Nucleon-exchange Terms Research Articles

Nucleus-nucleus scattering in the high-energy approximation and optical folding potential

A microscopic complex folding-model potential that reproduces the scattering amplitude of Glauber-Sitenko theory in its optical limit is obtained. The real and imaginary parts of this potential are dependent on energy and are determined by known data on the nuclear-density distributions and on the nucleon-nucleon scattering amplitude. For the real part, use is also made of a folding potential involing effective nucleon-nucleon forces and allowing for the nucleon-exchange term. Three forms of semimicroscopic optical potentials where the contributions of the template potentials—that is, the real and the imaginary folding-model potential—are controlled by adjusting two parameters are constructed on this basis. The efficiency of these microscopic and semimicroscopic potentials is tested by means of a comparison with the experimental differential cross sections for the elastic scattering of heavy ions 16O on nuclei at an energy of E ∼ 100 MeV per nucleon.

Knockon exchange contribution in the resonating-group study of the nucleus-nucleus interaction.

The properties of the type-c nucleon-exchange term in a resonating-group formulation that takes into account the clustering nature of the nuclei involved are investigated. The results indicate that these properties are weakly affected by the degree of clustering, and the one-exchange term makes the dominant contribution among all class-A exchange terms. The equivalent type-1c, or knockon, exchange potential is found to have a characteristic range shorter than the direct potential and a characteristic energy that has a large value around 50 MeV/nucleon.

Classical solutions to topologically massive Yang-Mills theory: Eric D'Hoker, Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139; and Luc Vinet, Laboratoire de Physique Nucléaire, Université de Montréal, Montréal, Québec H3C3J7, Canada

The effects of internuclear antisymmetrization in nucleus-nucleus scattering are studied by examining the structure of the exchange-Hamiltonian kernel function in the resonating group formulation. By investigating the features of the effective local potentials which are constructed to yield the same Born scattering amplitudes as the various nucleon-exchange terms in this kernel function, it is found that, among all exchange terms, the one-exchange and core-exchange terms have the largest influence. In addition, this investigation shows that the one-exchange terms, giving rise to a Wigner-type effective potential, are generally important in all scattering systems and over a wide energy range, while the core-exchange terms, giving rise to a Majorana-type effective potential, are generally important only when the nucleon-number difference of the interacting nuclei is rather small. Based on these results, it can therefore be concluded that, if a local-potential model is adopted to analyze experimental scattering results, then the real central part of the effective potential in this model must, in general, contain a Majorana exchange component or an odd-even l-dependence. Explicit resonating-group calculations in 3He + α and α + 16O systems, where contributions from individual exchange terms are studied, have also been performed. From this study, one finds that the conclusions mentioned above, reached in the Born approximation, may in fact be valid even in the lower-energy region.

Multiconfiguration resonating-group theory of the seven-nucleon system with realistic cluster wave functions.

The properties of the seven-nucleon system are examined with a multiconfiguration and multi- channel resonating-group calculation. The cluster internal functions employed explain the charge-form-factor data over a wide range of ${q}^{2}$ and satisfy the variational stability condition quite well. The model space used is spanned by $^{3}$H+\ensuremath{\alpha}, n${+\mathrm{}}^{6}$Li, n${+\mathrm{}}^{6}$${\mathrm{Li}}^{\mathrm{*}}$, and d${+\mathrm{}}^{5}$He cluster configurations. The result shows that the specific distortion of the $^{3}$H+\ensuremath{\alpha} system is quite significant. With our multiconfiguration calculation, the ground-state energy is improved by more than 1 MeV. The calculated level spectrum agrees well with the level spectrum empirically determined. The energy positions of both natural-parity and unnatural-parity levels are reasonably explained. In addition, we find that, because of centrifugal-barrier effects, the aligned configuration generally makes the most sig- nificant contribution. The characteristics of nucleon-exchange terms are also briefly examined. Here it is found that, at sufficiently high energies where sharp resonance levels do not exist, the essential properties of these terms can already be learned by performing relatively simple single-configuration calculations.

