# Properties of Hot Nuclear Matter

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Nuclear Hamiltonian

^{3}He and

^{4}He and the empirical equilibrium density of isospin-symmetric matter—such as the widely used Urbana IX (UIX) model [16,17]—have been shown to possess a remarkable predictive power. The results of Quantum Monte Carlo (QMC) calculations, extensively reviewed in Ref. [18], demonstrate that the AV18 + UIX Hamiltonian is capable of describing the energies of the ground and low-lying excited states of nuclei with mass number $A\le 8$ with an accuracy within a few percent.

#### 2.1. Renormalisation of the Nucleon–Nucleon Interaction

#### 2.2. The CBF Effective Interaction

## 3. Many-Body Perturbation Theory at Finite Temperature

#### 3.1. Perturbative Expansion

#### 3.2. Thermodynamic Consistency

## 4. Equilibrium Properties of Hot Nuclear Matter

## 5. Thermal Effects on Nuclear Matter Properties

#### Charge-Neutral $\beta $-Stable Matter at Finite Temperature

## 6. Bulk Viscosity of Neutron Star Matter

#### 6.1. Dissipative Processes in Fluids

#### 6.2. Bulk Viscosity of $\beta $-Stable Matter

#### 6.3. Calculation of the Bulk Viscosity Coefficient

## 7. Discussion

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Note

1 | In this article, we adopt the system of natural units, in which $\hslash =c={k}_{B}=1$, and, unless otherwise specified, neglect the small proton–neutron mass difference. |

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**Figure 1.**Radial dependence of the CBF effective potential in the spin–isospin $S=0$, $T=1$ channel. The solid, dashed, and dot-dash lines correspond to baryon number densities $\varrho =$ 0.04, 0.32, and 0.48 ${\mathrm{fm}}^{-3}$. For comparison, the thick solid line shows the bare AV6P potential.

**Figure 2.**Density and temperature dependence of the free energy per nucleon of SNM (

**A**) and PNM (

**B**), computed using Equations (30)–(37), with the CBF effective interaction discussed in Section 2.2.

**Figure 3.**Density dependence of the proton fraction in charge-neutral $\beta $-stable matter. Solid lines marked with triangles and circles correspond to $npe\mu $ matter at $T=$ 0 and 50 MeV, respectively. The same quantities in $npe$ matter are represented by dashed lines. From Ref. [14].

**Figure 4.**Momentum dependence of the proton spectrum in charge-neutral $\beta $-stable matter at baryon density $\varrho =2{\varrho}_{0}$ and temperature $T=0$ (

**A**) and 50 MeV (

**B**). The solid and dashed lines represent the results of full microscopic calculations and the approximation of Equation (41), respectively. The open circles in panel (

**B**) have been obtained using the quadratic approximation with ${m}_{0}^{\u2605}$ replaced by the effective mass computed at $T=50$ MeV.

**Figure 5.**Density dependence of the bulk viscosity coefficient of $\beta $-stable matter associated with a density fluctuation of frequency $\omega =2\pi \times 1\phantom{\rule{4pt}{0ex}}\mathrm{kHz}$. The results were obtained by performing the derivatives of Equation (60) using both the isothermal (solid lines and open circles) and adiabatic (dashed lines) definitions. The labels specify the temperature in units of MeV.

**Figure 6.**Temperature dependence of the bulk viscosity coefficient $\zeta $ corresponding to $\omega \phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}2\pi \times \phantom{\rule{3.33333pt}{0ex}}1\phantom{\rule{4pt}{0ex}}\mathrm{kHz}$ and different densities.

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**MDPI and ACS Style**

Benhar, O.; Lovato, A.; Tonetto, L.
Properties of Hot Nuclear Matter. *Universe* **2023**, *9*, 345.
https://doi.org/10.3390/universe9080345

**AMA Style**

Benhar O, Lovato A, Tonetto L.
Properties of Hot Nuclear Matter. *Universe*. 2023; 9(8):345.
https://doi.org/10.3390/universe9080345

**Chicago/Turabian Style**

Benhar, Omar, Alessandro Lovato, and Lucas Tonetto.
2023. "Properties of Hot Nuclear Matter" *Universe* 9, no. 8: 345.
https://doi.org/10.3390/universe9080345