D-wave Resonances Research Articles

Quantum mechanical streamlines. IV. Collision of two spheres with square potential wells or barriers

Quantum mechanical streamlines and probability density contours help in the understanding of collision dynamics by showing what happens during the collision. This is illustrated by considering the elastic scattering of two particles which interact with a spherically symmetric square potential, V (r) =0 when r≳a and V (r) =C when r<a, where the constant C is negative for a potential well and positive for a barrier. The streamlines and density contours completely determine the wavefunction (which is separable in r and ϑ and independent of φ) since the pre-exponential factor is the square root of the density and the phase is everywhere perpendicular to the streamlines. The streamlines often form quantized vortices surrounding wavefunction nodes. Since the nodal regions are circular rings, the vortices are toroidal (like smoke rings). If one or both of the particles is charged, the vortex ring corresponds to a collisional magnetic moment. The distortion of the streamlines provides a visual explanation of the large collision cross sections. In S-wave resonances 4πr2=σ0, where r is the distance from the origin to the center of the outermost vortex and σ0 is the cross section of the S-wave component. Thus, r is essentially the ’’scattering length.’’ In P-wave resonances (where again r is the radial distance to the outermost vortex), 1.85πr2?σ1 and in D-wave resonances, 1.45πr2?σ2. In the square well resonances, the density inside of the interaction sphere has the shape of the dominant wave and often has maxima hundreds to thousands of times greater than the density of the incident wave. By happenstance, whenever the potential well has the proper depth to form a newly bound D state, there is a Ramsauer–Townsend effect so that (for small energy of the incident wave) the total scattering cross section is very small;outside the interaction zone, the streamlines are only slightly deflected by the potential well;inside, the streamlines are deflected towards the symmetry axis and the probability density is concentrated near this axis

Resonant neutron capture in 40Ca

The neutron capture cross section of 40Ca has been measured with ≈ 0.2 % energy resolution below E n = 300 keV. Resonance parameters have been extracted for many new p- and d-wave resonances. Gamma-ray spectra were also measured following capture in one doublet and two resolved resonances below 50 keV. Strong feeding of low-lying p-wave levels was observed in all cases. Calculations showed that valence transitions were inadequate to account for the observed dominance of these transitions and a further mechanism is required. The average resonance parameters obtained from the data are as follows: 〈 D〉 = 37 + 4keV, 10 4 S 1 = 0.16 ± 0.05, 10 4 S 2 = 2.0 ± 0.7. The average radiative widths and standard deviations of their distributions were found to be strongly l-dependent as follows: 〈 Γ γ 〉 s = 1.5 ± 0.9 eV, 〈 Γ γ 〉 p = 0.36 ± 0.09 eV and 〈 Γ γ 〉 d = 0.7 ± 0.4 eV.

S- and p-wave neutron spectroscopy Xc. Intermediate structure: 88Sr

Neutron total cross section measurements of natural Sr were made from 50–875 keV using a high resolution proton beam and the 7Li( p, n) reaction as a neutron source. These data were analyzed with the help of an R-Matrix code to extract resonance (energies and other) parameters up to about 850 keV. 2 p-1 h and particle-vibration doorway interpretation of the s-, p- and d-wave resonances is attempted in terms of the sum rule Σ γ n 2 = γ d 2. Predictions based on both of these models agree with the experimental results. As expected the p-wave resonances are stronger than either s- and d-wave structure. Theory accounts for the p-wave strength remarkably well. Possible location of the p-wave s.p. resonance is reproduced with a real potential and its damping due to the imaginary potential is calculated. More fragmentation of the strong p-wave doorways is observed than was expected for a compound nucleus so near 90Zr, but a larger strength function is observed apparently due to the p-wave giant resonance.

Yang-Mills fields and pseudoscalar meson scattering

We have studied a model for pseudoscalar meson scattering ( π, K, η) based on a Lagrangian in which the mesons are coupled through massive Yang-Mills fields, identified with the physical (ϱ, K ∗, ϕ) vector meson resonances. The calculation of the various two-body scattering amplitudes has been performed, in perturbation, in the one loop approximation and the Padé summation method has been applied. As a result all the well-known d-wave resonances f o, f′, A 2 and K ∗(1420) have been generated. No exotic states have been found. The ππ and K K s-wave phase shifts are in excellent agreement with experimental data; in particular the strong K K threshold effect in the ππ scattering can be reproduced. Very broad σ, κ, δ resonances are obtained. In the last section it is shown that our model, which is not renormalizable, is a limit of renormalizable model containing Higgs-Kibble mesons which would lead to similar results.

