${}^{48}\mathrm{Ca}$-induced reaction on the lanthanide target ${}^{154}\mathrm{Gd}$ and its decay to ground and metastable states within the dynamical cluster-decay model

The decay mechanism of compound nucleus (CN) ${}^{202}\mathrm{Po}^{*}$, formed in ${}^{48}\mathrm{Ca}+{}^{154}\mathrm{Gd}$ reaction, is studied within the dynamical cluster-decay model (DCM) at various excitation energies $E_{\mathrm{CN}}^{*}$, where neutron emission $xn$, $x=3\text{–}5$, are the predominant decay modes. The study is of interest since ${}^{202}\mathrm{Po}^{*}$ decays to the ground state (g.s.) of ${}^{198}\mathrm{Po}$ by emission of $4n$ and to metastable states ${}^{199m}\mathrm{Po}$ and ${}^{197m}\mathrm{Po}$ via ($3n,5n$) emission, respectively. The DCM is applied here for the first time to the decays of metastable states. Both types of decays are analyzed separately, using neck-length $\mathrm{\Delta }R$ (equivalently, barrier-lowering) parameter, the only parameter in the DCM, to best fit the evaporation residue or channel cross section (${\sigma }_{xn}$) data and predict the quasifissionlike (qf-like) noncompound (${\sigma }_{\mathrm{qf}}$) and fusion-fission (${\sigma }_{\mathrm{ff}}$) cross sections. For g.s. to g.s. decay of ${}^{202}\mathrm{Po}^{*}$, possibly due to involving the deformed rare-earth lanthanide target ${}^{154}\mathrm{Gd}$, the observed $4n$ decay channel requires the noncompound nucleus (nCN) contribution, treated as the qf-like process. On the other hand, the decay mechanism of ${}^{202}\mathrm{Po}^{*}$ to metastable states (m.s.) ${}^{199m}\mathrm{Po}$ and ${}^{197m}\mathrm{Po}$, is a pure CN decay, i.e., the ${\sigma }_{\mathrm{qf}}$ is zero. In this study, we have included the deformation effects up to quadrupole deformations ${\beta }_{2i}$ and optimum orientations ${\theta }_i^{\mathrm{opt}.}$ for coplanar ($\mathrm{\Phi }=0^0$) nuclei, using hot-compact configurations, supporting asymmetric fission of CN ${}^{202}\mathrm{Po}^{*}$. The variation of CN formation probability $P_{\mathrm{CN}}$ and survival probability $P_{\mathrm{surv}}$ with excitation energy $E_{\mathrm{CN}}^{*}$ is in complete agreement with the known systematic of other radioactive CN studied so far, thereby giving credence to the predicted ${\sigma }_{\mathrm{qf}}$ in g.s. to g.s. decay and fusion-fission cross section ${\sigma }_{\mathrm{ff}}$ of ${}^{202}\mathrm{Po}^{*}$. Interestingly, both the observed g.s. to g.s. and g.s. to m.s. processes occur at a fixed $\mathrm{\Delta }R=2.45\pm 0.20\mathrm{fm}$, which is within the nuclear proximity limit of $\sim 2.5\mathrm{fm}$, and hence useful for making predictions.

Figure 1

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

Figure 2

The temperature ($T$) and $\ell$-dependent scattering potential $V\left(R\right)$ in (a) the g.s. decay of ${}^{202}\mathrm{Po}^{*}$ to ${}^{201}\mathrm{Po}+1n$, and (b) the decay of ${}^{202}\mathrm{Po}^{*}$ to metastable ${}^{197m}\mathrm{Po}$ state, i.e., ${}^{202}\mathrm{Po}^{*}\to {}^{197m}\mathrm{Po}+5n$ decay channel, both at $E_{\mathrm{CN}}^{*}=50.10\mathrm{MeV}$ ($T=1.60$ MeV). The first and second turning points $R_a$ and $R_b$ are labeled, and the barrier lowering parameter $\mathrm{\Delta }{V}_B=V\left(R_a\right)-V_B$ shown for both the ${\ell }_{max}=150\hslash$ and ${\ell }_{min}=19\hslash$ values. The scattering potential from touching radius $R_t$ up to spherical CN radius $R_o$ is extrapolated as a polynomial. The decay path, defined by $V(R_a,\ell )=Q_{\mathrm{eff}}$ for g.s. to g.s., and by $V(R_a,\ell )=Q_{\mathrm{eff}}^{*}$ for g.s. to m.s. is shown to begin at $R_a$ ($=R_t+\mathrm{\Delta }R$) for both cases.

