Multiconfiguration Resonating-group Research Articles

Scattering and Reaction Cross Sections in the p + System with the Multiconfiguration Resonating-Group Method

He cluster configurations, supplemented by their associated pseudo­ inelastic configurations. With the Minnesota nucleon-nucleon potential and a total of 25 cluster configurations, the results show that, with no adjustable parameters, the calculation can satisfactorily explain all the essential features of the measured scattering and reaction angular distributions, such as the angular positions of cross-section maxima and minima, the strong cross-section rise at backward angles, and so on. The only defect is that the calctdated values of the cross sections are on-the-average somewhat too large, which is correlated with the finding that the calculated p+ a total reaction cross sections are not yet large enough, being equal to only about 70-80% of the measured values. The way to improve the calculation is also discussed. The ultimate aim of an investigation with the resonating-group method 1 > (RGM) is to understand, in a completely microscopic way without any phenomenological adjustment, all the essential properties of the nuclear system under consideration. In particular, the experimental data on the total reaction cross section should be satisfac­ torily explained through the introduction of explicit reaction channels into the formu­ lation, rather than by the adoption of a phenomenologically determined imaginary potential which is an entity not compatible with the microscopic nature of the RGM. To achieve this aim, one must necessarily carry out the calculation in an extensive model space spanned by a sufficiently large number of cluster configurations, chosen according to physical intuition, energetical arguments, and the relative ease in the analytical derivation of the kernel functions. In the 6-nucleon system, for instance, a careful study 2 > has recently been performed, with the model space consisting of d +a, p+ 5 He and n+ 5 Li cluster configurations, supplemented by pseudo-inelastic configurations (PIC) involving pseudo-excited states of the deuteron cluster. The results obtained show that the d +a bound-state energy, differential scattering and reaction cross sections can all be well explained in a unified manner. The calculated d +a total reaction cross sections exceed 90 % of the measured values, indicating that the 6-nucleon calculation can be considered to be essentially complete.*> Similar *> The 6-nucleon calculation was performed with a purely central nucleon-nucleon potential in order to save computational effort. The use of a potential containing spin-orbit and tensor components will certainly be necessary for the discussion of the detailed features of the experimental data, but are not essential for extracting general information which is of interest to us, i.e., to study the cluster structures of bound and resonance levels, to determine the important mechanisms occurring in nuder reactions, and to learn the basic behavior of the intricate interplay among various cluster configurations.

Reaction Cross Sections in Light Nuclear Systems with the Multiconfiguration Resonating-Group Method

Differential cross sections for various reactions in the 6-, 7-, 8- and 10-nucleon systems, obtained by using multiconfiguration resonating-group calculations, are compared with experimental results. These comparisons show that the calculation can explain quite well the general features of the measured angular distributions, such as the cross-section rise at backward angles, the angular positions of cross-section maxima and minima, and so on. Discrepancies with experiment, none serious, can all be readily and satisfactorily explained. These findings, together with previous discussions on level spectra and scattering cross sections, indicate that there is now enough evidence to confidently support the assertion that the resonating-group method is a sound microscopic method built on firm physical foundation, and can be successfully used to treat nuclear bound-state, scattering, and reaction problems from a unified and consistent viewpoint.

Reaction Cross Sections in Light Nuclear Systems with the Multiconfiguration Resonating-Group Method

Differential cross sections for various reactions in the 6-, 7-, 8- and 10-nucleon systems, obtained by using multiconfiguration resonating-group calculations, are compared with experimental results. These comparisons show that the calculation can explain quite well the general features of the measured angular distributions, such as the cross-section rise at backward angles, the angular positions of cross-section maxima and minima, and so on. Discrepancies with experiment, none serious, can all be readily and satisfactorily explained. These findings, together with previous discussions on level spectra and scattering cross sections, indicate that there is now enough evidence to confidently support the assertion that the resonating-group method is a sound microscopic method built on firm physical foundation, and can be successfully used to treat nuclear bound-state, scattering, and reaction problems from a unified and consistent viewpoint.

Resonating-Group Study of Three-Nucleon Bound State and p + d Scattering

The multi-configuration resonating-group method is employed to study the properties of the three-nucleon system. The model space is spanned by p+d, p+d', n+ 2p, and a large number of their associated pseudo-inelastic configurations. The nucleon-nucleon potential used is the Minnesota potential which contains nuclear central, Coulomb, and spin-orbit components. The results show that the calculated p+d complex phase shifts agree well with the values obtained by an empirical analysis of experimental data. Differential scattering and total reaction cross sections in the p+d system are calculated at centre-of-mass energies up to 32 MeV. Without adjusting any parameter, it is found that the agreement between calculation and experiment is quite satisfactory. The effects of successively enlarging the model space have also been examined. Here the finding is that, in order to obtain reliable results, all three types of cluster configurations must be included in the calculation.

