Physical properties of hot,dense matter: The general case

The thermodynamic properties of hot, dense matter are examined in the density range 10^?5 fm^?3 ? n ? 0.35 fm^?3 and the temperature range 0 ? T ? 21 MeV, for fixed lepton fractions Y_? = 0.4, 0.3 and 0.2 and for matter in β-equilibrium with no neutrinos. Three phases of the matter are considered: the nuclei phase is assumed to consist of Wigner-Seitz cells with central nuclei surrounded by a nucleon vapor containing also α-particles; in the bubbles phase the cell contains a central spherical bubble of nucleon vapor surrounded by dense nuclear matter; the third phase is that of uniform nuclear matter. All are immersed in a sea of leptons (electrons and neutrinos) and photons. The nuclei and bubbles are described by a compressible liquid drop model which is self-consistent in the sense that all of the constituent properties — bulk, surface, Coulomb energies and other minor contributions — are calculated from the same nuclear effective hamiltonian, in this case the Skyrme 1' interaction. The temperature dependence of all of these energies is included, for bulk and surface energies by direct calculation, for the Coulomb energy by combining in a plausible way the usual electrostatic energy and the numerical results pertaining to a hot Coulomb plasma. Lattice contributions to the Coulomb energy are an essential ingredient, and lattice modifications to the nuclear translational energy are included. A term is constructed to allow also for the reduced density of excited states of light nuclei. All of these modifications incorporate necessary physical effects which modify significantly the matter properties in some regions.     

Mechanism of 3He-mediated nuclear spin-lattice relaxation at surfaces

We measured the nuclear spin-lattice relaxation time T₁, of several surface-bound nuclei, ¹H, ¹⁹F, ¹¹B, ¹³C, ²⁹Si, and ²H, immersed in liquid ³He over the temperature range 0.01 K ⩽ T < 1 K. The Larmor frequencies of these nuclei in a 3.39 T field extended from 22 to 144 MHz. All T₁ values were temperature-independent and ranged from a few seconds to several hours, depending on the particular nucleus and the surface geometry of the sample. The results indicate that the coupled relaxation of surface spins is a phenomenon occurring in all solids immersed in ³He and thus provides a general mechanism for obtaining high nuclear polarization in solids, that the relaxation is controlled by direct dipole-dipole interactions between the surface spins and ³He in the first surface layer, that the ³He motion dynamics do not change appreciably from one surface to another, and that measurements of T₁ may thus be useful for determining the structure of surfaces.     

Sensitivity of reaction cross sections to halo nucleus density distributions

In order to clear up the sensitivity of the nucleus-nucleus reaction cross sections σ _R to the nuclear matter distributions in exotic halo nuclei, we have calculated the values of σ _R for scattering of ⁶He, ¹¹Li, and ¹⁹C nuclei on several nuclear targets at the energy of 0.8 GeV/nucleon. The calculations were performed in the “rigid target” approximation to the Glauber theory, different shapes of the nuclear density distributions in ⁶He, ¹¹Li, and ¹⁹C being assumed.     

Phase transition and relaxation processes by 87Rb and 39K nuclear magnetic measurements of RbKSO4 single crystals

⁸⁷Rb and ³⁹K nuclear magnetic resonance (NMR) spectra of RbKSO₄ single crystals were measured at room temperature. ⁸⁷Rb central line has the angular dependences of second-order quadrupolar shifts. From these results, the quadrupole coupling constant and the asymmetry parameter were determined at room temperature. In addition, the spin–lattice relaxation rate, 1/T₁, and the spin–spin relaxation rate, 1/T₂, were measured as a function of temperature. The values of 1/T₁ for the ⁸⁷Rb and ³⁹K nuclei were found to increase with increasing temperature, and 1/T₁ was determined to be proportional to Tⁿ. Therefore, for the ⁸⁷Rb and ³⁹K nuclei, Raman processes with n=2 are more significantly in nuclear quadrupole relaxation than direct processes.     

On the nuclear interaction potential in the reactions with heavy ions

The interaction potential of heavy ions⁴He,⁶Li,¹²C and¹⁶O is constructed in the folding model. The density distribution of nuclear matter for these nuclei is calculated in the framework of the hyperspherical function method. For the calculation of the folding potentials we have employed the Skyrme nucleon-nucleon forces. The influence of several effects on the results of calculations is studied: the role of the three-body forces of the nucleon-nucleon interaction, dependence of the folding potential on the mass numbers of the colliding nuclei and the possibility of observing the monopole resonance in the ion inelastic scattering. Using our folding potential as a real part of the optical potential we have calculated the differential cross section of elastic scattering of⁶Li from¹²C at laboratory energy of lithium ionsT _L =90.0 MeV. Reasonable agreement with experiment is obtained.     

