Resonating-group Calculations Research Articles

Publisher's Note: Mesonic content of the nucleon and the Roper resonance [Phys. Rev. C 75, 067001 (2007)

We investigate colorless (mesonic) 3q-q qbar components in the nucleon and the Roper resonance N*(1440). Starting from constituent quarks and gluons we estimate the excitation of quark-antiquark pairs in a gluon exchange model with the strong coupling constant extracted from a comparison with a non-perturbative resonating group calculation of the pi, eta, rho and omega content of the nucleon. Applying the same model to the Roper resonance, we find as the most striking result a very strong scalar-isoscalar sigma content of the N*(1440) with a strength of the 3q-q qbar configurations comparable to the 3q component itself.

Mesonic content of the nucleon and the Roper resonance

We investigate colorless (mesonic) 3q-qq components in the nucleon and the Roper resonance N*(1440). Starting from constituent quarks and gluons we estimate the excitation of qq pairs in a gluon exchange model with the strong coupling constant extracted from a comparison with a nonperturbative resonating group calculation of the {pi},{eta},{rho}, and {omega} content of the nucleon. Applying the same model to the Roper resonance, we find as the most striking result a very strong scalar-isoscalar {sigma}-content of the N*(1440) with a strength of the 3q-qq configurations comparable to the 3q component itself.

Integral equations in the Fock-Bargmann space and the generator-coordinate method

In the generator-coordinate method, the norm kernel built as a Slater determinant of the Brink-Bloch orbitals plays a role of unity for the complete set of orthonormalized states defined in the Fock-Bargmann space and satisfying the Pauli exclusion principle. The closure condition is then written as the Hilbert-Schmidt expansion of the norm kernel and can be derived by a simple algebraic procedure. A basis of eigenstates of the norm kernel is shown to be a powerful tool in resonating-group calculations.

Resonating-Group Calculations with New Cluster Wave Function for p+3,4He Elastic Scattering

A new type of cluster internal wave function that can produce improved results, especially for the cluster binding energy, has been proposed. As a first application, we have carried out calculations for the case of p+3He and p+4He elastic scattering on the basis of the resonating group method with this type of wave function. The agreement of the calculated results and the experimental data is quite satisfactory.

Resonating-Group Calculations with a New Type of Cluster Internal Wave Function

Resonating-Group Calculations with a New Type of Cluster Internal Wave Function

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.

Differential cross section and analyzing power for elastic scattering of protons on 6Li below 2.2 MeV

Differential cross section dσdΩ and analyzing power Ay of elastic 6Li(p,p)6Li scattering have been measured in the energy range 0.4 MeV ⩽ Ep ⩽ 2.2 MeV. The angular distributions were obtained at thirteen different angles between θlab = 40° and 160° with statistical uncertainties of less than 2 × 10−3. The data show a resonance-like behaviour in the excitation functions for dσdΩ and Ay near Ep = 1.8 MeV (i.e. Ec.m. = 1.56 MeV). An energy-dependent phase-shift analysis has been performed from which resonance parameters have been deduced. The analysed data are well described in the whole energy range and support the predictions of recent refined resonating-group calculations.

Van der Waals forces in nonrelativistic quark models of the NN interaction.

The van der Waals force induced by color-dependent confining potentials in nonrelativistic quark models of the NN interaction is investigated through a full resonating group calculation where the NN channel is coupled to a channel of two orbitally polarized color octets. While exchange terms can be neglected at low energies, they prove to be essential at higher energies, where the short and intermediate ranges of the induced interaction are probed. The extent to which the latter can be simulated by effective local potentials is examined. Finally, the van der Waals force induced by a strong enough confining potential is shown to give rise to unphysical bound states.

Multiconfiguration Resonating-Group Study of Nuclear Reaction Mechanisms

Two important subjects in the field of the microscopic resonating-group method are discussed. These subjects are: (1) the study of reaction mechanisms in nuclear systems, and (2) the study of exchange effects in nuclear reactions. Both of these studies are motivated by the desire to perform simplified resonating-group calculations in medium- and heavy-weight systems. With the findings obtained from these studies, it is our opinion that the resonating-group method can now be utilized to make systematic and large-scale investigations of nuclear properties in mass regions that have hitherto been examined by only macroscopic, phenomenological means

Multiconfiguration Resonating-Group Study of Nuclear Reaction Mechanisms

Two important subjects in the field of the microscopic resonating-group method are discussed. These subjects are: (1) the study of reaction mechanisms in nuclear systems, and (2) the study of exchange effects in nuclear reactions. Both of these studies are motivated by the desire to perform simplified resonating-group calculations in medium- and heavy-weight systems. With the findings obtained from these studies, it is our opinion that the resonating-group method can now be utilized to make systematic and large-scale investigations of nuclear properties in mass regions that have hitherto been examined by only macroscopic, phenomenological means.

