Nuclear notation

For chemical purposes, the most important types of radiation are alpha and beta particles. An alpha particle (a) is a )He nucleus with 2 protons and 2 neutrons. This nuclear notation uses a subscript to the lower left to record the number of protons, whereas the superscript to the upper left is the mass number, the total number of nucleons. The number of protons... 

Look up sodium in the periodic table and write its nuclear notation. 

Discovery of Radioactivity Nuclear Notation Radioactive Decay Detecting Radioactivity Half Life and Radioisotope Dating ChemLab The Radioactive Decay of Pennium ... 

In nuclear notation, the element symbol refers to the nucleus only, so a proton is also sometimes represented as jH.) The number of neutrons N) in a nucleus is the mass number (/ ) minus the atomic number (Z) N = A — Z. The two naturally occurring isotopes of chlorine, for example, have 17 protons (Z = 17), but one has 18 neutrons (nCl, also written Cl) and the other has 20 ( Cl, or Cl). Nuclides can also be designated with the element name followed by the mass number, for example, chlorine-35 and chlorine-37. Despite some small variations, in naturally occurring samples of an element or its compounds, the isotopes of the element are present in particular, fixed proportions. Thus, in a sample of sodium chloride (or any Cl-containing substance), 75.77% of the Cl atoms are chlorine-35 and the remaining 24.23% are chlorine-37. 

To understand this chapter, it s very important that you are comfortable with nuclear notations, so please take a moment to review Sample Problem 2.2 and Problems 2.23 to 2.30 at the end of Chapter 2. 

Figure 2-1 shows the nuclear notation (a way of writing elements that gives information about the nucleus of element) for the 82 polyatomic ion with 16 neutrons on each sulfur atom, or nuclide. 

Nuclear notation forSr polyatomic ion with 16 neutrons on each sulfur atom. 

Atomic number 0ower left, IQ This is the number of protons within the nuclide. As the atomic number tells you the element, which is also represented by the element s symbol at the center of the nuclear notation (in this case, S for sulfur), it s commonly not included. All atoms that have 16 protons are sulfur atoms. 

Harris R K 1996 Nuclear spin properties and notation Encyclopedia of NMRvo 5, ed D M Grant and R K Harris (Chichester Wiley) pp 3301-14... 

The symbol M represents the masses of the nuclei in the molecule, which for simplicity are taken to be equal. The symbol is the Kionecker delta. The tensor notation is used in this section and the summation convention is assumed for all repeated indexes not placed in parentheses. In Eq. (91) the NACT appears (this being a matrix in the electronic Hilbert space, whose components are denoted by labels k, m, and a vector with respect to the b component of the nuclear coordinate R). It is given by an integral over the electron coordinates... 

The mixed, v t — % notation here has historic causes.) The Schrodinger equation is obtained from the nuclear Lagrangean by functionally deriving the latter with respect to t /. To get the exact form of the Schrodinger equation, we must let N in Eq. (95) to be equal to the dimension of the electronic Hilbert space (viz., 00), but we shall soon come to study approximations in which N is finite and even small (e.g., 2 or 3). The appropriate nuclear Lagrangean density is for an arbitrary electronic states... 

Nuclear Magnetic Resonance. The iateraction of a nucleus with Bq is usually described usiag vector notation and models as ia Figure 2 where the bulk magnetization, Af, and the static field Bq are initially parallel to A radio frequency pulse is appHed ia the xy plane for a duration of t p.s,... 

R. A. Abramovitch, Giam Choo-Seng, and A. D. Notation, Gan. J. Chem. 38,761(1960) L. M. J ackman, Applications of Nuclear Magnetic Resonance Spectroscopy to Organic Chemistry. Pergamon Press, New York, 1959. 

Uranium in the fuel of a nuclear power plant is designated U. The 92 protons and 143 neutrons in a U nucleus sum to 235, the number in the U notation. Through interaction with a neutron the 92 protons and 144 neutrons involved are rearranged into other nuclei. Typically, this rearrangement is depicted as... 

In the discussion that follows we refer to nuclear activation detection reactions in lieu of analysis reactions since the signals that are measured are not necessarily always from a radioactive product. Again, we will use standard nuclear physics notation in specifying nuclear reactions, namely ... 

During the red giant phase of stellar evolution, free neutrons are generated by reactions such as C(a,n) and Ne(a,n) Mg. (The (ot,n) notation signifies a nuclear reaction where an alpha particle combines with the first nucleus and a neutron is ejected to form the second nucleus.) The neutrons, having no charge, can interact with nuclei of any mass at the existing temperatures and can in principle build up the elements to Bi, the heaviest stable element. The steady source of neutrons in the interiors of stable, evolved stars produces what is known as the "s process," the buildup of heavy elements by the slow interaction with a low flux of neutrons. The more rapid "r process" occurs in... 

Introducing the Dirac bra and ket notation for operators and states of the electrons, while explicitly stating the nuclear coordinates, the operator t Q,Q, t) is then expanded in the states Xn(Q))- The Lagrangian functional becomes... 

This treatment differs from the usual approach to molecule-radiation interaction through the inclusion of the contribution from the electric field from the beginning and by not treating it as a perturbation to the field free situation. The notation 7/ei(r R, e(f)) makes the parametric dependence of the electronic Hamiltonian on the nuclear coordinates and on the electric field explicit. 

The term causes a uniform shift of the nuclear energy states which, however, is different for the ground and excited state because the nuclear volume and, therefore, also the entity R ) are different for ground and excited states. This gives rise to the isomer shift 6 of the Mbssbauer spectrum. The notation 6E = E is introduced to emphasize the very small change in energy ( 10 eV), which is only a fraction (about 10 ) of the transition energy. The isomer shift will be discussed in detail in Sect. 4.2. 

Here, we have removed the factor 1 /47ieo because in atomic units (a.u.) its value is unity. We have also used the short-hand notation Ex r) = ZxIi x2 for the nuclear electric field. Furthermore, we use the following two identities to arrive at the above expression ... 

The formal vector cp (K) denotes the set of atomic orbital basis functions with centers at the original nuclear locations of the macromolecular nuclear configuration K, where the components cp(r, K) of vector q(K) are the individual AO basis functions. The macromolecular overlap matrix corresponding to this set cp (K) of AO s is denoted by S(K). The new macromolecular basis set obtained by moving the appropriate local basis functions to be centered at the new nuclear locations is denoted by cfcK ), where the notation cp(r, K ) is used for the individual components of this new basis set overlap matrix is denoted by S(K ). 

For compactness and clarity, Eq. (2.11) is written in matrix notation. It is similar to the more familiar case of a time-independent basis set expansion but with two important differences The AIMS basis is time-dependent and nonorthogonal. As a consequence, the proper propagation of the coefficients requires the inverse of the (time-dependent) nuclear overlap matrix... 

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