Competition between neutron-proton rescattering and deuteron break-up in (d, np) reactions

Existing final-state interaction (FSI) theories predict observable rescattering effects in low-energy nuclear reactions with three or more particles in the final state. Obvious yields which could be attributed to this effect have only been reported in (d, np) reactions. However,n-p rescattering might be confused with the neutron-proton FSI following deuteron break-up since both contribute strongest at low relative neutron-proton energies. We have re-examined the (d, np) reactions on¹²C and⁴⁰Ca in a kinematically complete experiment making special effort to try to distinguish between rescattering and then-p FSI. Data have been taken within and outside the reaction plane at different bombarding energies. Attempts to simultaneously fit the detailed shapes of the proton spectra and the azimuthal angularn-p correlations with theoretical predictions in a consistent way were unsuccessful forboth reaction mechanisms. Improvements in the fits at particular energy and angle combinations were always at the expense of the agreement at other angles or energies. Therefore it must be concluded from our analysis that on the basis of calculations available at present the contributions fromn-p rescattering and deuteron break-up cannot be distinguished in a conclusive manner in the (d, np) experiments performed to date.     

The effect of the D-state of the deuteron in (d,p) and (p,d) reactions

The effect of the D-state of the deuteron in (d, p) and (p, d) reactions is discussed within the framework of the distorted waves Born approximation. Numerical estimates with plane waves are used to suggest that the D-state may play an important role in certain reactions. The necessary modifications of previous work on polarization effects in the distorted waves theory are discussed in detail.     

The neutron-proton scattering length in the reaction9Be(p,np)8Be at 7.5 MeV

The relative differential cross section of the⁹Be(p, np)⁸Be _gs reaction at 7.5 MeV has been measured in an FSI geometry. A strongn-p FSI peak was observed with virtually no sequential decay modes interfering. The Watson-Migdal analysis of this peak yields the scattering lengtha _np =–23.8_–1.2 ^–1.1 fm with the effective ranger _np =2.76 fm.     

Alpha-cluster break-up and reaction mechanism in (p, α) reactions on light nuclei

The differential cross sections for the ¹¹B(p, α)⁸Be and ²³Na(p, α)²⁰Ne reactions were measured at bombarding energies between 6 and 24 MeV. The observed angular distributions can be divided into two domains: at low energies the shapes vary rapidly with incident energy indicating a compound nucleus reaction ; at higher energies rather stable diffraction patterns are seen exhibiting a direct reaction mechanism and DWBA calculations are able to describe the shapes. The change from one region to the other is rather abrupt and this behaviour seems typical for reactions having an α-like compound nucleus. The energy at which this change occurs corresponds to an excitation energy in the compound nucleus of about 20 MeV above the α-threshold.     

Competition cusps in (α, γ) reactions

Absolute cross sections are presented for the reactions ³⁷Cl(α, γ)⁴¹K for 2.90 MeV ≦ E^lab_α ≦ 5.23 MeV, ${}^{62}\text{Ni}\text{(α, γ)}{}^{66}\text{Zn}\text{for}\text{5.07}\text{MeV}\text{≦ E}{}_{\mathrm{\alpha }}{}^{\mathrm{?2}}\text{lab}\text{≦ 8.64}\text{MeV}\text{,}{}^{62}\text{Ni}\text{(α,}\text{n}\text{)}{}^{65}\text{Zn}$ for energies near the (α, n₀) threshold at $\text{E}{}_{\mathrm{\alpha }}{}^{\mathrm{<mtext>lab</mtext>}}\text{= 6.90}\text{MeV up to}\text{8.76}\text{MeV}\text{,}{}^{64}\text{Ni}\text{(α, γ)}{}^{68}\text{Zn for}\text{4.50 ≦ E}{}_{\mathrm{\alpha }}{}^{\mathrm{<mtext>lab</mtext>}}\text{≦ 7.45}\text{MeV}$, and for ⁶⁴Ni(α, n)⁶⁷N from E_α^lab = 5.30 MeV up to E_α = 7.45 MeV. Substantial competition cusps were observed in the excitation function for all three (α, γ) reactions. The data were found to be in reasonable agreement with the predictions of the current versions of global Hauser-Feshbach models used in nucleosynthesis calculations. Including width fluctuation corrections and realistic neutron strength functions generally improves the ability of the models to predict the depth of the (α, γ) competition cusps; the depths of the predicted (α,γ) cusps are insensitive to the degree of isospin mixing. Taken together with studies of competition effects in proton-induced reactions, the present data confirm the importance of width fluctuation and strength function effects, and indicate essentially complete isospin mixing between T^< and T^> states in the compound nucleus.     

