Nuclear calculations results

As mentioned, most calculations we have done so far have concerned molecular systems. However, prior to development of the non-BO method for the diatomic systems, we performed some very accurate non-BO calculations of the electron affinities of H, D, and T [43]. The difference in the electron affinities of the three systems is a purely nonadiabatic effect resulting from different reduce masses of the pseudoelectron. The pseudoelectrons are the heaviest in the T/T system and the lightest in the H/H system. The calculated results and their comparison with the experimental results of Lineberger and coworkers [44] are shown in Table 1. The calculated results include the relativistic, relativistic recoil. Lamb shift, and finite nuclear size corrections labeled AEcorr calculated by Drake [45]. The agreement with the experiment for H and D is excellent. The 3.7-cm increase of the electron affinity in going from H to D is very well reproduced by the calculations. No experimental EA value is available for T. 

A breakthrough was achieved a few years ago when it was realized that an anal dic calculation of the deuterium recoil, structure and polarizability corrections is possible in the zero range approximation [76, 77]. An analytic result for the difference in (12.29), obtained as a result of a nice calculation in [77], is numerically equal 44 kHz, and within the accuracy of the zero range approximation perfectly explains the difference between the experimental result and the sum of the nonrecoil corrections. More accurate calculations of the nuclear effects in the deuterium hyperfine structure beyond the zero range approximation are feasible, and the theory of recoil and nuclear corrections was later improved in a number of papers [78, 79, 80, 81, 82]. Comparison of the results of these works with the experimental data on the deuterium hyperfine splitting may be used as a test of the deuteron models and state of the art of the nuclear calculations. 

In an attempt to relate calculated results to experimental findings for monomeric, lignin model compounds, preliminary work has compared theoretically determined electron densities and chemical shifts reported from carbon-13 nuclear magnetic resonance spectroscopy (62). Although chemical shifts are a function of numerous factors, of which electron density is only one, both theoretical and empirical relationships of this nature have been explored for a variety of compound classes, and are reviewed by Ebra-heem and Webb (63), Martin et al. (64), Nelson and Williams (65), and Farnum (66). 

The results presented here show that the energy distributions of the parent molecular species, e.g. benzene, are narrower than those of atomic species, even though the ejection processes in both cases arise from energetic nuclear collisions. The bonding geometry also Influences the ejection yield and angular distribution. The specific case of it-bonded and o-bonded pyridine on a metal surface is discussed with comparisons between the calculated results and experimental data. 

For the trimethylspironaphthoxazine, ab initio molecular orbital (MO) calculations indicated that the most stable colored form is the trans-trans-cis- form - about 7 kcal-mol 1 endothermic relative to the spiro form. Measurement of the proton NMR nuclear Overhauser effect experimentally confirmed this calculated result. The structural calculations indicate that the colored form is essentially quinoidal, rather that zwitterionic.186... 

The coefficients bi, (i = 1, 2, 3, 15), in the expansion of the nuclear shielding factor fi in powers of R, Equation (77), are also listed in Table 10, and Table 13 presents a comparison of our perturbation theory and numerical values with other calculated results [33,37]. We note that perturbation theory provides at least 6 figure accuracy up to R = 3, and we also observe that our numerical and other calculated data are in harmony for all values of R for which comparisons are available. f) behaves as R/3 as R 0 [6]. 

Table II. Calculated Results for Tbermal Rate Constant Ratios Determined by the Moderated Nuclear Recoil Method in Model Systems...

Abstract A consistent relativistic energy approach to the calculation of probabilities of cooperative electron-gamma-nuclear processes is developed. The nuclear excitation by electron transition (NEET) effect is studied. The NEET process probability and cross section are determined within the S-matrix Gell-Mann and Low formalism (energy approach) combined with the relativistic many-body perturbation theory (PT). Summary of the experimental and theoretical works on the NEET effect is presented. The calculation results of the NEET probabilities for the y Os, yy Ir, and yg Au atoms are presented and compared with available experimental and alternative theoretical data. The theoretical and experimental study of the cooperative electron-gamma-nuclear process such as the NEET effect is expected to allow the determination of nuclear transition energies and the study of atomic vacancy effects on nuclear lifetime and population mechanisms of excited nuclear levels. 

For microscopic nuclear structure work, it is important that the NN potential applied is able to reproduce the known facts about the two-nucleon system correctly. Therefore, in Section 3, we will make some comments on how to test the quantitative nature of a two-nucleon potential properly. Most relevant for this conference is the question to which extent nuclear structure results depend on the kind of potential used as input in the calculations. We will discuss this in Section 4. Our contribution finishes with summary and conclusions given in Section 5. 

In microscopic nuclear structure calculations, the off-shell behavior of the NN potential is important (see Section 4 for a detailed discussion). The fit of NN potentials to two-nucleon data fixes them on-shell. The off-shell behavior cannot, by principle, be extracted from two-body data. Theory could determine the off-shell nature of the potential. However, not any theory can do that. Dispersion theory relates observables (equivalent to on-shell T-matrices) to observables e.g., nN to NN. Thus, dispersion theory cannot, by principle, provide any off-shell information. The Paris potential is based upon dispersion theory thus, the off-shell behavior of this potential is not determined by the underlying theory. On the other hand, every potential does have an off-shell behavior. When undetermined by theory, then the off-shell behavior is a silent by-product of the parametrization chosen to fit the on-shell T-matrix, with which the potential is identified, by definition. In summary, due to its basis in dispersion theory, the off-shell behavior of the Paris potential is not derived on theoretical grounds. This is a serious drawback when it comes to the question of how to interpret nuclear structure results obtained by applying the Paris potential. 

Thus, the represents only one aspect among several others that need to be considered simultaneously when judging the quality of a NN potential. Other aspects of equal importance are the theoretical basis of a potential model (see the previous section) and (closely related) its off-shell behavior (that can, of course, not be tested by calculating the x with regard to the on-shell NN data). This latter aspect is important, particularly, for the application of a NN potential to nuclear structure. In fact, in Section 4 we will give an example, in which the variation of the f /datum between 1 and 6 affects nuclear structure result only in a negligible way, while off-shell differences are of substantial influence. 

The nuclear matter results for the average potential energy for the partial wave Si obtained with potentials A, B and C are displayed in Fig. 2 for a BHF calculation considering various values of the Fermi momentum kp. The traditional choice for the single-particle spectrum above the Fei mi momentum has been used in this calculation, i.e. the particle energies for k > kp are given by a pure kinetic term, yielding an undesirable gap at k = kp. Several improvements to this choice can be found in the literature, see e.g. Refs. [24-26]. However, since we here are merely interested in... 

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