How the Pauli exclusion principle affects fusion of atomic nuclei

The Pauli exclusion principle induces a repulsion between composite systems of identical fermions such as colliding atomic nuclei. Our goal is to study how heavy-ion fusion is impacted by this “Pauli repulsion.” We propose a new microscopic approach, the density-constrained frozen Hartree-Fock method, to compute the bare potential including the Pauli exclusion principle exactly. Pauli repulsion is shown to be important inside the barrier radius and increases with the charge product of the nuclei. Its main effect is to reduce tunneling probability. Pauli repulsion is part of the solution to the long-standing deep sub-barrier fusion hindrance problem.

Figure 1

(a)–(c) Nucleus-nucleus potential without (FHF) and with (DCFHF) Pauli exclusion principle between nucleons of different nuclei. Potentials from a Gram-Schmidt antisymmetrization (dotted-dashed line) and from DCFHF without rearrangement of the spin-orbit density (thin dashed line) are shown in (a). M3Y (dotted line) and M3Y+rep (dotted-dashed line) phenomenological potentials [45] are shown in (c). (d)–(f) Experimental [13, 46, 47, 48] and theoretical (coupled-channel calculations with couplings to low-lying collective $2^{+}$ and/or $3^{-}$ states) fusion cross sections ${\sigma }_{\mathrm{fus}}$ vs center-of-mass energy $E_{\mathrm{c}.\mathrm{m}.}$. (g)–(i) Logarithmic slopes of ${\sigma }_{\mathrm{fus}}{E}_{\mathrm{c}.\mathrm{m}.}$ vs $E_{\mathrm{c}.\mathrm{m}.}-V_B$ where $V_B$ is the barrier energy. In (g)–(i), FHF and DCFHF cross sections are obtained without couplings, the latter being included via a shift in $E_{\mathrm{c}.\mathrm{m}.}$ (see text).

Figure 2

${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ nucleus-nucleus potential without (FHF) and with (DCFHF) Pauli exclusion principle between nucleons of different nuclei.

Figure 3

Same as Fig. 2, but for ${}^{48}\mathrm{Ca}+{}^{208}\mathrm{Pb}$.

Figure 4

Same as Fig. 2, but for ${}^{40}\mathrm{Ca}+{}^{48}\mathrm{Ca}$. DCFHF potentials of the other ${}^A\mathrm{Ca}+{}^A\mathrm{Ca}$ are also reported.