible. The value of the polarization asymmetry A is positive for electric transitions and negative for magnetic transitions, and is given by [21]
N ⊥ and N are the numbers of γ rays Compton scattered in the perpendicular and parallel directions with respect to the beam axis. The factor, a is a correction term that is defined at A = 0 as
The data was sorted into two hits for the clover detectors placed at 90 • for polarization asymmetry; one parallel to the beam direction, and the other perpendicular
0 500 1000 1500 2000 2500 3000 3500 E γ (keV) -0.2 0 0.2 Asymmetry (a) 59 Co 1460 1995 2261 2384 2630 2719 2979 1893 1539 1584 457 653 695 1026 1095 1191 2654 Electric Magnetic 0 500 1000 1500 2000 2500 3000 3500 E γ (keV) -0.2 0 0.2 Asymmetry (b) 59 Ni 1121 1151 582 807 787 536 765 876 897 3142 2959 2878 2651 2010 2139 1368 1106 1239 1429 1402 1223 1339 1555 1769 1718 1751 1950 1936 2289 2336 797 Electric Magnetic 0 500 1000 1500 2000 2500 3000 3500 E γ (keV) -0.2 0 0.2 Asymmetry 436 709/710 753 457 1013 1132 1267 1665 1808 2076 Magnetic (c) 61 Co Magnetic Electric FIG. 2. The plot of polarization asymmetry vs. energy of γray for (a) 59 Co, (b) 59 Ni and (c) 61 Co. Point 709/710 in (c) represents the two transitions 709 keV and 710 keV which are magnetic in nature. The points in red are electric transitions while the points in blue represent magnetic transitions.
to the beam direction. Using a 152 Eu unpolarized source, we measured the factor a, for different energy which was then fitted with a linear equation to obtain the factor a, as a function of energy.
For all the γ transitions with good statistics, we calculated their polarization asymmetry and classified them as either electric or magnetic depending on the sign of A.
200 400 600 800 1000 1200 5 1 2 761 796 850 927 964 994 1095 1200 1400 1600 1800 2000 2200 4 8 Counts/keV 2200 2400 2600 2800 3000 3200 3400 E γ (keV) 1 2 729 712 1026 1047 1172 1191 1240 1460 236 269 303 457 653 1438 1478 1509 1539 1623 1645/1649 1690 1972 2025 2079 2261 2384 2630 2794 2979 3290 3420 334 1584 511* 1325 FIG. 3. 695-keV gate showing the γ ray energy peaks in 59 Co coincident with it. All the peaks labeled in red were newly discovered in this study. The 511-keV peak due to pair production is also shown; differentiated from other peaks with the * sign. Other peaks not labeled are possible contaminants from other nuclei also produced in the reaction. 0 200 400 600 800 1000 3 5 236 269 303 334 695 796 994 1041 1026 1000 1200 1400 1600 1800 2000 1 2 Counts/keV 1095 1191 1438 1460 1478 1509 1539 1645 1765 1690 1893 1972 1995 2000 2200 2400 2600 2800 3000 E γ (keV) 1 2 3 2184 2261 2384 2630 2654 2719 2979 2025 FIG. 4. 653-keV gate showing the γ ray energy peaks in 59 Co coincident with it. All the peaks labeled in red were newly discovered in this study. Other peaks not labeled are possible contaminants from other nuclei also produced in the reaction.
The combination of γγ coincidence analysis, R DCO measurement, and polarization asymmetry measurements allowed us to build new expanded level schemes for the three nuclei in this study, 59 Co, 59 Ni, and 61 Co.
In a previous study by Warburton et al. [14] using the 48 Ca( 14 N, 3n) 59 Co reaction, a maximum spin of 23/2 at an excitation energy of about 7.5 MeV was attained. In this current work, we have been able to confirm states predicted in the previous study and assigned parities to them. We have also extended the negative parity states to 27/2 -at around 9.6 MeV, while identifying positive parity states upto a J π = 31/2 + which had not been observed in any previous study of 59 Co. The multipolarity of the transitions in this study based on the value of the R DCO and polarization asymmetry are given in Table I. Figures 1(a) and 2(a) display the numbers for 59 Co. The R DCO value for the new transitions as seen in Figure 1(a) is based on the fact that the transition gated upon is a quadrupole transition. The expanded level scheme of 59 Co can be seen in Figure 5.
Figures 3 and 4 show the coincident γ ray peaks when gates were defined on the 695-keV and the 653-keV transitions. These two gates show most of the transitions already known (labeled in black), and the new ones observed in this study (labeled in red). The unlabeled peaks in the figures are mostly from other contaminants produced in this reaction. There are a few peaks that might be in 59 Co but we were unable to place them in the level scheme.
We have made an adjustment to two energy levels from the published level scheme in Ref [14]. The 3326-keV and 4087-keV levels have now been replaced with the 2915-keV and 3628-keV levels. This is driven by the fact that the observed intensities for the γ rays feeding the levels did not support the arrangement in the previous study. There are closeby 1168-keV and 1177-keV γ transitions observed in 56 Mn and 60 Co respectively, which influence the intensity of the 1172-keV γ transition observed in 59 Co. These nuclei are all produced in the reactions 14 C + 48 Ti (this current study) and 14 N + 48 Ca (previous study by study by Warburton et al. [14,22]) according to PACE calculations [23]. The intensity of the 1172-keV transition in 59 Co according to this study was used to determine its placement, and hence changed from where it was placed in the level scheme of Ref [14] as seen in Figure 5.
