Unexpectedly enhanced $\alpha$-particle preformation in ${}^{48}\mathrm{Ti}$ probed by the ($p,p\alpha$) reaction

The formation of $\alpha$ particles on nuclear surfaces has remained a fundamental problem since the dawn of nuclear physics. This $\alpha$-particle formation strongly affects the $\alpha$-decay lifetimes of heavy and superheavy elements, level scheme of light nuclei, and synthesis of elements in stars. However, despite its importance, the $\alpha$-particle formation in medium-mass nuclei is seldom investigated. Based on the ${}^{48}\mathrm{Ti}(p,p\alpha ){}^{44}\mathrm{Ca}$ reaction analysis, this study reports that $\alpha$-particle formation in the medium-mass ${}^{48}\mathrm{Ti}$ nucleus is pronounced more compared to that expected through mean-field approximations. Moreover, the estimated average distance between the $\alpha$ particle and residue equals approximately 4.5 fm. This result poses a challenge to describe the four nucleon correlations using microscopic nuclear models.

Figure 1

Wave-function density distributions for RWA calculation—(a) mean-field solution; (b)–(f) $\alpha +{}^{44}\mathrm{Ca}$ system with different internuclear distances $d$.

Figure 2

(a) RWA values calculated from $\alpha +{}^{44}\mathrm{Ca}$ ($d=3.0\text{–}5.0\text{fm}$) and mean-field wave functions shown in Fig. 1; (b) TMD values of ${}^{48}\mathrm{Ti}(p,p\alpha ){}^{44}\mathrm{Ca}$ reaction at $T_p=63$ MeV. The TMD values were calculated using the mean-field solution, and the $d=3.0$ fm wave function was multiplied by 10 and 5, respectively. The arrow indicates the sum of $\alpha$ and ${}^{44}\mathrm{Ca}$ charge radii, which approximately correspond to the nuclear surface.

Figure 3

Triple-differential cross section of ${}^{48}\mathrm{Ti}(p,p\alpha ){}^{44}\mathrm{Ca}$ reaction via DWIA calculations using RWAs of the $\alpha +{}^{44}\mathrm{Ca}$ ($d=3.0\text{–}5.0\text{fm}$) and mean-field wave functions shown in Fig. 2 and their comparison against experimental results reported by [20]. The incident-proton energy as well as values of the proton and $\alpha$-particle emission angles equal $E_p=101.5$ MeV, ${\theta }_p=-70.0^{\circ }$, and ${\theta }_{\alpha }=45.0^{\circ }$, respectively.

Figure 4

(a) Binding energy, (b) charge radii, and (c) E2 transition matrix of ${}^{44}\mathrm{Ti}$ calculated using mean-field solution and $\alpha +{}^{44}\mathrm{Ca}$ wave function, as well as their comparison against experimental data [38, 39, 40]. The binding energy is relative to the $\alpha +{}^{44}\mathrm{Ca}$-decay threshold.