Ab initio calculations of forbidden transition amplitudes and lifetimes of the low-lying states in ${\mathrm{V}}^{4+}$

We report electric quadrupole $\left(E2\right)$ and magnetic dipole $\left(M1\right)$ transition amplitudes of the first few low-lying states of quadruply ionized vanadium $\left({\mathrm{V}}^{4+}\right)$, which are important in various experimental applications and astrophysics. To our knowledge, most of these presented results are determined for the first time in the literature. A relativistic multireference Fock-space coupled-cluster theory with single $\left(S\right)$, double $\left(D\right)$, and partial triple $\left(T\right)$ excitations is employed to compute the forbidden transition probabilities and lifetimes of the low-lying states in ${\mathrm{V}}^{4+}$. Estimations of different correlation effects arising through the above formalism have been highlighted by investigating core and valence electron excitations. A long lifetime is found for the first excited $3d{}^{2}D_{5∕2}$ state, which suggests that ${\mathrm{V}}^{4+}$ may be one of the useful candidates for many important studies.