Compound nuclear decay and the liquid-vapor phase transition: A physical picture

Analyses of multifragmentation in terms of the Fisher droplet model (FDM) and the associated construction of a nuclear phase diagram bring forth the problem of the actual existence of the nuclear vapor phase and the meaning of its associated pressure. We present here a physical picture of fragment production from excited nuclei that solves this problem and establishes the relationship between the FDM and the standard compound nucleus decay rate for rare particles emitted in first-chance decay. The compound thermal emission picture is formally equivalent to an FDM-like equilibrium description and avoids the problem of the vapor while also explaining the observation of Boltzmann-like distribution of emission times. In this picture, a simple Fermi gas thermometric relation is naturally justified and verified in the fragment yields and time scales. Low-energy compound nucleus fragment yields scale according to the FDM and lead to an estimate of the infinite symmetric nuclear matter critical temperature between 18 and 27 MeV depending on the choice of the surface energy coefficient of nuclear matter.

Figure 1

Effective temperature of a Fermi system with three exit channels ($a,b$, and n) as a function of initial excitation energy for two cases: (1) barriers $B_a$ and $B_b$ are large (crosses) compared to $B_n=6$ MeV, and (2) $B_a$ or $B_b$ is similar (solid circles) to $B_n$. Initial temperature as a function of initial excitation energy is shown by the open circles.

Figure 2

Mean emission times (in fm/$c$) of fragments with atomic number $4\le Z\le 9$ (solid symbols) vs inverse temperature for the reaction π + Au at 8 GeV/$c$ [18, 19], and Average yields of the same fragments vs $1/T$ (solid symbols). The line represents a Boltzmann fit to the fragment yields. This same line has been superimposed (shifted) onto the emission times.

Figure 3

Results for the FDM-scaled yield distribution for the ${}^{64}\mathrm{Ni}{+}^{12}$C compound nucleus decay data. See text for details.

Figure 4

Solid line shows the ratio of $c_0\varepsilon$ (the surface free energy coefficient) for the two estimates of the nuclear binding energy used as a function of temperature. Dashed lines show the error arising from the errors on the $T_c$ values returned by the fitting procedure. Dotted vertical lines show the temperature range covered by the compound nucleus experiment.