Direct Interaction Mechanism Research Articles

Isospin Selection Rule in theC12(d,α)B10Reaction

The violation of the isospin selection rule has been studied in the reaction ${\mathrm{C}}^{12}(d,\ensuremath{\alpha}){\mathrm{B}}^{10}$ with deuteron energies between 9 and 12.5 MeV. The differential and total cross sections of the isospin-forbidden transition to the first $T=1$ state in ${\mathrm{B}}^{10}$ (the ${J}^{\ensuremath{\pi}}={0}^{+}$ state at 1.74-MeV excitation) have been compared with the cross sections of the isospin-allowed transitions to the ground state (${J}^{\ensuremath{\pi}}={3}^{+}$, $T=0$), the first excited state (${J}^{\ensuremath{\pi}}={1}^{+}$, $T=0$ at 0.72 MeV), and the third excited state (${J}^{\ensuremath{\pi}}={1}^{+}$, $T=0$ at 2.14 MeV). Mostly the intensity of the $T=1$ alpha group is less than 1% of the yield of the $\ensuremath{\alpha}$ groups leading to the neighboring $T=0$ states. This reduction is due not only to isospin forbiddenness but also to angular-momentum and parity selection rules which apply in this particular ($d,\ensuremath{\alpha}$) reaction for which both the initial and the final state have ${J}^{\ensuremath{\pi}}={0}^{+}$. These weighting factors have been calculated by use of the statistical theory of nuclear reactions. After these factors have been applied, the $T=1$ alpha group has an intensity of about 10% relative to the other three $T=0$ transitions at a deuteron energy of 9 MeV and 1-2% at an energy of 11 MeV. The small yield is ascribed to the isospin selection rules that to some extent govern this $T=1$ transition. In the energy range from 9 to 11 MeV, the angular distribution of the $T=1$ state stays fairly constant and is nearly symmetric around 90\ifmmode^\circ\else\textdegree\fi{}. The yield decreases steadily. At deuteron energies higher than 11.5 MeV, the angular distribution changes drastically and becomes strongly forward peaked and asymmetric around 90\ifmmode^\circ\else\textdegree\fi{}, and the total yield increases slightly. We assume that this behavior indicates a direct-interaction mechanism in which the process of mixing the isospins takes place at the surface of the nucleus. Coulomb excitation during the process of $d$ capture or $\ensuremath{\alpha}$ emission might be responsible for the isospin violation at these higher deuteron energies.

Double transfer processes in direct interactions

The reactions between complex nuclei, in which transfer of two different particles leads to the same pair of product nuclei, are investigated on the basis of the direct interaction mechanism. Assuming the cluster-model picture, the resulting theoretical formulae obtained in the plane wave Born approximation are compared with some experimental data. Good agreement is obtained.

Some cross-sections for the inelastic scattering reaction 180Hf( p, p′γ) 180 mHf with 16–62 MeV protons

Cross-sections for the reaction 180Hf( p, p′γ) 180 m Hf have been measured radiochemically in the energy range of 16 MeV to 62 MeV. The results are discussed in the light of Monte Carlo calculations performed by Bertini on the same system of target and range of proton energies, and seem to imply a pure direct interaction mechanism.

(He3,n) Reactions with 19- to 25-MeVHe3Ions

Three threshold detectors with thresholds at 1, 4.5, and 12 MeV have been used to investigate neutron emission from 10 targets (Be, C, N, O, Al, Fe, Ni, Cu, Mo, Ag) when bombarded by 19-, 22-, and 25-MeV ${\mathrm{He}}^{3}$ ions. Laboratory angular distributions and production cross sections have been measured. The results are compared with an evaporation spectrum and it is concluded that a direct-interaction mechanism operates in the production of neutrons with energies greater than 12 MeV.

