A comparison of the He(p, 2p)d and He(p, pd)p reactions

The ³He(p, 2p)d and ³He(p, pd)p reactions have been compared at three bombarding energies from 65 to 100 MeV. A comparison of plane wave impulse approximation calculations to the experimental data indicates that multiple scattering effects are large and energy dependent but that they primarily produce a uniform reduction in cross section. Although multiple scattering effects are large the ratio of the cross sections for the two reactions is in agreement with that predicted by the impulse approximation.     

The study of (d,t) and (d, 3He) reactions in several 1p shell nuclei using vector-polarized beams

Cross-section and vector analyzing power angular distributions using 15 MeV deuterons were taken over an angular range of θ_1ab = 20–100° for the ¹⁰B(d, t)⁹B_{g.s.and 2.36 Mev state}, ¹⁰B(d, ³He)⁹Be_{g.s. and 2.43 Mev state}, ¹³C(d, t)¹²C_g.s., ¹⁴N(d, t)¹³N_g.s., and¹⁴N(d, ³He)¹³C_g.s. reactions, and vector analyzing power data alone were taken for the ¹⁶O(d, t)¹⁵O_g.s. and ¹⁶O(d, ³He)¹⁵N_g.s. reactions. Beams of vector-polarized deuterons were used for the vector analyzing power determinations. A comparison is made of the results for (d, t) and (d, ³He) reactions leading to mirror states when the self-conjugate targets ¹⁰B and ¹⁴N are used. The reactions provide evidence for a j-dependence of the vector analyzing power for l = 1 transfers in 1p shell nuclei. When the reactions involve a j-value admixture, the vector analyzing powers are used to attempt to determine percentage admixtures involved in the population of several final states.     

The (d,t) and (d,t) reactions on 18O and the 1p spin-orbit splitting

The reactions ¹⁸O(d, t)¹⁷O and ¹⁸O(d, τ)¹⁷N have been investigated at ifE_{d = 52 MeV}. Energy spectra of tritons and τ particles have been measured up to excitation energies of 25 MeV in ¹⁷O and 12 MeV ¹⁷N, respectively, and spectroscopic factors have been obtained by a DWBA analysis of the measured angular distributions. From a comparison of the t-and τ-spectra the distribution of $\text{T =}\text{1}\text{2}\text{and}\text{3}\text{2}$ spectroscopic strengths in ¹⁷O could be deduced and analog relations between $\text{T =}\text{3}\text{2}$ states in ¹⁷N and ¹⁷O could be established. Nearly the total $\text{T =}\text{3}\text{2}$ strengths of the $\text{1}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{and}\text{1}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ shells and nearly the complete $\text{T =}\text{1}\text{2}$ strength of the $\text{1}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ shell have been found, whereas only one third of the $\text{T =}\text{1}\text{2}$ strength of the $\text{1}\text{p}\text{3}\text{2}$. Shell could be clearly identified. The observed centroid energies are understood from the different $\text{1}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$$\text{1}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^{\mathrm{?}}\text{1)}$ and $\text{1}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ effective residual interactions. This supports a strong isospin dependence of the 1p spin-orbit splitting.     

A study of the Ti(He, t) and Ni(He, t) reactions to isobaric analogue states

The (³He, t) reaction populating 0⁺ and 2⁺ states in ^{58, 60}Cu and ^{46, 48}V which are isobaric analogue states (IAS) of the 0⁺ ground states and 2⁺ first excited states in ^{58, 60}Ni and ^{46, 48}Ti have been studied at an incident ³He energy of 24.6 MeV. Triton spectra were measured for the targets ^46,48Ti, ^natNi and ⁵⁸Ni and angular distributions for the 0⁺ and 2⁺ IAS of ^{46, 48}Ti and ^{58, 60}Ni determined. The data were obtained using a magnetic spectrometer and position-sensitive detectors. The results have been analysed using DWBA theory. The 0⁺ → 0⁺ transitions to analogue states are described quite well using a microscopic form factor derived from a nucleon-nucleon interaction. However, with a Gaussian form, the m.s. radius of this interaction is only limited to the region 0–9 fm². Comparisons with data at other incident energies indicate that the strength of the effective interaction is strongly energy dependent. The Coulomb energies and (³He, t) angular distributions of the states assigned as the 2⁺ analogues in ⁴⁸V and ^58,60Cu are not described well by the models investigated. The ⁴⁶V 2⁺ IAS angular distribution is reproduced by a microscopic calculation, however. The ratios of the 0⁺ → 2⁺ IAS to the 0⁺ → 0⁺ IAS transitions are used to deduce a quadrupole deformation for the valence neutrons. The difference in the quadrupole deformations of the matter and proton distributions, as determined by other means, is found to be correlated with those of the valence neutrons. Several transitions to non-analogue states are also investigated.     

