Effect of the shell structure of nuclei on p 15C and p 15N scattering within diffraction theory

The differential cross sections for elastic proton scattering on ¹⁵C and ¹⁵N nuclei at energies of 150 and 800 MeV were calculated within the diffraction theory of Glauber multiple scattering. Shellmodel wave functions were used in these calculations, and particular attention was given to analyzing the sensitivity of the calculated features to distinctions between the shell structure of the ¹⁵C nucleus and the shell structure of the ¹⁵N nucleus. The calculations were performed in the approximation of double scattering. The multiple-scattering operator was written in a form that permits taking into account collisions with nucleons belonging to different shells. It is shown that the difference in structure between the two nuclei in question leads to substantial distinctions between the differential cross sections for scattering at an energy of 800 MeV and scattering angles larger than 25°.     

Neutron-neutron quasifree scattering in the 2H(n,nn)p reaction at En = 14.1 MeV

Neutron-neutron quasifree scattering has been studied in the deuteron break-up reaction ²H(n, nn)p at E_n = 14.1 MeV. Two coplanar and symmetric configurations have been investigated in a kinematically complete experiment where the detection of the spectator particle was not possible. The experimental cross sections are compared with “exact” calculations derived from Faddeev-type equations solved with S- and P-wave nucleon-nucleon separable interactions. These calculations agree both in shape and magnitude with the differential cross section for the θ₁ = ? θ₂ = 40° configuration (E_p^min = 0). At θ₁ = ? θ₂ = 30° (E_p^min = 180 keV). however, the absolute value of the measured cross section is too high and an observed structure in the shape of the differential cross section is in sharp conflict with the now available “exact” calculations.     

Differential cross section,analyzing power and phase shifts for p-3He elastic scattering below 1.0 MeV

Differential cross sections and analyzing powers for the elastic scattering of polarized protons by unpolarized ³He nuclei have been measured at eight energies between 0.3 MeV and 1.0 MeV for scattering angles θ_c.m. = 52.4°–173.3°. The cross-section values were normalized to the Rutherford cross section for proton-krypton scattering. The analyzing powers have been measured with a statistical accuracy of about 0.001. The phase-shift analysis based on these data included all phases for orbital angular momenta l ≦ 1 and the channel-spin mixing parameter for the P waves. An energy parametrization of the phase shifts by an effective-range approximation allowed a simultaneous utilization of all data.     

Sub-barrier interaction between deuterons and 58, 62Ni nuclei

The interaction between deuterons and ^{58, 62}Ni nuclei at energies of E _d = 3.5, 4.5 and 5.16 MeV is investigated. The discrepancy between measured scattering elastic cross section and the Rutherford ones is higher than the value calculated theoretically by considering deuterons polarization and Coulomb breakup. Analysis of measured cross section of ^{58, 62}Ni(d, p) reaction and the results of calculation of Coulomb breakup cross section integrated over neutron emission angles shows that that the dominant mechanism of proton formation is the reaction of neutron transfer to the target nucleus.     

Observation of deuteron D-state and compound nucleus effects in (d,p) reactions on 46Ti and 52Cr with a polarized deuteron beam

The cross section and the vector and tensor analyzing powers have been measured for ⁴⁶Ti(d, p)⁴⁷Ti at deuteron energies of 6 and 10 MeV and ⁵²Cr(d, p)⁵³Cr at 6 MeV. Transitions were observed to the states at E_x=0.159, 1.549 and 1.793 MeV in ⁴⁷Ti and the states at E_x=0.0, 0.564, 1.006 and 2.321 MeV in ⁵³Cr. In addition, the cross sections and vector analyzing powers for deuteron elastic scattering were measured for the same targets and deuteron energies and compared to optical model calculations. The choice of optical parameters for the DWBA analysis of the (d, p) reactions is discussed. Calculations made with the DWBA method show that the deuteron D-state must be included to reproduce even qualitatively the (d, p) tensor analyzing power measurements. The j-dependence of the tensor analyzing power T₂₂ is discussed. The validity of the local energy approximation (which was used to incorporate the deuteron D-state into the DWBA calculations) is evaluated by comparison to finite range calculations. The contribution of compound nucleus reactions to the measured cross sections and analyzing powers was investigated. In order to determine the compound cross section, the Ericson fluctuations in excitation functions of cross section and vector analyzing power were measured from 5 to 7 MeV on each target. The formulas used to calculate the polarization observables from the Hauser-Feshbach theory are presented.     

