Angular Distributions Of Deuterons Research Articles

Energy and angular distributions of deuterons from the D + D → p + n + d reaction

The energy and angular distributions of deuterons from the D + D → p + n + d reaction are experimentally and theoretically studied. The experiment is conducted on the U-240 cyclotron at the Institute for Nuclear Research in an extracted beam of deuterons with energy E D = 36.9 MeV. A theoretical analysis has been performed using the microscopic diffraction nuclear model, within which the final-state interaction is considered and simple expressions for internal wave functions and approximations that include quasibinary mechanisms are employed.

Differential cross sections for the reactions 6Li(n, d) 5He and 6Li(n, t) 4He at 14.1 MeV

The energy spectra and the angular distributions of deuterons, tritons and α-particles from the reactions 6Li(n, d) 5He and 6Li(n, t) 4He at 14.1 MeV have been measured at several angles up to 60° in the laboratory system. The measured energy spectrum of deuterons from the 6Li(n, d) 5He reaction was in agreement at each angle with the prediction of a simple final-state interaction theory. The measured absolute differential cross sections for the reactions 6Li(n, d) 5 He and 6Li(n, t) 4He, which are in good agreement with those of Valković et al. using 14.4 MeV neutrons, were compared with DWBA calculations. Spectroscopic factors have been deduced.

Studies of (α, d) Reactions on N=28 Nuclei. II. 52Cr(α, d)54Mn

Angular distributions of deuterons from the 52 Cr(α, d) 54 Mn reaction at E α =24 MeV have been measured and are analyzed in terms of the zero-range DWBA theory. Transferred angular momenta are assigned for 20 transitions up to 4.72 MeV excitation in 54 Mn. Strong transitions to the 0.363 and 4.715 MeV states in 54 Mn are interpreted as due to high angular momentum transfers, and these levels are assigned J π =5 + and 8 - , respectively. Seven L =0 transitions leading to E x =1.449, 1.623, 1.777, 1.913, 2.126, 2.873 and 3.835 MeV states in 54 Mn have been observed, and these levels are assigned as J π =1 + . The transition strengths for the low-lying states are discussed on the basis of a simple shell model and are found to be in good agreement with the shell model predictions.

NLi6(α,d)Be8reaction and the importance of exchange processes

The $^{6}\mathrm{Li}(\ensuremath{\alpha},d)^{8}\mathrm{Be}_{\mathrm{g}.\mathrm{s}.}$ reaction is studied in the expectation that exchange contributions will be enhanced relative to the more usual light particle stripping process. Angular distributions of deuterons were measured at bombarding energies of 20 and 24 MeV and are found to exhibit back-angle peaking characteristic of the exchange process. Calculations including only a direct stripping mechanism are not able to account for the back-angle peaking and disagree with the back-angle data by more than two orders of magnitude. A two-mode finite-range distorted-wave Born-approximation analysis including cluster exchange contributions accurately describes the observed backward peaking at both energies. The importance of exchange contributions is attributed to favorable kinematic conditions and large cluster amplitudes associated with the exchange process.

Direct processes in the 6Li(α, d) 8Be reaction

The angular distributions of deuterons from the 6Li(α, d) 8Be reaction corresponding to the 0 + ground state and the 2.9 MeV (2 +) state in 8Be have been measured at E α = 17.3, 23.3 and 25.1 MeV. The excitation functions for this reaction have been measured at seven emission angles in the region from 12 up to 25 MeV. The experimental angular distributions are compared with theoretical predictions obtained using DWBA stripping calculations and the plane wave approximation (PWA) for various direct processes. It is shown that the experimental angular distributions can be described throughout the angular region using the simple mechanisms associated with the break-up of the 6Li target nuc clusters and heavy-particle stripping. The interference of these processes is taken into account.

