Even-odd staggering of the spectroscopic factor as new evidence for $\alpha$ clustering

We evidence a staggering effect of the experimental spectroscopic factors corresponding to even-even and odd-mass (odd-mass and odd-odd) $\alpha$ emitters. The comparison to the theoretical estimate within the standard Bardeen-Cooper-Schrieffer (BCS) approach reveals a similar staggering, but with a different behavior. It turns out that the ratio between corresponding experimental and theoretical spectroscopic factors is proportional to the experimental reduced decay width. A similar dependence was found in a previous work between the strength of the quadrupole-quadrupole $\alpha$-core interaction, describing the $\alpha$-decay fine structure and the reduced width. Thus, the even-odd staggering effect in the spectroscopic factor is a new evidence of the $\alpha$-clustering phenomenon in medium and heavy nuclei.

Figure 1

(a) The experimental spectroscopic factors for even-even and odd-mass nuclei pertaining to various even-$Z$ isotope chains versus the neutron number. (b) Same as in (a), but for the corresponding BCS quantities.

Figure 2

Same as in Fig. 1, but for odd-$Z$ isotope chains.

Figure 3

The ratio between experimental and BCS spectroscopic factors versus the reduced width multiplied by 100.

Figure 4

The ratio between experimental and BCS spectroscopic factors versus the difference between neutron number and the closest magic number.

Figure 5

(a) QQ coupling strength versus the reduced width multiplied by 100 for even-even emitters. (b) QQ coupling strength versus $N-N_{\mathrm{magic}}$ for even-even emitters. (c) Same as in (a), but for odd-mass emitters. (d) Same as in (b), but for odd-mass emitters.