Refractive scattering and reactions,comparison of two systems:16O+16O and20Ne+12C

Elastic, inelastic scattering as well as one-neutron transfer channels have been measured over a wide angular range for systems¹⁶O+¹⁶O at the incident energy of 350 MeV and²⁰Ne+¹²C at 390 MeV, respectively, using the Q3D magnetic spectrometer. In both cases differential cross sections have been measured down to about 50 nb/sr (or d/d _R10^–4) at large angles. For the¹⁶O+¹⁶O system refractive contributions are found at the level of these cross sections, whereas in the²⁰Ne+¹²C case a steeper decrease of the differential cross section with the angle is observed and the refractive contribution can not be determined. The elastic scattering data have been analyzed using standard Woods-Saxon potentials and potentials calculated in different versions of the double-folding model. Some properties of these potentials are tested in the calculations for inelastic scattering and one-neutron transfer within the DWBA. With the refractive pattern observed for the¹⁶O+¹⁶O system, the scattering and transfer data are found to be sensitive to the interaction potential at small internuclear distances down to about 2.5 fm.It should be acknowledged that part of the folding analysis reported here was done while one of the authors (D.T.K.) was staying at the Institute for Theoretical Physics, University of Tübingen. We also thank Prof. H. Clement and H. Abele for numerous discussions and contributions and Prof. G.R. Satchler for helpful comments on the use of the DWBA code PTOLEMY.     

Threshold anomaly in doubletn-d scattering

The behaviour of the doubletn-d scattering phase shift ₂(k) at energies close to the three-particle threshold is studied analytically and numerically. The scattering parameters possess an anomaly associated with the low energy of the singletN-N virtual state. The anomaly manifests itself both as a bend in the energy dependence of the functionk cot(Re ₂) in the range around 0.5 MeV and in the nonstandard behaviour of the break-up cross section near the threshold.     

Analyzing power for elasticn-d scattering at 13 MeV

The analyzing power for elasticn-d scattering was measured atE _n=13 MeV. The result is in good agreement with experimental data atE _n =12 MeV andE _n =14.1 MeV. At backward angles the data are well above the predictions of a rigorous Faddeev calculation using the Paris potential.     

Quasi-free scattering in the 3-N continuum

The interaction of a nucleon with the deuteron leading to break-up at the quasi-free scattering (QFS) condition is studied atE _N ^lab =12.0, 22.7, 68.0, and 140.0 MeV. Results of rigorous Faddeev calculations and of the impulse approximation (IA) are compared at these energies for bothn-p andp-p QFS in order to study the importance of rescattering terms. For the two-nucleon interaction the Paris potential is used. It is restricted to act in two-body states with total angular momentumj2. Also we compare the Faddeev calculations with experimental data for the QFS cross section and analyzing powerA _y and find overall agreement. The behaviour of scattering observables turns out to be different forn-p andp-p QFS. Also the energy dependence of rescattering terms is different in the two cases. For all energies studied the IA is not reliable.     

Analysis of <Emphasis Type="Italic">p</Emphasis><Superscript>10</Superscript>B scattering within Glauber theory

The differential cross sections for p ¹⁰B scattering are calculated at the energies of 197, 600, and 1000 MeV within Glauber theory. The contributions of single and double collisions are taken into account in the multiple-scattering operator. The contributions of proton collisions with nucleons belonging to various (1s, 1p) shells are estimated in the single-scattering cross sections. A comparison with experimental data and with the result of calculations in the distorted-wave Born approximation (DWBA) at 197 MeV showed that the differential cross sections for p ¹⁰B scattering are adequately described in the region forward scattering angles.     

Quasi-free scattering of polarized protons

Cross section and analyzing power, energy-sharing spectra have been measured for the ¹⁶O($\text{p}$, 2p) reaction at an incident energy of 200 MeV for twenty-four different pairs of angles of the detected final-state protons. This general survey is intended to test the validity of the distorted wave impulse approximation (DWIA), particularly with respect to the predicted j-dependent analyzing power caused by the distorting optical potentials and nuclear spin-orbit coupling. Although the data in general confirm this j-dependence, agreement in detail between DWIA calculations and the analyzing power data becomes worse as the momentum of the recoiling nucleus increases. Predictably, the cross-section calculations show more sensitivity to the optical-model parameters than do the analyzing powers. Within the present limits imposed by scanty elastic scattering data, there seems to remain a choice between predicted ($\text{p}$, 2p) cross sections which either are unreasonably large or which have the incorrect energy-sharing shapes. More comprehensive elastic scattering and total reaction cross section data are clearly needed.     

Small-angle scattering in a Reissner-Nordstrem field. Quasiclassical approximation

Phases, amplitude and differential cross section of charged particle scattering by a Reissner-Nordstrem black hole are obtained for small scattering angles in a quasiclassical approximation of the Klein-Gordon equation. The approximation is legitimate in the shortwave case, where the situation is considered when the Coulomb and gravitational effects are commensurate in magnitude. It is shown that for relativistic particles the angular scattering distribution differs from the Rutherford distribution in terms ^–3.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 33–37, July, 1988.     

Comparisons of vector analyzing-power data and calculations for neutron-deuteron elastic scattering from 10 to 14 MeV

High-accuracy analyzing-powerA _y() data forn-d elastic scattering at 12 MeV have been measured using the polarized-neutron facilities at the Triangle Universities Nuclear Laboratory (TUNL). The present data have been combined with our previousn-d measurements at 10, 12, and 14.1 MeV to form the highest-accuracyA _y() data set forn-d elastic scattering below 20 MeV. These data are compared to recent Faddeev-based neutron-deuteron (n-d) calculations which use the Paris and Bonn equivalent separable potentials PEST and BEST, as well as Doleschall's representation of theP- andD-wave nucleon-nucleon interactions. None of these models adequately describe the data in the angular region around the maximum ofA _y(). Possible reasons for the discrepancies are discussed. The sensitivity of the present Faddeev-based calculations to various angular momentum components of the nucleon-nucleon interaction are examined.     

