1. Introduction

Neutron stars are among the densest known objects in the universe, withstanding pressures of the order of 10<sup>34</sup>Pa: However, it turns out that protons [1], the fundamental particles that make up most of the visible matter in the universe, contain pressures 10 times greater, [2, 3] 10<sup>35</sup>Pa: This has been verified from two perspectives at the Jefferson Laboratory, MIT [1–5]. High-energy physics continue to guide the study of the mechanical properties of the subatomic world.

Viscosity is a characteristic physical property of all fluids, which emerges from collisions between fluid particles moving at different speeds, causing resistance to their movement (Figure 1). When a fluid is forced to move by a closed surface, similar to the atomic nucleus, the particles that make up the fluid move slower in the center and faster on the walls of the sphere. Therefore, a shear stress (such as a pressure difference) is necessary to overcome the friction resistance between the

are required to accept as valid a solution to the Navier–Stokes 3D Equation [16–18]. An understanding of the mechanics of the atomic nucleus cannot do without fluid

Exergy: Mechanical Nuclear Physics Measures Pressure, Viscosity and X-Ray Resonance…

where P xð Þ , <sup>y</sup>, <sup>z</sup>, <sup>t</sup> is the logistic probability function P xð Þ¼ , <sup>y</sup>, <sup>z</sup>, <sup>t</sup> <sup>1</sup>

analyze the dynamics of an incompressible fluid [12–14].

<sup>þ</sup> ð Þ <sup>u</sup>:<sup>∇</sup> <sup>u</sup> <sup>¼</sup> <sup>ν</sup>∇<sup>2</sup>

Where speed u<sup>0</sup> must be C<sup>∞</sup> divergence-free vector.

�≤CαKð Þ <sup>1</sup> <sup>þ</sup> <sup>r</sup> �<sup>K</sup>

and the finite energy condition [14–16].

Nuclear reaction velocity coefficient.

expected value E rð Þ <sup>j</sup>r≥<sup>0</sup> <sup>&</sup>lt;<sup>C</sup> exist. The term <sup>P</sup> is defined in ð Þ <sup>x</sup>, <sup>y</sup>, <sup>z</sup> <sup>∈</sup> <sup>3</sup>

<sup>u</sup> � <sup>∇</sup><sup>p</sup> ρ0

viscosity, <sup>ν</sup> cinematic viscosity, and pressure <sup>p</sup> <sup>¼</sup> <sup>p</sup>0<sup>P</sup> in ð Þ <sup>x</sup>, <sup>y</sup>, <sup>z</sup> <sup>∈</sup> <sup>3</sup>

where constants k>0, μ>0 and P xð Þ , y, x, t is the general solution of the Navier– Stokes 3D equation, which has to satisfy the conditions (1) and (2), allowing us to

With, u∈ <sup>3</sup> an known velocity vector, ρ<sup>0</sup> constant density of fluid, η dynamic

Where velocity and pressure are depending of r and t. We will write the

<sup>∇</sup>:<sup>u</sup> <sup>¼</sup> <sup>0</sup> ð Þ <sup>x</sup>, <sup>y</sup>, <sup>z</sup> <sup>∈</sup> <sup>3</sup>

as <sup>r</sup> ! <sup>∞</sup>: We will restrict attention to initial conditions <sup>u</sup><sup>0</sup> that satisfy.

The initial conditions of fluid movement <sup>u</sup><sup>0</sup>ð Þ <sup>x</sup>, <sup>y</sup>, <sup>z</sup> , are determined for <sup>t</sup> <sup>¼</sup> 0.

For physically reasonable solutions, we make sure uð Þ x, y, z, t does not grow large

The Clay Institute accepts a physically reasonable solution of (1), (2) and (3),

The problems of Mathematical Physics are solved by the Nature, guiding the understanding, the scope, the limitations and the complementary theories. These guidelines of this research were: the probabilistic elements of Quantum Mechanics,

the De Broglie equation and the Heisenberg Uncertainty principle.

<sup>u</sup>ð Þ¼ <sup>x</sup>, <sup>y</sup>, <sup>z</sup>, 0 <sup>u</sup><sup>0</sup>ð Þ <sup>x</sup>, <sup>y</sup>, <sup>z</sup> ð Þ <sup>x</sup>, <sup>y</sup>, <sup>z</sup> <sup>∈</sup> <sup>3</sup> � � (3)

<sup>P</sup> , with a radius noted as <sup>r</sup> <sup>¼</sup> <sup>x</sup><sup>2</sup> <sup>þ</sup> <sup>y</sup><sup>2</sup> <sup>þ</sup> <sup>z</sup><sup>2</sup> ð Þ1=<sup>2</sup>

ð Þ <sup>x</sup>, <sup>y</sup>, <sup>z</sup> <sup>∈</sup> <sup>3</sup>

<sup>1</sup>þekt�μ<sup>r</sup> , and the

, t≥0 � �,

, t≥ 0 � � (1)

, t≥ 0 � �.