A major addition from the current work for 59 Co, is the identification of positive parity states which clearly form a cascade. The transitions at 2654-, 1995-and 2261-keV were already known from previous studies and their placement could be verified in the current study. From the present R DCO values these transitions were confirmed to be dipole transitions, but further, the polarization asymmetry measurements suggest that they are of electric nature, making them E1 transitions. This implies that they connect states with opposite parities. With the parities of the lower levels being negative we can conclude that the 2654-keV transition links the 11/2 + to the 9/2 -state, the 1995-keV transition links 13/2 + to 11/2 - state and the 2261-keV transition links the 15/2 + to the 13/2 -state. Beyond the 15/2 + a series of strong M1 transitions were observed connecting the positive parity states with no crossover E2 transitions. The multipolarities concluded for all the transitions based on R DCO
0 7/2 -1460 11/2 -2155 13/2 -2915 15/2 -3628 17/2 (-) 4490 15/2 (-) 4800 19/2 (-) 5445 17/2 (-) 5575 15/2 (-) 6422 19/2 (-) 6879 21/2 (-) 7904 23/2 (-) 8119 23/2 (-) 8868 25/2 (-) 9553 27/2 (-) 3225 13/2 (-) 3738 15/2 -4785 17/2 (-) 1191 9/2 -2184 11/2 -3083 11/2 -3844 11/2 + 4179 13/2 + 4415 15/2 + 4718 17/2 + 5371 19/2 + 6365 21/2 + 7460 23/2 + 7843 23/2 (+) 8898 25/2 (+) 9105 25/2 (+) 9344 25/2 (+) 9815 27/2 (+) 10073 27/2 (+) 10091 27/2 (+) 10889 31/2 (+) 11140 31/2 (+) values and polarization asymmetry are listed in Table I with some plotted in Figures 1(a) and 2(a). In all, 22 new transitions were observed which resulted in 20 new energy levels. Nine of these new energy levels are of positive parity, in addition to seven existing energy levels have now been identi ed as positive parity states.
In an earlier study by S. Juutinen et al. [24] in 1989, using the reaction 58 Ni( 3 He, 2p) 59 Ni, negative parity states were observed upto an excitation energy of 7.9 MeV with likely spin of 19/2 or 21/2 . Positive parity states were also identi ed in the study, and the band built on the 9/2 + state at 3057 keV was expanded to an energy level of around 6 MeV, though de nitive spin assignments were not made.
In a more recent study by C. -H. Yu et al. [17], using the reaction 40 Ca( 29 Si, 2 2p) 59 Ni, four rotational bands were established with the highest spin observed to be 43/2. The two strongest bands, 1 and 2, are proposed to be generated by exciting one neutron and one neutron + one proton to the g 9 2 orbital respectively. They also indicated that the transition quadrupole moments of these bands decrease with spin suggestive of band termination.
The expanded level scheme of 59 Ni as a result of this work is shown in Figure 9 where red indicates new additions. In the present study, new transitions were established which were instrumental in the extension of the existing band of negative-parity states to around 12 MeV with spin 31/2 earlier known only till 23/2 at an energy of 7954 keV from Ref. [24]. There is a new doublet of -ray transitions, 677-keV and 678-keV which appear in this band and can be seen in Figure 6 where the gate made on the 678-keV transition clearly shows the other
200 400 600 800 1000 1200 5 10 3 1 10 4 2 10 4 Counts/keV 1200 1400 1600 1800 2000 E γ (keV) 3 10 3 5 10 3 Counts/keV 340 427/429 582 662 677 765 787 807 797 855 938 998 1106 1121 1223 1239 1279 1339 1368 1402 1429 1555 1610 1718 1751 1793 1918 1936 779 511* 1918 1918 1918 1912 FIG. 6. Gate on 678-keV transition in 59 Ni. Another new 677-keV transition can be seen here. All the peaks labeled in red are some of the new transitions just observed in this study, including the 1918-keV transition. The 511-keV peak due to pair production is also shown; differentiated from other peaks with the * sign. Other peaks not labeled are possible contaminants from nuclei also produced in the reaction. 500 1000 1500 5 10 3 1 10 4 Counts/keV 1500 2000 2500 3000 E γ (keV) 1 10 3 2 10 3 3 10 3 Counts/keV 340 429 677/678 938 897 876 787 998 1106 1189 1223 1339 1368 1402 1429 1610 1718 1751 1769 1912 1950 2010 2139 2289 2506 2372 2878 1239 779 511* 759 2184 1584 FIG. 7. Gate on 797-keV transition in 59 Ni. All the new transitions are labeled in red, including the 1912-keV transition.
The 511-keV peak due to pair production is also shown; differentiated from other peaks with the * sign. Other peaks not labeled are possible contaminants from nuclei also produced in the reaction.
peak measured as 677-keV. The intensity of the 677-keV implies the two transitions when arranged in the level scheme should be in close proximity. Figure 6 also shows some of the other new transitions: 779-keV, 1121-keV and 1918-keV associated with this band of negative parity states. There is also a connection observed to the 17/2 + state at 5255 keV via a new 1912-keV transition. Though this transition is close in value to other new transition, 1918-keV which exists in the band, the gate made on the 797-keV transition as seen in Figure 7 validates the placement of the 1912-keV transition. From the 807-keV gate shown in Figure 8, we could see some of the existing transitions and some of the new transitions placed in the 59 Ni level scheme.
500 1000 1500 5 10 3 1 10
4 Counts/keV 1500 2000 2500 3000 E γ (keV) 1 10 3 2 10 3 Counts/keV 303 340 429 536 582 662 677/678 765 787 779 855 876 938 997/998 1106 1029 1131 1189 1339 1368 1429 1555 1610/1612 1793 1950 2223 2139 2372 2878 1223 749 1718 1751 2193 897 511* 1918 FIG. 8. Gate on 807-keV transition in 59 Ni. All the new transitions from the two negative bands show up here except for the 1918-keV transition. The 511-keV peak due to pair production is also shown; differentiated from other peaks with the * sign. Other peaks not labeled are possible contaminants from nuclei also produced in the reaction.
A new sequence of negative-parity states is also proposed and built on the 17/2 + state at 5255 keV up to an energy of 9167 keV with a spin of 27/2. The new transition 2139 keV was clearly established to be an E1 transition according to Figures 1(b) and 2(b) and it connects the negative-parity state 19/2 -to the 17/2 + state. The 897-keV transition placed above the 2139-keV transition to link the 23/2 -to 19/2 -was further established as an E2 transition. We could not estimate the polarization asymmetry of the last transition 876-keV in the sequence though we could confirm it to be quadrupole in nature from the R DCO value. Two new transitions were also added to the band of negative-parity states that terminated at 5.9 MeV in the previous study by C. -H. YU et al., [17]. No spin or parity was assigned to the 5.9-MeV state then, but we have been able to assign a 17/2 (-) to it in this study. We assumed that the dipole transition 997 keV is most likely to be magnetic in nature, in line with the multipolarity of the 807-keV, 582-keV, and 536-keV transitions placed below and above it. The band was extended to 7.2-MeV at 21/2 -by the 536-keV and 749-keV transitions.
