Phenomenological Imaginary Potential Research Articles

Mean free path of nucleons in a Fermi gas at finite temperature

The mean free path of a nucleon in a nuclear Fermi gas at finite temperature is calculated by utilizing the free nucleon-nucleon cross section modified to suppress final states excluded by the Pauli principle. The results agree with an earlier zero-temperature calculation but yield substantially smaller values than a previous finite-temperature analysis. The Fermi gas mean free paths are some two to four times shorter than those implied by phenomenological imaginary optical potentials, suggesting that the present Fermi gas model fails to adequately describe the physical processes determining the mean free path. Even so, the present results, taken as lower bounds on the mean free path, require temperatures of some 4.5 MeV before the mean free path of bound nucleons becomes as short as the nuclear diameter. It follows that very high excitation energies are prerequisite to any short mean free path assumption in nuclear heavy-ion collisions.

Resonating-group study and odd-even features in theHe3+Li6system

The resonating-group method in the single-channel approximation is used to investigate the $^{3}\mathrm{He}$ + $^{6}\mathrm{Li}$ system. The result shows that there exist a number of bound and sharp resonance levels in the energy region below about 10 MeV. In addition, it is found that, with the introduction of a phenomenological imaginary potential to take reaction effects into account, the calculation can yield differential cross sections in satisfactory agreement with experimental data. The effect of the Pauli principle is also examined. Here one finds that the odd-even feature is rather prominent and, similar to the $d$+$^{3}\mathrm{He}$ case, has distinctly different behavior in the two channel-spin states.NUCLEAR REACTIONS $^{6}\mathrm{Li}$($^{3}\mathrm{He}$, $^{3}\mathrm{He}$); calculated phase shifts and $\ensuremath{\sigma}(\ensuremath{\theta})$. Resonating-group method and effects of Pauli principle.

Resonating-group study of theα+N15system

The resonating-group method is used to study the $\ensuremath{\alpha}$+$^{15}\mathrm{N}$ system. The result shows that, with the use of a reasonable nucleon-nucleon interaction and a phenomenological imaginary potential, the calculation can yield a differential cross section which agrees rather well with experimental data. In addition, one learns from this study useful information concerning the cluster structures of many bound and resonance levels in the compound nucleus $^{19}\mathrm{F}$.NUCLEAR REACTIONS $^{15}\mathrm{N}$($\ensuremath{\alpha}$,$\ensuremath{\alpha}$); calculated level structure, phase shifts, and $\ensuremath{\sigma}(\ensuremath{\theta})$. Resonating-group method.

Resonating-group study of then+Li6system

The resonating-group method, together with a complex-generator-coordinate technique, is used to investigate the n + /sup 6/Li scattering problem. The result shows that, by including a phenomenological imaginary potential in the formulation to take approximate account of reaction effects, a good agreement with experiment can be obtained for both the differential scattering and the total reaction cross sections. The effect of the Pauli principle on the nature of the effective internuclear potential is also examined. Here it is found that the blocking effect, arising from the presence of two nucleons in the nonclosed 1p shell of /sup 6/Li, has a profound influence on the odd-even orbital-angular-momentum dependence of this potential.

Resonating-group study of d + α scattering

The resonating-group method is used to examine the d + α scattering problem over a wide energy range. The nucleon-nucleon potential employed contains both central and spin-orbit components. The result shows that, with the inclusion of a phenomenological imaginary potential to take account of reaction effects, the calculation does yield satisfactory agreement with experiment both at low energies and at a rather high energy of 53.9 MeV.

Study of theα+O16system with the resonating-group method

The resonating-group method is used to study the ..cap alpha..+/sup 16/O system. The cluster internal functions used are translationally invariant antisymmetrized products of single-particle wave functions of the lowest configuration in harmonic-oscillator wells, with width parameters chosen to yield the correct rms radii of both the ..cap alpha.. and the /sup 16/O clusters. A generator-coordinate technique is employed to derive the integrodifferential equation which governs the relative motion between the clusters. The result shows that a fairly satisfactory description of the /sup 20/Ne rotational bands can be obtained. In addition, it is found that, with the introduction of a phenomenological imaginary potential to take reaction effects into account, the calculation also yields differential scattering cross sections which agree rather well with experimental data. (AIP)

Alpha-Ca40optical potentials: Density dependent interactions

A linear density dependent effective nucleon-nucleon interaction is used in a folding model to analyze 166 MeV $\ensuremath{\alpha}$-particle elastic scattering data from $^{40}\mathrm{Ca}$. A phenomenological imaginary potential is added to the real potential generated by the model. The density dependence used is insufficient to fit the experimental angular distribution quantitatively. We point out the nature of the change in the optical potential required to achieve better results.