, t ≥0 � � (2)

on <sup>3</sup> for anyαandK (4)

<sup>p</sup>, <sup>u</sup>∈C<sup>∞</sup> <sup>3</sup> � 0, <sup>∞</sup> � �<sup>Þ</sup> (5)

dxdydz ≤C for all t≥ 0 bounded energy � �: (6)

equations.

2. Model

The velocity defined as <sup>u</sup> ¼ �2<sup>ν</sup> <sup>∇</sup><sup>P</sup>

DOI: http://dx.doi.org/10.5772/intechopen.95405

∂u ∂t

condition of incompressibility.

∂α xu<sup>0</sup> � � �

j j <sup>u</sup>ð Þ <sup>x</sup>, <sup>y</sup>, <sup>z</sup>, <sup>t</sup> <sup>2</sup>

only if it satisfies:

ð 3

2.1 Definitions

25

#### Figure 1.

Obtaining nuclear viscosity and nuclear pressure from the speed of the neutron particles in the disintegration of chemical element. Figure 1a. indicates that the BE=A ratio is proportional to the nuclear pressure, p<sup>0</sup> represented in Figure 1b. Figure 1c is the graph of the viscosity in equilibrium and out of equilibrium, the viscosity in equilibrium is greater than the viscosity at the moment of nuclear decay. Figure 1d is the average half-time of each isotope, 9≤Z ≤92 and 9≤ N ≤200:

layers of the nuclear fluid. For the same radial velocity profile, the required tension is proportional to the viscosity of the nuclear fluid or its composition given by ð Þ Z, N [6–8].

Radioactive decay is a stochastic process, at the level of individual atoms. According to quantum theory, it is impossible to predict when a particular atom will decay, regardless of how long the atom has existed. However, for a collection of atoms of the same type [8], the expected decay rate is characterized in terms of its decay constant <sup>k</sup> <sup>¼</sup> <sup>1</sup> T1=<sup>2</sup> . The half-lives of radioactive atoms do not have a known upper limit, since it covers a time range of more than 55 orders of magnitude, from almost instantaneous to much longer than the age of the universe [8, 9].

Other characteristics of the proton such as its size have been studied in many institutes such as Max Plank, where it has been measured with high precision ranges rp <sup>¼</sup> <sup>0</sup>:84184 67 ð Þfm , providing new research methods [10, 11].

The atomic nucleus is an incompressible fluid, justified by the formula of the nuclear radius, <sup>R</sup> <sup>¼</sup> <sup>1</sup>:2A<sup>1</sup> 3, where it is evident that the volume of the atomic nucleus changes linearly with A ¼ Z þ N, giving a density constant [11]. All incompressible fluid and especially the atomic nucleus comply with the Navier Stokes equations. We present a rigorous demonstration on the incomprehensibility of the atomic nucleus, which allows to write explicitly the form of the nuclear force F<sup>N</sup> ¼

� <sup>g</sup>μ<sup>2</sup> <sup>8</sup><sup>π</sup> ð Þ A � 1 Pð Þ 1 � P ∇r, which facilitates the understanding of nuclear decay.

The Navier Stokes equations are a problem of the millennium [12, 13], that has not been resolved yet in a generalized manner. We present a solution that logically meets all the requirements established by the Clay Foundation [14, 15]. This solution coherently explains the incompressible nuclear fluid and allows calculations of the nuclear viscosity and nuclear pressure [1, 2].

The alpha particle is one of the most stable. Therefore it is believed that it can exist as such in the heavy core structure. The kinetic energy typical of the alpha particles resulting from the decay is in the order of 5 MeV.

For our demonstrations, we will use strictly the scheme presented by Fefferman in http://www.claymath.org/millennium-problems [13, 14], where six demonstrations Exergy: Mechanical Nuclear Physics Measures Pressure, Viscosity and X-Ray Resonance… DOI: http://dx.doi.org/10.5772/intechopen.95405

are required to accept as valid a solution to the Navier–Stokes 3D Equation [16–18]. An understanding of the mechanics of the atomic nucleus cannot do without fluid equations.