The sequence of positive parity states seen in the level scheme of 59 Ni (Figure 9) is analogous to band 1 and band 2 in Ref. [17] built on the 9/2 + state, though we found differences in some of the proposed spins and parities. The three transitions, 1106-keV, 1718-keV and 1751-keV had been identified as dipole transitions in previous studies. Based on our polarization asymmetry measurements we further confirmed them to be electric in nature and assigned them as E1 transitions. With that the spin-parities of the 9/2 + and 13/2 + are confirmed. Further up the 979-, 2878-and 1769-keV transitions build the band to 25/2 + at 9902 keV. We firmly established 2878 keV and 1769 keV as E2 transitions. Beyond that we see disagreements with the level structure proposed
0 3/2 -340 5/2 -1189 5/2 -1339 7/2 -1769 9/2 -1950 7/2 -2530 9/2 -2707 11/2 -3057 9/2 + 3127 11/2 -3378 11/2 -3562 11/2 -4105 11/2 + 4144 13/2 -4419 13/2 -4458 13/2 + 4727 11/2 + 4911 11/2 + 4951 15/2 -5100 13/2 (-) 5255 17/2 + 5295 15/2 -5383 15/2 + 5948 17/2 (-) 5992 17/2 + 6079 17/2 -6506 19/2 -6750 15/2 (-) 6484 19/2 (-) 7168 21/2 (-) 677 9753 7233 21/2 (-) 7954 23/2 (-) 8133 21/2 + 8632 25/2 (-) 2223 7394 9902 25/2 + 15179 (41/2 + ) 10089 27/2 (-) 12008 29/2 (-) 11912 29/2 + 13229 27/2 14284 29/2 + 11645 33/2 (+) 10422 33/2 (+) 340 1189 1339 1950 998 1610 1429 2193 759 1718 1368 429 1191 3142 2959 2651 938 1358 1610 1793 2336 1106 1612 1029 1751 1435 855 674 1402 434 1571 765 858 582 1 5 3 9 1279 807 1936 1 2 3 9 1151 1534 797 303 1555 997 1 1 3 1 1650 2878 1912 1 1 2 1 31/2 (-) 427 749 662 536 787 8291 678 1769 1918 2289 1747 2 0 1 0 1223 779 1584 2372 2506 2139 897 9167 876 2393 2783 19/2 -23/2 -37/2 (+) 9310 7637 21/2 (-) 27/2 (-) 17685 610 1950 25/2 + 2184 16468 (37/2 + ) FIG. 9. Level scheme of 59 Ni showing the existing transitions and the new transitions observed in this study. All the energy levels in red are the newly established levels in this study. The thickness of the line arrows are approximately proportional to the intensity of the transitions.
in Ref. [17]. In the gate of 1106 keV we could see the 1747 keV transitions and its R DCO suggests it to be quadrupole and not dipole as in Ref. [17]. Similarly, the 2289-keV transition is established as a E2 transition opposite to Ref. [17] where it was thought to be an E1 transition though no polarization measurements are reported there. The R DCO value for 2289-keV transitions was ascertained from two gates (both con rmed E2) namely 797 keV and 2878 keV making it a E2 transition. We further con rmed that the 2010-keV and 1223-keV transitions are E2 transitions. The 2372-keV transition was shown to a quadrupole transition, though its asymmetry would not be found. Using all this information, we established a sequence of E2 transitions connecting all positive parity states extending to 17.7 MeV with spin 41/2 + .
Overall, we observed 15 new transitions, and these in addition to some rearrangements brought about 14 new energy levels in the level scheme of 59 Ni.
In a previous detailed study by Ayangeakaa et al. [18], the multinucleon transfer reaction, 26 Mg( 48 Ca, 2 4np ) 61 Co in inverse kinematics was used to study the excited states of 61 Co. Six bands were identi ed as shown in the level scheme from that study, and all levels were assigned negative parity. In the current work, following the reaction 50 Ti( 14 C, 2np) 61 Co, we were able to observe ve of the six bands previously identi ed. The level scheme as ascertained in this work is shown in Figure 11 where the bands are referred to as 1 to 5 going from left to right. We were able to verify most of the transitions though we could not add any new -ray transitions. Figure 10 shows some of the transitions seen when a gate was made on the 1665-keV transition. Only two of the bands in this current study terminated on similar energy levels as in Ref. [18]. This is because of the higher -ray detection efficiency of Gammasphere used in Ref. [18] compared to the FSU γ array of primarily 6 clovers. Conversely the use of Clover detectors as Compton polarimeters in the current study allowed us to examine the parities of the levels.
Consistent with the previous study, only in the fifth band starting with the 17/2 -state quadrupole transitions were observed connecting the exited states; all the other bands have a series of dipole transitions. We were able to clearly show that the 1267-keV has a E2 multipolarity, though for the 1008 keV we could only get a R DCO value (Figure 1(c)) suggesting it to be quadrupole in nature. This band in Ref. [18] had 5 more transitions going upto a spin of 41/2 which we did not observe. But with the additional information from the current experiment, we can confirm that this band consists of E2 transitions.
As mentioned before, the inclusion of polarization measurements in this study to determine which transition is electric or magnetic in nature brought about a major change to the level scheme of 61 Co. The strong 1808-keV transition (see Fig. 10) connecting the states at 3473 keV and 1665 keV has now been confirmed to be dipole in nature as seen in the Figure 1(c). The polarization asymmetry measurement suggested that this transition is electric in nature as shown in Figure 2. This ascribes 1808-keV as an E1 transition which would link states of opposite parity. Hence it can be confirmed that the 1808-keV transition starts from a 13/2 + state at 3473 keV feeding the 11/2 -state at 1665 keV. The transition at 1132 keV was also confirmed to be dipole and electric in nature, thus making it an E1 transition. This served as an additional confirmation of the 13/2 + state in this study as it ends on the 11/2 -level. The 2076-keV transitions which links bands 2 and 4 is also shown to be of E1 in nature for further consistency. With the 3473 keV levels firmly assigned a positive parity, the transitions above it namely 186-, 436-and 709 keV are confirmed to be M1. Beyond that it was difficult to get both R DCO and polarization asymmetry for all the transitions in the band because of low statistics and in the case of 1462 keV being a doublet. In view of all the experimental observables from this work and Ref. [18], we can confidently state that band 2 starting at the 13/2 + state (3473 keV) is a sequence of M1 transitions connecting states with positive parity. It also agrees very well with shell model calculations as will be discussed next.
