اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدNew Wrinkles on an Old Model: Correlation Between Liquid Drop Parameters and Curvature Term
59
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The relationship between the volume and surface energy coefficients in the liquid drop A^{-1/3} expansion of nuclear masses is discussed. The volume and surface coefficients in the liquid drop expansion share the same physical origin and their physical connection is used to extend the expansion with a curvature term. A possible generalization of the Wigner term is also suggested. This connection between coefficients is used to fit the experimental nuclear masses. The excellent fit obtained with a smaller number of parameters validates the assumed physical connection.
قيم البحث
اقرأ أيضاً
We consider a variant of Gamows liquid drop model with an anisotropic surface energy. Under suitable regularity and ellipticity assumptions on the surface tension, Wulff shapes are minimizers in this problem if and only if the surface energy is isotr
opic. We show that for smooth anisotropies, in the small nonlocality regime, minimizers converge to the Wulff shape in $C^1$-norm and quantify the rate of convergence. We also obtain a quantitative extension of the energy of any minimizer around the energy of a Wulff shape yielding a geometric stability result. For certain crystalline surface tensions we can determine the global minimizer and obtain its exact energy expansion in terms of the nonlocality parameter.
The nuclear binding energies for 28 nuclei including several isotopic chains with masses ranging from A=64 to A=226 were evaluated using the Skyrme effective nucleon-nucleon interaction and the Extended Thomas-Fermi approximation. The neutron and pro
ton density distributions are assumed in the form of Fermi functions the parameters of which are determined so as to minimize the total binding energy of any given nucleus. The present study is restricted to quadrupole shapes, but the neutron and proton density distributions are free to have different deformations. A simple expression for the variation of the nuclear energy with the neutron--proton deformation difference is derived.
The coefficients of different mass formulae derived from the liquid drop model and including or not the curvature energy, the diffuseness correction to the Coulomb energy, the charge exchange correction term, different forms of the Wigner term and di
fferent powers of the relative neutron excess $I=(N-Z)/A$ have been determined by a least square fitting procedure to 2027 experimental atomic masses. The Coulomb diffuseness correction $Z^2/A$ term or the charge exchange correction $Z^{4/3}/A^{1/3}$ term plays the main role to improve the accuracy of the mass formula. The Wigner term and the curvature energy can also be used separately for the same purpose. The introduction of an $|I|$ dependence in the surface and volume energies improves slightly the efficiency of the expansion and is more effective than an $I^4$ dependence. Different expressions reproducing the experimental nuclear charge radius are provided. The different fits lead to a surface energy coefficient of around 17-18 MeV and a relative equivalent rms charge radius r$_0$ of 1.22-1.23 fm.
Longitudinal ternary and binary fission barriers of $^{36}$Ar, $^{56}$Ni and $^{252}$Cf nuclei have been determined within a rotational liquid drop model taking into account the nuclear proximity energy. For the light nuclei the heights of the ternar
y fission barriers become competitive with the binary ones at high angular momenta since the maximum lies at an outer position and has a much higher moment of inertia.
Using the model of hexagonal clusters we express the surface, curvature and Gauss curvature coefficients of the nuclear binding energy in terms of its bulk coefficient. Using the derived values of these coefficients and a single fitting parameter we
are able to reasonably well describe the experimental binding energies of nuclei with more than 100 nucleons. To improve the description of lighter nuclei we introduce the same correction for all the coefficients. In this way we determine the apparent values of the surface, curvature and Gauss curvature coefficients which may be used for infinite nuclear matter equation of state. This simple model allows us to fix the temperature dependence of all these coefficients, if the temperature dependence for the bulk term is known. The found estimates for critical temperature are well consistent both with experimental and with theoretical findings.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