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.     

Rescattering and neutron-proton final-state interaction in the 12C(d,pn)12C reaction

The ¹²C(d, pn)¹²C reaction has been studied in a kinematically complete experiment at several energies and angles suitable for observing proton-neutron rescattering and sequential decay final-state interactions (FSI), with the aim of investigating the relative importance of the two reaction mechanisms. An increase of yield has been observed for all spectra in the region of low relative proton-neutron energy where both rescattering and sequential decay leading to the ¹S₀ final-state interaction are possible. No consistent fits to the data using only the rescattering graph were found and interference with other diagrams must be assumed to occur. The effect of isospin non-conservation is discussed. It is concluded that no reported measurements on this reaction require an exclusive interpretation in terms of a rescattering mechanism and therefore no reliable information on nuclear lifetimes can be obtained from these experiments.     

A systematic study of (n,d), (n,n' p) and (n,pn) reactions at 14.7 MeV

Cross sections for [(n, d) + (n, n′p) + (n, pn)] reactions induced by 14.7 ± 0.3 MeV neutrons on ⁴⁴Ca, ⁴⁹Ti, ⁵⁰Cr, ^{67, 68}Zn, ⁹²Zr and ^{97, 98}Mo have been measured by the activation technique using enriched isotopes as target materials, modern radiochemical separations and high-resolution counting methods. A brief summary of the literature data and our own earlier measurements is given. Our activation data are generally in agreement with those deduced from emitted charged particle characterisation. Some systematic trends in the activation cross-section data were analysed. Similar to other (n, charged particle) reactions, the [(n, d) + (n, n′p) + (n, pn)] reaction cross section decreases as a function of (N?Z)/A; the data, however, fall on two curves, one for nuclei with neutron separation energies (S_n higher than the proton separation energies (S_p) and the other for nuclei with S_n < S_p. For nuclei with S_n ? S_p the (n, n′p) process is very important. Detailed Hauser-Feshbach calculations show that in general contributions of statistical processes to the (n, d) reaction cross section are very small.     

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.     

The (p,t) reactions on nuclei in the rare earth region

The (p, t) reactions on isotopic targets of ^{178, 180}Hf and all the stable isotopes of Yb and on natural targets of Gd, Dy, Er, Hf, Ta, W, Os and Au were studied at a beam energy of 19 MeV with an average resolution of 12 keV. A split-pole magnetic spectrometer was used to measure (p, t) Q-values and absolute differential cross sections. On the basis of angular distribution shapes definite 0⁺ and tentative 2⁺ assignments were made. Rotational bands were identified assuming an I(I+1) spacing. The (p, t) reaction populates excited 0⁺ states strongly in ¹⁷⁴Yb, ¹⁷⁶Hf, ¹⁶⁶Yb and several Gd, Dy and Er isotopes. The ¹⁷⁴Yb and ¹⁷⁶Hf 0⁺ states are discussed in terms of the pairing phase transition and in terms of Nilsson orbitals with unequal (p, t) reaction amplitudes. Members of gamma and octupole vibrational bands were observed in the even-N nuclei. The lowest L = 0 transfers to states in ^{169, 171}Yb were found to have less than 55% of the strength to ground states in adjacent even-N nuclei. A strong L = 0 transfer to a state at 1513 keV in ¹⁷¹Yb indicates the presence of a possible K = 0 core vibration coupled to the unpaired $\text{5}\text{2}$[512] neutron. The natural targets have furnished information on trends in cross sections for members of ground bands, gamma bandheads, 3^? octupole states, and strongly excited 0⁺ states.     