The odd A nuclei studied in this work all have their valence nucleons occupying the f p shell according to the simple shell model picture. The Co isotopes, 59 Co and 61 Co have their unpaired 27 th proton in the f 7/2 orbital, leading to a ground state spin/parity of 7/2 -. 59 Ni on the other hand has a closed shell for protons but its unpaired valence neutron lies in the p 3/2 orbital, so its ground state is 3/2 -. Since the parity of the ground state energy level is negative, the confirmation of positive parity of some of the high spin states corresponds to excitations across the N=40 shell gap into the positive parity g 9/2 orbital. The excitations into the g 9/2 orbitals can generate high spin and are also responsible for generating collective motion.
The shell model calculations were performed utilizing the M-scheme code KSHELL on the Oakbridge-CX supercomputer at the University of Tokyo [25]. Both negative and positive parity states were generated from this shell model calculation. The model space was taken as f p shell for the negative states and the GXPF1Br interaction was used for that. For the positive states however, the model space was taken as the f p shell, 0g 9/2 , and 1d 5/2 orbits, restricting one neutron excitation to the 0g 9/2 , and 1d 5/2 orbits. In addition, up to 6-particle 6hole excitation from the 0f 7/2 orbit is allowed for the case of 59 Ni and 59 Co. The GXPF1Br+VMU interaction was used for the full calculation [26]. The predictions of the shell model calculation for the three nuclei in consideration align well with the experimental results. The rootmean-square (RMS) difference between the experimental results and the theoretical calculation averages below 200 keV. Figures 12,13 and 14 show the comparison between the calculation and experiment. The asterisks in red represent the experimental results and the squares in blue are the results from the shell model calculation for the yrast states. Figures 12 (a), 13 (a) and 14 (a) additionally include the yrare states (2nd excited state of each spin), with the experimental values represented by green circles, and the calculation represented by the green line. The details of the calculations will be discussed in greater
0 7/2 -1286 9/2 -1665 11/2 -2339 11/2 -2374 13/2 -3127 15/2 -3473 13/2 + 3659 15/2 + 4094 17/2 + 4804 19/2 + 5833 21/2 + 6895 23/2 + 8217 25/2 + 9678 27/2 + 4485 15/2 -4871 17/2 -5348 19/2 -5956 21/2 -6749 23/2 -3159 13/2 -3911 13/2 -4118 15/2 -4388 17/2 -5119 19/2 -6067 21/2 -6171 19/2 -6710 21/2 -7506 23/2 -8408 25/2 -5723 17/2 -5814 17/2 -6823 21/2 -8090 25/2 -1665 1286 378 1054 710 753 1462 1132 1098 1808 531 186 967 436 709 1030 1062 1322 1462 1013 1358 386 1212 477 609 793 1744 457 2246 208 1495 957 728 270 731 837 948 7 5 4 2076 540 796 902 2065 445 6 5 3 1008 1267 2156 7703 25/2 -954 FIG. 11. Level scheme of 61 Co con rming the existing transitions and energy levels. The spin and parity shown in red are the new important features added to this level scheme. The thickness of the line arrows are approximately proportional to the intensity of the γ-ray transitions.
detail below, in relation to the experimental results for each.
59 Co has 27 protons and 32 neutrons, leading to all its valence nucleons in the f p shell. With 7 protons outside the closed sd shell at Z = 20, we expect an unpaired proton in the 0f 7 2 orbit. The 12 neutrons on the other hand outside the closed sd shell are all paired and not contribute to the ground state spin value expected to be 7/2 because of the unpaired proton. Of the 12 neutrons, 8 neutrons ll the 0f 7 2 orbit, while the remaining 4 neutrons are expected to ll the 1p 3 2 orbit. However, as 1p 3 2 and 0f 5 2 levels are close in energy, both levels share the 4 neutrons in the ground state as per the calculations performed. This ground state con guration is veri ed by picturing 60 Co as 59 Co + n in the 59 Co (d,p) reaction studied by Roy et. al., to produce 60 Co [27]. If the four neutrons outside the closed 0f 7 2 shell lled up the 1p 3 2 orbit, then the (d,p) reaction leading to the ground state of 60 Co should be characterised by an = 3 transition (coming from the 0f 5 2 level). But all (d,p) reactions leading to the ground state and the isomeric state at 60 keV have = 1 (coming from the 1p 3 2 level), therefore pointing to the fact that there is a vacancy in the 1p 3 2 orbit in 59 Co to accommodate a neutron. We conclude therefore that in the ground state, 59 Co likely has 2 valence neutrons each in the 1p 3 2 and 0f 5 2 levels consistent with the shell model calculations.
The excitations at low spin to negative parity states are likely single particle excitations within the f p shell, i.e. 0p0h excitations. The shell model calculations for the 0p0h negative-parity states align well with the experimental result up till the 27/2 level as seen in Fig- ure 12. The positive parity states arise from 1p1h excitations where a nucleon is excited to the g 9 2 orbit leaving an even number of neutrons in the f p shell for a positive state to be formed. From Figure 12, we can see a very good agreement between the shell model calculation and the experimental result. The 9/2 + state predicted by the calculation as the lowest positive parity state was not observed in the experiment because it is not yrast. The positive parity states in 59 Co form a regular pattern with a series of strong M1 transitions from the 11/2 + state upwards to the 21/2 + state. Thus they can also be viewed in terms of collective excitation because of the regularity observed in the transitions linking the states. The presence of strong M1 transitions points to the possibility of a magnetic rotation band. In magnetic transition bands, the magnetic transition probability, experimentally indicated by transition intensities is expected to decrease until the band terminates. The g involved in the formation of positive states allows high spin to be generated and also ful lls the neutron particle, proton hole coupling condition for magnetic rotation as explained by R. M. Clark, and A. O. Macchiavelli [13]. The con guration for the proposed bandhead at 11/2 + according to the shell model calculation is (f p) 7 ⊗ ((f p) 11 g 1 9 2 ) with a neutron excited to the g 9 2 orbit.
