Effects of formation properties in one-proton radioactivity

It is shown that the proton formation probability, extracted from experimental data corresponding to one-proton radioactivity, is divided into two regions when plotted as a function of an universal parameter. This parameter is derived from a microscopic description of the decay process. In this way we explain the systematics of proton emission half-lives. At the same time the formation probability is shown to be a useful quantity to determine the deformation property of the mother nucleus.

Figure 1

Upper: UDL proton decay half-lives. Dots are experimental values while the straight line is $a{\chi }^{\prime }$ with $a$ provided by the parameter set I of Table . $e$ is given by $e=b{\rho }^{\prime }+dl(l+1)/{\rho }^{\prime }+c$. Lower: $\mathcal{R}=T_{1/2}^{\mathrm{expt}.}/T_{1/2}^{\mathrm{calc}.}$ as a function of the charge number $Z$. Within the dashed lines is the region where the data is reproduced by the calculation within a factor of 4.

Figure 2

Proton-decay formation amplitudes ${\log }_{10}{\left|RF\left(R\right)\right|}^2$ extracted from experimental data as a function of ${\rho }^{\prime }$. Squares correspond to nuclei with $N<75(Z⩽67)$ while circles are for $N⩾75(Z>67)$.

Figure 3

The parameter ${\rho }^{\prime }$ vs the fragmentation potential [Eq. (6)] for nuclei with $Z⩽67$ (open circles) and $Z>67$ (solid circles).

Figure 4

The formation amplitudes $|F_l\left(R\right)|$ extracted from experimental data for proton decays of nuclei $N⩾75(Z>67)$ as a function of $u$ calculated from BCS calculations using for the Woods-Saxon mean field the universal parameters [23] (upper) and the Cherpunov parameters [24] (lower).

Figure 5

Single-proton wave functions in ${}^{151}$Lu for different channels calculated with the universal Woods-Saxon parameter. The inserted plot shows the wave functions of the $0h_{11/2}$ orbital with different energies derived by changing the depth of the potential.