Compound Nucleus Contributions Research Articles

The Ca 40(d, α)K 38 reaction and the nuclear structure of K 38

Natural Ca-targets were bombarbarded with 7.7 MeV deutereons. Magnetic analysis was used to obtain α-particle spectra at angles of 50°, 70° and 90°. About 35 levels in K 38 were found up to an excitation energy of 4.8 MeV. There are the following low-lying states: ( E exc, Jπ, T) = (0.00 MeV, 3 +, 0); (0.12 MeV, 0 +, 1); (0.43 MeV, 1 +, 0); (1.69 MeV, 1 +, 0); (2.41 MeV, 2 +, 1). They are in agreement with recent intermediate coupling shell model calculations. Most of the levels above 2.5 MeV result from configurations with one or more nucleons raised into the f 7 2 shell. The nuclear temperature derived from an Ericson plot is 1.05 ± 0.15 MeV. Angular distributions for the low excited states were measured from 10° to 165°. The angular distributions and the total cross section show the effect of the ΔT = 0 isobaric spin selection rule which inhibits direct interaction leading to T = 1 final states. Compound nucleus transitions to the T = 1 states take place, however, because of isobaric spin mixing in the intermediate nucleus, and the selection rule seems to be completely violated. The total cross sections are in agreement with the theory of Hauser and Feshbach. This theory also makes it possible to estimate the compound nucleus contributions for the transitions leading to T = 0 states. About 2 3 of the total cross section for these transitions are due to direct interaction, which produces a pronounced structure of the angular distributions in the forward and backward hemisphere. The significance of this structure in terms of the various direct interaction modes is discussed.

Activation Cross-Section Survey of Deuteron-Induced Reactions

A survey was made of activation cross sections for various nuclear reactions induced by 20-MeV deuterons. The ($d,p$) and ($d,t$) cross sections increase monotonically with increasing mass number, and in one case (${\mathrm{Ni}}^{58}$) the absolute ($d,p$) cross section is closely predicted by a distorted-wave Born approximation calculation. They are undoubtedly stripping and pickup reactions with little or no compound nucleus contribution. The fact that Coulomb barriers do not affect ($d,t$) cross sections indicates that the pickup occurs far outside the nucleus. The cross sections for ($d,2p$) reactions are consistent with a model wherein the second proton is "evaporated" from a compound nucleus, but the level density parameters needed to fit this theory are somewhat lower than expected; this may indicate a contribution from a mechanism in which both protons are emitted in a direct interaction. Excluding the lightest element studied, ${\mathrm{Cl}}^{35}$, the $(d,p\ensuremath{\alpha})+(d,\ensuremath{\alpha}p)$ activation cross sections are consistent with calculations assuming a reaction path that is predominantly ($d,p\ensuremath{\alpha}$) with evaporation of the second particle (i.e., one alpha) from a compound nucleus; however the reaction on ${\mathrm{Cl}}^{35}$ seems to proceed by the path ($d,\ensuremath{\alpha}p$) with both particles being evaporated. Cross sections for ($d,2n$) and ($d,n\ensuremath{\alpha}$) reactions in the mass range 60 to 90 indicate that many more low-energy neutrons than low-energy protons are emitted as first particles in deuteron-induced reactions; this indicates that compound nucleus formation is more important than stripping in these reactions.

Reaction mechanisms in low energy inelastic proton scattering

A number of (p, p′) angular distributions and (p, p′γ) angular correlations have been measured in order to investigate the reaction mechanisms involved in inelastic proton scattering at low energies. Angular distributions were measured for the following nuclei at the energies (centre-of-mass) indicated: A 40 6.14 MeV (first, second, and third excited states); Ni 58 4.70, 5.64, 6.65–6.80 MeV (first excited state); Ni 60 4.69, 5.63, 6.65–6.80 MeV (first excited state); Cu 65 6.83 MeV (second and third excited states). Angular correlations between protons leading to the first excited state and subsequent decay gamma rays were measured for the following nuclei: Si 28, 5.66, 6.70 MeV,θ p′ = 45°, 90°, 135°; S 22 5.66 MeV, θ p′ = 90°, 135°; Ti 48 5.72, 6.77 MeV,θ p′ = 90°, 135°; Ni 58 5.73, 6.80 MeV,θ p′ = 45°, 90°,135°; Ni 60 5.73, 6.80 MeV,θ p′ = 50°, 90°, 135°. For the odd-mass nucleus Cu 65, the angular distributions show a prominent forward peaking, suggesting the importance of a direct interaction mechanism at this energy. For the even nuclei in the neighbourhood of A = 60, both angular distributions and correlations show agreement with the predictions of the statistical compound nucleus model for proton energies less than 6 MeV but indicate an appreciable direct interaction contribution at 7 MeV. Angular correlations for Si 28 show that direct interactions are important in this case at both 5.66 and 6.70 MeV. It appears that the importance of direct interaction relative to compound nucleus contributions increases rapidly as the energy of the incident and emergent protons approaches the height of the Coulomb barrier, though it is clear that the structure of the nuclear states involved is also important in determining this ratio.

