Nuclear constant

Remarkably, only one nuclear constant, Q, is needed in (4.17) to describe the quadrupole moment of the nucleus, whereas the full quadrupole tensor Q has five independent invariants. The simplification is possible because the nucleus has a definite angular momentum (7) which, in classical terms, imposes cylindrical symmetry of the charge distribution. Choosing x, = z as symmetry axis, the off-diagonal elements Qij are zero and the energy change caused by nuclear... 

The fc0-NAA method has been developed to overcome the labour-intensive and time-consuming work of preparing multi-element standards when routine multielement or panoramic analyses are required [447]. It is intended to be an absolute technique in which uncertain nuclear data are replaced by a composite nuclear constant, the T 0-factor, which has been determined experimentally for each radionuclide with high accuracy. This k0 is given by ... 

In the expression for the isomer shift, the term [c — nuclear measurement or by the measurement of the isomer shift for compounds with known electronic structures (57). Ideally then, a measure of 8 provides a determination of 0S(O) 2, the latter related to the electronic structure as expressed, for example, by the occupation numbers of the various orbitals, e.g., 3d74s1 for metallic iron (Fig. 7) (52). In this manner, it is often possible to identify the oxidation state of the Mossbauer atom and to deduce information concerning the bonding of this atom to its surroundings. In some cases, different electronic structures may have similar values of 0S(O) 2 (the low-spin Fe2+ and Fe3+ pair is an example), and electronic structure information from Mossbauer spectroscopy is most... 

In Table 2.1 are listed many of the common isotopes examined by NMR techniques, together with their nuclear constants. Notice that a bare proton has the largest y value of any nuclear particle, while heavier nuclei, surrounded by many subvalence electrons, tend toward lower values. This... 

Hq = strength of the magnetic field, in gauss y — a. nuclear constant, the gyromagnetic ratio,... 

Maeck WJ, Spraktes FW, Tromp RL, Keller JH (1975) Analytieal results, reeoimnended nuclear constants and suggested eorrelations for the evaluation of Oklo fission produet data Oklo Phenomenon. IAEA, Vienna, p 319-339... 

The magnitude of the quadrupole interaction is a product of two factors, eQ is a nuclear constant for the resonant isotope, while eq is a function of chemical environment. For a 4 transition it is not possible to determine... 

As already discussed in some detail in Chapter 3, the magnitude of the chemical isomer shift depends not only on the values of the electron density at the tin nucleus for the compounds being compared, but also on the value of the fractional change in nuclear radius on excitation to the 23-88-keV level, 6R/R. Determination of the sign and magnitude of the nuclear constant dR/R has proved more difficult for Sn than for Fe because of the initial lack of accurate electronic wavefunctions for tin compounds. The various values which have been proposed are given in Table 14.1 in approximate chronological order [1, 23-29]. 

The first excited state of I can be populated by decay of 33-day Te or 70-minute Te. Both parents are conveniently produced by the Te(n, y) reaction. The decay scheme (shown in simplified form in Fig. 15.17a) is very complex, and there is some divergence of opinion regarding the details. We have adapted the recent work of Berzins et al. [69]. Early I measurements were made using inaccurate values for some of the relevant nuclear constants. The currently accepted value for the I MOssbauer y-ray energy is = 27-72(6) keV [70]. The excited-state lifetime is = 16-8(2) ns, giving a natural width of 0-59 mm s" [70]. The y-ray has nearly pure Ml multipolarity, and the nuclear spin states are and /g =... 

Interest in the actinides stems from the importance of measuring the physical nuclear constants required for the study of the nuclear structure in this region of comparative instability. Few low-energy levels are conveniently populated by a radioactive parent, but the successful and detailed studies with Np using both and Am parents have stimulated the use of more difficult techniques such as Coulomb excitation. Consequently the 2 Th, Pa, U, and Am resonances have now also been detected. Full details of the known nuclear parameters of these nuclides are tabulated in Appendix I. 