Resonating-group calculation ofn+H3scattering

The single-channel resonating-group method with a central nucleon-nucleon potential is used to study the $n$ + $^{3}\mathrm{H}$ system up to a c.m. energy of about 17 MeV. The specific distortion of the triton in this system is investigated, and it is found that its effect on the $n$ + $^{3}\mathrm{H}$ phase shifts is small. A phenomenological imaginary potential is included in the calculation in order to account approximately for the effects of reactions on the elastic channel. The strength of this potential is chosen to reproduce measured total reaction cross sections for the charge-conjugate system $p$ + $^{3}\mathrm{He}$. The results of the calculation are in satisfactory agreement with measured $n$ + $^{3}\mathrm{H}$ elastic differential cross sections.NUCLEAR REACTIONS $^{3}\mathrm{H}(n, n)$, ${E}_{\mathrm{c}.\mathrm{m}.}=4.5\ensuremath{-}17.25$ MeV; calculated phase shifts and $\ensuremath{\sigma}(\ensuremath{\theta})$; studied specific distortion. Resonating-group method with imaginary potential.

Odd-even absorption and Coulomb-exchange effects in theHe3+He4andH3+He4systems

Differential cross sections for $^{3}\mathrm{He}$ + $^{4}\mathrm{He}$ elastic scattering are calculated at c.m. energies up to 44.5 MeV using the one-channel resonating-group method. A phenomenological imaginary potential, whose strength depends on whether the relative orbital angular momentum is even or odd, is included in the calculation in order to account approximately for open reaction channels. Exchange terms which arise from the nucleon-nucleon Coulomb interaction also are included. The introduction of both the odd-even absorption and the Coulomb-exchange terms is found to lead to significantly improved agreement with experiment. In addition, the use of improved rms matter radii for $^{3}\mathrm{He}$ and $^{3}\mathrm{H}$ is found to yield $^{2}P_{J}$ bound-state energies for the $^{3}\mathrm{He}$ + $^{4}\mathrm{He}$ and $^{3}\mathrm{H}$ + $^{4}\mathrm{He}$ systems which are more consistent with experiment than found previously.[NUCLEAR STRUCTURE, REACTIONS $^{7}\mathrm{Li}$, $^{7}\mathrm{Be}$; calculated $^{2}P_{J}$, $^{2}F_{J}$ levels. $^{4}\mathrm{He}$($^{3}\mathrm{He}$, $^{3}\mathrm{He}$), ${E}_{\mathrm{c}.\mathrm{m}.}=1.7\ensuremath{-}44.5$ MeV; calculated $\ensuremath{\sigma}(\ensuremath{\Theta})$; deduced imaginary-potential strength, space-exchange mixture. Resonating-group method.]

Microscopic coupled-channel study of the five-nucleon system with the resonating-group method

A coupled-channel study of the five-nucleon system is performed with the resonating-group method. The channels which are explicitly considered are the $d+^{3}\mathrm{He}$ (or $d+^{3}\mathrm{H}$) and the $p+\ensuremath{\alpha}$ (or ($n+\ensuremath{\alpha}$) channels. Three- and more-body breakup channels are not included in the calculation, but their effects are crudely taken into account by the introduction of phenomenological imaginary potentials into the formulation. The nucleon-nucleon potential used is purely central, but does yield correct values for the two-nucleon effective-range parameters. Differential scattering and reaction cross sections are calculated at various energies. The result shows that for the $d+^{3}\mathrm{He}$ and $p+\ensuremath{\alpha}$ differential scattering cross sections, the calculated values in general agree quite well with the experimental data. For the $d+^{3}\mathrm{He}\ensuremath{\rightleftarrows}p+\ensuremath{\alpha}$ differential reaction cross sections, the comparison between theory and experiment is somewhat less satisfactory. Although the general features of the experimental angular distributions are well reproduced, the magnitude of the calculated cross section is somewhat too low.[NUCLEAR REACTIONS $^{3}\mathrm{He}(d,d)$, $^{3}\mathrm{He}(d,p)$, $^{4}\mathrm{He}(p,d)$, $^{4}\mathrm{He}(p,p)$, $E=0\ensuremath{-}50$ MeV; calculated $\ensuremath{\sigma}(\ensuremath{\theta})$. Resonating-group method; coupled-channel calculation.]

Effects of imaginary potentials on spurious resonances in resonating-group calculations

By studying the coupled-channel d + 3He and p + α resonating-group calculation, it is found that the introduction of phenomenological imaginary potentials is a simple way to eliminate spurious resonances from resonating-group and perhaps other microscopic reaction calculations.

