Isochronous mass measurements of $T_z=-1fp$-shell nuclei from projectile fragmentation of ${}^{58}\mathrm{Ni}$

Atomic masses of seven $T_z=-1$, $fp$-shell nuclei from ${}^{44}\mathrm{V}$ to ${}^{56}\mathrm{Cu}$ and two low-lying isomers, ${}^{44m}\mathrm{V}$ ($J^{\pi }=6^{+}$) and ${}^{52m}\mathrm{Co}$ ($J^{\pi }=2^{+}$), have been measured with relative precisions of $1\text{–}4\times {10}^{-7}$ with isochronous mass spectrometry (IMS) at the Cooler Storage Ring (CSRe), Lanzhou. The masses of ${}^{56}\mathrm{Cu}$, ${}^{52g,52m}\mathrm{Co}$, and ${}^{44m}\mathrm{V}$ were measured for the first time in this experiment. The mass excesses ($\text{ME"}\mathrm{s}$) of ${}^{44}\mathrm{V}$, ${}^{48}\mathrm{Mn}$, ${}^{50}\mathrm{Fe}$, and ${}^{54}\mathrm{Ni}$ are determined with an order of magnitude improved precision compared to the literature values. ${}^{52g,52m}\mathrm{Co}$ and ${}^{56}\mathrm{Cu}$ are found to be 370 and 400 keV more bound, respectively, while ${}^{44g,44m}\mathrm{V}$ are $\sim 300$ keV less bound than the extrapolations in the Atomic-Mass Evaluation 2012 ($\mathrm{AME}\text{"}12$). The masses of the four $T_z=-1/2$ nuclei ${}^{45}\mathrm{V}$, ${}^{47}\mathrm{Cr}$, ${}^{49}\mathrm{Mn}$, and ${}^{51}\mathrm{Fe}$ are re-determined to be in agreement, within the experimental errors, with the recent JYFLTRAP (University of Jyväskylä, Finland) measurements or with the previous IMS measurements in CSRe. Details of the measurements and data analysis are described, and the impact of the new $\text{ME}$ values on different aspects in nuclear structure are investigated and discussed.

Figure 1

Layout of the high-energy part of the HIRFL-CSR complex at IMP including the synchrotron CSRm, the in-flight fragment separator RIBLL2, and the experimental storage ring CSRe.

Figure 2

The revolution time spectra zoomed in around ${}^{52}\mathrm{Co}$ before (a) and after (b) time shift correction. The isomeric state ($T_{1/2}=104$ ms) at $E_x\sim 390$ keV is clearly resolved from the ground state ($T_{1/2}=115$ ms) after the correction.

Figure 3

Part of the revolution time spectrum at a time window of $602\le t\le 621$ ns. The red and blue peaks represent the $T_z=-1$ and $-1/2$ nuclei, respectively.

Figure 4

Plot of the calculated standard deviations or RMS of the revolution time peaks in Fig. 3. The black circles are the values deduced from the time-shift-correction method, while the red triangles are the values deduced directly from the two ions of same species stored simultaneously in the ring. Note that the latter are independent of the correction methods. The labels (gs+isomer) indicate that the RMS values are deduced from the mixed peaks of ground state and a low-lying isomer; the label (corrected) corresponds to the extrapolated RMS.

Figure 5

Distribution of the revolution time difference, $\mathrm{\Delta }t=t_1-t_2$, obtained from injections where two ${}^{23}\mathrm{Mg}$ ions were stored simultaneously. The RMS divided by $\sqrt{2}$ is plotted in Fig. 4.

Figure 6

Differences between experimental $\text{ME}$ values determined in this work and those from the Atomic-Mass Evaluation $\mathrm{AME}\text{"}12$ [43] and Ref. [62] for ${}^{45}\mathrm{V}$ and ${}^{49}\mathrm{Mn}$. The nuclides indicated by the filled symbols are used for calibration, which allowed for the mass determination of the nuclides indicated by open symbols. The value of each filled symbol corresponds to the redetermined mass using the other nuclides as calibrants except for itself. The green shadows indicate the $1\sigma$ error in $\mathrm{AME}\text{"}12$. The error bars in this figure represent the uncertainties in this measurement. The inset compares the uncertainties of our measurements with those in $\mathrm{AME}\text{"}12$ [43].

