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Decay of neutron-rich Mn nuclides and deformation of heavy Fe isotopes

The use of chemically selective laser ionization combined with beta-delayed neutron counting at CERN/ISOLDE has permitted identification and half-life measurements for 623-ms Mn-61 up through 14-ms Mn-69. The measured half-lives are found to be significantly longer near N=40 than the values calculated with a QRPA shell model using ground-state deformations from the FRDM and ETFSI models. Gamma-ray singles and coincidence spectroscopy has been performed for Mn-64 and Mn-66 decays to levels of Fe-64 and Fe-66, revealing a significant drop in the energy of the first 2+ state in these nuclides that suggests an unanticipated increase in collectivity near N=40.

Until recently, the principal data available for neutronrich nuclides between 48 Ca and 78 Ni were the γspectroscopic data obtained in the 1980's at GSI [1,2] and the nuclear masses reported by Seifert et al. [3]. During the past three years, however, a number of new experimental studies on level structures and decay properties on Fe-group nuclei have been performed [4][5][6][7][8][9]. On the theoretical side, nuclear masses, ground-state (g.s.) deformations and β-decay properties were calculated by Möller et al. [10] on the basis of the FRDM mass model and the QRPA shell-model. Aboussir et al. [11] also calculated masses and g.s.-deformations on the basis of the ETFSI-1 approach that are not always in agreement with those of the FRDM for the Fe-group nuclides considered here. Earlier, Richter et al. [12] had performed fully microscopic shell-model calculations in this mass region and significantly underpredicted the measured [3] binding energies for the Cr to Fe isotopes with N>36. In addition to the clear nuclear-structure interest, the neutron-rich Fe-group nuclei may also play an important role as possible seed nuclei in the astrophysical r-process [13]. In the present paper, we report new measurements for the halflives of heavy Mn nuclides up to 69 Mn and for the level structure of 64,66 Fe populated in the decays of 64,66 Mn.
Manganese isotopes were produced at CERN by 1-GeV proton-induced spallation of uranium in a thick UC 2 target at the ISOLDE facility. The ionisation of the Mn atoms was accomplished using a chemically selective, three-step laser resonance excitation scheme as described in detail earlier [14].
Beams of Mn nuclides with masses differing by ∆A≥4 were transported separately to two different beam lines equipped with moving tape systems where β-delayed neutron (d.n.) multiscaling and γ-ray singles and coincidence measurements could be performed independently. In both cases, counting took place directly at the point of deposit, and the tape systems were used to remove the daughter nuclides as well as unavoidable surface-ionized isobaric Ga activities. Because the Mn half-lives being sought are in the millisecond range, data acquisition in both systems was initiated by the CERN-PSB proton pulses, separated by a multiple of 1.2 s, and continued for 1.0 s for each cycle.
Beta-delayed neutron data of high statistical quality were collected by multiscaling measurements using the Mainz 4π 3 He neutron counter. The time dependence of the counting rates for 65−69 Mn is shown in Figure 1. The decay curves were fitted with a constant small d.n.background component up through A=65. Because there exist no measured d.n.-emission probabilities (P n -values) for the A>65 daughter and grand-daughter isobars, for the fits of the heavier isotopes were performed using theoretical P n -values [10] along with the known half-lives [5,7,8,15]. For A=66 to 68, the contributions from d.n.emission of the Fe and Co isobars are quite small and actually do not affect the Mn half-life fits. For A=69, however, a multi-component fit was necessary to account for the significant Fe and Co d.n.-branches. The resulting data are summarized in Table 1, and are compared to literature values and QRPA predictions using experimental masses as far as they are available [15] and g.s.deformations of the β-decay daughter isotopes from the FRDM [10] and ETFSI [11] models.
For 61−63 Mn, the half-lives that we have observed are somewhat shorter than the literature values and have considerably smaller uncertainties. In a recent report of a parallel experiment at Ganil, Sorlin et al. [5] found half-lives similar to ours for 64−66 Mn. However, neither our nor their data are in agreement with those reported by Ameil et al. at ENAM'95 [7] and cited in NUBASE [15]. In a subsequent publication the same authors report somewhat shorter half-lives for these nuclides [16], however still exceeding our and Sorlin's values. Similarly, Franchoo et al. found systematic differences between their Ni half-lives [8] and those reported in [7,16]. These deviations gain particular importance when considering the conclusion of Ameil et al. that recent theoretical half-lives are not an improvement over calculations made almost a decade ago [16].
