Novel Role of Superfluidity in Low-Energy Nuclear Reactions

We demonstrate, within symmetry unrestricted time-dependent density functional theory, the existence of new effects in low-energy nuclear reactions which originate from superfluidity. The dynamics of the pairing field induces solitonic excitations in the colliding nuclear systems, leading to qualitative changes in the reaction dynamics. The solitonic excitation prevents collective energy dissipation and effectively suppresses the fusion cross section. We demonstrate how the variations of the total kinetic energy of the fragments can be traced back to the energy stored in the superfluid junction of colliding nuclei. Both contact time and scattering angle in noncentral collisions are significantly affected. The modification of the fusion cross section and possibilities for its experimental detection are discussed.

Figure 1

Schematic picture of the situation we examine in the present Letter: a collision of two superfluid nuclei with different phases of the pairing fields. Each disc represents a cross section of a nucleus. The arrows inside the nucleus indicate the pairing field ${\mathrm{\Delta }}_i(\mathit{r})$, where the length of the arrow indicates its absolute value $|{\mathrm{\Delta }}_i(\mathit{r})|$, while the direction indicates its phase ${\phi }_i(\mathit{r})$ ($i=1$, 2). In the ground state, the phase is uniform across each nucleus ${\phi }_i(\mathit{r})={\phi }_i$ and the phase difference $\mathrm{\Delta }\phi$ ($\equiv {\phi }_1-{\phi }_2$) is well defined. We will show how the phase difference affects the reaction dynamics.

Figure 2

Snapshots from the collision of ${}^{240}\mathrm{Pu}+{}^{240}\mathrm{Pu}$ for two extreme values of the relative phase differences ($\mathrm{\Delta }\phi =0$ and $\pi$) at the energy $E\simeq 1.1V_{\text{Bass}}$, where $V_{\text{Bass}}$ represents the phenomenological fusion barrier [23]. Left panels show the total density distribution, whereas the right panels show the neutron paring field of two colliding nuclei. Top half of each panel corresponds to the phase difference $\mathrm{\Delta }\phi =\pi$ case, while the bottom half corresponds to the case without phase difference $\mathrm{\Delta }\phi =0$. Contact time is about $550–600\mathrm{fm}/c$ depending on the phase difference. For movies and plots showing the phase evolution see Ref. [17].

Figure 3

Results of the TDSLDA simulations for ${}^{240}\mathrm{Pu}+{}^{240}\mathrm{Pu}$ head-on collisions at various collision energies. (a) Total kinetic energy (TKE) of the outgoing fragments is shown. Line shows fit to the data by a formula $\alpha +\beta {\sin }^2(\mathrm{\Delta }\phi /2)$ with respect to parameters $\alpha$ and $\beta$. (b) The average number of transferred neutrons from the left nucleus to the right nucleus due to the Josephson current is shown. The horizontal axis is the relative pairing phase $\mathrm{\Delta }\phi$. Note that the change of TKE has different phase dependence, and cannot be explained by the Josephson effect.

Figure 4

Results of the TDSLDA simulations for ${}^{90}\mathrm{Zr}+{}^{90}\mathrm{Zr}$ head-on collisions. Fusion threshold energy $B$ is shown as a function of the relative pairing phase $\mathrm{\Delta }\phi$. For this reaction the barrier height is $V_{\text{Bass}}\simeq 192\mathrm{MeV}$. The phase difference prevents fusion for energies up to 15% above the barrier.