Figure 7

Excited low-spin states in the mirror nuclei ${}^{56}\mathrm{Cu}$ and ${}^{56}\mathrm{Co}$. The excited states in ${}^{56}\mathrm{Cu}$ are from Ref. [52] but shifted by 36 keV upward according to our ground-state mass of ${}^{56}\mathrm{Cu}$. The data for ${}^{56}\mathrm{Co}$ are from Ref. [53].

Figure 8

The revolution time spectrum zoomed in around ${}^{52}\mathrm{Co}$. The red solid line represents the fitted result using two Gaussian distributions shown as black dotted lines.

Figure 9

(a) The revolution time spectrum zoomed in around ${}^{44}\mathrm{V}$. The red solid line represents the fitted result using two Gaussian distributions shown as black dashed lines. (b) Decomposed time spectra of the ground state ${}^{44}\mathrm{V}$ and its $\left(6^{+}\right)$ isomer according to the fitted Gaussian distributions.

Figure 10

Plots of (a) vector and (b) tensor Coulomb energies as a function of $A$. The solid lines represent the calculated results based on Eq. (17). The dashed line in the upper panel is from the same calculations by replacing the coefficient 0.46 of the second term in Eq. (17) by 0.828. The dashed line in the lower panel is from the same calculations by replacing the coefficient 0.15 of the third term in Eq. (17) by 0.075.

Figure 11

Mass differences between the experimental values and those from different model predictions for the $T_z=-1$ nuclei.

Figure 12

Reconstructed partial decay scheme of ${}^{52}\mathrm{Ni}$ compared to that of ${}^{52}\mathrm{Mn}$, where energies are in keV. For ${}^{52}\mathrm{Co}$, the red levels are deduced from the $\text{ME}$ values of ${}^{52g}\mathrm{Co}$, ${}^{52m}\mathrm{Co}$ (this work), and the $\gamma$-ray energies reported in Ref. [49]; the black ones are determined from the ground state $\text{ME}$ of ${}^{51}\mathrm{Fe}$ [43] and the $\beta \text{−}p$ decay of ${}^{52}\mathrm{Ni}$ in Ref. [49]. For ${}^{52}\mathrm{Mn}$, the $1^{+}$ states and IAS are inferred from Ref. [80], while the lowest two levels ($6^{+}$ and $2^{+}$ states) and the $\gamma$-transition energies are from Ref. [58]; the latter lead to $E_x\left(\mathrm{IAS}\right)=2925\left(5\right)$ keV [58]. This inconsistency needs a precise determination for the decay $\gamma$-ray energies in ${}^{52}\mathrm{Mn}$.

Figure 13

Differences between experimental mass excesses and IMME fit for the $A=52$, $T=2$ multiplet in keV. The mass values in [43] are used in the fit (black filled circles); the red filled squares correspond to the fit when $E_x\left(\mathrm{IAS},{}^{52}\mathrm{Mn}\right)=2923\left(5\right)$ keV [43] is replaced by $E_x\left(\mathrm{IAS},{}^{52}\mathrm{Mn}\right)=2938\left(2\right)$ keV [80].

Figure 14

Experimental $\delta V_{pn}$ values in keV for odd-odd nuclei in a small part of the chart of nuclides. The numbers in parentheses are the errors of $\delta V_{pn}$. Four quadrants are defined by the $Z=28$ proton and $N=28$ neutron shell closures. Schematic shell model single-particle orbitals are shown in the left part of this figure. The $\delta V_{pn}$ value for ${}^{56}\mathrm{Cu}$ (indicated with a red square) is the first experimental result in the upper-left quadrant. It has a similar magnitude as the $\delta V_{pn}$ values in the lower-right quadrant.

Figure 15

Same as Fig. 14 but for four odd-odd nuclei around the doubly magic nuclei ${}^{40}\mathrm{Ca}$, ${}^{48}\mathrm{Ca}$, ${}^{56}\mathrm{Ni}$, and ${}^{208}\mathrm{Pb}$ marked with red filled circles.