Mass measurements for the $T_z=-2fp$-shell nuclei ${}^{40}\mathrm{Ti}$, ${}^{44}\mathrm{Cr}$, ${}^{46}\mathrm{Mn}$, ${}^{48}\mathrm{Fe}$, ${}^{50}\mathrm{Co}$, and ${}^{52}\mathrm{Ni}$

By using isochronous mass spectrometry at the experimental cooler storage ring in Lanzhou, China, masses of short-lived ${}^{44}\mathrm{Cr}$, ${}^{46}\mathrm{Mn}$, ${}^{48}\mathrm{Fe}$, ${}^{50}\mathrm{Co}$, and ${}^{52}\mathrm{Ni}$ were measured for the first time and the precision of the mass of ${}^{40}\mathrm{Ti}$ was improved by a factor of about 2. Relative precisions of $\delta m/m=\left(1\text{–}2\right)\times {10}^{-6}$ have been achieved. Details of the measurements and data analysis are given. The obtained masses are compared with the Atomic-Mass Evaluation 2016 and with theoretical model predictions. The new mass data enable us to extract the higher-order coefficients, $d$ and $e$, of the quartic form of the isobaric multiplet mass equation for the $fp$-shell isospin quintets. Unexpectedly large $d$ and $e$ values for the $A=44$ quintet are found. By revisiting the previous experimental data on $\beta$-delayed protons from ${}^{44}\mathrm{Cr}$ decay, it is suggested that the observed anomaly could be due to the misidentification of the $T=2$, $J^{\pi }=0^{+}$ isobaric analog state in ${}^{44}\mathrm{V}$.

Figure 1

Schematic view of the time-of-flight detector [24] installed inside the CSRe aperture. The electric field is generated by the potential plates and an equalizing ring. The magnetic field is produced by Helmholtz coils (not shown) placed outside the ultra-high-vacuum environment of the CSRe.

Figure 2

A part of the measured revolution-time spectrum. $T_z=-2$ nuclei are indicated with red color. The inset shows an expanded time range around ${}^{44}\mathrm{Cr}$ and ${}^{33}\mathrm{Ar}$ illustrating that the corresponding revolution-time peaks are well resolved.

Figure 3

Obtained standard deviations (rms) of the revolution-time peaks shown in Fig. 2. Red squares are the values for $T_z=-2$ nuclides. The label Al-24 (g.s. $+$ isomer) indicates that the corresponding peak represents a mixture of the ground- and low-lying isomeric state. The label S-30 $+$ Cr-45 corresponds to the rms value deduced from the peak of unresolved ${}^{30}\mathrm{S}$ and ${}^{45}\mathrm{Cr}$ nuclei.

Figure 4

Experimental mass excess values determined in this paper compared with the literature values from the latest Atomic-Mass Evaluation 2016 (${\mathrm{AME}}^{\prime }16$) [27] and Ref. [30] for ${}^{27}\mathrm{P}$. The $T_z=-1$ nuclides (red filled circles) were used as calibrants. The shaded area indicates the time range where no systematic deviations were observed (see text). The gray shadowed areas indicate the $1\sigma$ mass uncertainty in ${\mathrm{AME}}^{\prime }16$ and in Ref. [30] for ${}^{27}\mathrm{P}$.

Figure 5

Differences between experimental ME values determined in this paper and those from the Atomic-Mass Evaluation ${\mathrm{AME}}^{\prime }16$ [27] and Ref. [30] for ${}^{27}\mathrm{P}$. Mass values for each of the ten reference nuclides (filled black circles) were redetermined by using the other nine nuclides as calibrants. The red circles correspond to the newly determined masses when all ten reference nuclides were employed for mass calibration. The gray shadowed areas indicate the $1\sigma$ mass uncertainty in ${\mathrm{AME}}^{\prime }16$ and in Ref. [30] for ${}^{27}\mathrm{P}$.

Figure 6

Comparison of the experimental ME values of ${}^{46}\mathrm{Mn}$ and ${}^{50}\mathrm{Co}$ with the IMME predictions.

Figure 7

Comparison of the new experimental mass values with predictions of several mass models for $T_z=-2$ nuclei. The adopted and extrapolated mass values from ${\mathrm{AME}}^{\prime }16$ [27] are presented with the filled and open black circles, respectively. The filled red circles indicate the new experimental masses of this paper.

Figure 8

Comparison of the new experimental ME values of $T_z=-2$ nuclei with predictions by local mass relations using the mass values from ${\mathrm{AME}}^{\prime }16$ [27, 33]. The literature masses [27, 33] are shown with black filled circles. The new masses from Table 1 are indicated with red symbols. The shaded areas represent $1\sigma$ uncertainty of the theoretical predictions.

Figure 9

$d$ and $e$ coefficients obtained from the least-squares fitting using the quartic (empty squares) form of the IMME. Results of four-parameter fitting with only $d$ or $e$ coefficient included are shown with filled symbols. ME values from the ${\mathrm{AME}}^{\prime }16$ (black symbols) [27, 33] and from this paper (red symbols) were used. For the $A=36$ quintet the mass value of ${}^{36}\mathrm{Ca}$ was taken from Ref. [62].

Figure 10

Left: Proposed partial decay scheme of ${}^{44}\mathrm{Cr}$. Right: The level structure of ${}^{44}\mathrm{Sc}$ identified in the ${}^{44}\mathrm{Ca}({}^3\mathrm{He},t){}^{44}\mathrm{Sc}$ reaction [67]. Only levels with $B\left(\text{GT}\right)\ge$ 0.1 are shown. The $\beta$ feedings $\left(I_{\beta }\right)$ and log $ft$ values of the ${}^{44}\mathrm{Cr}\beta$ decays are deduced from the branching ratios of $\beta$-delayed protons and $Q$ values suggested in this paper. The $\beta$-decay $B\left(\text{GT}\right)$ values are calculated from Eq. (4). The levels shown in green color indicate the excited $T=2,J^{\pi }=0^{+}$ IAS. All energies are in keV.