Nucleons and electrons

Another difference between nucleons and electrons is that nucleons pair whenever possible. Thus, even if a particular energy level can hold more than two particles, two particles will pair when they are present. Thus, for two particles in degenerate levels, we show two particles as II rather than II. As a result of this preference for pairing, nuclei with even numbers of protons and neutrons have all paired particles. This results in nuclei that are more stable than those which have unpaired particles. The least stable nuclei are those in which both the number of neutrons and the number of protons is odd. This difference in stability manifests itself in the number of stable nuclei of each type. Table 1.3 shows the numbers of stable nuclei that occur. The data show that there does not seem to be any appreciable difference in stability when the number of protons or neutrons is even while the other is odd (the even-odd and odd-even cases). The number of nuclides that have odd Z and odd N (so-called odd-odd nuclides) is very small, which indicates that there is an inherent instability in such an arrangement. The most common stable nucleus which is of the odd-odd type is 147N. 

The internal energy is sometimes called chemical energy because it is the consequence of all the motions of particles and forces between particles molecules, atoms, nucleons, and electrons. 

Table 1 Mass, charge, and energies of nucleons and electrons...

Matter is composed of atoms. An atom consists of a nucleus containing protons (Z) and neutrons (N), collectively called nucleons, and electrons rotating around the nucleus. The sum of neutrons and protons (total number of nucleons) is the mass number denoted by A. The properties of neutrons, protons, and electrons are listed in Table 1.1. The number of electrons in an atom is equal to the number of protons (atomic number Z) in the nucleus. The electrons rotate along different energy shells designated as A -shcll, L-shell, M-shell, etc. (Fig. 1.1). Each shell further consists of subshells or orbitals, e.g., the L-shell has s orbital the L-shell has s and p orbitals the M-shell has s, p, and d orbitals, and the A-shell has s, p, d, and / orbitals. Each orbital can accommodate only a limited number of electrons. For example, the s orbital contains up to 2 electrons the p orbital, 6 electrons the d orbital, 10 electrons and the / orbital, 14 electrons. The capacity number of electrons in each orbital adds up to give the maximum number of electrons that each energy shell can hold. Thus, the L-shell contains 2 electrons the L-shell 8 electrons, the M-shell 18 electrons, and so forth. 

The standard model of the electroweak interaction introduces an effective interaction between nucleons and electrons which violates parity-reversal symmetry. This P-odd interaction, Hp, is given by... 

For instance, in the Hamiltonian 2.1, it is assumed that whatever might happen to our system, the numbers of the nucleons and electrons will remain constant. 

The wavelength of an electron is larger than its radius, while the wavelength of the baseball is insignificant compared with the size of the ball. Therefore, the wavelike nature of matter is only important for extremely small objects, such as atoms, nucleons, and electrons. 

In most cases the emission of nucleons and electrons leads to an excited state of the resulting new nucleus. The excitation energy is given off in the form of one or several gamma-ray photons. In most cases this de-excitation takes place within an extremely short period of time (less than 10 s) but in some cases this transition is delayed. Such a type is called an isomeric state of a nuclide. 

In the following paragraphs we shall start with the so-called elementary particles (not so elementary since there are quite a few of them and there is a whole chemistry of their reactions and disintegrations), and recall how some of the most stable (nucleons and electrons) build up a few scores of atoms, which constitute a kind of alphabet that makes up all usual matter on earth. Then we shall recall how some of the molecules (sentences) built up with a few of these atoms (letters) constitute a higher-level alphabet which makes up all molecules of life (paragraphs). These molecules assemble in cells (chapters), tissues, organisms (books), species, and ecosystems (libraries). 

The difference between the sum of the masses of the nucleons and electrons in an atom and the actual mass of an atom is the mass defect, or nuclear binding energy. 

It is possible to correlate the molecular electronic states with the states of the separated atoms and independently, with the united atom having the same number of nucleons and electrons as the molecule. This correlation proceeds according to the Wigner-Witmer rules.and will be outlined in Appendix C. 

