Multinucleon transfer in ${}^{16,18}\mathrm{O},{}^{19}\mathrm{F}+{}^{208}\mathrm{Pb}$ reactions at energies near the fusion barrier

Background: Nuclear reactions are complex, involving collisions between composite systems where many-body dynamics determines outcomes. Successful models have been developed to explain particular reaction outcomes in distinct energy and mass regimes, but a unifying picture remains elusive. The irreversible transfer of kinetic energy from the relative motion of the collision partners to their internal states, as is known to occur in deep inelastic collisions, has yet to be successfully incorporated explicitly into fully quantal reaction models. The influence of these processes on fusion is not yet quantitatively understood.

Purpose: To investigate the population of high excitation energies in transfer reactions at sub-barrier energies, which are precursors to deep inelastic processes, and their dependence on the internuclear separation.

Methods: Transfer probabilities and excitation energy spectra have been measured in collisions of ${}^{16,18}\mathrm{O},{}^{19}\mathrm{F}+{}^{208}\mathrm{Pb}$, at various energies below and around the fusion barrier, by detecting the backscattered projectile-like fragments in a $\mathrm{\Delta }E\text{−}E$ telescope.

Results: The relative yields of different transfer outcomes are strongly driven by $Q$ values, but change with the internuclear separation. In ${}^{16}\mathrm{O}+{}^{208}\mathrm{Pb}$, single nucleon transfer dominates, with a strong contribution from $-2p$ transfer close to the Coulomb barrier, though this channel becomes less significant in relation to the $-2p2n$ transfer channel at larger separations. For ${}^{18}\mathrm{O}+{}^{208}\mathrm{Pb}$, the $-2p2n$ channel is the dominant charge transfer mode at all separations. In the reactions with ${}^{19}\mathrm{F},-3p2n$ transfer is significant close to the barrier, but falls off rapidly with energy. Multinucleon transfer processes are shown to lead to high excitation energies (up to $\sim 15$ MeV), which is distinct from single nucleon transfer modes which predominantly populate states at low excitation energy.

Conclusions: Kinetic energy is transferred into internal excitations following transfer, with this energy being distributed over a larger number of states and to higher excitations with increasing numbers of transferred nucleons. Multinucleon transfer is thus a mechanism by which energy can be dissipated from the relative motion before reaching the fusion barrier radius.

Figure 1

Schematic diagram of the experimental setup. The monitor detectors are placed perpendicular to the plane containing the $\mathrm{\Delta }E\text{−}E$ telescope.

Figure 2

$\mathrm{\Delta }E\text{−}{E}_{\text{Si}}$ spectra obtained for (a) ${}^{16}\mathrm{O}+{}^{208}\mathrm{Pb}$, (b) ${}^{18}\mathrm{O}+{}^{208}\mathrm{Pb}$, (c) ${}^{19}\mathrm{F}+{}^{208}\mathrm{Pb}$ at $E_{\text{c.m.}}/V_B\approx 0.98$. Main intense spots correspond to elastically scattered beam species. Products are shown to be well separated in charge, with the carbon band also showing separation of species by mass. Black dashed lines are srim [19] calculations showing the expected locus of $\alpha$ particles in the $\mathrm{\Delta }E\text{−}E$ telescope. In the ${}^{18}\mathrm{O}+{}^{208}\mathrm{Pb}$ (b) and ${}^{19}\mathrm{F}+{}^{208}\mathrm{Pb}$ (c) reactions, we observe a small number of events corresponding to charge pickup by the projectile. However, the vast majority of events correspond to charge stripping from the projectile, elastic/inelastic scattering, and neutron transfer reactions.

Figure 3

Mapping of ${}^{12}\mathrm{C},{}^{18}\mathrm{O}$, and ${}^{19}\mathrm{F}$ locii in the $\mathrm{\Delta }E\text{−}{E}_{\text{Si}}$ spectrum. The intense bands of events are from scattering of each projectile from a thick tantalum target. The positions of the elastic peaks for scattering of each projectile from the thin Pb target are indicated by the blue circles, and are used to map the locii to higher energies. The locii determined through this method are shown in the figure by the solid black lines. The intensity scale on the right of the figure applies only to the ${}^{19}\mathrm{F}$ band.

