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The study of properties of nuclei under extreme conditions of temperature and density has been the subject of many investigations in recent decades, since they are very important in the study of the process of supernovae, neutron stars and nuclei. Heavy-ion collision experiments are often employed to determine these properties. We present a short and limited review of the theoretical and experimental status of determining the temperature and density of the disassembling hot nucleus from ratios of the yields of emitted fragments.

The multipole response of nuclei at temperatures T = 0 − 2 MeV is studied using a self-consistent finite-temperature RPA (random phase approximation) based on relativistic energy density functionals. Illustrative calculations are performed for the isoscalar monopole and isovector dipole modes and, in particular, the evolution of low-energy excitations with temperature is analyzed, including the modification of pygmy structures. Both for the monopole and dipole modes, in the temperature range T = 1 −2 MeV additional transition strength appears at low energies because of thermal unblocking of single-particle orbitals close to the Fermi level. A concentration of dipole strength around 10 MeV excitation energy is predicted in 60,62 Ni, where no low-energy excitations occur at zero temperature. The principal effect of finite temperature on low-energy strength that is already present at zero temperature, e.g. in 68 Ni and 132 Sn, is the spreading of this structure to even lower energy and the appearance of states that correspond to thermally unblocked transitions.

The problem of the damping of the Giant Dipole Resonance (GDR) at finite temperature at T>2 MeV is discussed here. The experimental results are based on fusion evaporation reactions. The most recent results on the mass region A = 132 ( Ce isotopes) obtained in exclusive measurements are compared with the existing results on the A = 110–120 region ( Sn isotopes). The comparison with the theoretical predictions based on thermal shape fluctuations is also discussed. The GDR width is found to increase also in the region T>2 MeV and this is accounted by the combined effect of the increase of the compound nucleus width (smaller lifetime) and to the increase of the average deformation of the nucleus.

The reactions Kr-84+Au-197 and Kr-84+U-nat were studied at an incident energy of E/A = 150 MeV employing the large-volume neutron multiplicity meter ORION, The observed correlations between the atomic number of projectile-like nuclei (PLN) and neutron multiplicity indicate large deposits of excitation energies in the primary fragments, Angular correlations between fragments from the fission of target-like nuclei (TLN) and secondary PLN show a memory of the reaction plane. No indications for spin effects were found in the TLN-fission fragment distribution.

The thermal evolution of the energies and free energies of a set of spherical and near-spherical nuclei spanning the whole periodic table are calculated in the subtracted finite-temperature Thomas- Fermi framework with the zero-range Skyrme-type KDE0 and the finite-range modified Seyler-Blanchard interaction. The calculated energies are subjected to a global fit in the spirit of the liquid-drop model. The extracted parameters in this model reflect the temperature dependence of the volume symmetry and surface symmetry coefficients of finite nuclei, in addition to that of the volume and surface energy coefficients. The temperature dependence of the surface symmetry energy is found to be very substantial whereas that of the volume symmetry energy turns out to be comparatively mild., Comment: 6 page including 5 figures, Phys. Lett. B (in press)

Gamma-ray energy spectra have been measured for the 16 O + 118 Sn reaction at incident beam energies of 200 and 280 MeV. Comparing the experimentally obtained spectra with statistical-model calculations shows that the width of the isovector giant dipole resonance saturates beyond excitation energies of 165 MeV in the compound nucleus.

The relativistic random phase approximation based on effective Lagrangian with density dependent meson-nucleon couplings has been extended to finite temperature and employed in studies of multipole excitations within the temperature range T = 1 − 2 MeV. The model calculations showed that isoscalar giant monopole and isovector giant dipole resonances are only slightly modified with temperature, but additional transition strength appears at low energies because of thermal unblocking of single-particle orbitals close to the Fermi level. The analysis of low-lying states shows that isoscalar monopole response in 132Sn results from single particle transitions, while the isovector dipole strength for 60Ni, located around 10 MeV, is composed of several single particle transitions, accumulating a small degree of collectivity.