Angular Distribution of the Ground-State Neutrons from theC13(p, n)N13andN15(p, n)O15Reactions

The angular distribution of the neutrons from the ${\mathrm{C}}^{13}(p, n){\mathrm{N}}^{13}$ and ${\mathrm{N}}^{15}(p, n){\mathrm{O}}^{15}$ ground-state reactions has been measured in 10\ifmmode^\circ\else\textdegree\fi{} steps from 0\ifmmode^\circ\else\textdegree\fi{} to 150\ifmmode^\circ\else\textdegree\fi{} for incident proton (laboratory) energies of approximately 6.5, 6.9, 7.5, 8.1, 8.6, 8.9, 9.4, 10.6, 11.4, and 12.2 Mev. Additional measurements were made for ${\mathrm{C}}^{13}$ at 5.0, 10.2, 10.9, and 13.3 Mev, and for ${\mathrm{N}}^{15}$ at 5.5, 7.7, 7.8, and 13.6 Mev. A calibrated plastic or stilbene scintillator was used in order to obtain absolute differential cross sections. Time-of-flight techniques on the Liver-more variable energy cyclotron allowed positive identification of the ground-state neutrons. The targets [C${\mathrm{O}}_{2}$ (58%${\mathrm{C}}^{13}$) and ${\mathrm{N}}_{2}$ (90% ${\mathrm{N}}^{15}$)] were sufficiently thick to average out the effects of possible compound-nucleus contributions. From preliminary fits to the ${\mathrm{C}}^{13}$ angular distributions, Glendenning and Bloom have inferred an effective neutron-proton interaction inside the nucleus.

Some Be 9(d, pγ)Be 10 angular correlation measurements off the stripping peak

Angular correlations, in the reaction and azimuthal planes, between protons and gamma rays from the first excited state of Be 10 in the reaction Be 9(d, pγ)Be 10, have been measured for four proton angles between 26° and 86° in the centre-of-mass system. For a pure stripping reaction, with l = 1 for the stripped neutron, only P 2 (cos θ p γ ) terms are allowed in the angular correlation function in the reaction plane. However, P 4 terms have been found, even on the stripping peak, indicating a compound-nucleus contribution to the reaction. Excitation functions for the reaction products of Be 9+d have been measured for incident energies from 3.8 to 6.3 MeV and these show an absence of resonances. Absolute differential cross-sections for the ground state and first excited state proton groups form the Be 9(d, p)Be 10 reaction have been measured at an incident energy of 5.86 MeV; these have been analysed in terms of the Butler stripping theory to give cut-off radii and reduced neutron widths.

ReactionC12(d, n)N13

The reaction ${\mathrm{C}}^{12}(d, n){\mathrm{N}}^{13}$ has $Q=\ensuremath{-}0.28$ Mev and so is expected to show strong direct interaction effects even at low energies of the bombarding deuterons. We have made an extensive study of this reaction at 14 values of the deuteron energy between ${E}_{d}=1.45$ Mev and ${E}_{d}=2.95$ Mev. At each deuteron energy the differential cross section was measured at about 20 angles between 0\ifmmode^\circ\else\textdegree\fi{} and 165\ifmmode^\circ\else\textdegree\fi{}. Neutron time-of-flight techniques were used and each point on each angular distribution represents the detection of at least ${10}^{3}$ neutrons. Direct interaction effects are seen at all bombarding energies in the backward as well as in the forward hemisphere. The differential cross section at 0\ifmmode^\circ\else\textdegree\fi{} shows very pronounced resonance structure but this largely disappears in the integrated cross section and is due chiefly to interference between the direct interaction term and the probably quite small compound nucleus contribution. A rough method for eliminating the interference terms between the two mechanisms in the differential cross section is proposed and applied. The resultant purified angular distribution is remarkably close, in the forward hemisphere, to that predicted by simple stripping theory. A backward maximum, much lower than the forward peak, is also present but not accounted for.