I knew very little at that time about the work that was being carried in Chicago and what I can say about it is necessarily very sketchy. It was only a short time ago that I found out that V. Wilson wrote a memorandum to Mr. Compton during the summer of 1940, that is, only about six months after Szilard sent his article to the Physical Review. In this memorandum Wilson attempted to calculate the multiplication constant if one uses beryllium instead of hydrogen as a moderator. On the basis of nuclear constants which we now know to be rather far from their actual values, he arrived at the conclusion that a chain reaction with unseparated uranium and beryllium as a moderator may just barely be possible. V. Wilson apparently was not familiar with the idea of the lattice as developed in Columbia but assumed a homogeneous mixture of beryllium and uranium. 

The so-called lattice calculations are designed to obtain the geometries (carbon to U ratio and size of lumps) in which the sum of the resonance and thermal losses is least. It turns out, for instance, that a carbon to uranium mass ratio of 6 with uranium spheres of 2" diameter gives a particularly small premature loss of neutrons. The calculations are based on numerous experimentally established nuclear constants. They have been, on the whole, well confirmed by direct observations. 

For an estimation of the breeding gain in thermally fissionable material, the geometry of the reactor and the pertinent nuclear constants must be considered. The following estimates have been made for the abovegeometry using reasonable values of the nuclear constants based on actual measurements ... 

Starting from the JEF2 European Data Bank (microscopic cross section data and nuclear constants) the codes NJOY and CALENDF are used to prepare the cross section data libraries used with the ERANOS scheme (see table 7.1)... 

Like in the derivation based on the height of the fission barrier, Z M appears as the parameter determining fissility. The minimum values obtained for Z A (39 or 47) should not be taken too strictly, as they are based on rather arbitrary assumptions for nuclear constants. 

The rest of the constants presented are grouped according to the scientific field where they belong. Physicochemical constants are given in Table 11.11, followed by atomic and nuclear constants in Tables 11.12 and 11.13, respectively. 

It may be difficult and/or time consuming to prepare accurate standards for all possible elements hence, a monostandard method has been introduced in neutron activation analysis. The so-called Ao-standardi2ation method is based on the recognition that the ratio of nuclear constants for analyte x and a chosen standard s in O Eq. (30.29) can be combined into a single constant (Simonits et al. 1975) ... 

All the nuclear factors are contained in the compound nuclear constant, ko- For a given gamma ray, y, of a given product nuclide, the ko factor is proportional to the isotopic abundance of the target nuclide, the thermal neutron activation cross section, and gamma ray emission probability, and inversely proportional to the atomic mass ... 

In the absolute method, the masses of certain components are determined. Assuming thin samples, peak areas are directly proportional to the masses, so the mass can be determined from nuclear constants and the conditions of the measurement based on Eq. (31.4) as follows ... 

Shlyakhter, A.I., Direct test of the constancy of fundamental nuclear constants. Nature 264, 340, 1976. 

It is anticipated teat the exchange of similar information, and tee collaboration with other installatiinis, may lead to a better determination of nuclear constants and to an improvement in the general capability of quantitative nunierical predictions for problems in neutron transport. 

A formalism has been developed for describing Inte- gral neutron experiments and corresponding calculational models. Provision has been made for specifying dimensions, material compositions, and relevant bulk parameters, using appropriate, assumptions, uncertainties, definitions, and comments. A library of calculational models for 113 evaluated spherical critical assemblies and for 37. subcrltical. bulk pulsed spheres has been prepared for testing of evaluated nuclear constants and calculational techniques, notably those employing Monte Carlo and S methods. " ... 

By choice we do not provitte an automatic feedback for the scaling and alteraUon of neutron cross-sections. Our basic axiom is that any computerized anMysis of evaluated nuclear constants most not offend tte physics of nuclear processes, must foke place within the constraints of experimentally measured or inferred uncertainties, be addressable selectively to any reaction and energy domain of an isotope, mid be.,subservlent to human judgment. 

---