A comparison of the experimental Mn half-lives with the predictions derived from QRPA calculations of Gamow-Teller (GT) strength functions [17] (see Table 1) indicates that the theoretical half-lives for the g.s.-decays of 61−66 Mn are on the average shorter than the measured ones by a factor of 2.6, whereas for the heaviest isotopes 67−69 Mn the agreement becomes gradually better. When looking in more detail into the theoretical β-strength distributions, it becomes evident that in the decay of all neutron-rich Mn isotopes considered here, the (low-lying) νf 5/2 →πf 7/2 transition is strongly dominating the GT-decay with I β ≃85-95% and log(ft)≃4.0, practically independent of the assumed g.s.-shape of the Fe daughters [10,11]. As will be discussed later, this GTpattern is, indeed, observed in the γ-data of 64 Mn and 66 Mn decay. With this rather "simple" decay pattern, already the differences between the experimental and theoretical half-lives seem to reflect the actual strength of this specific spin-flip transition.
The γ-ray data were written in event-by-event mode for β-gated γ-singles as well as γγ(t) coincidences with time recorded relative to each proton pulse. In this way, consecutive spectra of variable time intervals could be reconstructed from the data. As considerable data exist for the structure of even-even Fe nuclides up to A=62, in the present study we have focused on the γ-spectra for decay of 89-ms 64 Mn and 66-ms 66 Mn.
At A=64, γ-ray peaks up to 4.2 MeV could be assigned to the decay of 64 Mn. More than 20 lines have been incorporated into a decay scheme of at least 8 excited levels [18]. In the upper part of Figure 2 are shown partial γray spectra, one for the time period from 40 ms to 140 ms after the PSB proton pulses, and a second for the time slice from 800 ms to 900 ms after bombardment. The most intense line in the early 64 Mn spectrum that decays with a short half-life is at 746 keV. With the intensity of this γ-line being more than five-times stronger than the next most intense peak, it is taken to be the 2 + to 0 + transition in the even-even daughter 64 Fe. As five of the eight levels appear to depopulate to both the g.s. and the first 2 + level, a low spin for the g.s. of 64 Mn is indicated. No candidate has so far been identified unambiguously for the 4 + to 2 + transition. On the basis of the observed γγ-coincidences, strong GT-feeding to levels near 3.5 MeV in 64 Fe is indicated [18], as predicted by our QRPA calculations.
More than 20 γ-ray lines with energies up to at least 4.2 MeV have also been observed in the decay of 66-ms 66 Mn and incorporated into a partial level scheme containing 11 levels. We show in the lower part of Figure 2 a portion of the first and of a late spectrum (see above) between 525 keV and 900 keV. In the early spectrum, the strongest line by far is at 573 keV which is -as in the above case of 64 Fe -taken as the g.s.-transition from the first 2 + state in even-even 66 Fe. The relatively weak γ line at 840 keV (also shown in Figure 2) is found in coincidence with the 573-keV level and decays with the same half-life. Hence, it is assigned as depopulating the second excited state at 1414 keV and given a tentative spin and parity of 4 + . A number of high-energy g.s.-transitions (E>2.7 MeV) again indicates strong GT-feeding to that energy region [18], as predicted by the QRPA.
At both A=64 and 66, it was also possible to identify the growth and decay of known daugther and granddaughter Fe and Co lines; whereas the lines from longlived, surface-ionized 64 Ga and 66 Ga showed no change in intensity in our 1.0 s measuring period.
The 2 + 1 energies and the E 4 /E 2 ratios for even-even 24 Cr to 32 Ge isotopes are shown in Figure 3. As is well established, the 2 + energy in the Z=28 Ni nuclides rises sharply at N=40 and exhibits clear evidence for a semidouble shell closure, similar to that for Z=40, N=50 in 90 Zr. Recent studies of the structure of 69 Ni and 69 Cu are consistent with the closed-shell character of 68 Ni [8,9].
