${\beta }^{-}$ decay study of the ${}^{66}\mathrm{Mn}\text{−}{}^{66}\mathrm{Fe}\text{−}{}^{66}\mathrm{Co}\text{−}{}^{66}\mathrm{Ni}$ decay chain

Background: Shell evolution can impact the structure of the nuclei and lead to effects such as shape coexistence. The nuclei around ${}^{68}\mathrm{Ni}$ represent an excellent study case, however, spectroscopic information of the neutron-rich, $Z<28$ nuclei is limited.

Purpose: The goal is to measure $\gamma$-ray transitions in ${}^{66}\mathrm{Fe},{}^{66}\mathrm{Co}$, and ${}^{66}\mathrm{Ni}$ populated in the ${\beta }^{-}$ decay of ${}^{66}\mathrm{Mn}$ to determine absolute $\beta$ feedings and relative $\gamma$-decay probabilities and to compare the results with Monte Carlo shell model calculations in order to study the influence of the relevant single neutron and proton orbital occupancies around $Z=28$ and $N=40$.

Method: The low-energy structures of ${}^{65,66}\mathrm{Fe},{}^{66}\mathrm{Co}$, and ${}^{66}\mathrm{Ni}$ were studied in the ${\beta }^{-}$ decay of ${}^{66}\mathrm{Mn}$ produced at ISOLDE, CERN. The beam was purified by means of laser resonance ionization and mass separation. The $\beta$ and $\gamma$ events detected by three plastic scintillators and two MiniBall cluster germanium detectors, respectively, were correlated in time to build the low-energy excitation schemes and to determine the $\beta$-decay half-lives of the nuclei.

Results: The relative small $\beta$-decay ground state feeding of ${}^{66}\mathrm{Fe}$ obtained in this work is at variant to the earlier studies. Spin and parity $1^{+}$ was assigned to the ${}^{66}\mathrm{Co}$ ground state based on the strong ground-state feeding in the decay of ${}^{66}\mathrm{Fe}$ as well as in the decay of ${}^{66}\mathrm{Co}$. Experimental log($ft$) values, $\gamma$-ray de-excitation patterns, and energies of excited states were compared to Monte Carlo shell model calculations. Based on this comparison, spin and parity assignments for the selected number of low-lying states in the ${}^{66}\mathrm{Mn}$ to ${}^{66}\mathrm{Ni}$ chain were proposed.

Conclusions: The $\beta$-decay chain starting ${}^{66}\mathrm{Mn}$ toward ${}^{66}\mathrm{Ni}$, crossing $N=40$, evolves from deformed nuclei to sphericity. The $\beta$-decay population of a selected number of $0^{+}$ and $2^{+}$ states in ${}^{66}\mathrm{Ni}$, which is understood within shape coexistence framework of Monte Carlo shell model calculations, reveals the crucial role of the neutron $0g_{9/2}$ shell and proton excitations across the $Z=28$ gap.

Figure 1

Single-$\gamma$ spectrum collected in the laser-on mode (black) and the laser-off mode (red [medium gray], enlarged five times for better visual comparison), and $\beta \text{−}\gamma$ coincidence spectrum collected in the laser-on mode (blue [light gray]) from 0 to 1500 keV (top panel) and 1500 to 3500 keV (bottom panel) with the mass separator set to $A=66$. Peaks attributed to the decay of ${}^{66}\mathrm{Mn}$ and daughter activities are marked.

Figure 2

The scheme of excited states in ${}^{66}\mathrm{Fe}$ populated in ${\beta }^{-}$ decay of ${}^{66}\mathrm{Mn}$. $Q_{{\beta }^{-}}$ and $S_n$ values are taken from Ref. [62]. The $\beta$ feeding of the states should be treated as upper limits and the log($ft$) values as lower limits due to the pandemonium effect. Half-life and $P_n$ are determined in the analysis. Spin assignments were made based on the experimental data and the Monte Carlo shell model calculations; see text for details. The level at 1413.9 keV is shifted 40 keV upward on the scheme for better visual representation.

Figure 3

A $\gamma \text{−}\gamma$ coincidence spectrum gated on the 574-keV transition. The most intense coincidences are labeled with the energy given in keV.

