Clustering effects and decay analysis of the light-mass $N=Z$ and $N\ne Z$ composite systems formed in heavy ion collisions

We investigate the clustering effects in light mass $N=Z$ and $N\ne Z$ composite systems ${}^{20}\mathrm{Ne}^{*}, {}^{28}\mathrm{Si}^{*}, {}^{40}\mathrm{Ca}^{*}$ and ${}^{21,22}\mathrm{Ne}^{*}, {}^{39}\mathrm{K}^{*}$, respectively, formed in low-energy heavy ion reactions at different excitation energies, within the collective clusterization approach of the dynamical cluster-decay model (DCM) of Gupta and collaborators based on quantum-mechanical fragmentation theory (QMFT). Considering quadrupole deformed and compact orientated nuclei, a comparative decay analysis of these systems has been undertaken for the emission of different intermediate mass fragments (IMFs) or clusters, specifically the IMFs having $Z=3$, 4, and 5 (or $Z=7$, 6, and 5 complimentary fragments from the ${}^{20}\mathrm{Ne}^{*}$ and ${}^{21,22}\mathrm{Ne}^{*}$ composite systems) which are having the experimental data available for their $Z$ distribution. Quite interestingly, the QMFT supports clustering in $N=Z$ (${}^{20}\mathrm{Ne}^{*}$ and ${}^{28}\mathrm{Si}^{*}$) and $N\ne Z$ (${}^{21}\mathrm{Ne}^{*}$ and ${}^{22}\mathrm{Ne}^{*}$) nuclear systems at excitation energies corresponding to their respective decay threshold or resonant-state energies for the $4\alpha , {}^{16}\mathrm{O}$ cluster and non-$\alpha$ cluster ${}^{14}\mathrm{C}$ (more so in ${}^{22}\mathrm{Ne}^{*}N\ne Z$ composite system), supported by the Ikeda diagrams, taking into account the proper pairing strength in the temperature-dependent liquid drop energies. Within the DCM, we notice that at higher excitation energies in addition to $x\alpha$-type (where $x$ is an integer) clusters from $N=Z$ composite systems and $xn-x\alpha$-type clusters from $N\ne Z$ composite systems, $np-x\alpha$-type clusters are relatively quite dominant, with larger preformation probability due to the decreased pairing strength at higher temperatures in the liquid drop energies. Also, the study reveals the presence of competing reaction mechanisms of compound nucleus (fusion-fission, FF) and of noncompound nucleus origin (deep inelastic orbiting, DIO) in the decay of very-light-mass composite systems ${}^{20,21,22}\mathrm{Ne}^{*}$ and ${}^{28}\mathrm{Si}^{*}$ at different excitation energies. The DIO contribution in the IMF cross section ${\sigma }_{\text{IMF}}$ is extracted for these composite systems, ${\sigma }_{\text{IMF}}$ is given as the sum of FF cross section ${\sigma }_{\text{FF}}$ and DIO cross section ${\sigma }_{\text{DIO}}$. The DCM calculated FF cross sections ${\sigma }_{\text{FF}}^{\text{DCM}}$ are in good agreement with the available experimental data.

Figure 1

Schematic configuration of two equal or unequal axially symmetric deformed, oriented nuclei, lying in the same plane (azimuthal angle $\varphi =0^{\circ }$) for various ${\theta }_1$ and ${\theta }_2$ values in the range $0^{\circ }$ to ${180}^{\circ }$. The ${\theta }_i$ are measured anticlockwise from the collision axis and angle ${\alpha }_i$ clockwise from the symmetry axis.

Figure 2

Variation of the preformation probability $P_0$ with fragment or cluster mass ($A_i, i=1,2$) for the decay of $N=Z$ or $\alpha$ conjugate systems (a) ${}^{20}\mathrm{Ne}^{*}$ and (b) ${}^{28}\mathrm{Si}^{*}$, and $N\ne Z$ or non-$\alpha$ conjugate systems (c) ${}^{21}\mathrm{Ne}^{*}$ and (d) ${}^{22}\mathrm{Ne}^{*}$, at $T$ values of their corresponding excited resonant states and the experimentally available excited state [13].