Second Quantized Description of a System of Noninteracting Spin Particles.—All the spin particles discovered thus far in nature have the property that particles and antiparticles are distinct from one another. In fact there operates in nature conservation laws (besides charge conservation) which prevent such a particle from turning into its antiparticle. These laws operate independently for light particles (leptons) and heavy particles (baryons). For the light fermions, i.e., the leptons neutrinos, muons, and electrons, the conservation law is that of leptons, requiring that the number of leptons minus the number of antileptons is conserved in any process. For the baryons (nucleons, A, E, and S hyperons) the conservation law is the... 

Table 2. Magnetic interaction energies /

We consider a system made up of N fermions (nucleons or electrons) interacting through two-body forces and with an external field, with respective potentials >(r,r ) and V(r). We assume there exists a possibility of decomposing the one-particle density matrix into an averaged part and an oscillating part, i.e. ... 

The atom as an ultimate and indivisible particle of matter was a venerable and a viable scientific notion for many years before and after Daltoa For example, Newton s speculations about matter in the Queries at the end of his Opticks included Particles so very hard, as never to wear or break in pieces no ordinary Power being able to divide what God himself made one in the first Creation (Newton, I. Opticks, London, 1704 Query 31). This chapter describes ideas and scientific evidence from the late 19 and early 20 centuries about the contrary notion, the divisibility of atoms. It is about the notion that the ultimate pieces of matter themselves have pieces. It focuses on the electron and the nucleus, with a few words about the proton and neutron as well it does not treat constituent pieces of nucleons and more exotic particles. 

The Nuclear Force. The nuclear forces and the interactions between pions and nucleons are strong the electron-electron and electron-photon interactions are electromagnetic the beta decay interactions are weak... 

Note how the nuclear equation for the radioactive decay of uranium-238 is written. The equation is not balanced in the usual chemical sense because the kinds of nuclei are not the same on both sides of the arrow. Instead, a nuclear equation is balanced when the sums of the nucleons are the same on both sides of the equation and when the sums of the charges on the nuclei and any elementary particles (protons, neutrons, and electrons) are the same on both sides. In the decay of 2 U to give He and 2 oTh, for example, there are 238 nucleons and 92 nuclear charges on both sides of the nuclear equation. 

Besides the photon-electron interactions, it will be assumed that the main phenomenon, that is taking place in the cesium cell, is an electron-cesium atom interaction. This interaction is assumed to be the result of the existence of STC around nucleons and atoms [5,16]. The momentum pstc will express the presence of STC around cesium atoms. 

Vertex B. Electron with momentum /v/.i interacts with momentum pstc- An important assumption is made here. It has already been mentioned that in Ref. 5 the possibility for existence of STC around nucleons and atoms is predicted, and elaborated on in Ref. 16. It is assumed that in the electron-cesium atom interactions, distortion of the STC around the atom is taking place. As a result of this STC distortion, the momentum Pstc is created, which is added to the electron momentum. The resultant momentum of the electron then will be pes = Pek +psic- As a result of STC distortion, the electron will be in motion with faster than light speed in the STC between cesium atoms. Hence, at the vertex B, the superluminal process is taking place. 

What is the loss of mass per nucleon for the HFe atom, compared with its component protons, neutrons, and electrons ... 

Nuclear binding energy This is the energy needed to disassemble a nucleus into its component nucleons, and is an important demonstration of Einstein s formula. It can best be understood by considering the nucleus 12C. The atomic mass unit, by being defined as i/l2th of the 12C atomic mass, causes A for 12C to be identically equal to zero thatis, A(12C) = o. But the 12C atom is assembled from six H atoms (sixprotons with their six electrons) and six neutrons, each of which is more massive than mu. Their atomic mass excesses are... 

In order to use the perturbation theory it is necessary that the state vectors in the matrix element Eq. (8) belong to the spectrum of the unperturbed Hamiltonian H0 only. However, this is usually not so, since, in p decay, the initial particles are not the same as the final products of the reaction the initial molecule containing the radioactive atom transforms into a different molecule besides, the ft electron and the neutrino appear. One of the ways to describe the initial and final states using only the H0 Hamiltonian is to use the isotopic spin formalism for both the nucleons and the leptons (/ electron and neutrino). In the appendix (Section V) we present the wave functions of the initial and the final states together with the necessary transformations, which one can use to factorize the initial matrix element Eq. (8) into the intranuclear and the molecular parts. Here we briefly discuss only the approximations necessary for performing such a factorization. 

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