Channel-coupling effects in the resonating-group study of the seven-nucleon system

A three-channel resonating-group calculation is performed to study the effects of channel coupling on the properties of the /sup 3/H+..cap alpha.. system. The channels included are /sup 3/H+..cap alpha.., n+ /sup 6/Li, and n+ /sup 6/Li( channels, with /sup 6/Li and /sup 6/Li( described by (1s)/sup 4/(1p)/sup 2/ harmonic-oscillator functions representing d+..cap alpha.. cluster configurations with relative orbital angular momenta equal to 0 and 2, respectively. By comparing with the /sup 3/H+..cap alpha.. single-channel result, it is found that the three-channel calculation improves the L = 1 ground state energy by 0.68 MeV and yields additional features such as cusps in the L = 0 and 2 phase shifts and a dispersionlike resonance structure in the L = 1 phase shift. In addition, it is noted that, in states with larger L values, the n+ /sup 6/Li( aligned configurations make particularly important contributions. Characteristics of nucleon-exchange terms have also been briefly investigated; here one finds that, as far as the /sup 3/H+..cap alpha.. system is concerned, the important one-exchange and core-exchange contributions are only weakly affected by the presence of other channels.

N+Lisystem investigated with the resonating-group method: Effects of target clustering and charge form factor

The influence of the clustering and charge-form-factor behavior of $^{6}\mathrm{Li}$ on the properties of the $n$+Li system is investigated. By examining the $n$+$^{6}\mathrm{Li}$ cross-section and phase-shift results, it is found that, in the low-energy region, a proper consideration of $n$+$^{6}\mathrm{Li}$ cluster correlations in $^{6}\mathrm{Li}$ is essential to explain the resonance structure, while in the high-energy region one must adopt in the calculation a $^{6}\mathrm{Li}$ internal function which yields the empirical form-factor values over a wide ${q}^{2}$ range. Contributions from various nucleon-exchange terms are also studied. Here one finds that the main characteristics of these contributions do not seem to depend sensitively on the detailed nature of the cluster internal function.NUCLEAR REACTIONS $^{6}\mathrm{Li}(n, n)$. Effects of target clustering and charge form factor. Resonating-group method with three-cluster formulation.

Study of Local Inter-Nucleus Potential on the Basis of the Resonating Group Method. I: General Discussion and Study of the - System

Under the purpose of obtaining the knowledge of the local inter· nucleus potential from the microscopic ground, it is proposed to analyse the equivalent local potentials obtained from the non-local potentials of the resonating group method. Our localization method has been already demonstrated in previous papers to be quite accurate. Classification of RGM kernels into Wigner and Majorana types and the properties of the spatial and energy range parameters of the kernels are discussed. It is shown from the analysis of the basic properties of RGM kernels that our localization method is a quite natural one. Highly non-local kernels coming from the exchange of nucleons whose number is near the reduced mass number are shown to have only small effects in the whole spatial region. Study of the a·a system is reported. One· nucleon exchange term is shown to be dominant in the exchange potential. Kinetic and norm exchange contributions are found to be comparable with the interaction exchange one. Knock-on exchange contribution is analysed in detail and it is stressed that it is not a dominant component of the exchange potential at low and medium incident energy.

Detailed investigation of exchange effects inHe3+αandα+O16scattering

The effects of intercluster antisymmetrization in $^{3}\mathrm{He}$+$\ensuremath{\alpha}$ and $\ensuremath{\alpha}$+$^{16}\mathrm{O}$ systems are examined. The result indicates that the characteristic quantities of the Born-equivalent local potentials can be reliably employed to predict the relative importance of the various nucleon-exchange terms. Based on these quantities and by studying the cross section or phase-shift behavior, it is noted that many exchange terms are of only minor significance when the energy is high or when the absorption is strong. Furthermore, one finds that, at an energy higher than about 25 MeV/nucleon, the features of the cross-section angular-distribution curve, which has a distinct V shape, can be simply explained. Here our investigation shows that the contribution to the cross section in the decreasing part of the V-shaped curve comes essentially from the direct term and the one-exchange terms (mainly the knockon exchange term), while the contribution to the cross section in the increasing part of this curve comes essentially from the core-exchange terms.