Figure 3

Scattering potential $V\left(R\right)$ for the symmetric decay of $\alpha$ conjugate systems (a) ${}^{20}\mathrm{Ne}^{*}$, (b) ${}^{28}\mathrm{Si}^{*}$, and (c) ${}^{40}\mathrm{Ca}^{*}$ at ${\ell }_{\min }$ and respective ${\ell }_c$ values.

Figure 4

Variation of the fragmentation potential $V$ with fragment charge $Z$ for $A_2=4$ fragment, for the decay of non-$\alpha$ conjugate system ${}^{22}\mathrm{Ne}^{*}$ at $T$ values of their corresponding excited resonant state and the experimentally available excited state [13].

Figure 5

Variation of fragmentation potential $V$ with fragment mass ($A_i, i=1,2$) for the decay of $\alpha$ conjugate systems (a) ${}^{20}\mathrm{Ne}^{*}$ (b) ${}^{28}\mathrm{Si}^{*}$, and (c) ${}^{40}\mathrm{Ca}^{*}$ at $\ell =0$ and respective ${\ell }_c$ values. The values of fitted $\mathrm{\Delta }R$ for the excitation energies in the figure for ${}^{20}\mathrm{Ne}^{*}$ are 2.12, 2.02, 1.781 (for $Z=5,6,7$, respectively), for ${}^{28}\mathrm{Si}^{*}$ they are 1.223, 1.542, 1.585 (for $Z=3,4,5$, respectively), and for ${}^{40}\mathrm{Ca}^{*}$ they are 1.14, 1.14, 1.34 (for $Z=3,4,5$, respectively); also given in Table 1.

Figure 6

Variation of preformation probability $P_0$ with fragment mass ($A_i, i=1,2$) for the decay of $\alpha$ conjugate systems (a) ${}^{20}\mathrm{Ne}^{*}$, (b) ${}^{28}\mathrm{Si}^{*}$, and (c) ${}^{40}\mathrm{Ca}^{*}$ at $\ell =0$ and respective ${\ell }_c$ values, calculated for fragmentation potentials in Fig. 5.

Figure 7

Variation of preformation probability $P_0$ with fragment mass ($A_i, i=1,2$) for the decay of non-$\alpha$ conjugate systems (a) ${}^{21}\mathrm{Ne}^{*}$, (b) ${}^{22}\mathrm{Ne}^{*}$, and (c) ${}^{39}\mathrm{K}^{*}$ at $\ell =0$ and respective ${\ell }_c$ values. The values of fitted $\mathrm{\Delta }R$ for the excitation energies in the figure for ${}^{21}\mathrm{Ne}^{*}$ are 2.0, 1.92, 1.78 (for $Z=5,6,7$ respectively), for ${}^{22}\mathrm{Ne}^{*}$ they are 1.765, 2.0, 1.82 (for $Z=5,6,7$ respectively), for ${}^{39}\mathrm{K}^{*}$ they are 0.97, 1.16, 1.78 (for $Z=3,4,5$, respectively). See also Table 2.

Figure 8

Variation of penetration probability $P$ with cluster mass ($A_i, i=1,2$) for the decay of $\alpha$ conjugate systems (a) ${}^{20}\mathrm{Ne}^{*}$, (b) ${}^{28}\mathrm{Si}^{*}$, and (c) ${}^{40}\mathrm{Ca}^{*}$ at ${\ell }_{\min }$ and respective ${\ell }_c$ values.

Figure 9

Variation of penetration probability $P$ with cluster mass ($A_i, i=1,2$) for the decay of non-$\alpha$ conjugate systems (a)${}^{21}\mathrm{Ne}$, (b) ${}^{22}\mathrm{Ne}^{*}$, and (c) ${}^{39}\mathrm{K}^{*}$ at ${\ell }_{\min }$ and respective ${\ell }_c$ values.