Three-nucleon interaction in 3-, 4- and ∞-body systems

We report results of variational calculations of ³H, ³He, ⁴He and nuclear matter with the Urbana v₁₄ two-nucleon interaction and realistic models of the three-nucleon interaction (TNI). These include the Tucson and isobar intermediate-state models of the two-pion exchange TNI. The latter is also studied with an intermediate-range three-nucleon repulsion. In general, realistic TNI helps to bring the theory closer to experiment by giving extra binding energy to the A = 3 and 4 nuclei and providing extra saturation to the nuclear matter binding energy. The Coulomb energy of ³He and the rms radii of A = 3, 4 nuclei are also well described. However, some problems remain unresolved. There is a slight overbinding of ⁴He, an underbinding of nuclear matter, and the charge form factors of ³He and ⁴He, calculated with impulse approximation, deviate from the experimental at q²>5 fm^?2.     

Variational calculations of asymmetric nuclear matter

We report on variational calculations of the energy E(ρ, β) of asymmetric nuclear matter having ? = ?_n + ?_p = 0.05 to 0.35 fm^?3, and β = (?_n ? ?_p/g9 = 0 to 1. The nuclear h used in this work consists of a realistic two-nucleon interaction, called v₁₄, that fits the available nucleon-nucleon scattering data up to 425 MeV, and a phenomenological three nucleon interaction adjusted to reproduce the empirical properties of symmetric nuclear matter. The variational many-body theory of symmetric nuclear matter is extended to treat matter with neutron excess. Numerical and analytic studies of the β-dependence of various contributions to the nuclear matter energy show that at ? < 0.35 fm^?3 the β⁴ terms are very small, and that the interaction energy EI(ρ, β) defined as E(ρ, β) ? T_F(ρ, β), where T_F is the Fermi-gas energy, is well approximated by EI₀(?) + β²EI₂(ρ). The calculated symmetry energy at equilibrium density is 30 MeV and it increases from 15 to 38 MeV as ? increases from 0.05 to 0.35 fm^?3.     

Zeeman exchange cross relaxation time TZX1 in BCC3 He

Measurements are reported of T^ZX₁ in BCC³ He whose molar volume dependence is obtained in high accuracy. This dependence is described with an empirical spectral density function different from the often used theoretical one consistently with the thermostatic results.     

Three-body continuum structure and response functions of halo nuclei (I): 6He

Three-body scattering states of the Borromean two-neutron halo nuclei are explored in a core + n + n model using the method of hyperspherical harmonics. We analyse the continuum structure (the properties of the continuum wave functions) separately from the continuum response (the magnitudes of one-step transitions from the ground state to the continuum). Predictions are made for the positions and strengths of the isoscalar monopole, electric dipole and quadrupole excitations, as well as for nuclear inelastic and charge-exchange response functions, for the ⁶He nucleus. The known 2⁺ resonance in ⁶He is reproduced. We find 1⁻ strength concentrations at lower energies in the proximity of the three-body threshold, and predict new 2⁺, 1⁺ (and possibly 0⁺) resonances at slightly higher energies in ⁶He.     

Dynamical treatment of binding,polarization and recoil in asymmetric ion-atom collisions

The cross sections for quenching the lowestn ² P states of the alkali atoms Li, Na, K., and Rb by the inert gases He, Ne, Ar, Kr, and Xe are presented for 5 eV≦E _c.m.≦ 100 eV. These cross sections are derived from the corresponding cross sections for collisional excitation by applying the principle of microreversibility. Upper estimates for the quenching cross sections at thermal energies are given; in all studied cases the quenching cross sections are <8·10^?3Ų. These new upper limits are in most cases much lower than those obtained from other methods previously.     

Correlation effects in the heat capacity of separating 3He-4He solid solutions

We propose to describe the impurity heat capacity of solid ³He-⁴He mixtures both below and above the phase separation temperature T ^s by an extension of the Bethe-Guggenheim approximation for the lattice gas model. It is shown that at T > T _s, the temperature behavior of the heat capacity is completely defined by correlation effects in the impurity subsystem. The developed theory enables us to explain from the common stand-point the experimental data by Edwards, McWilliams, and Daunt for all concentrations of ₄He and make some conclusions about the structure of second phase nuclei.     

Determination ofn-4He observables fromp-4He scattering data between 20 and 55 MeV

We usep-⁴He data to determinen-⁴He observables, i.e. differential cross sections and polarizations, in the energy range between 20 and 55 MeV. Comparison of our calculations with experimental values at 23 MeV shows good agreement. In addition we also present examples of polarizationsT _z,z andT _z,x .     