Resonating-group study and importance of exchange effects in the α + 6Li system

The resonating-group method in the one-channel approximation is used to investigate the α + 6Li system. The result shows that, especially at relatively high energies, reasonable agreement with experiment can be obtained. In particular, the cross-section rise in the backward angular region is well accounted for. The effects of internuclear antisymmetrization, represented by various nucleon-exchange terms in the kernel function, have also been carefully examined. Here some of the interesting findings are that the blocking effect is quite significant in this system and the two-exchange terms (sometimes even the three-exchange terms) seem to have only minor influence on the scattering cross section.

Antisymmetrization effects on the effective internuclear potential

The effects of internuclear antisymmetrization in nucleus-nucleus scattering are studied by examining the structure of the exchange-Hamiltonian kernel function in the resonating group formulation. By investigating the features of the effective local potentials which are constructed to yield the same Born scattering amplitudes as the various nucleon-exchange terms in this kernel function, it is found that, among all exchange terms, the one-exchange and core-exchange terms have the largest influence. In addition, this investigation shows that the one-exchange terms, giving rise to a Wigner-type effective potential, are generally important in all scattering systems and over a wide energy range, while the core-exchange terms, giving rise to a Majorana-type effective potential, are generally important only when the nucleon-number difference of the interacting nuclei is rather small. Based on these results, it can therefore be concluded that, if a local-potential model is adopted to analyze experimental scattering results, then the real central part of the effective potential in this model must, in general, contain a Majorana exchange component or an odd-even l-dependence. Explicit resonating-group calculations in 3 He + α and α + 16 O systems, where contributions from individual exchange terms are studied, have also been performed. From this study, one finds that the conclusions mentioned above, reached in the Born approximation, may in fact be valid even in the lower-energy region.

Exchange effects in nucleus-nucleus interaction

The effects of antisymmetrization, represented by various nucleon-exchange terms in a resonating-group formulation, are studied in the case of nucleus-nucleus scattering. By examining the features of the effective local potentials which are constructed to yield the same Born scattering amplitudes as these exchange terms, it is found that the one-exchange and the core-exchange terms are the most important. In addition, this study shows that in scattering systems the one-exchange term has generally a substantial influence over a wide range of energies. On the other hand, the core-exchange term is important only when the nucleon-number difference of the interacting nuclei is rather small. Based on the results of this investigation, it can also be concluded that if a local-potential model is employed to phenomenologically analyze experimental scattering results, then the effective potential in this model may need to have an odd-even l-dependent character.

Nucleon transfer calculation in reactions induced by12C to22Ne ions

A classical-statistical model is presented here in order to predict the isotopic production in light heavy ion reactions. The dynamical approach includes a nucleon exchange term. Such transfer is made possible through a window and a simple gas theory argument. The distribution of the cross section among all the allowed exit channels is then calculated within the statistical assumption. Excellent agreement is obtained with light heavy ion experimental cross section. The neck configuration is shown to be in reasonable agreement with the one deduced from Nix's liquid drop model.

Cluster Model Wave Function and the r.m.s. Radius of 7Li

The ground state wave function of 7Li, considered to be made of an alpha particle and a triton cluster configuration, including all the nucleon exchange terms arising out of the antisymmetrization of a two oscillator shell model wave function, is used in the calculation of the root mean square (r.m.s.) radius of 7Li with a view to determine the range of the parameters in the wave function.

Role of the Nucleon Exchange in the Diffraction Dissociation N-> (N )

Properties of the nucleon exchange and the direct nucleon pole terms are studied in the diffraction dissociation JrN~>r. (N7r). It is shown that contrary to the naive expectation, the nucleon exchange term with the s-channel helicity conserving 7rN scattering amplitude cannot give the maximum at ¢aJ=O in the ¢aJ distribution. The transverse momentum distributions in the lab. frame reflect well the cos eaJ but not the ¢aJ distributions. We need something besides the pion exchange term to enhance the backward side, cos !JaJ<O, bnt it is questionable whether the nucleon exchange term plays the role of something completely. Including cross-over phenomena, it is qualitatively examined that the resonance production term plays the role of the something.

ABSORPTIVE CORRECTIONS TO THE NUCLEON EXCHANGE TERM IN ELASTIC πN SCATTERING

The absorption model of Gottfried and Jackson is justified in the case of backward elastic scattering. The model is then applied to the nucleon exchange term in π+p scattering at 4 and 8 BeV. It is found that the data can be fitted only if a phenomenological form factor is introduced.