Figure 4

A portion of the $\gamma$-delayed-$\gamma$ spectrum with background subtraction gated on the 364-keV transition (coincidence window: $-5$ to $-0.5\mu \mathrm{s}$). A peak at 163 keV is visible.

Figure 5

The excited states in ${}^{65}\mathrm{Fe}$ populated in ${\beta }^{-}$-delayed-neutron decay of ${}^{66}\mathrm{Mn}$. Dotted lines represent transitions reported in Ref. [64], not observed in our analysis, and their energies are the differences between levels energies. Intensities are normalized to 100 units of the 364-keV transition. Spin assignments and half-lives of the states in ${}^{65}\mathrm{Fe}$, except the half-life of 398-keV level, are taken from Ref. [64].

Figure 6

Time behavior of the 364-keV $\gamma$-ray transition as a function of time after the $\beta$ signal with the fitted function. Insert: posterior probability density function of the half-life of the second isomeric state in ${}^{65}\mathrm{Fe}$ ($T_{1/2}={409}_{-27}^{+29}$ ns). The 16th, 50th, and 84th percentiles are indicated with vertical, dotted lines.

Figure 7

The scheme of excited states in ${}^{66}\mathrm{Co}$ populated in ${\beta }^{-}$ decay of ${}^{66}\mathrm{Fe}$. The $\beta$ feeding of the states should be treated as upper limits and the log($ft$) values as lower limits due to the pandemonium effect. The $Q_{{\beta }^{-}}$ value is taken from Ref. [62] and the limit for the half-life of the second isomeric state from Ref. [40]. The half-life of the parent nucleus and the first excited state at 176 keV come from our analysis. The spin and parity assignments are made based on the experimental results and the Monte Carlo shell model calculations; see text for details. When indicated with an asterisk (*), the log($ft$) value was calculated assuming second-forbidden unique transition.

Figure 8

A portion of the $\gamma \text{−}\gamma$ coincidence spectrum gated on the 471-keV transition. Beyond 600 keV, no peaks were observed.

Figure 9

A portion of the $\gamma$-delayed-$\gamma$ coincidence spectrum gated on the 176-keV transition (coincidence time window $-2.5$ to $-0.2\mu \mathrm{s}$). The coincide transitions are labeled with the energy in keV.

Figure 10

A portion of the $\gamma \text{−}\gamma$ coincidence spectrum gated on the 511-keV transition. Transitions at 371 and 471 keV are assigned to the decay of ${}^{66}\mathrm{Fe}$. There are also visible transitions assigned to the decay of ${}^{66}\mathrm{Mn}$: escape peaks (ep) of the high-energy $\gamma$-ray transition and their coincidences (the transition at 574 keV).

Figure 11

Counts in the peak area of the 176-keV $\gamma$-ray transition as a function of time after the $\beta$ particle (red circles) with the fitted function (black straight line) and counts in the background area (blue squares) with the fitted function (blue dash-dotted line). Insert: a portion of the $\beta$-delayed-$\gamma$ spectrum (coincidence time 0.5 to 10 $\mu \mathrm{s}$) in the 176-keV $\gamma$-ray transition region with marked peak area (dark shade) and background areas (light shades). See text for details.

Figure 12

Time behavior of the 176-keV $\gamma$-ray transition as a function of time after the 806-keV $\gamma$-ray transition. Insert: posterior probability density function of the half-life of the first isomeric state in ${}^{66}\mathrm{Co}$ ($T_{1/2}={823}_{-21}^{+22}$ ns). The 16th, 50th, and 84th percentiles are indicated with vertical dotted lines.

Figure 13

The scheme of excited states in ${}^{66}\mathrm{Ni}$ populated in ${\beta }^{-}$ decay of ${}^{66}\mathrm{Co}$. The spin assignments and the energies of the unobserved states are taken from Refs. [35, 69, 73]. The $\beta$ feeding of the states should be treated as upper limits and the log($ft$) values as lower limits due to the pandemonium effect.

Figure 14

A portion of the $\gamma \text{−}\gamma$ coincidence spectrum gated on the 1425-keV transition. The coincide transitions are labeled with the energy in keV.