Measured hard photon multiplicities from second-chance nucleon-nucleon collisions are used in combination with a kinetic thermal model, to estimate the break-up times of excited nuclear systems produced in nucleus-nucleus reactions at intermediate energies. The obtained nuclear break-up time for the $^{129}${Xe} + $^{nat}${Sn} reaction at 50{\it A} MeV is $\Delta$$\tau$ $\approx$ 100 -- 300 fm/$c$ for all reaction centralities. The lifetime of the radiating sources produced in seven other different heavy-ion reactions studied by the TAPS experiment are consistent with $\Delta$$\tau$ $\approx$ 100 fm/$c$, such relatively long thermal photon emission times do not support the interpretation of nuclear breakup as due to a fast spinodal process for the heavy nuclear systems studied., Comment: 11 pages, 9 figures, submitted to EPJA

The fragment yields from the multifragmentation of gold, lanthanum and krypton nuclei obtained by the EOS Collaboration are examined in terms of Fisher's droplet formalism modifed to account for Coulomb energy. The critical exponents sigma and tau and the surface energy coefficient c0 are obtained. Estimates are made of the pressure-temperature and temperature-density coexistence curves of finite neutral nuclear matter as well as the location of the critical point., Comment: 14 pages, 13 figures, 6 tables, submitted to Phys. Rev. C

The reactions Kr-84+Au-197 and Kr-84+U-nat were studied at an incident energy of E/A = 150 MeV employing the large-volume neutron multiplicity meter ORION, The observed correlations between the atomic number of projectile-like nuclei (PLN) and neutron multiplicity indicate large deposits of excitation energies in the primary fragments, Angular correlations between fragments from the fission of target-like nuclei (TLN) and secondary PLN show a memory of the reaction plane. No indications for spin effects were found in the TLN-fission fragment distribution.

The violence of collisions induced by Pb-208 projectiles bombarding a Au-197 target at 29 MeV/u has been deduced by detecting the accompanying neutrons. With this filter, the temperature of the projectile-like fragments formed in very dissipative collisions has been extracted from the slope of the alpha-particle energy spectra. Temperatures of the order of 7 MeV are found, in very good agreement with the energy dissipations deduced from an energy balance assuming binary kinematics. The associated neutron multiplicities are well reproduced by a standard evaporation model, despite the dissociation into intermediate mass fragments observed in previous experiments. However, the measured temperatures exceed by a significant amount the limits predicted by theoretical calculations.

Photon emission in proton-induced reactions at 50 MeV with In-115 was studied. Analyses of the measured photon spectrum show that the GDR couples to the compound states as well as to pre-equilibrium states. The centroid and width of the GDR strength function were determined as E(GDR) = 15.4 +/- 0.7 MeV and GAMMA(GDR) = 6.2 +/- 0.5 MeV. From the measured gamma-ray yield above E(gamma) = 30 MeV, a value of (7.1 +/- 1.4) x 10(-5) for the hard-photon emission probability per single proton-neutron collision is inferred.

The measured properties of the Giant Dipole Resonance in hot rotating nuclei are successfully described with the model of thermal fluctuations, even though there are still some open problems especially at very low (T < 1.2MeV), very high (T > 2.5MeV) temperatures and missing data in some mass regions. Recent experimental works have addressed more specific problems regarding the nuclear shape and its behaviour in very particular and delimited phase space regions. In this paper will be discussed new exclusive measurements of the GDR decay in heavy 216Rn nuclei (where the shape of nuclei surviving fission have been probed) and some preliminary data on the 132Ce nuclei at very high excitation energy.

The fully self-consistent finite temperature relativistic random phase approximation (FTRRPA) has been established in the single-nucleon basis of the temperature dependent Dirac- Hartree model (FTDH) based on effective Lagrangian with density dependent meson-nucleon couplings. Illustrative calculations in the FTRRPA framework show the evolution of multipole responses of 132Sn with temperature. With increased temperature, in both monopole and dipole strength distributions additional transitions appear in the low energy region due to the new opened particle-particle and hole-hole transition channels.