Isobaric-spin violation in the reactionB10(d,d′)B10

The reaction $^{10}\mathrm{B}(d,{d}^{\ensuremath{'}})^{10}\mathrm{B}$ was investigated to determine the isobaric-spin violation in exciting the lowest $T=1$ state of $^{10}\mathrm{B}$ at an excitation energy of 1.74 MeV. The extent and nature of the isobaric-spin-forbidden reaction was obtained by measuring yield curves at laboratory angles of 30, 45, and 77\ifmmode^\circ\else\textdegree\fi{}, using deuteron bombarding energies from 5 to 12 MeV and at 140\ifmmode^\circ\else\textdegree\fi{} from 6.5 to 16 MeV. Simultaneously, data were obtained on the nearby isobaricspin-allowed $T=0$ state at 2.15 MeV. Generally, broad structure dominates the excitation functions at all angles but tends to disappear at higher bombarding energies. Angular distributions of deuterons leading both to the $T=0$ and $T=1$ states were obtained at five bombarding energies between 6.5 and 12.0 MeV. The angular distributions both for the forbidden ($T=1$) and allowed ($T=0$) state are characterized by a trend to forward peaking with increasing bombarding energies although much less so for the $T=1$ state. The total cross sections were measured, and the ratios of the forbidden yield to allowed yield were found to decrease linearly from 0.69% at 6.5 MeV to 0.16% at 12 MeV. In an attempt to describe the angular distributions in terms of a direct-reaction mechanism, distorted-wave Born-approximation (DWBA) calculations were performed assuming collective excitations for the residual nucleus. No clear physical interpretation could be derived from these calculations. Indications are that the reaction $^{10}\mathrm{B}(d,{d}^{\ensuremath{'}})^{10}\mathrm{B}$ proceeds through states very high in the compound nucleus $^{12}\mathrm{C}$, where the isobaric-spin violation originates in Coulomb mixing of $T=1$ and $T=0$ states of the same spin and parity. In view of the very small yield of deuterons leading to the lowest $T=1$ state in $^{10}\mathrm{B}$, and in view of the background difficulties anticipated and experienced, a specialized charged-particle detection system was used, consisting of a position-sensitive gas proportional counter mounted on the focal surface of a broad-range magnetic spectrograph. This constitutes the first observation of the lowest $T=1$ state in $^{10}\mathrm{B}$ by the present reaction.

Optical model and coupled-channel analysis of 60–90 mev deuteron scattering from24Mg and89Y

Angular distributions of deuterons scattered from24Mg and89Y in the angular range 12 °→100 ° have been measured atEd=60, 77 and 90 MeV. With some exceptions the elastic and inelastic data were found to be described consistently by the optical model approach and by coupled-channel analysis, respectively. Collective model features of24Mg are derived from the inelastic scattering results.

Octupole excitation of the 6.88 level of28Si by deuteron inelastic scattering at 29.5 MeV

The experiments have been performed with the Grenoble Isochronous Cyclotron beam, focused on a 4 mg/cm ~ thin foil target of natural silicon. The scattered deuterons are detected by two 3 mm thick Si(Li) detectors, mounted on the two rotable arms of a chamber of 65 cm internal diameter. The positioning accuracy of the arms is 0.05 ~ Each detector has an angular resolution of • ~ delimited by a 4 • 8 mm tanta lum diaphragm. A monitoring detector is fixed at 45 ~ and a Faraday cup collects the beam charge. The detectors are cooled to about 2 0 ~ Each detector is connected to a charge preamplifier which gives rise to an analogue channel and a logic channel. This logic channel used an antipile-eup circuit which eliminates the pile-up effects by cancelling the pulse arriving at interval of t ime less than 30 ~s. The spectra from the multichalmel analyser are stored on magnetic tapes and handled by a PD1)-9 computer. An example of the spectra obtained is given in Fig. I. The overall energy resolution is (I00--150) keV. The beam energy is measured with a (CD2) ~ thin foil target, by crossover techniques. The angular distributions of deuterons scattered from the ground state, the first 2+-state and the 6.88 MeV level are shown in Fig. 2 together with the optical model and DWBA calculations. The first excited level of 2ssi has been well explained by Hartree-Fock and HartreeFoek-Bogoliubov calculations (1) as a rotational state of the ground band. Some recent experiments and calculations suggested an oblate deformation (2.3). :For the 6.88 level, gamma-ray double and triple angular-correlation measurements (4) from the 2:Al(p, T)2sSi reaction let to the spin-3 assignment and suggested the od,t narity, supported by some transfer reactions, particularly the 27 Al(aiie, d)2ssi reaction (a). According to the Blair

Neutron-Hole-State Structure inN=81Nuclei. II.Ce140andBa138(p,d)

