Nucleons defined

As we have noted, nuclear binding energy is an indication of the stability of a nucleus. However, in comparing the stability of any two nuclei we must account for the fact that they have different numbers of nucleons. For this reason it is more meaningful to use the nuclear binding energy per nucleon, defined as... 

The proposed (Manuel et al., 2006) nuclear cycle that powers the cosmos has many elements in common with some of our arguments. Not unlike the periodic model of stable nuclides and the notion of cosmic self-similarity these authors suggest that stars are subject to the same types of interaction that occur in radioactive nuclides, which depend on the relative amounts of nucleons defined by the numbers A, Z and N. Because of chemical layering an accumulation of neutrons that resembles a neutron star develops at the core of an ordinary star. This core is left behind as the remains of a supernova. 

Moreover, for monoenergetic heavy ions of the same energy per nucleon, the average number of ion pairs increases with a corresponding decrease in the deviation about the mean, so we have a higher modal value with a more sharply defined Bragg peak. 

The number of nucleons is equal to the sum of the number of protons (Z = atomic number) and number of neutrons (N) in the nucleus and is defined as the mass number (A = nucleon number)... 

In many tabulations of nuclear properties, such as that in Appendix B, the quantity that is tabulated is the mass excess or mass defect rather than the mass. The mass excess, A, is defined as M(A, Z) — A, usually given in units of the energy equivalent of mass. Since in most, if not all calculations, the number of nucleons will remain constant, the use of mass excesses in the calculations will introduce an arithmetic simplification. Another term that is sometimes used is the mass excess per nucleon or the packing fraction [=(M — A)/A]. 

Extending these ideas to nucleons, we can define the nuclear magneton, pN as (eh /2mp), which has the numerical value of 3.15 x 10-8 eV/tesla or... 

As we have seen, the nucleons reside in well-defined orbitals in the nucleus that can be understood in a relatively simple quantum mechanical model, the shell model. In this model, the properties of the nucleus are dominated by the wave functions of the one or two unpaired nucleons. Notice that the bulk of the nucleons, which may even number in the hundreds, only contribute to the overall central potential. These core nucleons cannot be ignored in reality and they give rise to large-scale, macroscopic behavior of the nucleus that is very different from the behavior of single particles. There are two important collective motions of the nucleus that we have already mentioned that we should address collective or overall rotation of deformed nuclei and vibrations of the nuclear shape about a spherical ground-state shape. 

The concept of the vectorial coupling of quasispin momenta was first applied to the nucleus to study the short-range pairing nucleonic interaction [117]. For interactions of that type the quasispin of the system is a sufficiently good quantum number. In atoms there is no such interaction - the electrons are acted upon by electrostatic repulsion forces, for which the quasispin quantum number is not conserved. Therefore, in general, the Hamiltonian matrix defined in the basis of wave functions (17.56) is essentially non-diagonal. 

For an additional degree of freedom of a particle that defines one of the two possible states in which it exists, we shall apply now the concept of isospin (in analogy with the theory of the nucleus where the isospin doublet includes protons and neutrons, which are treated as two states of the same particle - the nucleon [122]). For a pair of states (a,/ ) we introduce the isospin operators... 

The approximation we explore is the one in which among all correlated pairs appearing in the commutators like (17)> we retain only one pair for each multipolarity, i.e. the collective pair which defines the collective subspace. This approximation appears consistent with the assumption,aiready implicit in the choice of the basis states, that only these pairs are essential for a description of the low-lying nuclear states. The important advantage of this approximation is that recursion formulas of the type (lU), in the case of nucleons moving in many j-orbits, become as easy to use as those in single j-orbit. 

Although there are particles not used here, the basic particles listed in Table 21-1 can be used to define and illustrate the concepts presented. Note that the proton and neutron are referred to as nucleons. The masses in Table 21-1 are presented in atomic mass units (u, Chapter 2) and their charges are expressed in multiples of the elementary charge (1.6022 x 10 19 C, Chapter 19). Note that the neutron has slightly more mass than the proton. Also, the mass of the electron is considered to be 1/1836 that of a proton or, if you prefer, the mass of 1 proton is 1836 times that of an electron. 

These three different types of natural isomers are present in the respective percentages of 99.76%, 0.04%, and 0.2%. Despite this difference in the number of nucleons, the number of electrons (e ) rotating around the nucleus is always eight, The e rotates in five different orbitals represented as IS, 2S, and 2Pz that each contain a couple of e", and as 2PX and 2Py that each contain one e only, Since every element that has a single e (unpaired) in an orbital is defined as a free radical, O by definition is a biradical,... 

Details of the elemental and neutron periodicities follow directly as subsets of the 24-fold periodic function of the nucleons. The periodic ordinal numbers, derived in this way, define the stability limits of nuclides in terms of, either atomic number or neutron number, as shown in Figures 4.4 and 4.11 respectively. 

For a given nucleus, having nuclear charge number (atomic number) Z representing its number of nuclear protons and nucleon number (mass number) A representing its total number of nucleons (neutrons + protons), the mass excess of atom (Z, A) is defined by... 

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... 

Separation energy This is defined as the energy to remove one nucleon from a nucleus. Consider an example of a neutron removed from a nucleus, taking that nucleus to be 29Si just for purposes of illustration. The 29Si nucleus is assembled from 14 protons and 15 neutrons. Removing one neutron can be represented by the nuclear-identity equation... 

The number 12, shown as a superscript, is called the mass number for the element. The mass number is the sum of the protons and neutrons in the nucleus of the atom. Recall from Rutherford s experiment that the nucleus contains the atom s mass. Because protons and neutrons are the particles in the nucleus of the atom, they make up the mass of the atom because the masses of the electrons are minimal in comparison. The number 6, shown as a subscript, is called the atomic number. This can be defined as the number of protons in the nucleus, the nuclear charge (protons are the only nucleons with a charge), or the number of electrons in a neutral atom. How many neutrons are in carbon-12 To find the number of neutrons in the atom, subtract the atomic number from the mass number. In this case there are 6 neutrons in this atom. 

Isotopes are nuclides which I lave the same number of Ijroiuns. but different numbers of neutrons, in their nuclei. An isotope is defined by two numbe s the mass number. A, which is total number of nucleons I protons and neutrons) in the nucleus, and the atomic number, Z, which is total nunber of protons in the nucleus. The value of A is written as a. superscript and of Z as a subscript proceeding the element symbol, e.g. Mo. U, - Pu. 

The binding energy per nucleon is defined as and is a better measure of the stability of... 

Define the term binding energy per nucleon. How can this quantity be used to compare the stabilities of nuclei ... 

---