Figure 4

(a) $\mathrm{\Delta }E\text{−}{E}_{\text{Si}}$ plot obtained in the reaction ${}^{16}\mathrm{O}+{}^{208}\mathrm{Pb}$ at $0.98 V_B$. The red line shows the ${}^{12}\mathrm{C}$ locus from which the relative energy loss $\left(\mathrm{\Delta }{E}_{\mathrm{rel}}\right)$ spectrum is calculated. The $\mathrm{\Delta }{E}_{\mathrm{rel}}$ spectrum is determined from events within the dashed contour. (b) Resulting $\mathrm{\Delta }{E}_{\mathrm{rel}}$ spectrum. Red curve shows the multiple Gaussian function fitted to the distribution. Black curves indicate the corresponding fitted components, which are attributed to yields of the expected isotopes, in this case ${}^{12,13,14}\mathrm{C}$. Vertical blue dashed lines show the gate limits for event-by-event analysis as determined by the intersections between adjacent fitted peaks.

Figure 5

Measured probabilities at $E_{\text{c.m}}\sim 0.95V_B$ for various transfer processes in the studied reactions and the associated effective $Q$ values, corresponding to the data shown in Table 2. Left hand panels (a–c) show the data for the reactions indicated. Right hand panels (d—f) show the data sorted by $\mathrm{\Delta }Z$ channel. The downward arrows indicate all of the modes that are within the shown range in $Q_{\text{eff}}$ but are not observed experimentally, thus their probabilities are much closer to zero.

Figure 6

(a) Ratio of the quasielastic and Rutherford scattering cross sections for all systems as a function of the surface separation parameter $\mathrm{\Delta }$. (b) Total transfer probability for each system. Key shown in the top panel is relevant to both panels. Open circles in the bottom panel show the sum of channel transfer probabilities in ${}^{19}\mathrm{F}+{}^{208}\mathrm{Pb}$ excluding the $-1p$ channel. Vertical red dashed line indicates the approximate location of the fusion barrier in the $\mathrm{\Delta }$ coordinate, where the probability for absorption $=0.5$.

Figure 7

(a) Measured one and two neutron pickup probabilities. Blue line is a fit to the 1n transfer data $\left(\mathrm{\Delta }N=+1\right)$, and the red dashed line is the expected pickup of two independent neutrons $\left(\mathrm{\Delta }N=+2\right)$ according to Eq. (5). (b) One proton stripping probability as a function of the separation (triangles), along with those reported in Ref. [17] (circles). The purple line is a fit to the data in the range 13.1 fm $\le r_{\text{min}} \le$ 14.5 fm. (c) Measured $\mathrm{\Delta }Z=-2$ channels in this experiment (diamonds), along with those reported in Ref. [17] (circles). Shown again is the fit to the $1p$ stripping data shown in (b), along with its square (green dashed line), which is the expected probability of stripping of two independent protons according to Eq. (5).

Figure 8

(a) shows measured neutron transfer probabilities. We show also the trends in the $-1p$ and $-2p2n \left(\alpha \right)$ modes for the sake of comparison by the solid purple and dashed green lines respectively. (b) shows measured probabilities for channels involving the transfer of one proton, again with the $-2p2n$ and $-1p$ trends for comparison. (c) shows $\mathrm{\Delta }Z=-2$ channels, along with the measured $-1p$ and $-2p2n$ trends.

Figure 9

(a) One proton and one neutron pickup probabilities. Note that we cannot unambiguously separate the neon products, so the square symbols represent the total $\mathrm{\Delta }Z=+1$ probabilities. (b) Measured $\mathrm{\Delta }Z=-1$ probabilities. Solid blue line and dashed blue line indicate $-1p$ and $-1p2n$ trends to guide the eye. (c) $\mathrm{\Delta }Z=-2$ probabilities. Shown also are the trend lines of the most significant $\mathrm{\Delta }Z=-1$ modes for comparison, with the trend in $-2p2n$ indicated by the purple dash dotted line. (d) $\mathrm{\Delta }Z=-3$ probabilities, along with the most significant $\mathrm{\Delta }Z=-1$ and $\mathrm{\Delta }Z=-2$ trends for comparison.

