Nuclear radii: A critique of the droplet model☆
Abstract
Equivalent sharp radii of a number of nuclei are calculated with the droplet model, using parameters that have been determined by the Hartree-Fock (HF) method with a given force (Gogny). They are found to be systematically smaller than the sharp radii given by direct HF calculations on the nucleus in question with the same force. This is shown to be a result of nuclear matter being squeezed by the surface tension much more in the droplet model than in the HF method. Inclusion of higher-order terms in the droplet model's expansion in powers of in no way helps to remove the anomaly, and in fact serious questions concerning the convergence of this expansion arise.
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Mass predictions in the infinite nuclear matter model
1999, Atomic Data and Nuclear Data TablesWe present here the binding energies and mass excesses of 7208 nuclei in the ranges 4 ≤ Z ≤ 120 and 8 ≤ A ≤ 270. Relative to our 1986–1987 mass table, the present results are obtained with the recently improved infinite nuclear matter model which has the desirable features of natural decoupling of the infinite part from the finite part of the ground state energy, together with the cancellation of the exchange Coulomb, finite-size proton form factor, and Nolen–Schiffer anomaly terms. In addition, we have developed a new scheme of an interactive network covering the entire nuclear chart to obtain the local energy (comprising shell, deformation, etc.) of a nucleus in a consistent manner, using the technique of ensemble averaging of a large number of values predicted with the help of recursion relations derived in the model. This has widened the scope for predictions of masses of nuclei far into the drip-line regions of the nuclear chart. On the basis of systematics of the two-neutron separation energies, several new islands of stability in the exotic regions are predicted. This model has only five parameters representing the properties of infinite nuclear matter, the surface tension, and the Coulomb and pairing terms, which are determined once and for all in least-squares fits to known nuclear masses. The root-mean-square deviation of the fit to 1884 known masses is 401 keV, while the mean deviation is a remarkably low 9 keV, indicating that remanent systematic effects are vanishingly small.
Finite nuclei to nuclear matter: A leptodermous approach
1999, Physics ReportThe liquid drop model (LDM) expansions of energy and incompressibility of finite nuclei are studied in an analytical model using Skyrme-like effective interactions to examine, whether such expansions provide an unambiguous way to go from finite nuclei to nuclear matter, and thereby can yield the saturation properties of the latter, from nuclear masses. We show that the energy expansion is not unique in the sense that, its coefficients do not necessarily correspond to the ground state of nuclear matter and hence, the mass formulas based on it are not equipped to yield saturation properties. The defect is attributed to its use of liquid drop without any reference to particles as its basis, which is classical in nature. It does not possess an essential property of an interacting many-fermion system namely, the single particle property, in particular the Fermi state. It is shown that, the defect is repaired in the infinite nuclear matter model by the use of generalized Hugenholtz–Van Hove theorem of many-body theory. So this model uses infinite nuclear matter with well defined quantum mechanical attributes for its basis. The resulting expansion has the coefficients which are at the ground state of nuclear matter. Thus a well defined path from finite nuclei to nuclear matter is found out. Then using this model, the saturation density 0.1620 fm−3 and binding energy per nucleon of nuclear matter 16.108 MeV are determined from the masses of all known nuclei. The corresponding radius constant r0 equal to 1.138 fm thus determined, agrees quite well with that obtained from electron scattering data, leading to the resolution of the so-called ‘r0-paradox’. Finally a well defined and stable value of 288±20 MeV for the incompressibility of nuclear matter K∞ is extracted from the same set of masses and a nuclear equation of state is thus obtained.
Nuclear data sheets update for A = 64
1991, Nuclear Data SheetsThe evaluated spectroscopic data are presented for eight known nuclides of mass 64 (Mn, Fe, Co, Ni, Cu, Zn, Ga, Ge). Excited-state data are nonexistent for 64Mn and 64Fe. Very little information is available for 64Ge and γ-ray data are scarce for 64Co and 64Ni. Some high-spin data are available for 64Ga and 64Ge, in spite of several in-beam γ-ray experiments on 64Zn and 64Cu. Further work on 64Zn and 64Ga seems to be in progress at Daresbury (90LiZS) through heavy-ion reactions. Radioactive decay data for 64Mn are not available and those for 64Fe, 64Co and 64Ge are not considered definitive.
Thomas-fermi approach to nuclear mass formula. (I). Spherical nuclei
1986, Nuclear Physics, Section AWith a view to having a more secure basis for the nuclear mass formula than is provided by the drop(let) model, we make a preliminary study of the possibilities offered by the Skyrme-ETF method. Two ways of incorporating shell effects are considered: the “Strutinsky-integral” method of Chu et al., and the “expectation-value” method of Brack et al. Each of these methods is compared with the HF method in an attempt to see how reliably they extrapolate from the known region of the nuclear chart out to the neutron-drip line. The Strutinsky-integral method is shown to perform particularly well, and to offer a promising approach to a more reliable mass formula.
Semi-classical nuclear properties from effective interactions
1986, Annals of PhysicsWe present a systematic study of average nuclear properties in the framework of an energy density formalism (EDF). The method provides a link between the mean field microscopic approach using effective interactions fitted to ground states of nuclei and the macroscopic approach such as the Droplet Model (DM). First, we concentrate on geometrical aspects of nuclear densities. We show that the semi-classical nuclear surface can be essentially characterized by two diffuseness coefficients: the inward one deseribes the (exponential) shoulder of the surface and the outward one the (exponential) fall-off; the ratio of these two coefficients is a measure of the skewness of the profile and is shown to be of the order of 1.5–2 in semiinfinite medium. The effect of a neutron excess is discussed and an explicit expression is given for the difference between neutron and proton surface thicknesses. The analysis answers a number of criticisms and misunderstandings concerning the relation between the neutron skin and the difference between neutron and proton root mean square (r.m.s.) radii. We then calculate the different coefficients appearing in the mass formula. We show in particular that within the present formalism, the curvature energy coefficient is necessarily large (i.e., in the range 10–15 MeV), in contradiction with the empirical estimates, which are compatible with a zero value; whether this discrepancy is due to the use of zero-range forces or should be attributed to the macroscopic models used in the fit to experimental masses remains to be seen. We also calculate the surface symmetry energy for which a simple expression is derived. Next, we show that the DM theorems can be established directly within the EDF and we study the breakdown of the leptodermous approximation in light systems. Concerning the squeezing of the bulk by the surface tension, the leptodermous expression overestimates EDF results in the region of mass . We review critically a number of recent studies devoted to the subject; we show that exponential terms in , which do not have an expansion, appear here, and we calculate the intensity and the range (close to 1) of these nonleptodermous terms. Similar terms appear also in the description of isovector properties (e.g., neutron skin) although less crucially. A better understanding of the presence of these terms in the total energy is, however, still needed and should provide a model describing correctly the average trends of physical properties of small as well as of large saturating systems.
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Work partially supported by NSERC of Canada.