Direct Interaction Mechanism in the Ionization FollowingβDecay

A method of estimating the contribution of the direct interaction mechanism (d.i.m.) to the ionization process in $\ensuremath{\beta}$ decay is proposed. It is restricted to the same energy range ${E}_{\ensuremath{\beta}}\ensuremath{\gg}{E}_{b}$ (${E}_{\ensuremath{\beta}}$ is the kinetic energy of the $\ensuremath{\beta}$-particle, ${E}_{b}$ is the binding energy of the atomic electron) as the conventional theory, but is based on independent information emerging from experimental impact cross-section data. Following Williams, the ionization by external impact is ascribed to two factors: (a) direct collisions, corresponding to low impact parameters; (b) glancing ("photoeffect") collisions corresponding to large impact parameters. We assume that the contribution of factor (a) to the ionization cross section is the same both in external impact and in $\ensuremath{\beta}$ decay, and evaluate the contribution of factor (b) to the impact cross section by means of the Weizs\"acker-Williams method. By subtracting this contribution from the experimental impact cross section, we get the d.i.m. cross section. We apply this procedure to the calculation of the d.i.m. ionization probabilities ${P}_{\mathrm{d}.\mathrm{i}.}$ of the following $\ensuremath{\beta}$-active isotopes: ${\mathrm{Na}}^{22}$, ${\mathrm{P}}^{32}$, ${\mathrm{Y}}^{90}$, ${\mathrm{Pr}}^{143}$, ${\mathrm{Ne}}^{23}$, and ${\mathrm{Ar}}^{41}$. In opposition to the predictions of the conventional theory, according to which $\ensuremath{\delta}\ensuremath{\equiv}\frac{{P}_{\mathrm{d}.\mathrm{i}.}}{{P}_{s}}\ensuremath{\ll}1$, (${P}_{s}$ is the shake-off probability), our results, although approximative, suggest that the $K$-shell ionization probabilities are affected, sometimes in a decisive manner, by the d.i.m.; we get for ${\mathrm{Y}}^{90}1<\ensuremath{\delta}<2$ and for ${\mathrm{Pr}}^{143}2<\ensuremath{\delta}<4$. This conclusion is in line with independent experimental results by Charpak, Suzor, and Spighel on low-energy electrons accompanying $\ensuremath{\beta}$ decay. Further experiments to check this conclusion are proposed, and possible explanations of the failure of the theory are suggested.

Polarization of protons from elastic and inelastic scattering on 24Mg

The angular distributions of the polarization of protons from elastic and inelastic scattering on 24Mg have been measured at E p = 5.8 MeV. The polarization of the elastically and inelastically scattered protons are of opposite sign. The results obtained are explained by a direct interaction mechanism with channel coupling.

Direct heavy ion induced excitation

Observation of the radionuclides 127Cs through 132Cs resulting from the reaction 133Cs + 14N at 140 MeV indicates that the more neutron deficient products are formed as a result of a direct interaction mechanism followed by neutron emission. Kinematic arguments based on the recoil momenta and angular distributions indicate that the formation of a highly excited intermediate state is required to account for the formation of 127Cs through 130Cs.

(d, α) reaktionen an leichten kernen

The analysed beam from the Heidelberg cyclotron has been used to investigate (d, α) reactions on 24Mg, 25Mg and 28Si targets at incident beam energies between 11.45 und 12.1 MeV. Angular distributions of α-particles corresponding to the excitation of the lowest six to ten levels of the residual nuclei have been measured in the range between 15° and 165°. The data suggest a mixed direct and compound nucleus interaction mechanism. The latter seems to be predominant in the 25Mg(d, α) reaction. The angular distributions have been analysed by double pick-up theory where feasible. The (2 I+1) rule has been observed to hold for 25Mg(d, α) and to a lower degree of accuracy for 28Si(d, α). From the viewpoint of this rule it is suggested that the well-known 2.07 MeV level in 26Al is a doublet state as proposed earlier. The integrated cross-sections of various α-particle groups from the (d, α) reactions on 9Be, 14N, 16O, 31P and 32S have also been measured. A pronounced odd-even effect has been observed not only for the transitions to the ground states but also for the transitions to the excited states up to about 3 MeV.

