Narrow Results

The influence of the isovector neutron–proton (np) pairing effect on nuclear statistical quantities is studied in N ≈ Z even–even systems. Expressions of the energy, the entropy, and the heat capacity are established using a recently proposed temperature-dependent isovector pairing gap equations. They generalize the conventional finite temperature BCS (FTBCS) ones. The model is first numerically tested using the schematic one-level model. As a second step, realistic cases are considered using the single-particle energies of a deformed Woods–Saxon mean-field. It is shown that: (i) the gap parameter Δ_np(T) behaves like Δ_tt(T), t = n, p, in the conventional FTBCS model and the critical temperature value T_cnp is such as T_cnp<T_cp<T_cn; (ii) the behavior of Δ_tt(T), t = n, p in the present model is different from that of the FTBCS one. This fact leads to a systematic discrepancy between the predictions of both models in the T_cnp<T<T_cn region for all studied statistical quantities; and (iii) in the 0≤T≤T_cnp region, the np pairing effect on the energy is a lowering of about 1%, on average, for all considered nuclei. Dealing with the entropy and the heat capacity, the np pairing effect appears only if the T_cnp value is sufficiently important.

Gap equations at finite temperature are established in the isovector plus isoscalar pairing case $(T=1+T=0)$ using a path integral approach. Expressions of the various statistical quantities, i.e., the energy, the entropy and the heat capacity are then deduced. It is shown that they do generalize the ones obtained in the pure isovector ($T=1$) pairing case, as well as those obtained within the conventional finite temperature Bardeen–Cooper–Schrieffer (FTBCS) theory in the pairing between like-particles case. A numerical study is then performed using the schematic one-level model.

It is shown that the isoscalar n–p gap parameter ${\mathrm{\Delta }}_{np}^{T=0}$ behaves as a function of the temperature, like its homologues ${\mathrm{\Delta }}_{pp}$ and ${\mathrm{\Delta }}_{nn}$ in the conventional FTBCS approach. As for the three other gap parameters, i.e., ${\mathrm{\Delta }}_{np}^{T=1}$, ${\mathrm{\Delta }}_{pp}$ and ${\mathrm{\Delta }}_{nn}$, their behaviors are clearly modified when the isoscalar pairing is taken into account. In particular, one observes a shift of the values of the critical temperatures.

Dealing with the statistical quantities, the inclusion of the isoscalar pairing, in addition to the isovector one, leads to a lowering of the energy as well as a change of the shapes of the curves of the energy, the entropy and the heat capacity as a function of the temperature.

Temperature is an important and commonly used parameter among others to study properties of matter created during high energy collisions of nuclei. Experimental data from JINR and UrQMD (version 3.3p2) model simulations have been used to estimate temperature and other properties of positive pions in collisions of deuteron with carbon nuclei at incident momentum of 4.2GeV/$c$ in this paper. Transverse mass and transverse momentum spectra have been used to get inverse slope parameter/temperature of said particles, with the help of some fitting equations. These equations are referred as Hagedorn Thermodynamic and Boltzmann Distribution functions. Such functions or equations are used to describe particles spectra. Temperature of positive pions has been found to be equal to $104\pm 2$ and $112\pm 2$MeV in experimental and model, respectively, using Hagedorn function. Results from both experimental and model calculations have also been compared with each other and thus most reliable fitting function has been suggested. It is found that Hagedorn Thermodynamic function is the most reliable function to get pions’ temperature in said collision system at given momentum. Similarly, results obtained in this paper have been compared with results from other experiments in the world and worthy conclusions have been reached and reported.

In this paper, we analyzed charged particle transverse momentum spectra in high multiplicity events in proton–proton and nucleus–nucleus collisions at LHC energies from the ALICE experiment using the color string percolation model (CSPM). The color reduction factor and associated string density parameters are extracted for various multiplicity classes in $pp$ collisions and centrality classes for heavy-ion collisions at various LHC energies to study the effect of collision geometry and collision energy. These parameters are used to extract the thermodynamical quantities temperature and the energy density of the hot nuclear matter. A universal scaling is observed in initial temperature when studied as a function of charged particle multiplicity scaled by transverse overlap area. From the measured initial energy density $𝜀$ and the initial temperature T, a dimensionless quantity $𝜀/T^4$ is constructed which is used to obtain the degrees of freedom (DOF) of the deconfined phase. A two-step behavior and a sudden increase in DOF of $\sim$47 for the ideal gas, above the hadronization temperature (T$\approx$ 210MeV), are observed in case of heavy-ion collisions at LHC energies.

An expression for the two-particle relaxation time of collective excitations on a distorted Fermi surface in the diffusion approach to kinetic theory is obtained. The general case of momentum-dependent diffusion and drift coefficients is considered. The temperature dependence of the obtained expression is established.

The nuclear structure and thermal quantities of the superheavy nucleus of ${}^{292}120_{172}$ are studied in a recent developed framework of the Finite-Temperature Hartree–Fock–Bogoliubov (FT-HFB) by using a zero-range pairing and including the continuum effects. Analyzing the shell structure of this nucleus at both zero and finite temperature shows a dependence on the various Skyrme-type forces used and a shell closure occurrence at Z = 120 for protons and N = 172 for neutrons with a large gap energy where the pseudo-spin-orbit effects play a primordial role in the shell sequence at finite temperature which confirm the double magicity of ${}^{292}120_{172}$. Thermodynamic quantities are also studied in the same framework where the results are qualitatively similar to what are obtained in case of the hot ordinary nuclei.

