High-precision mass measurements of the isomeric and ground states of ${}^{44}\mathrm{V}$: Improving constraints on the isobaric multiplet mass equation parameters of the $A=44$, $0^{+}$ quintet

Background: The quadratic isobaric multiplet mass equation (IMME) has been very successful at predicting the masses of isobaric analog states in the same multiplet, while its coefficients are known to follow specific trends as functions of mass number. The Atomic Mass Evaluation 2016 [Chin. Phys. C 41, 030003 (2017)] ${}^{44}\mathrm{V}$ mass value results in an anomalous negative $c$ coefficient for the IMME quadratic term; a consequence of large uncertainty and an unresolved isomeric state. The $b$ and $c$ coefficients can provide useful constraints for construction of the isospin-nonconserving Hamiltonians for the $pf$ shell. In addition, the excitation energy of the $0^{+},T=2$ level in ${}^{44}\mathrm{V}$ is currently unknown. This state can be used to constrain the mass of the more exotic ${}^{44}\mathrm{Cr}$.

Purpose: The aim of the experimental campaign was to perform high-precision mass measurements to resolve the difference between ${}^{44}\mathrm{V}$ isomeric and ground states, to test the IMME using the new ground state mass value and to provide necessary ingredients for the future identification of the $0^{+}$, $T=2$ state in ${}^{44}\mathrm{V}$.

Method: High-precision Penning trap mass spectrometry was performed at LEBIT, located at the National Superconducting Cyclotron Laboratory, to measure the cyclotron frequency ratios of [${{}^{44g,m}\mathrm{VO}]}^{+}$ versus [${{}^{32}\mathrm{SCO}]}^{+}$, a well-known reference mass, to extract both the isomeric and ground state masses of ${}^{44}\mathrm{V}$.

Results: The mass excess of the ground and isomeric states in ${}^{44}\mathrm{V}$ were measured to be $-23804.9\left(80\right)$ keV/$c^2$ and $-23537.0\left(55\right)$ keV/$c^2$, respectively. This yielded a new proton separation energy of $S_p=1773\left(10\right)$ keV.

Conclusion: The new values of the ground state and isomeric state masses of ${}^{44}\mathrm{V}$ have been used to deduce the IMME $b$ and $c$ coefficients of the lowest $2^{+}$ and $6^{+}$ triplets in $A=44$. The $2^{+}c$ coefficient is now verified with the IMME trend for lowest multiplets and is in good agreement with the shell-model predictions using charge-dependent Hamiltonians. The mirror energy differences were determined between ${}^{44}\mathrm{V}$ and ${}^{44}\mathrm{Sc}$, in line with isospin-symmetry for this multiplet. The new value of the proton separation energy determined, to an uncertainty of 10 keV, will be important for the determination of the $0^{+}$, $T=2$ state in ${}^{44}\mathrm{V}$ and, consequently, for prediction of the mass excess of ${}^{44}\mathrm{Cr}$.

Figure 1

Schematic diagram of the experimental setup including the beam stopping area, low energy transport/mass separation, LEBIT cooler/buncher, and 9.4 T Penning Trap system.

Figure 2

A 100-ms ${\left[{}^{44}\mathrm{VO}\right]}^{+}$ time-of-flight cyclotron double resonance used for determining the ${\nu }_c$ of ${\left[{}^{44}\mathrm{VO}\right]}^{+}$. The line shape is a theoretical curve described in [39]. Both the isomer and the ground state of ${}^{44}\mathrm{V}$ are visible.

Figure 3

Experimental (square) and theoretical (circle) $b$ and $c$ coefficients of the lowest triplets in the $pf$ shell, as a function of mass number $A$. The experimental information came from references [28, 29, 30, 44] and this work on $A=44$ ground state mass measurements. Theoretical calculations have been performed with cdGX1A Hamiltonian [45].

Figure 4

Mirror and triplet energy differences as a function of J for $A=44$. Experimental values (square) are compared with those obtained with two different shell model calculations: (circle) with the cdGX1A effective interaction [45] and (triangle) using Eqs. (4), (6) [12]. See text for details.

Figure 5

Experimental partial decay scheme of ${}^{44}\mathrm{Cr}$, including new results calculated with the new precise mass measurements of the ground and isomeric states of ${}^{44}\mathrm{V}$. The experimental information came from Refs. [28, 29, 30]. The level denoted $(T=1)$ refers to the unknown $J=1^{+},T=1$ state (or states) that can undergo proton emission, in the vicinity of the IAS. The red dashed transition represents the isospin-forbidden transition to ${}^{43}\mathrm{Ti}$.