Reaction cross sections in the ten-nucleon system

The properties of the 10-nucleon system are investigated with a multiconfiguration resonating-group method, which consists of α+6Li,d+8Be,d+8Be*, and α+6Li* cluster configurations, where6Li* and8Be* represent the rotational excited-states of6Li and8Be with orbital angular momentum equal to 2. The results show that, among reactions initiated from the α+6Li incident channel, the inelastic-scattering process6Li(α,α′)6Li* dominates. The α-transfer reactions6Li(α,d)8Be and6Li(α,d)8Be* have smaller cross sections, but still contribute, on the average, to about one-third of the α+6Li total reaction cross sections in the centre-of-mass energy region between 12 and 24 MeV. The calculated α+6Li total reaction cross section at 27 MeV is equal to around 70% of the empirical value obtained by analyzing α+6Li differential scattering cross-section data. This is a respectable amount, considering the complexity of the problem and that no adjustable parameters are involved in the calculation. Based on the findings of this and previous investigations, some general criteria which govern the importance of cluster-transfer processes in light nuclear systems have also been obtained. These criteria should be very useful in qualitatively understanding the behaviour of other systems that have hitherto not been studied with the multi-configuration resonating-group method.

Multi-Configuration Resonating-Group Study of p+α and d+^3He Scatterings(Microscopic Cluster Models of Light Nuclei and Related Topics)

Multi-Configuration Resonating-Group Study of p+α and d+^3He Scatterings(Microscopic Cluster Models of Light Nuclei and Related Topics)

Reaction mechanisms in the six-nucleon system with the multi-configuration resonating-group method

The properties of the six-nucleon system are examined with a multi-configuration resonating-group method consisting of thed+α configuration, thep+5He andn+5Li configurations, and deuteron pseudo-inelastic configurations. The main purpose is to study the reaction mechanisms in this system. The results obtained are quite satisfactory, with the calculatedd+α total reaction cross sections equal to around 90% of the empirically determined values. The one-nucleon transfer process turns out to be significantly more important than the deuteron direct-breakup process; however, the latter process must still be properly taken into consideration, since it does contribute to about one third of thed+α total reaction cross section. The process of one-nucleon transfer is shown to occur mainly in the peripheral region, while the process of deuteron direct-kreakup is found to take place predominantly in the interior region of the compound nucleus. The convergence property with respect to the number of deuteron pseudo-inelastic configurations has also been investigated. Here it is found that, with the dominant configurations included, the number of such configurations required can be rather small, which is an important finding because it greatly simplifies the computational aspects of multi-configuration resonating-group calculations.

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

The three-nucleon system is studied within the multi-configuration resonating-group method. The model space is spanned byp+d,p+d′, and their associated pseudo-inelastic configurations. The results show that, at lower energies less than about 15 MeV, the calculatedp+d differential scattering and total reaction cross sections agree well with experiment, suggesting that the use of pseudo-inelastic configurations can yield an adequate description of deuteron direct-breakup processes. At higher energies, the agreement is less satisfactory, owing mainly to the adoption of a relatively small number of pseudo-inelastic configurations in our formulation. Thep+d inter-cluster interactions are found to be appreciably odd-evenL-dependent and are characteristically different in channel spinS=3/2 and 1/2states. Specific distortion effects of the deuteron cluster are also studied. For relative orbital angular momentumL=0, these effects turn out to be small in theS=3/2 state but are quite large in theS=1/2 state.

Reaction cross sections in the four-nucleon system with the multiconfiguration resonating-group method.

