$\alpha$-cluster formation and decay in the quartetting wave function approach

We present a microscopic calculation of $\alpha$-cluster formation in heavy nuclei by using the quartetting wave function approach. The interaction of the quartet with the core nucleus is taken in local density approximation. The $\alpha$-cluster formation is found to be particularly sensitive to the interplay of the mean field felt by the $\alpha$-cluster and the Pauli blocking as a consequence of antisymmetrization. The striking feature of $\alpha$-cluster formation probability across the major shell closures of 82 protons and 126 neutrons is reproduced. The shell (or subshell) effects on the $\alpha$-cluster formation in superheavy nuclei are also analyzed.

Figure 1

Comparison of the c.m. effective potentials, the c.m. wave functions, and the Fermi energies for two neighboring $\alpha$ emitters ${}^{210}\mathrm{Po}$ and ${}^{212}\mathrm{Po}$.

Figure 2

$\alpha$-cluster preformation probability $P_{\alpha }$ of even-even Po isotopes by the quartetting wave function approach. For comparison, the empirical analysis of $\alpha$ decay reduced width ${\delta }^2$ taken from Ref. [13] are given in the insert.

Figure 3

The quantity $E_{\mathrm{tunnel}}-{\mu }_4$ as a function of the neutron number $N$ for the Po isotopes.

Figure 4

$\alpha$-cluster preformation probability $P_{\alpha }$ of even-even $N=126$ isotones by the quartetting wave function approach.

Figure 5

The comparison of experimental and calculated half-lives for the Po isotopes by using linear mass-dependent parametrization of M3Y interaction strengths.

Figure 6

The comparison of experimental and calculated half-lives for the superheavy nuclei by using linear mass-dependent parametrization of M3Y interaction strengths.