Nucleonic density

Brueckner, K. A., Phys. Rev. 103, 1121, "Relation between nucleon density and nuclear potential."... 

The nature of spheron-spheron interactions is such that maximum stability is achieved when each spheron ligates about itself the maximum number of neighbors, to produce a nucleus with a closest-packed structure. A simple argument (12) leads to the conclusion that the spherons in a nucleus are arranged in concentric layers. The packing radius of a spheron varies from 1.28 f for the dineutron to 1.62 f for the helion. The radius (to nucleon density half that of the inner region) of the largest nucleus is 6.8 f... 

In the right panel of Fig. 4 we display the symmetry energy as a function of the nucleon density p for different choices of the TBF. We observe results in agreement with the characteristics of the EOS shown in the left panel. Namely, the stiffest equation of state, i.e., the one calculated with the microscopic TBF,... 

Figure 6. The single-particle potentials of nucleons n, p and hyperons , A in baryonic matter of fixed nucleonic density pN = 0.4 fm-3, proton density pp/pN = 0.2, and varying density pz/pN = 0.0, 0.2, 0.5. The vertical lines represent the corresponding Fermi momenta of n, p, and . For the nucleonic curves, the thick lines represent the complete single-particle potentials Un, whereas the thin lines show the values excluding the contribution, i.e., U + uffi.

They carry the stamp of the Big Bang, whence their great interest for cosmology. Their lithium content in particular is a precious clue as to the nucleonic density of the Universe, combined with deuterium and helium abundances measured in extremely metal-poor media (see Appendix 1). 

It is easy to see why the results of primordial nucleosynthesis, and in particular the final abundance of deuterium, should be so sensitive to the nucleonic density of the Universe. For this reason, deuterium, made up of one proton and one neutron, can be considered as an excellent cosmic densimeter. The disparate abundances for their part are related to specific nuclear properties of the isotopes under consideration. 

A single parameter, the nucleonic density, is thus sufficient to explain the proportions of the light elements in the Universe, from helium at 10% of the number of hydrogen atoms to lithium at one ten-thousandth. However, the number of neutrino species must be at most three in order to avoid an overproduction of helium-4. Since each neutrino belongs to a single particle family, the number of particle farmlies in the Universe must... 

The Symmetry of Cluster Structures of Nuclei was discussed by Brink who showed contour plots of nucleon density obtained from Har-tree-Fock calculations for simple nuclei such as 8Be, l2C, and 20Ne. 

Recall that X rays are diffracted by the electrons that surround atoms, and that images obtained from X-ray diffraction show the surface of the electron clouds that surround molecules. Recall also that the X-ray diffracting power of elements in a sample increases with increasing atomic number. Neutrons are diffracted by nuclei, not by electrons. Thus a density map computed from neutron diffraction data is not an electon-density map, but instead a map of nuclear mass distribution, a "nucleon-density map" of the molecule (nucleons are the protons and neutrons in atomic nuclei). 

The primordial abundances of D, 3He, and 7Li(7Be) are rate limited, depending sensitively on the competition between the nuclear reactions rates and the universal expansion rate. As a result, these nuclides are potential baryometers since their abundances are sensitive to the universal density of nucleons. As the universe expands, the nucleon density decreases so it is useful to compare the nucleon density to that of the CMB photons r) = n /n7. Since this ratio will turn out to be very small, it is convenient to introduce... 

In contrast to the other light nuclides, the primordial abundance of 4He (mass fraction Y) is relatively insensitive to the baryon density, but since virtually all neutrons available at BBN are incorporated in 4He, it does depend on the competition between the weak interaction rate (largely fixed by the accurately measured neutron lifetime) and the universal expansion rate (which depends on geff)- The higher the nucleon density, the earlier can the D-bottleneck be breached. At early times there are more neutrons and, therefore, more 4He will be synthesized. This latter effect is responsible for the very slow (logarithmic) increase in Y with rj. Given the standard model relation between time and temperature and the nuclear and weak cross sections and decay rates measured in the laboratory, the evolution of the light nuclide abundances may be calculated and the frozen-out relic abundances predicted as a function of the one free parameter, the nucleon density or rj. These are shown in Fig. 1. 

This expression assumes equal distributions for protons and neutrons, or alternatively an averaged nucleon density. The nucleon density, nuc( )> generally representable for every nucleus a as... 

Generally speaking, the density p ri —ta)-, which appears in the nuclear spin-dependent terms, does not coincide with the nucleon density relevant for the nuclear spin-independent term (see for instance also equation 26 in ref. [90]). The situation is reminiscent of the magnetic moment distribution... 

FIGURE 8.22 The lower well rises strongly with increasing primary nucleon density, and even gets supercritical (spontaneous nucleon emission and creation of bound antinucleons). Supercriticality denotes the situation, when the lower well enters the upper continuum. 

The mechanism is similar for the production of multi-hyper nuclei A, E, S, Q). Meson field theory predicts also for the A energy spectrum at finite primary nucleon density the existence of upper and lower wells. The lower well belongs to the vacuum and is fully occupied by yl s. 

FIGURE 8.27 Contour plot of nucleon densities for Be without (left) and with (right) antiproton calculated with the parametrization NL3. The maximum density of normal Be is 0.20 fm , while for the nucleus with the antiproton it is 0.61 fm. ... 

In order to study the compression modulus of the finite nucleus 0 let us consider as a model wave function the Slater determinant appropriate to describe the ground-state of 0 in terms of harmonic oscillator functions for a given oscillator length b. For each oscillator length one can calculate the radial density distribution pb(r) and the average nucleon density... 

The observed constant nucleonic density suggests that the nucleons are packed together in a nucleus in a way resembling the packing of molecules in a liquid, rather than in a gas (see Section 20-21). 

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