Antisymmetrization Effects Research Articles

Optimal approximation to elastic and inelastic scattering on a bound nucleon system.

An approximation to scattering on a bound system which minimizes the correction term is derived. This ``optimal'' approximation is found to be more precise and more simple for application than the weak binding impulse approximation. The derivations are presented in the framework of a local many-body nuclear interaction for the elastic and inelastic single scattering amplitude for the first-order optical potential and for distorted wave approximations. A simple formula for the correction terms to the optimal approximation is obtained. Pauli antisymmetrization effects and spin-orbit forces are not considered.

Modified momentum distribution of quarks in a two-nucleon system

The average quark momentum in a two-nucleon system is calculated using the quark cluster model approach. Its relation to the rescaling model of the EMC effect is discussed. We emphasize that the effect of quark antisymmetrization is supressed by exchange factors for the internal degrees of freedom. Color-magnetic gluon exchange is found to modify the individual nucleon size significantly.

Antisymmetrization effects in radiative capture reactions

The role played by the Pauli principle in low-energy radiative capture reactions is investigated through a comparison between a microscopic model-the generator coordinate method-and two of its approximations based on an orthogonality condition. The electromagnetic transition matrix element is shown to contain a dominant local term and a smaller residual-antisymmetrization term. The validity of the approximations is studied for the 16O(α, γ) 20Ne reaction under conditions of calculation leading to spectroscopic and elasticscattering properties as close as possible to those of the microscopic model. Nonnegligible differences are found between the three calculations. The local approximation is not significantly less accurate than the more complicated nonlocal one. A simple criterion is proposed to determine the validity of both approximations for other radiative capture reactions. At very low energies, the variation of the astrophysical factor can be well reproduced by the extranuclear capture model. The slope of the S-factor at zero energy is explained qualitatively for different reactions by a simple analytical formula. © 1985 Academic Press, Inc. All rights reserved.

Antisymmetrization effects in radiative capture reactions: D. Baye and P. Descouvemont. Physique Théorique et Mathématique CP 229, UniversitéLibre de Bruxelles, Belgium

Antisymmetrization effects in radiative capture reactions: D. Baye and P. Descouvemont. Physique Théorique et Mathématique CP 229, UniversitéLibre de Bruxelles, Belgium

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.

Wolfenstein parameters in the helicity representation for intermediate-energy proton-nucleus scattering

The reorientation of proton spin polarization as a result of scattering from a 0 + target is studied in a distorted-wave formulation using the momentum helicity representation. The relations between Wolfenstein parameters are examined including antisymmetrization effects.

One-pion exchange potential based on a quark model

Employing a quark model where massless quarks are confined by a scalar potential, the effect of quark antisymmetrization on one-pion exchange potential between two nucleons is investigated. It is found that the effect is very large at short distances. The resulting potential has a state independent strong repulsion at short distances and the usual Yukawa form with σ·στ·τ dependence at long range.

Deuteron distorting potentials for (d, p) and (p, d) reactions

A simple treatment of deuteron stripping is developed in which the deuteron distoring potential is constructed so as to include some higher-order processes and effects of antisymmetrization between the deuteron and the target. The resulting potential consists of the usual adiabatic potential and Pauli correction terms. The failure of the adiabatic prescription for 54Fe(d, p) 55Fe reactions is solved when the Pauli correction terms are included.

Time-dependent variational description of αα scattering

The time-dependent variational principle is applied to the simple but quite realistic situation of αα scattering. The effects of antisymmetrization are included and we show that they lead to a change in the structure of the phase space of relative motion. The main new feature is the appearance of forbidden regions in the phase space which have, in the quantum treatment, a close connection with states excluded by the Pauli principle. The elastic phase shifts are evaluated semiclassically in the distorted phase space and compared to a quantum calculation by the resonating group method.