Analyzing powers and cross sections in elastic p-d scattering at 65 MeV

Analyzing powers and differential cross sections for $\text{p}\text{-}\text{d}$ elastic scattering have been measured at 64.8 MeV. The angular distributions cover center-of-mass angles between 8° and 169°. The relative uncertainties of the analyzing power measurement are typically ± 0.005 at c.m. angles less than 80° and are in general ± 0.015 at the remaining angles. The absolute scale of the analyzing power measurement has an uncertainty of ± 0.013. The data are compared with three-body calculations based on the Faddeev theory. In contrast with the differential cross sections, the analyzing powers could not be reproduced without the D-wave nucleon-nucleon interactions.     

Elastic, inelastic scattering and fusion of the 14N +59Co system at energies close to the coulomb barrier

Elastic and inelastic scattering differential cross sections were measured in the energy range 30 MeV ≤ E _lab ≤ 55 MeV, for the ¹⁴N +⁵⁹Co system. Ambiguities of the optical potential derived from the analysis of the elastic scattering data were removed by performing calculations at the radius of sensitivity and by comparison with the available fusion cross section data. A simultaneous analysis of the three mechanisms was performed by coupled channel calculations, and a unique energy independent nuclear potential was found to be able to fit the data. Discussions and comparisons concerning the optical model, the threshold anomaly, full and approximated coupled channel calculations are presented. Received: 6 February 1997 / Revised version: 1 August 1997     

Suppression of the Coulomb interaction in the off-energy-shell p - p scattering from the p + d --> p + p + n reaction

Off-energy-shell effects in p - p scattering have been investigated at p - p relative energies from 600 down to 80 keV applying the Trojan horse method (THM) to the p + d --> p + p + n reaction at 5 MeV. In contrast with the on-energy-shell case, no Coulomb-nuclear interference minimum has been found in the extracted THM p - p cross section, due to the suppression of the Coulomb amplitude as predicted by the half-off-energy shell calculations. This hypothesis is strengthened by the agreement between THM p - p data and calculated on-energy-shell n + n, n + p and nuclear p + p cross sections.     

Three-body calculation of neutron-deuteron elastic scattering in the energy region from 2.5 MeV up to 50 MeV

The three-body Faddeev equations for neutron-deuteron scattering are solved in the energy region from 2.5 MeV to 50 MeV of the incident neutron energy with small energy steps. Higher-rank separable potentials are used in the¹ s ₀ wave and in the³ s ₁—³ d ₁ waves, while rank-1 separable potentials are used in¹ p ₁,³ p _0,1,2 ¹ d ₂ ³ d _2,3 waves. The calculation is compared with experiments for the total cross section, the total break-up cross section, the differential cross section and the analyzing power of neutron-deuteron scattering. The improvements in the agreement as compared to previous calculations are impressive in many cases. Especially, the calculated total cross section agrees with the experiment below 30 MeV within the error bars, which are as small as 1%. A discussion on the numerical accuracy is given. General aspects of the calculated cross section are discussed. It is pointed out that thes-wave asymptotic normalization of the deuteron wave function (A _s ) is important.     

Deuteron d-state effects for the reactions 117Sn(d, p)118Sn and 119Sn(d, p)120Sn

Angular distributions of the differential cross section and the three tensor analyzing powers were measured for the reactions ¹¹⁷Sn($\text{d}$, p)¹¹⁸Sn and ¹¹⁹Sn($\text{d}$, p)¹²⁰Sn at E_d = 12 MeV. In addition, excitation functions of the tensor analyzing power T₂₀ were measured at proton lab angles of 0° and 5° for energies ranging from 10 to 12 MeV. At forward angles, the tensor analyzing powers for the ground state (l_n = 0) transitions are more than an order of magnitude larger than the predictions of distorted-wave calculations which neglect the deuteron D-state. Qualitative agreement with the measurements is obtained when the D-state is included.     

Analysis of <Superscript>4</Superscript>He+<Superscript>40</Superscript>Ca and <Superscript>4</Superscript>He+<Superscript>44</Superscript>Ti scattering using different optical model potentials

Elastic scattering of ⁴He+⁴⁰Ca and ⁴He+⁴⁴Ti reactions at backward angles has been analyzed using two differentmodels, microscopic and semimicroscopic folding potentials. The derived real potentials supplemented with phenomenological Woods–Saxon imaginary potentials, provide good agreement with the experimental data at energy E_c.m. = 21.8 MeV without need to renormalize the potentials. Coupledchannels calculations are used to extract the inelastic scattering cross section to the low-lying state 2+ (1.083 MeV) of ⁴⁴Ti. The deformation length is obtained and compared with the electromagnetic measurement values as well as those obtained from previous studies.