Tsuneo Kaneko

Specific distortion effects in 3H + α and 3He + α systems☆

Abstract In this investigation, the effects of specific distortion in the 3 H+ α and 3 He+ α systems are examined within the framework of the resonating-group method. The nucleon-nucleon potential employed contains a weakly repulsive core and a spin-orbit component; it yields a satisfactory description of not only the two-nucleon low-energy scattering data, but also the essential properties of the deuteron, 3 H, 3 He and the α-particle. The result shows that such effects are only moderately important in these systems; they are appreciably stronger than those in the α + α system, but considerably weaker than those in the d + α system. In addition, it is shown that the influence of specific distortion is significant mainly in Pauli-favored l = 1 and 3 states, but rather weak in states having other values for the relative orbital angular momentum. Phase shifts, differential cross sections, and polarizations are computed at various energies, and are found to agree quite well with empirically determined values. With the resultant wave function, the 7 Li charge form factor is also studied for q 2 = 0 to 7 fm −2 . Here one finds that there is a reasonable over-all agreement with the experimental result in the whole range of q 2 considered.

Microscopic study of the d + α scattering system with the multi-channel resonating-group method

Abstract Specific distortion effects of the deuteron and α-clusters in the d + α system are examined by requiring that the stability conditions for both clusters are satisfied. The results show that these effects for the deuteron cluster are very important; on the other hand, specific distortion for the α-cluster seems to have a rather minor influence. In this system, virtual-breakup effects of the deuteron are also examined within the framework of the multi-channel resonating-group method. It is noted that these effects are quite significant. Almost forbidden states which result from the coupling among various channels and spurious states which are caused by the choice of bound-state boundary conditions for excited channels are almost smeared out by introducing these effects. In addition, one notes that one can obtain a fairly good description of the experimental data on the 2 + excited states of 6 Li, the differential scattering cross section, and the vector and tensor polariz-ations. In this analysis, two types of nucleon-nucleon potential are adopted to examine the potential dependence of the calculated results. It is found that this kind of dependence is rather weak.

Specific distortion effects in the d + α system and charge form factor of 6Li☆

Abstract The effects of specific distortion in the d + α system are examined. The result shows that, because of the high compressibility of the deuteron cluster, these effects are very important in this system. By properly considering such effects within the resonating-group framework, it is noted that one can obtain a satisfactory description of the experimental data on differential cross sections, vector and tensor polarizations, and the effective nucleon-nucleon (NN) potential required is very similar to those required in the p + α, 3 H + α, and α + α systems. With the resultant wave function, the charge form factor of 6 Li is also studied for q 2 values up to about 14 fm −2 . Here one finds that there is a good agreement with experiment in the higher- q 2 region; in particular, the position of the diffraction minimum and the height of the diffraction maximum are well reproduced. The calculated charge rms radius, however, is only 2.31 fm, which is somewhat too small.

Characteristic features of specific distortion in light nuclear systems

Abstract The pseudo-state method is used to examine the specific distortion of the deuteron cluster in the channel spin- 3 2 state of the d + 3 He system. From the results obtained here and in previous investigations of many other light nuclear systems, we extract the characteristic features of specific distortion. These features are: (i) the importance of specific distortion is sensitively correlated with the cluster compressibility and the nucleon number of the companion cluster, (ii) specific distortion effects are both l - and energy-dependent, and (iii) specific distortion effects are much stronger in Pauli-favored l -states than in Pauli-unfavored l -states.

Multi-configuration resonating-group study of the five-nucleon system

Abstract The properties of the five-nucleon system is investigated with a multi-configuration resonating-group method. The model space adopted is spanned by p + α, d + 3 He and deuteron pseudo-inelastic configurations. The results indicate that, with no adjustable parameters, the main characteristics of the p + α and d + 3 He differential scattering and reaction angular distributions can be reasonably well explained. Calculated total reaction cross sections in the p + α channel are found to be generally higher than experimental values, while the opposite is true in the d + 3 He channel. These latter findings are correlated with the observation that the general magnitudes of the calculated differential scattering cross sections in the p + α and d + 3 He channels are, respectively, smaller and larger than the measured results. Defects in the present model are also discussed, and a way to correct these defects is proposed.