Direct-Interaction (p,α) Reactions inY89andZr90

Alpha-particle energy spectra from ($p,\ensuremath{\alpha}$) reactions in $^{89}\mathrm{Y}$ and $^{90}\mathrm{Zr}$ were obtained at 5-deg intervals between 15 and 90 deg. Bombarding energies of 20.2 and 22.5 MeV were used. Differential cross sections for reactions leading to the ground states and first excited states were determined. Distorted-wave calculations were done for the angular distributions for the reactions leading to each of the ground states and the 0.38-MeV first excited state in $^{87}\mathrm{Y}$. The calculated angular distributions reproduce the general features of the experimental angular distributions. Spectroscopic factors, obtained from normalization of the calculated angular distributions to the experimental data, are consistent with triton pickup as the dominant mechanism for direct-interaction ($p,\ensuremath{\alpha}$) reactions. The normalization factors also indicate the $^{90}\mathrm{Zr}$ ground-state proton configuration to be 70% ${(2{p}_{\frac{1}{2}})}^{2}$ and 30% ${(1{g}_{\frac{9}{2}})}^{2}$.

Evidence for Nucleon Clustering from High-Energy Reactions

The telescope method was used with solid-state detectors for measuring angular and energy distributions of complex particles emitted in nuclear reactions induced by 157-MeV protons on heavy nuclei (Ag, Au, Bi, Th). Both an isotropic and a forward-peaked emission of $^{4}\mathrm{He}$, tritons, and deuterons were observed. Yields of $^{3}\mathrm{He}$ were found to be very low at the back angles. The components of the above particle spectra emitted at forward angles are interpreted in terms of a direct-interaction mechanism on "$\ensuremath{\alpha}$ clusters" in the surface, and a Monte Carlo calculation was performed to compute the yield of "$\ensuremath{\alpha}$ clusters" knocked out by prompt cascade nucleons. The tritons and $^{3}\mathrm{He}$ particles might partly be ejected by a double pickup process, partly by a stripping mechanism on "$\ensuremath{\alpha}$ clusters."

Study of theMg26(p, p′γ)Reaction Mechanism at Low Energies

The angular distribution and ${p}^{\ensuremath{'}}\ensuremath{-}\ensuremath{\gamma}$ angular correlations of the protons inelastically scattered on the first two ${2}^{+}$ excited states of ${\mathrm{Mg}}^{26}$ were measured at several energies of the incident protons between 5.67 and 6.46 MeV. The angular correlation of the inelastically scattered protons on the ${\mathrm{Mg}}^{26}$ second excited state is of the type ${0}^{+}\ensuremath{\rightarrow}{J}^{\ensuremath{\pi}}\ensuremath{\rightarrow}{2}^{+}\ensuremath{\rightarrow}{2}^{+}\ensuremath{\rightarrow}{0}^{+}$, where the heavy arrow indicates the unobserved cascade $\ensuremath{\gamma}$ rays. The angular distributions and correlations corresponding to the second level of ${\mathrm{Mg}}^{26}$ ($Q=\ensuremath{-}2.94$ MeV) are in good agreement with the predictions of the statistical model. In the case of the protons which populate the first level ($Q=\ensuremath{-}1.81$ MeV) the angular distribution varies strongly with the energy, indicating a violation of the hypotheses on which the statistical model is based. The angular correlations corresponding to the excitation of this level likewise agree only in some cases with the predictions of the statistical model. The difference in behavior of the angular distribution and angular correlations on the two levels is attributed to the differences in value of the transmission coefficients ${T}_{l}(E)$. Angular correlations for ${\mathrm{Mg}}^{26}(p, {p}^{\ensuremath{'}}\ensuremath{\gamma})$, $Q=\ensuremath{-}1.81$ MeV at energies higher than 6 MeV also suggest some contribution of the direct-interaction mechanism.