Energy-dependent signature of the spin-orbit interaction in inelastic nucleon-nucleus scattering

The two-body spin-orbit term in the nucleon-nucleon transition operator responsible for intermediate-energy nucleon-nucleus inelastic scattering is studied. It is shown that the simple characteristic energy dependence of the spin-orbit contribution at fixed momentum transfer q is largely maintained in the presence of antisymmetrization, distortion, and other energy-dependent effects. Fixed-q variable-energy plots of cross sections may therefore be useful as a diagnostic tool for important spin-orbit contributions for isoscalar transitions in the range 100< or =E/sub p/< or =400 MeV.

The hyperspherical harmonics method applied to 12C

We apply the hyperspherical harmonics method to the low-lying T = 0 states in 12C, using the 3-α model. With the results from ref. 1) we are able to investigate all states up to the 4 + level at 14.1 MeV, except for the broken symmetry 1 + state at 12.7 MeV. Antisymmetrization effects are included by adopting the local potential approximation 2). Energy levels and electron scattering form factors are calculated.

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.

Effect of deuteron breakup on the 24Mg(p, d) 23Mg( [formula omitted]+, 2.36 MeV) cross section

The “spectacular” failure of the conventional DWBA to fit this Δl = 0 pick up reaction, first pointed out by Shepard et al. is not removed by inclusion of breakup. The calculation is approximate in that it includes only one breakup bin, and neglects spins as well as Pauli antisymmetrization effects.

Calculation of the energy dependence of the ion-ion potential using the Negele force

The energy dependence of the real part of the ion-ion interaction potential is studied using an energy density functional derived from the Negele realistic nucleon-nucleon interaction. It is found that the Negele force produces an ion-ion potential which varies slowly with energy compared to that derived using a simple two-body effective interaction.NUCLEAR REACTIONS Antisymmetrization effects, Fermi gas model, momentum density, Negele force, energy dependence of ion-ion potential.

Exact multiple scattering theory of two-nucleus collisions including the Pauli principle

Exact equations for two-nucleus scattering are derived in which the effects of the Pauli principle are fully included. Our method exploits a modified equation for the scattering of two identical nucleons, which is obtained at the beginning. Considering proton-nucleus scattering we found that the resulting amplitude has two components, one resembling a multiple scattering series for distinguishable particles, and the other a distorted ($A\ensuremath{-}1$) nucleon cluster exchange. For elastic $\mathrm{pA}$ scattering the multiple scattering amplitude is found in the form of an optical potential expansion. We show that the Kerman-McManus-Thaler theory of the optical potential could be easily modified to include the effects of antisymmetrization of the projectile with the target nucleons. Nucleus-nucleus scattering is studied first for distinguishable target and beam nucleus. Afterwards the Pauli principle is included, where only the case of deuteron-nucleus scattering is discussed in detail. The resulting amplitude has four components. Two of them correspond to modified multiple scattering expansions and the others are distorted ($A\ensuremath{-}1$)- and ($A\ensuremath{-}2$)- nucleon cluster exchange. The result for $d\ensuremath{-}A$ scattering is extended to the general case of nucleus-nucleus scattering. The equations are simple to use and as such constitute an improvement over existing schemes.

Antisymmetrization and density-dependent effects within the folding model approach to α-nucleus scattering

The real α-nucleus interaction is investigated within the framework of the folding model. First the non-local α-nucleon interaction is calculated in the Hartree-Fock approximation and then folded in with the target matter density. The resulting α-nucleus potential is non-local but a local equivalent potential is obtained within the Perey-Saxon approximation. The calculations are performed both with density-independent and density-dependent forces. The rearrangement terms, arising from the density dependence of the force, which are usually neglected, are calculated and found to be significant at small distances. The local density appearing in the density-dependent part of the force is evaluated using a prescription which avoids explicit contradiction of the Pauli principle, in contrast to many earlier calculations where it is calculated as the sum of the densities of the colliding nuclei. However our prescription is expected to underestimate the density-dependent effects. The calculated potentials are used to fit elastic α-particle scattering from 40 Ca at 104 MeV incident energy. Good agreement with experimental data is obtained after renormalizing the theoretical potentials by a factor ranging from 0.6 to 0.9. Finally the E - and A -dependences of the volume integral per nucleon pair of the calculated potentials are investigated and found to be in good qualitative agreement with the available phenomenological results.