Approximate treatment of the deuteron + nucleus interaction in the resonating-group formulation

Abstract A simplified version of the microscopic resonating-group method (RGM), called model K, is formulated for the deuteron + nucleus problem by making the simplifications of approximately treating the total center-of-mass motion and keeping only the direct and knockon-exchange terms. For these terms, the important point is that they can be analytically derived without much difficulty, with the consequence that the adoption of this model can enhance the general utility of the RGM by rendering the calculations feasible even in heavy nuclear systems. By utilizing the information obtained from previous investigations in the nucleon + nucleus case and by studying the analytical structure of the RGM kernel functions, it can be determined that this model for deuteron + nucleus scattering should work well when the nucleon-number ratio of the target and incident nuclei is larger than about 10 and when the scattering energy is higher than about 20 MeV/nucleon. A test comparison with exact RGM results for d + 16 O scattering at 30 MeV and a fit to experiment for d + 40 Ca scattering at 49.52 MeV yield rather convincing evidence that this model has great simplicity and generality, and can be employed to conduct a systematic and large-scale study of existing data on deuteron + nucleus scattering.

Resonating-group study of the parameters in the local nucleon-nucleus optical-model potential

The general characteristics of the nucleon-nucleus interaction in a recently proposed microscopic model, called model K, are examined. The procedure used is to first construct an equivalent local potential (ELP) of the model-K nonlocal interaction by a WKB method, and then study the features of the ELP by expressing its depth as the sum of an overall-strength term, an energy-dependence term, an asymmetry term, and a Coulomb-correction term, characterized by the parameters V0, Ve, Vt, and Ve, respectively. The results obtained are compared with the corresponding parameters in the real nuclear-central part of a global optical-model potential, called the CH89 potential. From this comparison, it is noted that our calculated results for V0 and Ve are quite satisfactory. The energy-dependence parameter Ve turns out to be equal to about 85% of the CH89 value, indicating that a proper consideration of antisymmetrization alone can already account for a major part of the empirically determined energy dependence. On the other hand, it is also found that our predictions do differ from the CH89 results in two respects: (i) our calculated asymmetry-potential depth Vt is nearly system- and energy-independent, but has a value which is almost twice as large as the CH89 value, and (ii) in contrast to the CH89 assumption of a constant value for the Coulomb-correction parameter Ve, our study indicates that Ve is energy-dependent, with about a 25% decrease as the scattering energy increases from 20 to 40 MeV. In addition to these results, our calculation also shows that the parameters V0, Ve, Vt and Ve are all essentially system-independent. This is clearly an important finding, since it provides a microscopic foundation for the validity of employing a global model with local potentials in the phenomenological analysis of nucleon-nucleus scattering data.

Approximate resonating-group calculations with Woods-Saxon target-nucleus wave functions

Abstract Differential cross sections and analyzing powers in n + 16 O and n + 40 Ca scattering are calculated with a simplified version of the reasonating-group method in the cases where the wave functions of the target nuclei are constructed with single-nucleon functions generated from Woods-Saxon and harmonic-oscillator potential wells (WS and HO models). A comparison of the calculated results shows that the angular distributions for these quantities obtained in the two models are characteristically similar in all respects. This suggests that scattering properties are mainly sensitive to the gross structure of the target-nucleus density distribution and computationally-simpler harmonic-oscillator wave functions may be reliably adopted in future resonating-group calculations when the scattering energy is not too low.

Analysis of deuteron + nucleus scattering data with a simplified resonating-group method

Abstract A simplified version of the microscopic resonating-group method, called model K, is used to analyze the data of deuteron scattering by a variety of target nuclei ranging from 28Si to 208Pb. The results indicate that, by simply using the same parameter values as those found previously in model-K studies of N + nucleus scattering, a satisfactory agreement between calculation and experiment can already be obtained, especially for the differential scattering cross section. To create a connection between the nonlocal interaction of model K and the local interaction of phenomenological optical-model analyses, we have constructed a d + nucleus equivalent local potential by using the WKB procedure. An examination of the properties of this equivalent potential reveals that a proper consideration of anti-symmetrization alone can account for most of the energy dependence of the empirically determined internuclear local interaction. The knockon-exchange term, arising from antisymmetrization, is shown to make an appreciable contribution; at 40 MeV, for example, it contributes to around 35% of the total volume integral per nucleon pair of the equivalent local potential.

Neutron and proton form factors of 7Li and 7Be

Abstract Proton and neutron form factors of 7 Li and 7 Be are computed with wave functions obtained from a multi-configuration resonating-group calculation. Results obtained for the RMS matter and charge radii are in accordance with conclusions reached recently by analyzing experiments utilizing exotic nuclear beams produced through projectile-fragmentation processes in high-energy heavy-ion reactions.