Figure 15

The fit results of the $\gamma$-decay curves to the number of $\beta$ particles registered in time (red circles). The $\beta$-decay curve [Eq. (6)] is plotted as a black straight line. The contribution of the ${}^{66}\mathrm{Mn},{}^{66}\mathrm{Fe}$, and ${}^{66}\mathrm{Co}$ decays is represented by the red straight line [Eq. (B1)], green dashed line [Eq. (B2)], and blue dash-dotted line [Eq. (B3)], respectively. The purple dotted line represents a constant from Eq. (6). Insert: posterior probability density functions of the direct feeding to the ground state of (from left) ${}^{66}\mathrm{Fe},{}^{66}\mathrm{Co}$, and ${}^{66}\mathrm{Ni}$, and the probability of $\beta$-delayed-neutron emission. The 16th, 50th, and 84th percentiles are indicated with vertical, dotted lines.

Figure 16

Time behavior of the 574-keV transition as a function of time after PP (red circles) with the fitted function (black straight line) and the background area of the 574-keV transition (blue squares) with the fitted function (blue dash-dotted line). Insert: posterior probability density function of ${}^{66}\mathrm{Mn}$ half-life. The 16th, 50th, and 84th percentiles are indicated with vertical, dotted lines.

Figure 17

Time behavior of the 471-keV transition as a function of time after PP (red circles) with the fitted function (black straight line) and the background area of the 471-keV transition (blue squares) with the fitted function (blue dash-dotted line). Insert: posterior probability density function of ${}^{66}\mathrm{Fe}$ half-life. The 16th, 50th, and 84th percentiles are indicated with vertical, dotted lines.

Figure 18

$T$-plots of the selected states in the $A=66$ chain.

Figure 19

The comparison of the observed states in ${}^{66}\mathrm{Fe}$, log($ft$) values, and relative branching ratios from selected levels with the MCSM calculations. The states up to 3.1 MeV are presented. The theoretical intensities are calculated by taking experimental energies and $B\left(M1\right)$ and $B\left(E2\right)$ values from MCSM. Dashed lines represent transitions which were not observed experimentally. Experimental levels at 1407 and 1414 keV are shifted for the better visual representation. The calculated $4_2^{-}$ level is shifted $-20$ keV.

Figure 20

The comparison of the observed states in ${}^{66}\mathrm{Co}$, log($ft$) values, and relative branching ratios from selected levels with the MCSM calculations. The states up to 1.2 MeV are presented. The theoretical intensities are calculated by taking experimental energies and $B\left(M1\right)$ and $B\left(E2\right)$ values from MCSM. Dashed lines represent transitions which were not observed experimentally. The spherical states are drawn in red, oblate in green, prolate in blue, and negative-parity states in brown. The calculated $4_1^{+}$ state is shifted $-10$ keV and the $6_1^{+}$ state is shifted $-20$ keV for better visual representation.

Figure 21

The comparison of the states in ${}^{66}\mathrm{Ni}$ observed in the ${\beta }^{-}$ decay of ${}^{66}\mathrm{Co}$ (straight lines) and other experiments (dashed lines) [35, 69, 73], and the log($ft$) values with the MCSM calculations. The states up to 4 MeV are presented. The experimental $3_1^{+}$ level is shifted $-20$ keV and the theoretical $6_1^{-}$ level is shifted 20 keV. The spherical states are drawn in red, oblate in green, prolate in blue, and negative-parity states in brown.

Figure 22

The $\beta$-gated-$\gamma$ counts in the 511-keV transition peak area as a function of time after PP (red circles) with the fitted function [Eq. (A1), black straight line] and the $\beta$-gated-$\gamma$ counts in the background area (blue squares) with the fitted function [Eq. (A4), blue dash-dotted line]. The contributions of the decay of ${}^{66}\mathrm{Fe}$ ($N_{\text{Fe}}$), ${}^{66}\mathrm{Mn}$ decay high-energy $\gamma$ rays ($N_{\text{Mn}}$), the environmental background ($N_{\mathrm{off}}$), and other sources ($N_o$) are represented by the red straight line, the green dashed line, the cyan dash-dotted line, and the purple dotted line, respectively. Insert: posterior probability density function of the 511-keV transition intensity. The 16th, 50th, and 84th percentiles are indicated with vertical, dotted lines.