In continuation of our program of neutron-hole-state studies in $N=81$ nuclei, angular distributions of deuterons from ($p,d$) reactions (energy resolution \ensuremath{\sim}35 keV) on $^{140}\mathrm{Ce}$ and $^{138}\mathrm{Ba}$ at ${E}_{p}=35$ MeV have been measured and compared with distorted-wave Born-approximation calculations including finite-range and nonlocality corrections. These calculations yield acceptable spectroscopic factors and are in fair agreement with the shapes of the experimental angular distributions. The neutron-single-hole energies have been determined. These energies (in MeV) are ${d}_{\frac{3}{2}}$, 0.0; ${s}_{\frac{1}{2}}$, 0.33; ${h}_{\frac{11}{2}}$, 1.07; ${d}_{\frac{5}{2}}$, 1.72; and ${g}_{\frac{7}{2}}$, 2.90 for $^{139}\mathrm{Ce}$; and ${d}_{\frac{3}{2}}$, 0.0; ${s}_{\frac{1}{2}}$, 0.54; ${h}_{\frac{11}{2}}$, 1.07; ${d}_{\frac{5}{2}}$, 1.71; and ${g}_{\frac{7}{2}}$, 2.93 for $^{137}\mathrm{Ba}$.Considerable fractionation of the ${(2{d}_{\frac{5}{2}})}_{\ensuremath{\nu}}^{\ensuremath{-}1}$ and the ${(1{g}_{\frac{7}{2}})}_{\ensuremath{\nu}}^{\ensuremath{-}1}$ states is observed while the ${(1{h}_{\frac{11}{2}})}_{\ensuremath{\nu}}^{\ensuremath{-}1}$ and the ${(3{s}_{\frac{1}{2}})}_{\ensuremath{\nu}}^{\ensuremath{-}1}$ states are each observed to split mostly into two components. Systematics of the energies and strengths of the various neutron-single-hole states and their components are presented for all $N=81$ nuclei from $^{137}\mathrm{Ba}$ through $^{143}\mathrm{Sm}$ and the significance of the systematics discussed. No measurable population of any neutron state in the $82<N\ensuremath{\le}126$ major shell has been observed.

A study of the 26Mg( 3He, d) 27Al reaction

Angular distributions of deuterons from the 26Mg( 3He, d) 27Al reaction have been analysed with DWBA calculations to extract spectroscopic factors for most states in 27Al up to 4.58 MeV excitation. Ground state occupation numbers for d 5 2 , s 1 2 and d 3 2 orbits in the 26Mg ground state, and the single-particle centroids in 27Al are obtained. The results are in reasonable agreement with the excited core model of the low-lying states of 27Al. The negative parity state at 4.05 MeV in 27Al is shown to be a 1p hole state rather than a 2p particle state. Finally, a previous estimate of the excitation of d 3 2 particles in the ground state of 28Si is shown to be questionable.

Study of states in 12C by the reaction 11B( τ, d) 12C

Angular distributions of deuterons from transitions to nine states of 12C are measured in the reaction 11B( τ, d) 12C; spectroscopic factors were extracted and compared to recent (d, n) measurements. For the 14.71 MeV state, negative parity and a probable spin of 1 or 2 were found.

Study of states in 15O by the reactions 14N(τ, d) and 16O(τ, α)

Angular distributions of deuterons and α-particles emitted in the reactions 14N(τ, d) and 16O(τ, α) going to the first seven states in 15O were measured between 5° and 120° at E τ = 11 Mev . DWBA calculations were performed and spectroscopic factors extracted and discussed.

Neutron-induced reactions on silicon: Deuteron and alpha particle angular distributions at En = 21.3 MeV

At a neutron energy of 21.3 MeV, the angular distributions of deuterons and alphas particles emitted in the reactions 28Si(n, d) and 28Si(n 0, α) were measured. DWBA fits were made, and spectroscopic factors extracted. The yield was also measured in the range E n = 14−22 MeV.

Untersuchung der Niveaustruktur von53Cr und52Cr mit (d, d?) und (d, t)-Reaktionen

Angular distributions of deuterons and tritons from the reactions52,53Cr(d,d),52,53Cr(d,d′),53,54Cr(d, t)52,53Cr have been measured at Ed=11.8 to 11.9 MeV. The elastic scattering data have been analyzed in terms of the optical model. The (d, d′) and (d, t) data have been compared with DWBA calculations. Deformation parameters and spectroscopic factors have been extracted. The results are qualitatively discussed in terms of different nuclear models.