The (τ,d), (d,p) and (d,n) reactions on28Si

The model of a three-particle proton cluster coupled to the quadrupole vibrational field is applied to¹²⁹I. The energy spectrum and spectroscopic factors, as obtained in a (³He,d) stripping reaction, are calculated and compared with experimental data. With the wave functions obtained magnetic-dipole and electric-quadrupole moments are derived.     

Four-body calculations of 3He(p,pp)d and 3He(p,pd)p break-up reactions

We calculate the differential cross sections at various angles for reactions ³He(p, pp)d and ³He(p, pd)p at 35 MeV and 45 MeV incident proton laboratory energy, solving the integral equations of four-body theory with separable, S-wave, spin-dependent two body forces.     

Deuteron breakup in the field of a heavy nucleus,Au(d,np)Au

The breakup of deuterons in the field of a gold nucleus has been measured at a deuteron energy of 12 MeV. The energy-angle correlations are compared with two different theoretical models which take into consideration only the Coulomb interaction.     

The Zr(d,n)Nb and Zr(d,n)Nb reactions

The (d, n) reaction on ⁹⁰Zr and ⁹⁶Zr has been studied at 12 MeV deuteron bombarding energy using the neutron time-of-flight technique with an overall neutron time resolution of 1.9 ns. Angular distributions of neutron groups leading to states in ⁹¹Nb and ⁹⁷Nb were measured in the angular range between 15° and 60°. The measured cross sections were analyzed in the framework of the distorted-wave theory of stripping reactions to deduce l-values and proton spectroscopic factors of states in the residual nuclei. The results are compared with the corresponding data available from (³He, d) studies. The fractionation of the single-particle proton states and their centroid energies are determined.     

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.     

Reactions p(d, p)d and p(d, p)pn as a tool for studying the short-range internal structure of the deuteron

In recent years, the deuteron structure at short distances has often been treated from the point of view of nonnucleonic degrees of freedom. In this study, measurements of T-odd polarization observables by using a tensorially polarized deuteron beam and a polarized proton target or a proton polarimeter are proposed as a means for seeking quark configurations inside the deuteron.     

Triton-emission cross sections with 30 MeV d(Be) break-up neutrons

Triton-emission cross sections were measured for Al, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Nb, Mo, Ag, Ta, Tl, Pb and Bi with a 30 MeV d(Be) break-up neutron spectrum characterized by a multiple-foil activation technique. The accumulated tritium was separated by vacuum extraction and measured by low-level gas-phase β^? counting. The systematic trend in the cross sections is somewhat similar to that in the 53 MeV d(Be) break-up neutron spectrum; apart from some initial decrease as a function of Z, the cross section is almost constant over the entire range of Z = 22 to 83. The magnitudes of the cross sections lie between those with 14 MeV neutrons and 53 MeV d(Be) break-up neutrons. Hauser-Feshbach calculations show that the statistical model describes the triton-emission cross sections for nuclei in the (2s, ld) shell within a factor of 2; for the heavier nuclei, however, the calculated cross sections are much smaller than the experimental values.     

Transition potentials for (d, p) reactions

Finite-range calculations are carried out in the distorted wave Born approximation to obtain the ²⁸Si(d, p)²⁹Si and ⁹⁰Zr(d, p)⁹¹Zr stripping differential cross sections at a number of different bombarding energies. The transition interaction responsible for the A(d, p)B reaction is assumed to be V_pn+V_pA−V_pB rather than just the proton-neutron interaction V_pn alone. Various assumptions are made about the forms of this interaction. The exact calculations are compared with second order approximate finite-range calculations employing a Hulthén form for V_pn.     