Capture of 10?100 keV Neutrons in Isotopes of Titanium

Gamma ray spectra are presented as functions of neutron energy for capture of 10?100 keV neutrons in natural titanium. The spectra are dominated by transitions to the first, third, and fifth excited states of 49Ti which show strong fluctuations with neutron energy. The nature of these fluctuations and their relation to the nature of the capture process is discussed. A small but measurable strength in the transition to the 7/2? ground state of 49Ti has been observed and this is interpreted as evidence for the existence of a d-wave resonance in the reaction 48Ti(n, ?)49Ti at 39 keV. Transitions at 8260 and 8380 keV are assigned to capture in 47Ti.

Vector-polarization measurements and phase-shift analysis for d-α scattering between 3 and 11 MeV

Vector-polarized deuterons from a tandem accelerator were used to measure the vector analysing power in d-α elastic scattering at deuteron energies from 3 to 11 MeV in steps of 1 MeV, for c.m. angles between 21° and 152°. A phase-shift analysis was carried out of the differential cross section and of tensor and vector polarization data. It was found that f-waves must be included above 8 MeV. The analysis confirms the presence of the two known d-wave resonances. The p-wave phase shifts were found to be small. An alternate solution with large p-wave phase shifts was found at 8 MeV.

Study of the d + d system using the method of resonating-group structure

The method of resonating-group structure with a one-channel approximation is used to study the d + d and d ∗ + d ∗ systems. The calculated 2H(d, d) 2H differential cross sections agree fairly well with those determined experimentally. Also, evidence is found for an l = 1 state near the d + d threshold and possibly, a D-wave resonance near 30 MeV excitation in 4He. Further, no indication of the existence of a bound 4n system is obtained.

KeV neutron capture in iron

Gamma ray intensities are given for capture of 15–80 keV neutrons in 54Fe, 56Fe and natural iron and for their variation with neutron energy. The results show a correlation with thermal capture and (d, p) results for low-lying final states in 55Fe and 57Fe thus suggesting that there is a considerable overlap of the configurations of the capturing and final states. However, reduced widths are not as large as would be expected for single-particle transitions. Limited evidence is observed of an anticorrelation between (d, p) and capture results, and the explanation in terms of possible doorway states can only apply to a small number of transitions. The observation of transitions to 5 2 − and 7 2 − final states is used to obtain evidence on the location of d-wave resonances in both 54Fe and 56Fe. Information on the isotopic allocation of resonances is also contained in the neutron energy spectra.

π−πScattering with Unitarity and Crossing

A model of pion-pion scattering is presented in which each partial-wave amplitude in the s channel satisfies unitarity including inelastic states. This is accomplished by the use of the N/D technique. The full amplitude, i.e., the explicit, continued, partial-wave sum does not satisfy unitarity in the t and u channels, but it does have the correct branch points in these channels. These characteristics are guaranteed by construction and do not depend on arbitrary parameters occurring in the N functions. The parameters are fixed by imposing the crossing relations and by demanding the existence of a Pomeranchuk trajectory in the T = 0 channel. The existence of the p is not assumed. Since crossing is not satisfied exactly, the parameters are determined as those that yield the best fit to the crossing relations. Once the parameters are fixed, the behavior of each partial wave in each isospin channel is determined. Phase shifts are presented for the S, P, and D waves. The P wave is repulsive at low energies but becomes quite attractive at higher energies due to inelastic effects. A resonance occurs at s = 33.7 mu 2 with a width about three times that experimentally observed; this width ismore » extremely sensitive to the parameters, the position is not. An S-wave ghost occurs at s = --57.1 mu 2 (whose residue is zero) as well as the Pomeranchuk trajectory at s - 0. The S waves are strongly repulsive at low energies. In fact, they are so repulsive that rather broad peaks are produced in their cross sections near 400 Mev when the phase shifts pass through -- pi /2. The peak in the T = 0 channel may very well correspond to the Abashian, Booth, and Crowe (ABC) anomaly. There are no resonances in the D waves. In panticular, the existence of an f/sub 0/ is incompatible with any choice of the parameters unless it is accompanied by another strong D-wave resonance at low energy, and even this possibility violates crossing badly. This may be due to a poor choice for the trial function. (auth)« less