The 14N(p, d) 13N reaction at 30 MeV

Energy spectra and angular distributions of deuterons from the 14N(p, d) 13N reaction have been measured at an incident proton energy of 30.3 MeV. The data indicate that the 13N levels at 0.0, 3.51, 7.38, 8.93 and 11.80 MeV correspond to the levels calculated by Cohen and Kurath at excitation energies of 0.0, 3.7, 7.4, 8.7 and 10.6 MeV with J π of 1 2 −, 3 2 −, 5 2 −, 1 2 − and 3 2 − , respectively. Spectroscopic factors obtained from DWBA analysis of the angular distributions are compared with theoretical predictions of intermediate coupling calculations. In addition, the excitation of positive parity states in this reaction indicates configuration admixtures of 2s-1d shell in the ground state of 14N.

Study ofN14by the ReactionC13(He3, d)N14

A thin carbon foil enriched to 91% in $^{13}\mathrm{C}$ was bombarded with 15-MeV $^{3}\mathrm{He}$ ions from a tandem electrostatic accelerator. Angular distributions of deuterons corresponding to the bound states of $^{14}\mathrm{N}$ were measured with a single-gap magnetic spectrograph. Distorted-wave calculations were performed and spectroscopic factors were extracted. Agreement with the predictions of intermediate-coupling theory is very good, indicating that this theory provides a good description of states arising from $p$-shell configurations.

Total Cross Sections and Angular Distributions of theC12(Li6, p)O17,C12(Li6, d)O16, andC12(Li6, α)N14Reactions from 4.5 to 5.5 MeV

The ${\mathrm{Li}}^{6}$+${\mathrm{C}}^{12}$ reaction has been studied for bombarding energies in the range 4.5 to 5.5 MeV. Angular distributions and total cross sections have been obtained at 100-keV intervals using a $\frac{\mathrm{dE}}{\mathrm{dx}}\ensuremath{-}E$ system coupled to a computer. The reaction products which have been studied are proton groups from the ground and first four excited states of ${\mathrm{O}}^{17}$, deuterons from the ground and first four excited states of ${\mathrm{O}}^{16}$ (the 6.05-6.13-MeV doublet unresolved), and alpha particles from the ground and second excited states of ${\mathrm{N}}^{14}$. The angular distributions of certain of the particle groups show a rather strong energy dependence. The total cross sections, however, are smoothly increasing functions of energy. There is no strong ($2J+1$) dependency in total cross sections that would imply a statistical compound-nucleus decay. The relatively smooth variation of the angular distributions of deuterons from the excited states of ${\mathrm{O}}^{16}$ and alpha particles from the second excited state of ${\mathrm{N}}^{14}$ suggests that these proceed predominantly via a direct reaction. The ground-state groups would appear to have significant compound-nucleus contributions.

Etude de la reaction Li 6 (α, d 0)Be 8 aux energies moyennes

The angular distributions of deuterons from the 6Li(α, d)8Be reaction corresponding to the 0+ ground state and the 2.9 MeV (2+) state in8Be have been measured at Eα = 17.3, 23.3 and 25.1 MeV. The excitation functions for this reaction have been measured at seven emission angles in the region from 12 up to 25 MeV. The experimental angular distributions are compared with theoretical predictions obtained using DWBA stripping calculations and the plane wave approximation (PWA) for various direct processes. It is shown that the experimental angular distributions can be described throughout the angular region using the simple mechanisms associated with the break-up of the 6Li target nuc clusters and heavy-particle stripping. The interference of these processes is taken into account.

Energy dependence of the deutron elastic scattering for nuclei in the region of A = 40

Previous work on the elastic scattering of deuterons on light nuclei indicates that the third maximum of the angular distribution vanishes at lower nuclei mass numbers as deuteron energy is lowered. To investigate this phenomenon, the angular distributions of deuterons elastically scattered on Ai, S, Ca, and Ti nuclei were measured for deuteron energies of 9.8, 11.4, 12.1, and 12.8 Mev. The measured differential cross sections are presented relative to Rutherford scattering. (H.D.R.)

Angular Distributions of Deuterons fromLi7(p, d)Li6Reactions

Angular distributions of deuterons from ${\mathrm{Li}}^{7}(p, d){\mathrm{Li}}^{6}$ reactions induced by 17.5-Mev protons on a natural lithium target have been observed at angles less than 50 degrees in the laboratory system. Deuteron groups leaving ${\mathrm{Li}}^{6}$ in its ground state and in states at 2.19 and 3.57 Mev were studied, and the branching ratios were compared with intermediate coupling shell theory. Pure or nearly pure $L\ensuremath{-}S$ coupling was found to be adequate to explain the observed ratios.