Resistible effects of Coulomb interaction on nucleus-vapor phase coexistence

We explore the effects of Coulomb interaction upon the nuclear liquid vapor phase transition. Because large nuclei $\left(A>30\right)$ are metastable objects, phases, phase coexistence, and phase transitions cannot be defined with any generality and the analogy to liquid vapor is ill posed for these heavy systems. However, it is possible to account for the Coulomb interaction in the decay rates and obtain the coexistence phase diagram for the corresponding uncharged system.

Figure 1

The droplet dependent caloric curve at constant pressure. The solid line shows the drop’s caloric curve and its dependence on radius. The scaled values of temperature, enthalpy, and radius are $T^{\prime }=T∕\Delta H_m^0$, $H^{\prime }=H{\left(\Delta H_m^0∕3c_s{V}_m^l\right)}^3∕\left(4\pi ∕V_m^l\right)$, and $r^{\prime }=r\Delta H_m^0∕\left(3c_s{V}_m^l\right)$, respectively (see Ref. 10). $\Delta H_m^0$ is the bulk molar enthalpy of vaporization, $c_s$ is the surface energy coefficient, and $V_m^l$is the molar volume of the liquid.

Figure 2

Top panel: the schematic potential of an uncharged and bound particle $\left(Q<0\right)$ leaving a nucleus. Bottom panel: the schematic potential of a bound charged particle. The charged particle must overcome a Coulomb barrier $B_c$ in order to leave the nucleus.

Figure 3

The schematic potential of an unbound charged particle.

Figure 4

A schematic representation of the Coulomb correction when the emitted fragment is bound (left panels) and unbound (right panels). In both cases one can remove the Coulomb energy of the saddle configuration and calculate the $Q$ value using surface energies only (bottom panels). The resulting hypothetical gas will be composed of fragments that are bound to the droplet $\left(Q_{\text{surface}}<0\right)$ for all fragment partitions.

Figure 5

The dependence of the saddle barrier ($B_s$, dotted line) is plotted as a function of atomic number for a schematic binding energy which includes only Coulomb and surface terms. Each saddle barrier consist of two parts: the $-Q$ value (short dash) and the Coulomb barrier $B_c$ (long dash). After correction for Coulomb, the relevant $Q$ value calculated using surface terms only binds the fragment to the drop and is shown by the solid line. This is calculated for a $Z=50$, $A=118$ nucleus.