Neutron skin

Abstract The hadronic equation of state for a neutron star is discussed with a particular emphasis on the symmetry energy. The results of several microscopic approaches are compared and also a new calculation in terms of the self-consistent Green function method is presented. In addition possible constraints on the symmetry energy coming from empirical information on the neutron skin of finite nuclei are considered. 

Green function method, that can be considered as a generalization of the BHF approach. The results are compared with those from various many-body approaches, such as variational and relativistic mean field approaches. In view of the large spread in the theoretical predictions we also examine possible constraints on the nuclear SE that may be obtained from information from finite nuclei (such the neutron skin). 

Relativistic mean field (RMF) models have been applied successfully to describe properties of rinite nuclei. In general ground state energies, spin-orbit splittings, etc. can be described well in terms of a few parameters ref. [18]. Recently it has lead to the suggestion that the bulk SE is strongly correlated with the neutron skin [19, 20] (see below). In essence the method is based upon the use of energy-density functional (EDF) theory. 

Recently in applying the non-relativistic Skyrme Hartree-Fock (SHF) model Brown [19] noted that certain combinations of parameters in the SHF are not well determined by a fit to ground state binding energies alone as a result a wide range of predictions for the EoS for PNM can be obtained. At the same time he found a correlation between the derivative of the neutron star EoS (i.e., basically the symmetry pressure po) and the neutron skin in 208Pb. 

Subsequently Furnstahl [20] in a more extensive study pointed out that within the framework of mean field models (both non-relativistic Skyrme as well as relativistic models) there exists an almost linear empirical correlation between theoretical predictions for both 04 and its density dependence, po, and the neutron skin, All lln — Rp, in heavy nuclei. This is illustrated for 208Pb in Fig. 5 (from ref.[20] a similar correlation is found between All and po). Note that whereas the Skyrme results cover a wide range of All values the RMF predictions in general lead to AR > 0.20 fm. 

Figure 5. Neutron skin thickness versus <24 for 208Pb for a variety of mean field models (from [20]). The circles correspond to results for the Skyrme force, the squares to RMF models with mesons, and the triangles to RMF with point couplings the shaded area indicates the range of NR values consistent with the present empirical information for 208Pb.

Figure 6. Neutron skin in 208Pb vs. the Landau-Migdal parameter /. ...

What are the experimental constraints on the neutron skin A variety of experimental approaches have been explored in the past to obtain information on AR. To a certain extent all analysis contain a certain model dependence, which is difficult to estimate quantitatively. It is not our intention to present a full overview of existing methods for the special case of 208Pb. In particular the results obtained in the past from the analysis of elastic scattering of protons and neutrons have varied depending upon specifics of the analysis employed. At present the most accurate value for AR comes from a recent detailed analysis of the elastic proton scattering reaction at E = 0.5 — 1 GeV [28], and of... 

We note that also other types of isovector giant resonances have been suggested as a source of information on the neutron skin, such as the spin-dipole giant resonance [33] and the isobaric analog state [34], At present studies of these reactions have not led to quantitative constraints for the neutron skin of... 

Neutron skin and neutron haio in heavy nuciei. The neutron radius of heavy nuciei is observed to be iarger than the proton radius. A uniformiy overhanging neutron distribution is caiied neutron skin (on the left), whereas a graduaiiy diminishing one is a neutron haio... 

W.D. Myers, Droplet model isotope shifts and the neutron skin, Phys. Lett. 30B 451 (1969) Droplet Model of Atomic Nuclei... 

Radionuclides that do not emit beta particles likely emit alpha particles. An alpha particle is, in effect, a helium atom (two protons and two neutrons) ejected from an unstable nucleus. An alpha particle can only travel a few inches in air and cannot penetrate the outer layers of dead skin cells. Therefore, alpha particles are not external hazards and produce tissue damage only if alpha-emitting radionuclides are ingested, inhaled, or injected. 

Two forms of gold provide medical treatments. The radioactive isotope Au-198, with a short half-life of 2.7 days, is used to treat cancer and is produced by subjecting pure gold to neutrons within a nuclear reactor. A gold salt, a solution called sodium thiosulfate (AuNa O Cl ), is injected as an internal treatment for rheumatoid arthritis. However, since gold and some of its compounds are toxic when ingested, this treatment may cause complications such as skin rashes and kidney failure. It is a less popular treatment, particularly with the development of newer and more effective medications. 

Toxicosis in animals has resulted from ingestion of boric acid or borax solutions, from topical applications of boric acid solutions to damaged skin, and from inhalation of boranes the exact mechanisms of action are not understood. Boron and its compounds are potent teratogens when applied directly to the embryo, bnt there is no evidence of mutagenicity or carcinogenicity. Boron s unique affinity for cancerons tissnes has been exploited in neutron capture radiation therapy of malignant hnman brain tnmors. 

Fig. 3.1 Dose-incidence curves for different neoplasms in animals exposed to external radiation (A) myeloid leukemia in x-irradiated mice (°) (Upton et al., 1958) (B) mammary gland tumors at 12 months in gamma-irradiated rats (A) (Shellabarger et al., 1969) (C) thymic lymphoma in x-irradiated mice ( ) (Kaplan and Brown, 1952) (D) kidney tumors in x-irradiated rats (o) (Maldague, 1969) (E) skin tumors in alpha-irradiated rats (percentage incidence x 10) ( ) (Bums et al., 1968) (F) skin tumors in electron-irradiated rats (percentage incidence x 10) (A) (Bums et al., 1968) (G) reticulum cell sarcoma in x-irradiated mice (0) (Metalli et al., 1974) (H) lung adenomas in neutron-irradiated mice ( ) (Ullrich et al., 1976) (Modified from UNSCEAR, 1972) (from Upton, 1984).

---