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

Differential cross sections and analyzing powers in n + 16O and n + 40Ca 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.

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.

The low-energyD(α, γ)6Li and6Li+208Pb→D+α+208Pb cross sections

We have calculated theE1 andE2 contributions to the low-energyD(α,γ)6Li fusion and to the6Li+208Pb →D+α+208Pb Coulomb dissociation cross sections within a multichannel Resonating Group calculation based on many-body deuteron+α configurations and pseudo-states. For both reactions experimentally determined cross sections are reasonably well reproduced. We find that dipole capture contributes noticeably to the fusion cross sections atE≦500 keV, while it is negligible in the Coulomb dissociation data.

Microscopic study of the low-energy3H(d, n)4He reaction

We have studied the3H(d, n)4He reaction at low energies within a multi-channel resonating-group calculation based on many-bodyn+α andd+3H configurations and pseudo-states as well as on an effective nucleonnucleon interaction containing central, spin-orbit, and tensor components. The low-energy fusion cross section is excellently reproduced within our approach.

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.

DETERMINATION OF THE TRANSITION AMPLITUDES OF THE D(d,n)3He AND D(d,p)3H H REACTIONS FOR Ed≤500 keV

An analysis of all available experimental data of the mirror reactions D(d,n)3He and D(d,p)3 H below 500 keV is presented. Account is taken of S-, P-, and D-waves in the input channels of the reactions. All 16 participating transition amplitudes are obtained by a fit to the experimental data. In accordance with refined resonating group calculations no suppression of quintet entrance-state transitions and therefore no neutron suppression in polarized fusion can be derived.

Microscopic study of p+ alpha bremsstrahlung.

Bremsstrahlung double cross sections for p+\ensuremath{\alpha} collisions are computed by using the wave functions obtained from a single-configuration resonating-group calculation. The photon-emission operator employed is translationally invariant and the center-of-mass motion is strictly eliminated from the transition amplitude. Analytical expressions for the reduced matrix elements are derived without invoking the long-wavelength approximation. With no adjustable parameters, it is found that there is a very good agreement between calculated and experimental values. Effects of the p+\ensuremath{\alpha}, 3/${2}^{\mathrm{\ensuremath{-}}}$ resonance show up distinctly in the cross-section curve when this resonance occurs in the final channel. On the other hand, the presence of the very broad 1/${2}^{\mathrm{\ensuremath{-}}}$ level becomes detectable from the bremsstrahlung cross-section result only when there is a proper choice of the geometrical arrangement of the particle detectors.

Consistent microscopic study of the low-energy 5Li spectrum.

We have studied the nucleus $^{5}\mathrm{Li}$ within a multichannel resonating group calculation based on many-body p+\ensuremath{\alpha} and d${+}^{3}$He configurations and pseudostates as well as on effective nucleon-nucleon interactions containing central, spin-orbit, and tensor components. The known levels in $^{5}\mathrm{Li}$, identified by the p+\ensuremath{\alpha} phase shifts and the $^{3}\mathrm{He}$(d,p${)}^{4}$He fusion cross section, can consistently be described by our approach. Special distortion effects in the sense of Tang and collaborators are discussed for these states.

Determination of the reaction-matrix elements of the D(d, n)3He and D(d, p)3H reactions forE d ?500 keV

All available data of the mirror fusion reactions D(d, n)3He and D(d, p)3H have been subjected to a new analysis in order to extract the matrix elements of all 16 transitions necessary for inclusion of alll≤2 waves. Their energy dependence was assumed to be governed solely by Coulomb penetrabilities. The Levenberg-Marquardt algorithm was used to fit all experimental data. The experimental data are reproduced satisfactorily. The results compare well with anR-matrix analysis and with refined resonating group calculations. No suppression of quintet entrance-state transitions and therefore no neutron suppression in “polarized fusion” can be derived from this analysis.