Entropy and caloric curve for mononuclei considering both surface diffuseness and self-similar expansion degrees of freedom

The caloric curve for mononuclear configurations is studied with a model that allows for both increased surface diffusness and self-similar expansion. The evolution of the effective mass with density and excitation is included in a schematic fashion. The entropies, extracted in a local-density approximation, confirm that nuclei posess a soft mode that is predominately a surface expansion. We also find that the mononuclear caloric curve (temperature versus excitation energy) exhibits a plateau. Thus a plateau should be the expectation with or without a multifragmentationlike phase transition. This conclusion is relevant only for reactions that populate the mononuclear region of phase space.

Figure 1

(Color online) Binding energy per particle for infinite matter from [14] as a function of reduced density for asymmetries $\delta =$ 0.0, 0.2, 0.4, and 0.6 (bottom to top).

Figure 2

(Color online) Binding energy per particle for the energy-density formalism used in this work [${\epsilon }_{\mathrm{ED}}(1,1),$ solid curve]. Also shown are the DROPLET model binding energy per particle (dashed curve) and the percentage of difference between the DROPLET model and ${\epsilon }_{\mathrm{ED}}$ (dotted curve) binding energies. The latter are referenced to the right-hand-side axis.

Figure 3

(Color online) Expansion energy (per particle) as a function of the self-similar expansion degree of freedom c for the energy-density formalism used in this work (solid curve), the scaling model of Myers and Świątecki [17] (dashed curve) and the form used in EES [16] (dotted curve).

Figure 4

(Color online) The expansion energy ${\varepsilon }_E$ used in this work as a function of the both increased surface diffuseness (b) and self-similar expansion degree of freedom (c). The contours are at 1-MeV increments, starting from 0, intersecting $(b,c)=$ (0,0), and increasing from that point to the upper-left-hand corner.

Figure 5

(Color online) (a) Effective mass profiles for ($b,c)=(1,1)$ (solid curve), self-similar expansion (1,0.85) (dashed curve), and increased surface diffuseness (2,1) (dotted curve). (b) Effective-mass profiles for $(b,c=(1,1)$) and $T=0.5$ (solid curve), 2 (dashed curve) and 4 MeV (dotted curve).

Figure 6

(Color online) Ratio of level-density constants a${}_{\mathrm{LDA}-F}/a_{\mathrm{SC}-F}$ (dotted curve) from [32] and $a_{\mathrm{LDA}-F}/a_{\mathrm{LDA}-S}$ (solid curve).

Figure 7

(Color online) The relative entropies per nucleon $s(b,c)/s(1,1)$ map as functions of expansion (c = abscissa) and surface diffuseness (b = ordinate) for excitation energies of $\varepsilon =2,3,4$, and 5 MeV A are shown in panels a, b, c, and d, respectively. The contours are in steps of 10%. The (unitless) absolute values of the entropy of the references states at (1,1), for each of these energies are 0.907, 1.134, 1.356, and 1.59, respectively.

Figure 8

(Color online) (a) Density profiles that maximizes the entropy for excitation energies of $\varepsilon =2,3,4$, and 5 MeV A. (b) Density profiles along the entropy ridge for $\varepsilon =3$ MeV A. The solid curves represents the entropy peak while the dotted and dashed curve are extremes of the entropy ridge.

Figure 9

(Color online) Caloric curve (for ${}^{197}\mathrm{Au}$) for a Fermi gas with fixed density and a level-density parameter $a=A/10$ (dotted curve), self-similar expansion (dashed curve), and both self-similar and surface expansion degrees of freedom (solid curve).

Figure 10

(Color online) Barrier-reduction factors $k(b,c)$. The contours are at 5% increments from 1.1 to 0.80 in the lower-right-hand and upper-left-hand corners, respectively.

Figure 11

(Color online) Barrier-reduction factors as functions of excitation energy per nucleon for the equilibrium shapes (circles) and those extracted from ISiS data [42] (squares with error bars.)