59 Ni has a full 0f 7 2 orbital for both protons and neutrons, leaving 3 extra neutrons to ll the 1p 3 2 orbit. With this con guration, the spin-parity of the ground state is 3/2 as a consequence of an unpaired neutron in the 1p 3 2 orbit. The rst excited state with 5/2 is generated by the unpaired neutron moving from the 1p 3 2 orbital to the 0f 5 2 and is seen experimentally at 340 keV. The low-lying negative parity excited states have irregular energy transitions linking them that are suggestive of single-particle excitations within the f p shell. Other nuclei in this A = 60 mass region have been found to exhibit similar single particle excitation for the low-lying states [9,18]. There is a very good agreement between the shell model calculations for the negative parity states (no particle allowed to leave the f p shell) and experimental results up until the 23/2 as seen in Figure 13. We however see a pronounced variation from the 25/2 state and beyond. This variation can be due to a di erent conguration for these high spin states which are favorable for collective excitations. The excitation energy needed to generate the states in the collective model is likely lower than in the shell model picture.
The rst excited positive parity state from the level scheme is a 9/2 + state and can be easily generated by having a neutron in the g 9 2 orbit while all the other nucleons are paired in the f p shell. The shell model calculation for the yrast positive states aligns well with the experimental results up till the 33/2 + state. Further up, starting from the 37/2 + state we see a clear discrepancy between the shell model calculations and experimental results. The discrepancy here may also be due to a change in the con guration not captured by the shell model calculations as we move from the 33/2 + level to 37/2 + . Such a change of con guration was also observed in rotational bands in the study of 61 Ni [9], where the two con gurations were illustrated by two ts to the rotational model.
Among the positive parity states, there is a sequence of regular E2 transitions from 9/2 + to 41/2 + which points to a rotational motion. Since it is the rotation of a deformed nucleus that gives rise to regular bands observed in the spectrum of nuclei [13], it suggests 59 Ni being somewhat deformed at high excitation energy. Deformed bands have been established in 59 Ni by C. -H. Yu et al. [17]. Cranked Nilsson-Strutinsky (CNS) calculations [28] were performed and there was an indication of substantial collectivity in the band structures of 59 Ni. Similar deformed bands with a sequence of E2 transitions were also established in the neutron-rich 61 Ni by Soumik Bhattacharya et al. [9]. The negative parity high spin states from 19/2 to 31/2 also show some regularity with strong M1 transitions connecting the states. This could be an indication of magnetic rotation, which we also observed in 59 Co. The con guration of the proposed bandhead at 19/2 from the shell model calculation is (f
) which makes it possible to generate high spin.
The implication of this result is that we have two modes of excitation in this nucleus competing; one driven by the deformation of the nucleus, and the other, magnetic rotation due to the angular momentum coupling of the protons and holes. Though this is not new as has been noted earlier in Refs [7 9, 18] in their study of 61 Co, 58 Fe, 60 Ni, and 61 Ni still it is interesting to see the extent of such a phenomenon with changing neutron numbers.
61 Co with 27 protons and 34 neutrons has a ground state spin-parity of 7/2 just like 59 Co. It can be seen as 59 Co + 2n, so it is expected that excitations for the two isotopes have similarities. The rst four excited states in the two nuclei are similar in energy levels. The rst excited state, 9/2 is at 1.19 MeV and 1.29 MeV in 59 Co and 61 Co respectively. The di erence in the energies of the yrast states are 95 keV at 9/2 , 205 keV at 11/2 , 219 keV at 13/2 and 211 keV at 15/2 . Therefore, it can be expected that the same pattern of excitation will follow at low spins before the additional neutron pair is broken, and its excitation contributes to the spin of the nucleus. These considerable similarities in the low-lying spins are in agreement with the conclusions of Ref. [15] on the similarities between the energy levels of the lowlying states of 57 Co, 59 Co and 61 Co.
The randomness of the transitions within the low-lying negative parity states in the level scheme suggests single particle excitation and seems to follow a 0p0h excitation pattern. Figure 14 shows the comparison between the shell model calculation and the experimental results. Overall, a good agreement is observed, except for negative parity states from around 21/2 upwards, where there seems to be a departure between the calculation and the experiment. It can be seen from the level scheme that the high-lying negative parity states are all linked by transitions to the 13/2 + , 15/2 + and 17/2 + states which are 1p1h excitation and hence they could possibly represent 2p2h excitations, with two nucleons residing in the g 9 2 orbit. Con gurations involving two g 9 2 neutrons were also suggested by ref [18] while discussing rotational bands in the high-lying negative states of 61 Co.
The positive parity states assigned in this study of 61 Co are a natural extension of what we observed in 59 Co. In Ref. [18] these were not proposed as positive parity states as linear polarization measurement was not performed in that study. They did though observe a difference in the excitation pattern above 4 MeV, (which corresponds to 17/2 + ) and therefore suggested that the description of higher-lying states in 61 Co should be carried out in an expanded model space beyond the f p shell [18], which has been done in this current study to predict the positive states. From Figure 14, we see an excellent agreement between the shell model calculations for the positive parity states and the experimental results. The regularity observed in this band of positive states which contains a series of strong M1 transitions is again an indication of magnetic rotation. The con guration for the proposed bandhead 13/2 + shows a neutron in the g 9 2 orbit just like in 59 Co. The other bands of high-lying negative states also have strong M1 transitions and could be candidates for magnetic rotation too. We also observe the established band of E2 transitions indicative of rotation due to deformation, but it terminates quickly in this study.
Just as was discussed for 59 Ni, di erent modes of excitations are observed in the case of 61 Co. Ref [18] concluded that in 61 Co, quadrupole collectivity associated with a prolate shape competes for yrast status with the magnetic rotation of a nearly spherical system. Our results in general also support the notion that there is a competition between the magnetic rotation and the rotation due to deformation in this nucleus.