Figure 10

Variation in the distribution of excitation energy following transfer reactions in ${}^{16}\mathrm{O}+{}^{208}\mathrm{Pb}$ (a), ${}^{18}\mathrm{O}+{}^{208}\mathrm{Pb}$ (b), and ${}^{19}\mathrm{F}+{}^{208}\mathrm{Pb}$ (c). Legend labels give bombarding energies in the center-of-momentum frame $E_{\text{c.m.}}$ as a factor of the barrier energy $V_B$.

Figure 11

(a–c) and (g–i) show the distribution of excitation energy in the $1p,2p$, and $2p2n$ channels (left to right) in the reaction ${}^{16}\mathrm{O}+{}^{208}\mathrm{Pb}$, measured relative to the ground state $Q$ values for those processes, at bombarding energies of 73 MeV and 69.3 MeV, respectively (corresponding to $E_{\text{c.m.}}/V_B$ of 0.98 and 0.93). Black dashed line shows total excitation energy of all channels (including transfers and inelastic scattering). The filled areas show events corresponding to the detected product listed in the legend. The solid black curves in (a) and (g) show a grazing calculation [44] of the excitation energy for the single proton stripping channel. (d–f) are contour plots showing the distribution in excitation energy of each product as the beam energy varies relative to the Coulomb barrier energy. Contours are drawn in increments of 0.0001 in $dP/d{E}_x$. Thick black dashed line in (e) and (f) shows the evolution of the optimal excitation energy with bombarding energy, which is derived from the optimal $Q$ value (see Appendix); in the case of the $1p$ stripping reaction shown in (d), the optimal $Q$ value is less than $Q_{\text{g.g.}}$ and thus is not shown.

Figure 12

(a–c) and (g–i) show the distribution of excitation energy in the $-1p,-1p2n$, and $-2p2n$ channels (left to right) in the reaction ${}^{18}\mathrm{O}+{}^{208}\mathrm{Pb}$, measured relative to the ground state $Q$ values for those processes, at bombarding energies of 73.6 MeV and 68 MeV, respectively (corresponding to $E_{\text{c.m.}}/V_B$ of 1.00 and 0.92). The black dashed line shows total excitation energy of all channels (including transfers and inelastic scattering). The filled areas show events corresponding to the detected product listed in the legend. The solid black curves in (a) and (g) show a grazing calculation [44] of the excitation energy for the single proton stripping channel. (d–f) are contour plots showing the distribution in excitation energy of each product as the beam energy varies relative to the Coulomb barrier energy. Contours are drawn in increments of 0.0001 in $dP/d{E}_x$. Thick black dashed line in (f) shows the evolution of the optimal excitation energy with bombarding energy, which is derived from the optimal $Q$ value (see Appendix); for modes shown in (d) and (e) the optimal $Q$ value is below $Q_{\text{g.g.}}$, and thus $E_{x\mathrm{opt}}$ is not visible.

Figure 13

(a–e) and (k–o) show the distribution of excitation energy in the $-1p,-1p2n,-2p,-2p2n$, and $-3p2n$ channels (left to right) in the reaction ${}^{19}\mathrm{F}+{}^{208}\mathrm{Pb}$, measured relative to the ground state $Q$ values for those processes, at bombarding energies of 83.3 MeV and 74.1 MeV, respectively (corresponding to $E_{\text{c.m.}}/V_B$ of 1.01 and 0.90). The black dashed lines show total excitation energy of all channels (including transfers and inelastic scattering). The filled areas show events corresponding to the detected product listed in the legend. The solid black curves in (a) and (k) show a grazing calculation [44] of the excitation energy for the single proton stripping channel. (f–j) are contour plots showing the distribution in excitation energy of each product as the beam energy varies relative to the Coulomb barrier energy. Contours are drawn in increments of 0.0001 in $dP/d{E}_x$. Thick black dashed line shows the evolution of the optimal excitation energy with bombarding energy, which is derived from the optimal $Q$ value (see Appendix).