The d+d and p+t partial and total reaction cross sections are computed with a multiconfiguration resonating-group method. The model space employed is spanned by p+t, n+h, d+d, and pseudoinelastic configurations involving deuteron pseudoexcited states. The results show that, at energies where the influence of relatively sharp resonance levels is small, the calculated cross sections for the reactions d(d,p)t, d(d,n)h, and p(t,n)h agree well with experiment. On the other hand, it is also found that, for d+d going into three- and four-particle channels, the calculated reaction cross sections are much too small, suggesting that the inclusion of direct-breakup processes alone through the use of deuteron pseudoinelastic configurations is not sufficient. Because of this, we conclude that the model space employed here is still not extensive enough, especially in the channel spin S=2 state, and should be further expanded to include cluster-rearrangement configurations p+${\mathit{t}}^{\mathrm{*}}$ and n+${\mathit{h}}^{\mathrm{*}}$, where ${\mathit{t}}^{\mathrm{*}}$ and ${\mathit{h}}^{\mathrm{*}}$ represent excited states of the three-nucleon systems having n+d and p+d cluster structures with relative orbital angular momentum I=1 and spin angular momentum S=3/2.

Multiconfiguration resonating-group study of the six-nucleon system with cluster-rearrangement and pseudo-inelastic configurations.

The six-nucleon system is studied with a multiconfiguration resonating-group calculation which consists of the dominant configuration {ital d}+{alpha}, the cluster-rearrangement configurations {ital p}+{sup 5}He and {ital n}+{sup 5}Li, and the pseudo-inelastic configuration {ital d}{sup *}+{alpha}. The result shows that, because the deuteron cluster is easily distortable, a {ital d}+{alpha} single-configuration study is inadequate. With the addition of the other cluster configurations, the {sup 6}Li ground-state energy is improved by a large amount equal to 1.76 MeV. From an overall viewpoint, the {ital p}+{sup 5}He and {ital n}+{sup 5}Li configurations are found to contribute more significantly than the {ital d}{sup *}+{alpha} configuration, thus confirming the findings from previous seven- and eight-nucleon investigations that single-nucleon transfer processes generally make important contributions and sequential-decay processes are more important than direct-breakup processes in the relatively low-energy region. The {ital d}+{alpha} total reaction cross sections have also been computed and found to agree rather well with empirical results. At 10 MeV, for example, the calculated total reaction cross section is equal to 85% of the empirical value, which is the highest percentage obtained in our six- to eight-nucleon microscopic resonating-group calculations containing no phenomenological imaginary potentials.

Multiconfiguration resonating-group theory of 8Li.

The nucleus $^{8}\mathrm{Li}$ is studied with a multiconfiguration resonating-group calculation which consists of n${+}^{7}$Li, t${+}^{5}$He, n${+}^{7}$${\mathrm{Li}}^{\mathrm{*}}$, and $^{4}$H+\ensuremath{\alpha} cluster configurations. With no adjustable parameters, the results show that the calculated level spectrum agrees well with experiment and with the empirical level spectrum obtained by Knox, Resler, and Lane using an extensive R-matrix analysis. A calculation employing only the n${+}^{7}$Li configuration is found to be generally inadequate. Among the configurations t${+}^{5}$He, n${+}^{7}$${\mathrm{Li}}^{\mathrm{*}}$, and $^{4}$H+\ensuremath{\alpha} which are employed to enlarge the model space, the n${+}^{7}$${\mathrm{Li}}^{\mathrm{*}}$ configuration is shown to be the most important from an overall viewpoint. Comparisons between calculated and experimental scattering and reaction cross sections have also been made. Here one finds that the calculation explains all the main features of measured results. In particular, the triton production cross section of the $^{7}\mathrm{Li}$(n,n't)\ensuremath{\alpha} reaction is well reproduced. The calculated n${+}^{7}$Li total reaction cross section turns out to be somewhat too small, being equal to around 75% of the experimental value.

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

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 + 3He and deuteron pseudo-inelastic configurations. The results indicate that, with no adjustable parameters, the main characteristics of the p + α and d + 3He 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 + 3He 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 + 3He 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.

Neutron and proton form factors of 7Li and 7Be

Proton and neutron form factors of 7Li and 7Be 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.

Microscopic theory of the sup3H+ alpha system with the multichannel resonating-group method.

The effects of specific distortion in the /sup 3/H+..cap alpha.. system are examined, within the framework of the multiconfiguration resonating-group method, by including a large number of pseudo-inelastic cluster configurations involving pseudo-states of both /sup 3/H and ..cap alpha.. clusters. In this investigation, the variational stability conditions for both /sup 3/H and ..cap alpha.. clusters are well satisfied. The result shows that the effects of distortion are important to explain the main characteristics of the /sup 3/H+..cap alpha.. system, and that the dependence of the distortion effect on the choice of the nucleon-nucleon potential is rather weak. In addition, it is found that the distortion effect of the ..cap alpha.. cluster is enhanced when the triton-cluster distortion is properly considered.

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.