(3He, α) Reactions on25Mg and26Mg at 5.50 MeV

Angular distributions of α-particles from the25Mg(3He, α)24Mg and26Mg(3He, α)25Mg reactions, leading to the ground and the low excited states of24Mg and25Mg, were measured at a bombarding energy of 5.50 MeV. Relative total cross-sections were obtained from the experimental results for transitions to the ground, 1.37, 4.12, 4.23, 5.22 and 6 MeV states of24Mg and for transitions to the ground, 0.58,0.98, 1.61 and 1.96 MeV states of25Mg. The ratios of the total cross-sections were compared with the predictions of the theory of Hauser and Feshbach and a satisfactory agreement has been found. In addition, the transition to the ground state of25Mg in the26Mg(3He, α)25Mg reaction seems predominantly due to a direct interaction mechanism.

The B 11(He 3, α)B 10 reaction between 2.2 and 5.5 MeV

The differential cross sections for the B 11(He 3, α)B 10 reactions leading to the ground state of B 10 and to excited states at 0.72, 1.74 and 2.15 MeV have been measured as a function of bombarding energy between 2.2 and 5.5 MeV at laboratory angles of 15°, 90° and 165°. Angular distributions have been measured at bombarding energies of 2.35, 2.86, 3.42, 3.93, 4.50, 5.02 and 5.51 MeV. The total cross sections for these reactions have been obtained by integration of the angular distributions. The small variation of the angular distributions with energy and the strong forward peaking at the higher energies suggest that a direct interaction mechanism predominates. A comparison with the B 11(p, d)B 10 and B 11(d, t)B 10 reactions indicate that this mechanism is probably pick-up. There is some evidence for a compound nucleus contribution in the case of the reaction which leaves B 10 in its second excited state at 1.74 MeV.

The (d, α) reaction on N 15 and O 16 in the deuteron energy range 1–2.5 MeV

Excitation functions and angular distribution for the first two α-groups from the N 15 (d, α)C 13 reaction and those for the α 0-group from the O 16(d, α)N 14 reaction have been observed. For the first reaction a broad maximum in the excitation curve has been observed for both α-groups at the deuteron energy 1.6–1.8 MeV. Slight irregularities were observed in the excitation function for α-particles of the second reaction at E d=1.2, 1.9, 2.1 and 2.4 MeV. Angular distributions of α-particles from the N 15(d, α)C 13 reaction show a mixing between compound nucleus and direct interaction mechanism. Angular distributions of the α 0-group from the O 16(d, α)N 14 reaction are typical of the compound nucleus mechanism. Differential cross-sections for all α-groups are given in a wide energy range.

Elastic and Inelastic Scattering at 168 MeV in theO16—C12System

Differential cross sections for the elastic scattering and the inelastic scattering to the most strongly excited states in the ${\mathrm{O}}^{16}$---${\mathrm{C}}^{12}$ system have been measured using the 168-MeV ${\mathrm{O}}^{16}$ beam from the Yale University heavy-ion linear accelerator. The states most strongly excited are the ${2}^{+}$ state in ${\mathrm{C}}^{12}$ at 4.43 MeV and the ${3}^{\ensuremath{-}}$ state in ${\mathrm{O}}^{16}$ at 6.14 MeV. The mutual excitation reaction wherein both these levels are excited ($Q=\ensuremath{-}10.57$ MeV) was also observed and measured. All of the angular distributions measured have an oscillatory behavior, a consequence of the strong absorption of the incident wave in the nuclear interior and indicative of a direct interaction mechanism. A distorted-wave Born approximation analysis of the data is obtained in order to extract reliable nuclear parameters. The results of this experiment are compared to previous elastic and inelastic scattering, from ${\mathrm{C}}^{12}$ in the adiabatic-Fraunhofer limit. Fair agreement in shown in spite of the variety of projectiles used in the comparison. The transition strengths for inelastic scattering are further compared to the electromagnetic transition probabilities and a scheme for relating the two quantities is presented.