Angular distributions for elastic and inelastic scattering of 40-MeV alpha particles by carbon, nitrogen, oxygen, and argon

Angular distributions for elastic and inelastic scattering of 40-MeV alpha particles by carbon, nitrogen, oxygen, and argon were obtained. Gas targets were used. Angles of observation ranged from 7° to 130° (laboratory) for carbon and over lesser intervals for the other elements. Elastic scattering angular distributions are characterized by sharply defined diffraction-like structure at the forward angles with maxima and minima spaced very regularly in sin 1 2 θ (c.m.), deep minima near 90° (c.m.), and appreciable cross sections at angles beyond 90°. A black nucleus diffraction interpretation gives reasonable absolute cross sections for the forward maxima and good agreement with observed locations of maxima and minima. Inelastic scattering angular distributions were obtained for C 12( Q = −4.43, −7.65 and −9.61 MeV); for O 16 [ Q = −6.06 and −6.14 MeV (unresolved), −6.91 and −7.12 MeV (unresolved)]; and A 40 ( Q = −1.462 MeV). Direct interaction analysis verifies previously assigned spins and parities and indicates an assignment of 0 + or 2 + to the 9.61-MeV level of C 12. Integrated cross sections for inelastic scattering to individual levels may be as high as 6 per cent of πR 2. Interaction radii determined from diffraction analysis of the elastic scattering data are (in units of 10 −13 cm) 5.11±0.20 for C 12, 5.37±0.17 for N 14, 5.64±0.29 for O 16, and 6.38±0.32 for A 40. Interaction radii calculated from inelastic scattering data are consistently larger. Compound nucleus contributions to observed cross sections appear to be small or zero.

Einteilchen-strahlungsübergänge im optischen modell des atomkerns

Using the “distorted wave approximation” and employing for the nuclear interaction a complex square well potential, the single particle contribution to the radiative capture of neutrons incident on a medium weight nucleus is calculated. Numerical results are obtained for the upper end of the γ-spectrum, d σ(n, γ)/d E γ , for an incident energy of 20 MeV, and for the integrated cross section, σ(n, γ)( E n), in the energy region 10 MeV ≦ E n ≦ 20 MeV. These results agree fairly well with experimental data on (p, γ)-reactions, available in this energy region (figs. 1, 5 and 6), and a closer agreement of the integrated cross sections is obtained by adding to the single particle part the compound nucleus contribution for the process in question. The radiation from compound nucleus states contributes a non negligible amount up to about 15 MeV incident energy. The presence of an absorbing part in the potential does not change the order of magnitude of the cross section compared to the value obtained in a real potential, up to an absorption strength of V 1 = 10.5 MeV.

Collision Matrix for (n, d) and (p, d) Reactions

The contributions to ($n, d$), ($p, d$) reactions and their inverses from the pickup and stripping mechanisms are considered as corrections to the compound-nucleus or $R$-matrix theory of nuclear reactions. In an ($n, d$) reaction, for example, the $R$-matrix theory neglects the interaction of the incident neutron with the target-nucleus proton "tails" which extend beyond the nuclear radius. The pickup correction to the collision-matrix component, or reaction amplitude, appears as the matrix element of the neglected interaction involving an exact wave function and the approximate wave function of the compound-nucleus system not having the interaction; a distorted-wave Born approximation is used in which the former exact wave function is replaced by one of the latter type with the appropriate radiation condition. An explicit expression is given for the collision-matrix component which, together with the compound-nucleus contribution, can be substituted directly into the formulas of Blatt and Biedenharn for total reaction cross sections and angular distributions. In general, the angular distributions contain interference terms in addition to the straight pickup and compound-nucleus contributions. If the distorted neutron and deuteron spherical partial waves are assumed to depend only on the angular momenta, and not explicitly on the total spin and the channel spins, the formula of Tobocman is obtained for the pickup contribution, while Butler's formula is obtained if plane waves are used instead of distorted waves. There are discussions of the various approximations, the exchange terms, and the question of the nuclear radius.