In the current work, we have studied the structure of three nuclei with A ≈ 60; namely 59 Co, 59 Ni and 61 Co using a 14 C beam on 48 Ti and 50 Ti targets. The level scheme of 59 Co now includes positive parity states which has been extended to 31/2 + at around 11 MeV. The positive parity states in the 59 Ni level scheme are now extended to 41/2 + at excitation energy 17.7 MeV. The negative parity states have also been extended to 31/2 at excitation energy of 12 MeV. There were no new transitions observed for 61 Co, but one of the major bands has been reassigned as positive parity states by reason of this study.
It can be concluded from this study that the low-lying negative states in the three nuclei represent single particle excitations with the nucleons limited to the f p shell. The positive parity states and possibly the high-lying negative states in these nuclei are highly in uenced by the presence of nucleons in the g 9 2 orbit. The presence of either strong E2 or M 1 transitions observed in these nuclei suggests a form of collective excitation; both magnetic rotation and rigid rotor-type rotation were observed. We conclude that collective excitation in 59 Co is dominated by magnetic rotation which can be explained by the shears mechanism. However, the collective excitations in 59 Ni and 61 Co are both in the form of magnetic rotation and rotations due to deformation. This implies that placing neutrons in the g 9 2 orbit creates deformation in 59 Ni and 61 Co which in turn brings about a rotation that competes with the magnetic rotation occurring with little to no deformation. The three nuclei studied highlight the competition between single particle excitations and collective excitations in the excited states observed. The large scale shell model calculations presented here do an excellent job of reproducing the excited states for the most part. However the departures at the very high spins clearly point to the need for re nements of calculation to include more than one nucleon moving to the g 9 2 orbit. TABLE I: This table show the details of the γ transitions observed in this present work on 59 Co. The DCO ratio (RDCO) was calculated for quadrupole transitions except for those with the D symbol which are from dipole transitions. Begin of Table Ei (keV) E f (keV) Eγ (keV) Branching Ratio J π i J π f RDCO Asymmetry Multipolarity 1190.7 (5) 0 1190.7 (5) 100 9/2 - 7/2 - 0.91 (6) D -0.014 (10) M1 1460.4 (5) 0 1460.4 (5) 100 (10) 11/2 - 7/2 - 1.63 (9) D 0.013 (13) E2 1190.7 269.2 (5) 8 (1) 11/2 - 9/2 - 1.26 (9) D D 2154.9 (7) 1460.4 694.5 (5) 100 13/2 -11/2 - 0.63 (5) -0.0077 (11) M1 2183.7 (8) 1190.7 993.0 (6) 100 (10) 11/2 - 9/2 - 1.03 (7) D D 0 2183.7 (8) 7 (1) 11/2 - 7/2 - 2915.4(10) 2154.9 760.5 (7) 100 15/2 -13/2 - 0.68 (5) -0.0005 (9) M1/E2 3083.4 (8) 1190.7 1892.7 (6) 100 11/2 - 9/2 - 1.04 (7) D -0.057 (18) M1 3224.9 (9) 2183.7 1041.2 (5) 100 (12) 13/2 (-) 11/2 -1.00 (14) D D 1460.4 1764.9 (9) 48 (5) 13/2 (-) 11/2 -1.07 (11) D D 3627.5(11) 2915.4 712.1 (5) 100 17/2 (-) 15/2 - 0.62 (5) D 3738.4(9) 2154.9 1583.5(5) 100 15/2 -13/2 - 0.71 (5) -0.0016 (10) M1 3844.3(10) 1190.7 2653.6 (6) 100 (13) 11/2 + 9/2 - 0.81 (6) D 0.075 (21) E1 1460.4 2383.9 (9) 89 (9) 11/2 + 11/2 - 0.98 (7) 0.075 (14) E2, J = 0 2154.9 1690.2 (8) 27 (3) 11/2 + 13/2 -0.79 (6) D D 4178.7(11) 2183.7 1995.3 (5) 100 (13) 13/2 + 11/2 -0.97 (7) D 0.066 (13) E1 3844.3 334.4 (5) 81 (11) 13/2 + 11/2 + 0.97 (7) D D 1460.4 2719.4 (5) 29 (5) 13/2 + 11/2 - 0.54 (5) 0.083 (22) E1 3083.4 1095.1 (5) 21 (5) 13/2 + 11/2 - 0.62 (5) D 2154.9 2025.3 (5) 14 (3) 13/2 + 13/2 - J = 0 4414.6(11) 4178.7 235.9 (5) 100 (11) 15/2 + 13/2 + 1.14 (3) D D 2154.9 2260.6 (5) 46 (9) 15/2 + 13/2 - 0.48 (5) 0.055 (13) E1 3224.9 1190.3 (6) 12 (3) 15/2 + 13/2 -0.91 (6) D D 4489.6(9) 1460.4 3029.2 (8) 100 15/2 (-) 11/2 -1.25 (18) Q 4717.5(12) 4414.6 302.9 (5) 100 17/2 + 15/2 + 0.68 (5) D 4785.2(13) 3738.4 1046.8 (9) 100 17/2 (-) 15/2 -1.23 (9) D D 4799.9(12) 3627.5 1172.4 (5) 100 19/2 (-) 17/2 (-) 0.67 (5) D 5370.6(13) 4717.5 653.1 (5) 100 19/2 + 17/2 + 0.58 (4) -0.017 (12) M1 5444.8(11) 2154.9 3289.9 (9) 100 17/2 (-) 13/2 -1.19 (13) Q 5574.8(11) 2154.9 3419.9 (9) 100 15/2 (-) 13/2 - 0.48 (5) D 6364.6(14) 5370.6 994.0 (6) 100 21/2 + 19/2 + 0.50 (5) D 6422.4(13) 4799.9 1622.5 (5) 100 (12) 19/2 (-) 19/2 (-) 1.14 (8) J = 0 3627.5 2794.0 (7) 65 (8) 19/2 (-) 17/2 (-) 0.70 (8) D 6878.7(14) 5370.6 1508.9 (5) 100 (13) 21/2 (-) 19/2 + 0.50 (5) D 4799.9 2078.8 (5) 73 (8) 21/2 (-) 19/2 (-) 0.54 (5) D 6422.4 457.1 (5) 69 (7) 21/2 (-) 19/2 (-) 0.68 (5) -0.0035 (10) M1 7459.7(15) 6364.6 1095.1 (5) 100 23/2 + 21/2 + 0.62 (5) -0.020 (13) M1 7842.7(15) 6364.6 1478.1 (5) 100 23/2 (+) 21/2 + 0.71 (5) D 7903.9(15) 6364.6 1539.3 (5) 100 (9) 23/2 (-) 21/2 + 1.16 (8) D 0.013 (12) E1 6878.7 1025.6 (6) 9 (1) 23/2 (-) 21/2 (-) 0.64 (5) -0.0080 (11) M1 8118.5(16) 6878.7 1239.8(8) 100 23/2 (-) 21/2 (-) 0.73 (5) D 8868.1 (16) 7903.9 964.2 (6) 100 25/2 (-) 23/2 (-) 0.66 (6) D 8898.2(16) 7459.7 1437.6 (6) 100 25/2 (+) 23/2 + 0.41 (5) D Continuation of Table I Ei (keV) E f (keV) Eγ (keV) Branching Ratio J π i J π f RDCO Asymmetry Multipolarity 9105.4(17) 7459.7 1644.8 (9) 100 25/2 (+) 23/2 + 1.14 (8) D D 9343.8(15) 6364.6 2979.2 (5) 100 25/2 (+) 21/2 + 2.08 (23) D 0.027 (15) E2 9552.9(16) 7903.9 1649.0 (5) 100 27/2 (-) 23/2 (-) 1.06 (11) Q 9815.1(16) 7842.7 1971.5 (5) 100 27/2 (+) 23/2 (+) 0.94 (7) 0.21 (4) E2 10073.2(16) 9343.8 729.4 (5) 100 27/2 (+) 25/2 (+) 0.68 (5) D 10091.0(16) 7459.7 2630.4 (6) 100 27/2 (+) 23/2 + 1.13 (13) 0.12 (5) E2 10888.7(17) 10091.0 795.7 (7) 100 31/2 (+) 27/2 (+) 1.25 (8) Q 11140.1(18) 9815.1 1325.0 (8) 100 31/2 (+) 27/2 (+) 1.64 (12) D Q End of Table
TABLE II: This table show the details of the γ transitions observed in this present work on 59 Ni. The RDCO was calculated for quadrupole transitions except for those with the D symbol which are from dipole transitions Begin of Table Ei (keV) E f (keV) Eγ (keV) Branching Ratio J π i J π f RDCO Asymmetry Multipolarity 339.5(5) 0 339.5(5) 100 5/2 - 3/2 - 0.74 (5) D 1189.0(5) 0 1189.0(5) 100 5/2 - 3/2 - 0.52 (6) D 1339.0(6) 339.5 998.0(5) 100 (10) 7/2 - 5/2 -0.96 (6) D D 0 1339.0(6) 42 (5) 7/2 - 3/2 -1.67 (16) D 0.053 (11) E2 1768.5(7) 339.5 1429.0(5) 100 (8) 9/2 - 5/2 -0.93 (13) 0.093 (13) E2 1339.0 429.1(8) 25 (3) 9/2 - 7/2 -0.87 (9) D D 1949.7(7) 0 1949.7(7) 100 (8) 7/2 - 3/2 - 0.94 (7) 0.079 (13) E2 339.5 1610.4(5) 58 (6) 7/2 - 5/2 - 0.58 (4) D 1189.0 759.0(5) 19 (2) 7/2 - 5/2 - 0.56 (7) D 1339.0 610.0 (5) 11 (2) 7/2 - 7/2 -1.79 (17) D J = 0 2530.0(8) 1339.0 1191.0(5) 100 (8) 9/2 - 7/2 -0.90 (9) D D 339.5 2193.0(6) 54 (6) 9/2 - 5/2 -1.74 (17) D Q 2707.0(7) 1339.0 1368.0(5) 100 (10) 11/2 - 7/2 -1.50 (14) D 0.13 (1) E2 1768.5 938.3(5) 21 (2) 11/2 - 9/2 - 0.42 (3) D 3056.6(7) 1949.7 1105.9(8) 100 (7) 9/2 + 7/2 - 0.57 (4) 0.086 (12) E1 1339.0 1717.6(5) 44 (5) 9/2 + 7/2 - 0.59 (4) 0.040 (12) E1 3126.5(9) 1768.5 1358.0(6) 100 (11) 11/2 - 9/2 -0.88 (11) D D 339.5 2783.0(7) 82 (12) 11/2 - 5/2 - 3378.2(9) 1768.5 1609.7(5) 100 (10) 11/2 - 9/2 - 0.66 (7) D 2707.0 674.0(5) 90 (10) 11/2 -11/2 -0.89 (9) J = 0 3561.8(8) 1768.5 1793.3 (5) 100 (7) 11/2 - 9/2 - 0.71 (5) -0.0040 (11) M1 2707.0 854.6(8) 70 (8) 11/2 -11/2 - J = 0 2530.0 1029.0(5) 39 (5) 11/2 - 9/2 -1.09 (11) D D 3126.5 433.6(5) 31 (5) 11/2 -11/2 -1.27 (13) J = 0 1949.7 1612.0(5) 24 (3) 11/2 - 7/2 - 1339.0 2223.2(6) 10 (3) 11/2 - 7/2 - 1.07 (8) Q 4104.7(9) 1768.5 2336.2(5) 100 11/2 + 9/2 - 0.76 (5) 0.062 (19) E1 4143.8(9) 3378.2 764.9(5) 100 (10) 13/2 -11/2 -0.99 (8) D -0.0005 (9) M1 3561.8 582.0(5) 12 (2) 13/2 -11/2 -0.90 (9) D -0.033 (9) M1 2707.0 1435.0(5) 0.4 (1) 13/2 -11/2 - 4419.0(10) 1768.5 2650.5(8) 100 (9) 13/2 - 9/2 -1.15 (10) 0.058 (18) E2 3561.8 858.0(8) 6 (1) 13/2 -11/2 - 4457.8(9) 3056.6 1401.5(5) 100 (7) 13/2 + 9/2 + 0.82 (6) 0.069 (12) E2 2707.0 1750.8(5) 94 (10) 13/2 + 11/2 -0.44 (6) 0.054 (12) E1 4727.2(9) 1768.5 2958.7(5) 100 11/2 + 9/2 - 0.56 (8) 0.030 (14) E1 4910.7(10) 1768.5 3142.2(7) 100 11/2 + 9/2 - 0.64 (9) 0.070 (24) E1 4950.5(10) 4143.8 806.7(5) 100 (9) 15/2 -13/2 -0.87 (9) D -0.055 (12) M1 3378.2 1571.0(6) 9 (2) 15/2 -11/2 - 5100.0(9) 3561.8 1539.0(7) 100 (7) 13/2 (-) 11/2 -1.27 (13) D D 2707.0 2393.0(6) 53 (5) 13/2 -11/2 - 5254.6(10) 4457.8 796.8(5) 100 (11) 17/2 + 13/2 + 1.00 (7) 0.051 (25) E2 4950.5 303.0(5) 9 (1) 17/2 + 15/2 -1.08 (11) D D TABLE III. This table show the details of the γ transitions observed in this present work on 61 Co. The RDCO was calculated for quadrupole transitions except for those with the D symbol which are from dipole transitions Ei (keV) E f (keV) Eγ (keV) Branching Ratio J π i J π f RDCO Asymmetry Multipolarity 1285.9(5) 0 1285.9(5) 100 9/2 -7/2 -1.11 (11) D D 1664.8(5) 0 1664.8(5) 100 (8) 11/2 -7/2 -2.16 (25) D 0.075 (12) E2 1285.9 378.4(5) 20 (3) 11/2 -9/2 - 0.54 (8) D 2339.4 (8) 1285.9 1053.5(6) 100 11/2 -9/2 - 0.60 (6) D 2374.4 (8) 1664.8 709.6(6) 100 13/2 -11/2 -0.66 (5) -0.036 (11) M1 3127.0 (9) 1664.8 1462.0(6) 100 (8) 15/2 -11/2 -1.19 (12) Q 2374.4 752.6(5) 51 (4) 15/2 -13/2 -0.66 (7) -0.041 (11) M1 3159.4(9) 1664.8 1494.6(8) 100 13/2 -11/2 -0.65 (6) D 3472.5(7) 1664.8 1807.7(5) 100 (4) 13/2 + 11/2 -0.59 (6) 0.030 (11) E1 2374.4 1097.6(9) 8 (1) 13/2 + 13/2 - J = 0 2339.4 1131.6(6) 27 (2) 13/2 + 11/2 -0.81 (8) D 0.044 (11) E1 3658.8(9) 3472.5 186.3(5) 100 (3) 15/2 + 13/2 + 0.55 (4) D 3127.0 531.2(5) 46 (4) 15/2 + 15/2 -0.84 (8) J = 0 3910.8(7) 1664.8 2246.0(5) 100 13/2 -11/2 - 4094.4(10) 3658.8 435.6(5) 100 (4) 17/2 + 15/2 + 0.68 (6) -0.047 (11) M1 3127.0 966.6(6) 14 (1) 17/2 + 15/2 -0.99 (10) D D 4117.9(11) 3159.4 956.5(7) 100 (10) 15/2 -13/2 - 2374.4 1743.5(8) 37 (4) 15/2 -13/2 -0.40 (5) D 3658.8 456.5(7) 37 (4) 15/2 -15/2 + 0.108 (13) J = 0 3910.8 208.2(6) 54 (6) 15/2 -13/2 -0.66 (6) D 4388.3(13) 4117.9 270.4(7) 100 (3) 17/2 -15/2 -0.44 (4) D 3658.8 728.3(7) 20 (2) 17/2 -15/2 + 0.56 (6) D 4485.4(8) 3472.5 1012.9(3) 100 (8) 15/2 -13/2 + 0.72 (8) 0.107 (13) E1 3127.0 1358.4(6) 25 (3) 15/2 -15/2 -1.28 (11) D J = 0 4803.6(12) 4094.4 709.2(6) 100 19/2 + 17/2 + 0.66 (5) -0.036 (11) M1 4871.2(10) 4485.4 385.8(6) 100 (9) 17/2 -15/2 -0.64 (8) D 3658.8 1212.4(6) 50 (5) 17/2 -15/2 + 0.87 (12) D D 5118.8(15) 4388.3 730.5(7) 100 19/2 -17/2 -0.56 (6) D 5347.8(12) 4871.2 476.6(6) 100 19/2 -17/2 -0.97 (14) D D 5723.3(13) 3658.8 2064.5(9) 100 17/2 -15/2 + 5814.3(11) 3658.8 2155.5(6) 100 17/2 -15/2 + 0.38 (5) D 5833.1(13) 4803.6 1029.5(6) 100 21/2 + 19/2 + 0.73 (7) D 5955.8(17) 5118.8 837.0(8) 100 (10) 21/2 -19/2 - 5347.8 608.5(5) 58 (6) 21/2 -19/2 -0.65 (6) D 6066.6(17) 5118.8 947.8(8) 100 21/2 -19/2 -0.83 (7) D D 6170.5(12) 4094.4 2076.1(6) 100 (11) 19/2 -17/2 + 0.67 (9) 0.045 (11) E1 5723.3 445.3(5) 80 (9) 19/2 -17/2 - 6710.4(13) 6170.5 539.9(6) 100 (12) 21/2 -19/2 -1.26 (18) D D 5955.8 754.0(9) 43 (5) 21/2 -21/2 - J = 0 6749.2(18) 5955.8 793.4(7) 100 23/2 -21/2 - 6823(13) 6170.5 652.5(6) 100 (11) 21/2 -19/2 -0.51 (10) D 5814.3 1007.9(11) 84 (9) 21/2 -17/2 -0.96 (10) Q 6894.9(14) 5833.1 1061.8(6) 100 23/2 + 21/2 + 0.50 (7) D 7506.6(15) 6710.4 796.2(7) 100 23/2 -21/2 -0.61 (6) D 7703.2(19) 6749.2 954.0(7) 100 25/2 -23/2 - 8089.5(14) 6823 1266.5(6) 100 25/2 -21/2 -0.93 (9) 0.099 (13) E2 8216.7(16) 6894.9 1321.8(8) 100 25/2 + 23/2 + 8408.1(16) 7506.6 901.5(6) 100 25/2 -23/2 - 9678.3(17) 8216.7 1461.6(7) 100 27/2 + 25/2 +