Angular distribution of tritons from the reaction B 10+n at 14.4 MeV

The angular distributions of tritons from the reactions B 10(n, t)Be g.s. 8 and B 10(n, t)Be 2.9 MeV 8 have been measured. Both angular distributions have two pronounced maxima, one at small angles and the other at about 80°. This indicates that the reaction proceeds via the direct interaction mechanism. The Butler theory fits the first maximum in the B 10(n, t)Be g.s. 8 angular distribution quite well. The deformation of Be 8 and B 10 nuclei makes the analysis more difficult, since higher values for the total angular momentum of the transferred deuteron are allowed. There is no possibility of distinguishing between the pickup (n, t) and the sequential pickup (n-d-t). The plane wave theory does not give a satisfactory explanation of the angular distribution of tritons from the reaction B 10(n, t)Be 2.9 MeV 8.

Angular correlations for C 12(p, p′ γ)C 12 in a resonance-free region

The reaction C 12(p, p′ γ)C 12 involving the first excited state at 4.43 MeV has been investigated experimentally by measurements of the p′- γ correlation and the proton angular distribution for an incident energy of 8.5 MeV. Although this energy corresponds to an energy region where there are no sharp resonances, the experimental results show that none of the simple models of the reaction mechanism are valid due to the important contributions from proton “spin-flip” during the inelastic scattering. The simplified distorted wave theory of direct interactions is improved by including the effects of spin-orbit distortion and an attempt is made with this theory to explain all the available data at 8.5 MeV. Partial success is achieved and it appears that the inelastic scattering in this energy region is dominated by a direct interaction mechanism. The inclusion of spin-orbit distortion is found to be important. In contrast to previous work the correlation function is found to be relatively insensitive to the detailed nature of the target nucleus wave functions.

Neutron slowing-down spectra in beryllium and beryllium oxide

The collision density of neutrons slowing down in an infinite homogeneous moderator has been obtained as a function of neutron energy for beryllium and beryllium oxide. The source fission neutrons were uniformly distributed in space. The spectra were obtained by solving the slowing-down integral equation numerically using a digital computer. The reactions considered were anisotropic elastic scattering in Be and O, (n, α) in Be and O and (n, 2n) in Be. Both the direct interaction and compound nucleus mechanisms were used for the (n, 2n) reaction.

The (p, pn) and (p, n) reactions on Sc 45 induced by high-energy protons

The reactions (p, pn) and (p, n) on Sc 45 have been investigated in the proton energy range of 120–670 MeV. The cross sections of these reactions decrease with proton energy from ≈ 70 mb and ≈ 4 mb at 120 MeV down to ≈ 40 mb and ≈ 1 mb at 670 MeV, respectively. The influence of the nuclear structure on the cross sections of the reactions under study is discussed under the assumption of a direct interaction mechanism. The experimental value of the production cross section ratio of Sc 44g and Sc 44m, which is 2.2, is compared to the calculated one and the parameter σ, entering into the expression for nuclear level density, is estimated.

Ne20(p, p′γ)Angular Correlations at Low Energy

${\mathrm{Ne}}^{20}(p, {p}^{\ensuremath{'}}\ensuremath{\gamma})$ 1.63-MeV angular correlations have been measured in the 5.2-6.10 MeV energy range, where the elastic and inelastic excitation functions vary in a compensating manner. The measurements have been made at 5.25-, 5.55-, and 6.10-MeV proton energies, the position of the proton detector being at 60\ifmmode^\circ\else\textdegree\fi{}, 90\ifmmode^\circ\else\textdegree\fi{}, and 120\ifmmode^\circ\else\textdegree\fi{}. One obtains strong angular correlation functions of the form $A+B{sin}^{2}2(\ensuremath{\theta}\ensuremath{-}{\ensuremath{\theta}}_{0})$, where ${\ensuremath{\theta}}_{0}$ defines the axis of symmetry. The angular correlation curves are insensitive to a change of the incident proton energy and ${\ensuremath{\theta}}_{0}$ is situated in the proximity of the recoil direction ${\ensuremath{\theta}}_{R}$ of the nucleus. These facts could constitute an argument in favor of the direct-interaction mechanism.