The masses of open bottom mesons ($B$($B^{+}$,$B^0$), $\bar{B}$($B^{-}$,$\overline{B^0}$), $B_s$(${B_s}^0$, $\overline{{B_s}^0}$)) and upsilon states ($\mathrm{{\rm Y}}(1S)$, $\mathrm{{\rm Y}}(2S)$, $\mathrm{{\rm Y}}(3S)$, $\mathrm{{\rm Y}}(4S)$ and $\mathrm{{\rm Y}}(1D)$) are investigated in the isospin asymmetric strange hadronic medium at finite temperature in the presence of strong magnetic fields using a chiral effective Lagrangian approach. Here the chiral SU(3) Lagrangian is generalized to include the bottom sector to incorporate the interactions of the open bottom mesons with the magnetized medium. At finite temperature, the number density and scalar density of baryons are expressed in terms of thermal distribution functions. For charged baryons, the magnetic field introduces contribution from Landau energy levels. The masses of the open bottom mesons get modified through their interactions with the baryons and the scalar mesons, which undergo modifications in a magnetized medium. The charged $B^{+}$, $B^{-}$ mesons have additional positive mass shifts due to Landau quantization in the presence of the magnetic field. The medium mass shift of the upsilon states originates from the modification of the gluon condensates simulated by the variation of dilaton field ($\chi$) and a quark mass term in the magnetized medium. The open bottom mesons and upsilon states experience a mass drop in the magnetized medium. The masses of these mesons initially increase with a rise in temperature, and beyond a high value of temperature, their masses are observed to drop. When the temperature is below 90MeV, the in-medium masses of the mesons increase with an increase in the magnetic field. However, at high temperatures (T > 90 MeV), the masses are observed to drop with an increase in the magnetic field. These in-medium modifications can have observable effects in asymmetric heavy-ion collisions experiments.

The shape evolution and potential energy surfaces of even–even ${}^{220-240}$Ra are investigated in the $({\beta }_2,{\beta }_3)$ plane by the covariant density functional theory. For octupole-deformed ${}^{222}$Ra, the free energy surfaces, the deformations, the pairing gaps, the excitation energy as well as the specific heat with increasing temperature are analyzed. Based on the specific heat, ${}^{222}$Ra exhibits three distinct discontinuities as the temperature rises. The first pairing transition occurs at $T=0.45$MeV, while the second one happens at $T=0.65$MeV when octupole deformation disappears, and the third one takes place at $T=0.80$MeV as quadrupole deformation approaches zero. The gaps at $N=132,136$ and $Z=88$ in the single-particle levels are responsible for the octupole global minima. The shape transitions not only occur between even–even ${}^{220-240}$Ra, but also occur with increasing temperature for ${}^{222}$Ra.

Higher-order approximation based on Taylor expansion over the saddle point is employed to approach the partition function of a hot nucleus in the presence of the like-particle pairing correlations. Analytical expressions have been derived for the correction terms of different thermodynamic quantities such as energy, entropy and heat capacity. Furthermore, the theory has been applied to the schematic and realistic models. It is found that the correction terms are temperature-dependent functions and are more deeply sensitive to the pairing gap in the vicinity of the critical temperature.

In this paper, we investigate the masses of the pseudoscalar ($D$($D^0$, $D^{+}$), $\bar{D}$($\overline{D^0}$, $D^{-}$) and vector open charm mesons ($D^{\ast }$($D^{\ast 0}$, $D^{\ast +}$), ${\bar{D}}^{\ast }$(${\bar{D}}^{\ast 0}$, $D^{\ast -}$) as well as the pseudoscalar (${\eta }_c(1S)$, ${\eta }_c(2S)$) and the vector charmonium states ($J∕\psi$, $\psi (2S)$, $\psi (1D)$) in the asymmetric hot strange hadronic medium in the presence of strong magnetic fields. In the magnetized medium, the mass modification of open charm mesons due to their interactions with baryons and the scalar fields ($\sigma$, $\zeta$, and $\delta$) is investigated in a chiral effective model. Moreover, the charged pseudoscalar meson ($D^{\pm }$), as well as the longitudinal component of charged vector meson ($D^{\ast \pm \parallel }$), experience additional positive mass modifications in the magnetic field due to Landau quantization. The effect of the modification of gluon condensates simulated by the medium change of dilaton field $\chi$ on the masses of the charmonia is also calculated in the chiral effective model. The contribution of masses of light quarks is also considered in the modification of gluon condensates. At high temperatures, the magnetically induced modifications of scalar fields significantly reduce the in-medium masses of mesons. The effects of magnetically induced spin mixing between the pseudoscalar and the corresponding vector mesons are incorporated in our study through a phenomenological effective Lagrangian interaction. The spin mixing result in a positive mass shift for the longitudinal component of the vector mesons and a negative mass shift for the pseudoscalar mesons in the presence of the magnetic field. From the obtained in-medium masses of charmonia and open charm mesons, we have also calculated the partial decay widths of $\psi (1D)$ to $D\bar{D}$, using a light quark pair creation model, namely, the ${}^3{P}_0$ model.

The emission angular distributions, the transverse momentum distributions and the temperature parameters of projectile fragments produced in fragmentation of ${}^{28}$Si on C target at 736AMeV are measured. It is found that the scattering angle of primary silicon ions is smaller than the emission angle of their fragments. The average value and the width of the angular distribution and the transverse momentum distribution are increased with the decrease of the charge of projectile fragments. The cumulative squared transverse momentum distribution of projectile fragments can be well fitted by a single Rayleigh distribution, which indicates that the projectile fragments are emitted from a single temperature emission source. Most of the temperature parameters of projectile fragments emission source are in the range of 2–5MeV, which does not obviously depend on the charge of the projectile fragments.