Study ofd+H3andd+He3Systems with the Resonating-Group Method

The one-channel resonating-group method, together with a phenomenological imaginary potential, is used to study the $d+^{3}\mathrm{H}$ and $d+^{3}\mathrm{He}$ systems. Our calculations show that, because of the Pauli exclusion principle, these systems possess the following rather interesting feature: In the $s=\frac{3}{2}$ state they behave similar to the $d+\ensuremath{\alpha}$ system, whereas in the $s=\frac{1}{2}$ state they behave more like the $^{3}\mathrm{He}$+$^{4}\mathrm{He}$ system. Phase shifts are computed up to $l=7$, and an $\mathbf{R}$-matrix analysis of these phases indicates that there are a large number of levels with resonance energies below 12 MeV. Differential scattering and total-reaction cross sections are compared with experimental data at several c.m. energies from about 2 to 14 MeV. This comparison shows that the introduction of an odd-even orbital-angular-momentum dependence into the imaginary potential can improve the agreement of the calculation with experiment.

Odd-even absorption in 3He + 3He scattering and level structure of 6Be

Differential cross sections for 3He + 3He elastic scattering are calculated at c.m. energies from 2.95 to 37.44 MeV using the one-channel resonating-group method. A phenomenological imaginary potential, whose strength depends on whether the relative orbital angular momentum is even or odd, is included in order to account approximately for open reaction channels. The introduction of such an odd-even feature leads to a significantly improved agreement with experiment, especially at the larger scattering angles. In addition, an analysis of the calculated resonant phase shifts confirms recent experimental observations of highly excited levels in 6Be.

Study of d + d scattering with the resonating-group method and an imaginary potential

The elastic scattering of deuterons by deuterons is considered with the resonating group method. The existence of reaction channels is approximately taken into account by introducing into the resonating-group formulation a phenomenological imaginary potential. For the deuteron wave function, a flexible three-Gaussian function is used, with the parameters adjusted to minimize the expectation value of the deuteron Hamiltonian. This particular deuteron function yields a very satisfactory behaviour for the form factor and its use in the d + d calculation is shown to produce results very close to those which would be obtained if the deuteron eigenfunction were used. Comparison with experiment is made at 6.9, 12.65, 17.45 and 19.9 MeV. At all these energies, rather good agreement with the experimental differential and reaction cross-section data can be obtained. The imaginary potential is found to be energy dependent and contain a strong odd-even orbital-angular-momentum dependence. Without this odd-even dependence, it is shown that the diffraction minimum, observed experimentally at around 70°, cannot be reproduced.

Imaginary potential in resonating-group calculation of 3He + 3He scattering

The 3He+ 3He differential scattering and reaction cross-section data in the energy range of 1.5 to 15 MeV (c.m.) is analyzed with a one-channel resonating-group method to which is added a phenomenological imaginary potential in order to approximately account for open reaction channels. With a nucleon-nucleon potential of near-Serber exchange mixture it is found that satisfactory results can be obtained with such a formalism. The presence of the imaginary potential is shown to be important, especially at higher energies; it affects the magnitude of the differential cross section mainly, but can also accentuate the diffraction features at certain energies.

Study ofp+He3andn+H3Systems with the Resonating-Group Method

The one-channel resonating-group method, together with a phenomenological imaginary potential, is used to study the $d+^{3}\mathrm{H}$ and $d+^{3}\mathrm{He}$ systems. Our calculations show that, because of the Pauli exclusion principle, these systems possess the following rather interesting feature: In the $s=\frac{3}{2}$ state they behave similar to the $d+\ensuremath{\alpha}$ system, whereas in the $s=\frac{1}{2}$ state they behave more like the $^{3}\mathrm{He}$+$^{4}\mathrm{He}$ system. Phase shifts are computed up to $l=7$, and an $\mathbf{R}$-matrix analysis of these phases indicates that there are a large number of levels with resonance energies below 12 MeV. Differential scattering and total-reaction cross sections are compared with experimental data at several c.m. energies from about 2 to 14 MeV. This comparison shows that the introduction of an odd-even orbital-angular-momentum dependence into the imaginary potential can improve the agreement of the calculation with experiment.

Evaluation of the imaginary part of the optical potential with a Monte-Carlo method

A study of the use of a Monte-Carlo method, in evaluating multi-dimensional integrals, where the domain of integration is restricted by the Pauli exclusion principle, is made. This method is applied to the evaluation of the imaginary part of the optical potential using the Fermi-gas model and experimental nucleon-nucleon cross sections. The results show that the discrepancy reported by Greenlees et al., between the calculated and phenomenological imaginary potentials is not due to the assumption of an isotropic angular distribution in the nucleon-nucleon differential cross sections.