Figure 3

Fragmentation potentials $V\left(A_2\right)$, as a function of light fragment mass number $A_2$, for (a) the g.s. decay of ${}^{202}\mathrm{Po}^{*}$ formed in ${}^{48}\mathrm{Ca}+{}^{154}\mathrm{Gd}$ reaction, plotted at ${\ell }_{min}$ and ${\ell }_{max}$ values, for best-fitted $\mathrm{\Delta }R$ values given in Table 1 Cal.2 for $xn$ decay channels, at $E_{\mathrm{CN}}^{*}=50.10\mathrm{MeV}$, using quadrupole deformations (${\beta }_{2i}$) alone with ${\theta }_i^{\mathrm{opt}.}$ orientations. The fusion-fission (ff) region is also marked; (b) decay of ${}^{202}\mathrm{Po}^{*}$ to metastable states, plotted at ${\ell }_{min}$ and ${\ell }_{max}$ values, for best-fitted $\mathrm{\Delta }R$ values given in Table 2 Cal.2. Figure 3 shows a magnified view of the fragmentation potential, modified due to $3n$ and $5n$ metastable states ${}^{199m}\mathrm{Po}$ and ${}^{197m}\mathrm{Po}$, i.e., how the respective metastable state energy difference (${\varepsilon }_j$) is added to their respective g.s., i.e., fragmentation potential $V^m\left(xn\right)=V\left(xn\right)+{\varepsilon }_j$, $j=xn$ (and their complementary heavy fragments), where ${\varepsilon }_j=0.31\mathrm{MeV}$ for $j=3n$ and 0.204 MeV for $j=5n$ [12].

Figure 4

The preformation probability $P_0$ vs. angular momentum $\ell$ for the fragmentation potential (a) for g.s. to g.s. decay of ${}^{202}\mathrm{Po}^{*}$, and (b) for g.s. to m.s. decays of ${}^{202}\mathrm{Po}^{*}$.

Figure 5

Same as for Fig. 4, but for penetrability $P$.

Figure 6

The $xn$ decay channel cross sections ${\sigma }_{xn}$, $x=1\text{–}5$, vs. angular momentum $\ell$ as per details in Fig. 4 for (a) g.s. to g.s. decay, and (b) g.s. to m.s. decays.

Figure 7

(a) DCM calculated ${\sigma }_{xn}$ excitation functions for g.s. decay of ${}^{202}\mathrm{Po}^{*}$ for best fitted $\mathrm{\Delta }R$'s in Table 1 Cal.2, composed of the pure CN contribution ${\sigma }_{xn}^{\mathrm{CN}}$ (dash-dot line with open stars) and the noncompound quasifission component ${\sigma }_{\mathrm{qf}}^{\mathrm{Cal}.}$ (dotted line with open down-triangles), and their sum ${\sigma }_{xn}^{\mathrm{Cal}.}$ (solid line with open squares; lines are a guide for the eyes), compared with experimental data (filled circles), and a statistical model calculation (dashed line [8]). (b) DCM calculated ${\sigma }_{xn}$ excitation functions of ${}^{202}\mathrm{Po}^{*}$ for decay to metastable state $x=3$ for best-fitted $\mathrm{\Delta }R$'s in Table 2 Cal.2 (open squares, with solid lines as a guide for the eyes), compared with experimental data (filled circles) and the above-stated statistical model calculation (dashed line [8]).

Figure 8

Variation of DCM calculated (a) $P_{\mathrm{CN}}$ and (b) $P_{\mathrm{surv}}$ as a function of excitation energy $E_{\mathrm{CN}}^{*}$ for the g.s. decay of ${}^{202}\mathrm{Po}^{*}$, for ${\beta }_{2i}$-deformed ${\theta }_i^{\mathrm{opt}.}$, and $\mathrm{\Phi }=0^0$ case, compared with another ${}^{48}\mathrm{Ca}$-induced reaction [10] forming ${}^{220}\mathrm{Th}^{*}$.

Figure 9

Variation of DCM calculated $\mathrm{\Delta }R$ with $E_{\mathrm{CN}}^{*}$ for the observed and unobserved g.s. to g.s. and g.s. to m.s. decays of ${}^{202}\mathrm{Po}^{*}$.