Effects of antisymmetrization in nuclear direct reactions

The effects of antisymmetrization in direct reactions are studied by examining the general properties of the coupling-hamiltonian kernel function occurring in a coupled-channel resonating-group formulation. Together with a previous investigation of the coupling-normalization kernel function, one finds from this study interesting systematics concerning the general behaviour of direct-reaction processes and some justification for the use of simple three-body models in phenomenological analyses. In addition, it is shown that certain coupling terms make comparatively insignificant contributions; these terms may, therefore, be frequently omitted in a resonating-group calculation, thus reducing to a considerable extent the computational effort required in such a calculation.

Alpha-cluster transfer from alpha-decaying nuclei

The (d, 6Li) α-cluster pickup reaction on targets of 144Nd, 148Sm, 152Gd, 208Pb, 232Th and 238U at bombarding energies from 33 MeV to 55 MeV as well as the α-cluster stripping reaction, 208Pb( 6Li, d) at 90 Mev have been analyzed and the results compared with the known α-decay properties of 144Nd, 148Sm, 152Gd, 212Po, 232Th and 238U, respectively. The dependence of the finite-range DWBA cross sections on a number of quantities was studied : (i) the optical model parameters; (ii) the α-cluster wave function in 6Li and the influence of α + d antisymmetrization effects; (iii) the effective interaction between the deuteron and the α-particle; (iv) the α-cluster wave function in the target nucleus and its relationship to the A-dependence of nuclear matter radii. Reduced widths and spectroscopic factors extracted independently for α-transfer and α-decay agree within a factor 1.4±0.5 for appropriate choices of parameters. This confirms the validity of the reaction and decay analyses and indicates that the g.s. → g.s. transitions proceed predominantly by a direct α-transfer. Antisymmetrization effects which may influence α-decay and α-transfer differently are weak as the latter takes place primarily in the surface region of nuclei. It is estimated that about 25 % of the nuclear matter in the surface at ρ nucl ( r)/ ρ nucl (0) ≈ 0.3% is associated with α-particle matter (α-particle condensation).

Energy dependence of the real part of ion-ion interaction potential

A simple derivation for the energy dependence of the real part of ion-ion interaction potential is given in the framework of Brueckner's energy density formalism. This is based on the decreasing effect of antisymmetrization on the kinetic energy densities of the two ions which is studied in a Fermi gas model and tends to make the ion-ion potential more and more attractive with increasing relative energy ${E}_{\mathrm{c}.\mathrm{m}.}$. On the other hand, the linear dependences of the kinetic energy densities and the momentum densities on ${E}_{\mathrm{c}.\mathrm{m}.}$, through the effective mass term in the energy density, introduce a repulsion which increases directly as the relative energy. At low values of ${E}_{\mathrm{c}.\mathrm{m}.}$ the first effect dominates over the second one, thereby making the ion-ion potential more and more attractive. However, at relatively high energies, the repulsion caused by the second effect dominates completely and makes the potential less and less attractive.NUCLEAR REACTIONS Antisymmetrization effects, Fermi gas model, momentum density, effective mass term, energy dependence of ion-ion interaction potential.

Antisymmetrization effects in bond-orbital models of internal rotation barriers

We exhibit a set of orthonormal CH bond orbitals, having high overlap (?0.998) with those of Hoyland and Sovers et al., but predicting an ethane rotation barrier of incorrect sign when employed in an antisymmetric wave function. Taken together with previous work of Levy et al., this indicates that wave function antisymmetry is neither necessary nor sufficient for the appearance of barrier forces in approximate quantum-chemical calculations.