La NMR and As NQR study of the As-based filled skutterudite LaOs4As12

We report experimental results of nuclear magnetic resonance (NMR) at the La site and nuclear quadrupole resonance (NQR) at the As site in the normal state of the superconducting compound LaOs₄As₁₂. Measurements have been performed on powder sample obtained from high quality single crystals. The temperature dependences of the nuclear spin-lattice relaxation rates, 1/T₁, of ⁷⁵As and ¹³⁹La nuclei were measured. No scaling between them was found indicating a local character of relaxation processes. The relaxation of ⁷⁵As nuclei can consistently be understood in terms of antiferromagnetic spin fluctuations, as deduced from the T-dependence of (1/T₁T)=C/(T−θ)^1/2.     

Is heavy lepton pair production on nuclei really independent of nuclear size?

We investigate the nuclear size dependence of the distribution of massive lepton pairs produced by hadronic beams. Our principle conclusion is that <p ² _T > of the lepton pair should have a substantial and readily observable component from nuclear rescattering even though the nuclear enhancement exponent α(p _T ) lies within present experimental limits. We indicate the relevance of these effects to the study of quark propagation through nuclear matter.     

Sensitivity of cross sections for elastic nucleus-nucleus scattering to halo nucleus density distributions

In order to clear up the sensitivity of the nucleus-nucleus scattering to the nuclear matter distributions in exotic halo nuclei, we have calculated differential cross sections for elastic scattering of the ⁶He and ¹¹Li nuclei on several nuclear targets at the energy of 0.8 GeV/nucleon with different assumed nuclear density distributions in ⁶He and ¹¹Li.     

Finite nuclei to nuclear matter: a leptodermous approach

The 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.     

Clustering aspects of light exotic nuclei

The discovery of light nuclei with neutron halos has opened new perspectives for nuclear structure and a possibility to study genuine few-body aspects of matter. A number of borromean systems where the system is bound but where no binary subsystems are bound, are realized by nature in the context of nuclei,¹¹Li being the nucleus which has had most recent attention. Although a large number of calculations have addressed the detailed structure of the¹¹Li neutron halo, no single model has yet explained all the data presently available. This is in part due to uncertainties in then+⁹Li interaction. For⁶He, also a borromean system, where then+core interaction is known, the best three-body and reaction models succeed in reproducing the data. In the¹¹Li case, a major uncertainty concerns the effect of possible 1s intruder states.     

Thermodynamics of 3He solid monolayers in the Heisenberg model

The two-dimensional Heisenberg model is applied to the interpretation of the experimental data on the thermodynamic and magnetic properties of ³He monoatomic films in the millikelvin temperature range, i.e., under conditions when these properties are completely governed by the dynamics of the nuclear spin subsystem. The theoretical results obtained make it possible to describe the internal energy E, the heat capacity C _s, and the magnetic susceptibility χ of the two-dimensional spin-1/2 Heisenberg ferromagnets and antiferromagnets on a triangular lattice within the unified approach over the entire range of temperatures. The data available in the literature on the heat capacity and magnetic susceptibility of ³He films are interpreted in the framework of the advanced theory. Most attention is concentrated on the layers characterized by the ferromagnetic exchange. Comparative analysis of theoretical and experimental data is carried out with the use of two fitting parameters: the exchange interaction constant J and the number of “active” spins n ₂ in the layer that is determined from the entropy of the system in the limit T → ∞. It is demonstrated that, for the ferromagnetic layers, the theoretical results obtained within the Heisenberg model are in very good agreement with the experimental data reported by different authors.     

rp-process nucleosynthesis at extreme temperature and density conditions

We present nuclear reaction network calculations to investigate the influence of nuclear structure on the rp-process between Ge and Sn in various scenarios. Due to the lack of experimental data for neutron-deficient nuclei in this region, we discuss currently available model predictions for nuclear masses and deformations as well as methods of calculating reaction rates (Hauser-Feshbach) and β-decay rates (QRPA and shell model). In addition, we apply a valence nucleon (N_pN_n) correlation scheme for the prediction of masses and deformations. We also describe the calculations of 2p-capture reactions, which had not been considered before in this mass region. We find that in X-ray bursts 2p-capture reactions accelerate the reaction flow into the Z ≥ 36 region considerably. Therefore, the rp-process in most X-ray bursts does not end in the Z = 32–36 region as previously assumed and overproduction factors of 10⁷–10⁸ are reached for some light p-nuclei in the A = 80–100 region. This might be of interest in respect of the yet unexplained large observed solar system abundances of these nuclei. Nuclei in this region can also be produced via the rp-proces in accretion disks around low mass black holes. Our results indicate that the rp-process energy production in the Z > 32 region cannot be neglected in these scenarios. We discuss in detail the influence of the various nuclear structure input parameters and their current uncertainties on these results. It turns out that rp-process nucleosynthesis is mainly determined by nuclear masses and β-decay rates of nuclei along the proton drip line. We present a detailed list of nuclei for which mass or β-decay rate measurements would be crucial to further constrain the models.