Raman et al. [19] have presented an extensive discussion of the relationship between 2 + energies, B(E2) values and collectivity. In particular, they have shown the inverse correlation between 2 + energies and deformation. Similar correlations of B(E2) values with energy have recently been presented by Azaiez and Sorlin [20]. Hence, the direct interpretation of the drop in 2 + energy from 877 kev in 62 Fe to 573 kev in 66 Fe would be an increase in deformation. Because of the large quantity of data available, including the B(E2) systematics [19], there is general agreement on deformation values of β 2 ≃ 0.18 for the lighter Fe nuclides. For the heavier isotopes where only few data are available, both the FRDM [10] and new calculations using the Relativistic Mean Field approach [21] indicate deformation of ∼0.21 for 62 Fe and then dropping toward values below 0.1 for 66 Fe. In contrast, the ETFSI calculations [11], show a value of β 2 =0.18 for 62 Fe that rises to 0.27 for 66 Fe.
The data in Figure 3 reveal that both the 2 + 1 energy and 4 + /2 + ratio for 66 Fe 40 are comparable to those of stable 76 Ge 44 . Extensive studies of the structure of the stable Ge nuclides [22,23] have indicated a range of deformation values between β 2 =0.22 and 0.28 for 76 Ge. Azaiez and Sorlin recently reported a β 2 -value of 0.23 for 72 Zn 42 that has a 2 + energy of 653 keV [20]. Combining all of the above approaches, we deduce a β 2 ≃ 0.26 for 66 Fe 40 . Thus, we conclude that the trends we observe for the Fe isotopes are reproduced only by the ETFSI calculations [11].
We attribute this increase of deformation to the strong proton-neutron (pn) interaction between the two f 7/2 proton holes and the g 9/2 neutrons, which results in a dramatic lowering of the energy of the νg 9/2 orbital. The effect of interactions between protons and neutrons in high-j orbitals has also been discussed in [8] for odd-mass Cu nuclides near N=40. In that paper, a sharp lowering of the energy of the πf 5/2 orbital was observed with increasing occupancy of the νg 9/2 state.
For the neutron-rich Fe and Mn nuclides, one effect of this strong pn-interaction is to lower the energy of the νg 9/2 orbital. For example, the recent report of a 9/2 + M2 isomer in 61 Fe 35 at 861 keV is well below the 1292-keV position of the νg 9/2 state in isotonic 63 Ni 35 [9]. Because of the lowered position of the base νg 9/2 orbital, it can be seen by reference to Figure 12 in [10] or Figure 7 in [5b] that, as the neutron number increases beyond 36, the down-sloping ν[440]1/2 + and ν[431]3/2 + orbitals are more likely to be occupied than the spherical orbitals thus generating increased deformation at N=40. This collectivity increase beyond N=36 can be seen to correlate with the difference between the masses calculated with a spherical model and the measured values shown by Richter et al. [12] in their Figure 1. From the trends in that figure, it can be expected that 64 Cr 40 may be even more deformed than 66 Fe 40 .
Moreover, such a change in neutron occupancy near N=40 may help to account for the retarded Mn β-decay rates described earlier. The decay of the odd-mass Mn nuclides would be considered as "even-jumping" transitions as described by Kisslinger and Sorensen [24]. For such transitions, the β-decay rate λ is proportional to (V n ·V p ) 2 ·M 2 , where M 2 is the pure decay matrix element and V represents the proton/neutron occupancy values. As noted earlier, the allowed GT β-decay is dominated by the νf 5/2 → πf 7/2 transition. Because of the increase in deformation, the negative parity orbitals ν[301]3/2 − and ν[303]5/2 − with νf 5/2 parentage are up-sloping and are thus displaced from the region near the Fermi surface. Instead, the 37th through 40th neutrons will preferentially fill the down-sloping low-j, positive-parity or-bitals with νg 9/2 origin that can only undergo forbidden β-decay. The lowered occupancy of the above critical negative-parity states may well be directly responsible for the observed retardation of the β-decay rates for Mn nuclides with N≃40. Moreover, the ultimate increase in occupancy for these orbitals that must occur for N>40 also accounts for the gradual convergence of the calculated half-lives and the newly measured values for 67−69 Mn 42−44 .
This work was supported by the German BMBF (06MZ864) and DFG (436RUS/17/40/97 and Kr806/3), the Russian Foundation for Basic Research (96-02-18331), the Belgian FWO, and the U.S. DOE.  2. Partial γ-ray spectra taken at A=64 (upper part) and A=66 (lower part), one for the time period from 40 ms to 140 ms after the PSB proton pulses, and a second for the time slice from 800 ms to 900 ms after bombardment.