Statistical analysis of the (d,p) and (d,d) reactions on 40Ca

Excitation functions of the ⁴⁰Ca(d, p)⁴¹Ca and ⁴⁰Ca(d, d)⁴⁰Ca reactions have been measured at 45°, 90°, 135° and 170° from E_d = 4.50 to 5.43 MeV in 10 keV steps. Angular distributions of these reactions have been taken at E_d = 4.70, 5.00 and 5.30 MeV from 25° to 170° in 5° steps. Transitions were observed to the excited states for the range 0.0 ≦ E_x ≦ 3.74 MeV in ⁴¹Ca. Rapid fluctuations in the excitation functions and strong variations of the angular distributions with the incident energy were observed, suggesting that the contribution from compound nucleus processes is very large. Various quantities extracted from the experimental data were compared to the predictions of the statistical theories combined with the DWBA theory for the calculation of the direct reaction amplitudes. The results of the present analysis are consistent with the predictions of the standard statistical theories based on the neglect of the channel-channel correlation.     

Studies on the Ne(p, d)Ne and Ne(d, p)Ne reactions

Angular distribution measurements have been performed on the ²¹Ne(p, d)²⁰Ne and ²¹Ne(d, p)²²Ne reactions at E_p = 20 MeV and E_d = 10.2 MeV, respectively. In the ²¹Ne(p, d) ²⁰Ne reaction, the prolific formation of the J^π = 2⁺, 1.63 MeV state was characterized by l_n = 2 pickup, and the distribution associated with the 4⁴, 4.25 MeV state was suggestive of a weak l_n = 2 pickup. All of the observed l_n = 1 pickup strength is associated with formation of the 2⁻, 4.97 MeV ²⁰Ne level. The ²¹Ne(d, p)²²Ne results indicate that l_n = 2 transfer is involved in the formation of the 1.28, 3.36, 5.52, 5.63 and 6.65 MeV ²²Ne states. The angular distribution observed for the 2⁺, 4.46 MeV state and also the unresolved 5.33, 5.36 MeV composite of states required both l_n = 0 and l_n = 2 components in the associated distorted-wave Born approximation fits. The spectroscopic factors extracted from the present results are compared with those predicted by the Nilsson model without mixing: Applications of the angular momentum projection rule to the ²¹Ne(d, p)²²Ne reaction are considered.     

Pion-transfer (n, d) and (d, He) reactions leading to deeply bound pionic atoms

Theoretical studies are given on the (n, d) and (d, ³He) reactions leading to deeply bound pionic atoms in heavy nuclei of configuration [(nl)_π·j_n⁻¹]J. The cross sections for various pionic and neutron-hole configurations in the case of a ²⁰⁸Pb target are calculated at incident energies 300–1000 MeV/u by using the effective number approach and the eikonal approximation for distortion. The effective number with a pion in the 1s or 2p state and a neutron hole in the orbit peaks around the same incident energy (T_n = 600 MeV) as the elementary cross section n+n→d+π⁻, where the momentum transfer matches the angular-momentum transfer of L = 5–7. The DWIA cross section for (n,d) producing a pion in the 1s or 2p orbit at T_n = 600 MeV is found to be around 42 or 75 μb/sr, respectively. At T_n = 350 MeV, where the momentum transfer is small, quasi-substitutional states of configurations and are preferentially populated with (n, d) cross sections of 95 and 190 μb/sr, respectively. The (d, ³He) cross sections are estimated to be an order of magnitude smaller than the (n, d) cross sections. Thus, the (n, d) and (d, ³He) reactions are found to be suited for the production of deeply bound pionic atoms.     

Effects of channel non-orthogonality in (d,p) reactions

Coupled channel calculations for (d, p) reactions were performed in which a strong coupling between the d and p channels was assumed. Reactions investigated were ¹⁶O(d, p) ¹⁷O(2s) and ⁴⁰Ca(d, p) ⁴¹Ca(2p) at E_d =10.5 MeV and the related (d, d) and (p, p) scattering processes. The nonorthogonality of the d- and p-channels were taken into account. The results of these calculations are presented and are compared with the coupled channel calculations neglecting the channel nonorthogonality and also compared with the DWBA and optical model calculations.