A study of the nucleus 107Ag in the core-excitation model with the (p,t) and (τ, d) reactions

The ¹⁰⁷Ag residual nucleus was studied in the core-excitation model using the (p, t) and (τ, d) reactions. The L, J, π of levels between 0.0 and 2.25 MeV was deduced from the combined reactions. The octupole state observed at 2.19 MeV in other experiments was resolved in (p, t) into a triplet of states at 2.182, 2.203 and 2.229 MeV; octupole strength was observed in (p, t) over a range from 1.144 to 2.229 MeV. Core-excitation wave functions for the quadrupole 2⁺ and 2'⁺ vibration doublets of ¹⁰⁷Ag were constructed using electromagnetic data. These wave functions, combined with data from the ¹⁰⁸Pd(p, t) core reaction, effectively reproduced the ¹⁰⁹Ag(p, t) differential cross sections to these states. The ground-state L = 0 transfer in (p, t) to ¹⁰⁷Ag was only 0.752±0.113 as strong as the corresponding transfer to ¹⁰⁶pd. this is an unexpectedly large blocking effect for an unpaired proton to exert upon a neutron-transfer reaction. An apparent dependence of the (p, t) angular distributions to states of ¹⁰⁷Ag built upon the same core excitation was observed, depending upon the J of the final state.     

Energy levels in even actinide isotopes from (t,p) reactions

Energy levels in^{232, 234}Th,^{236, 238, 240}U and in²⁵⁰Cm have been measured using the (t, p) reaction. Angular distributions were obtained for the^{234, 238}U targets and evidence for second order effects in the direct reaction mechanism was found.     

Study of the reactions 118Sn(d,t) and98Mo(d,t): (I). Spectroscopy of 117Sn and 97Mo

The vector analyzing power and differential cross section have been measured at a deuteron energy of 12.0 MeV for ${}^{118}\text{Sn}\text{(}\text{d}\text{,}\text{t}\text{)}$ transitions to six states of ¹¹⁷Sn (E_x = 0.0, 0.16, 0.31, 0.71, 1.02 and 1.18 MeV), for ${}^{98}\text{Mo}\text{(}\text{d}\text{,}\text{t}\text{)}$ transitions to eight states of ⁹⁷Mo (E_x = 0.0, 0.68, 0.72, 0.89, 1.12, 1.28, 2.39 and 2.52 MeV), and for ${}^{118}\text{Sn}\text{(}\text{d}\text{,}\text{d}\text{)}\text{and}{}^{98}\text{Mo}\text{(}\text{d}\text{,}\text{d}\text{)}$. Deuteron optical model potentials were obtained from analysis of the elastic scattering measurements, and were used in a DWBA analysis of the $\text{(}\text{d}\text{,}\text{t}\text{)}$ results. Comparison of the measurements and DWBA predictions for σ(θ) and for iT₁₁(θ) allows unambiguous determination of tl_n and j_n for all ¹¹⁸Sn(d, t) and most ⁹⁸Mo(d, t) transitions. Differences in the triton energy relative to the Coulomb barrier cause marked qualitative differences in the measured cross sections and analyzing powers between ${}^{118}\text{Sn}\text{(}\text{d}\text{,}\text{t}\text{)}\text{and}{}^{98}\text{Mo}\text{(}\text{d}\text{,}\text{t}\text{)}$ transitions of the same l_n and j_n.     

Effects of exchange and final-state interactions in the reactions 2H(3He, 3H p)p and 2H(3He, 3He p)n

Absolute coincidence cross sections for the ²H(³He, ³He p)n and ²H(³He,³H p)p reactions were measured at E_He = 35.9 MeV. Spectra dominated by the nucleon-nucleon final-state interaction (FSI) are fitted by a fully antisymmetrized PWBA theory which includes the effects of FSI in all its matrix elements. Previously reported 26.8 MeV data showing both FSI and quasi-elastic scattering (both with and without charge exchange) are also fitted by the theory, which qualitatively describes the shapes of all these spectra and the ratios of the cross sections for the various processes. Predictions of Watson-Migdal theory are fitted to the FSI spectra and differences between the two theories are analyzed.     

Compound nucleus contribution and even-odd effect for (3He,p) reactions in the Ni region

The compound nucleus contributions to the proton spectra from 8 MeV and 10 MeV ³He induced (³He, p) reactions on even-A Ni isotopes were obtained. The relative cross sections for ⁵⁸Ni/⁶⁰Ni/⁶²Ni in the high excitation region are in fair agreement with predictions of statistical theory, but the absolute cross sections in the same region are smaller than the prediction by a factor of 3 to 8, and the shapes of the measured spectra for heavier isotopes do not agree with the prediction. These discrepancies between experiment and theory are in sharp contrast to the situation in (p, p′), (p, α), (α, p) and (α, α′), where good agreement was found.The proton spectra from (³He, p) reactions on nuclei in the A = 54–68 mass range have a systematic difference in slope between even-A targets and odd-A targets; it is similar to the systematic difference found previously in (p, p′) and (α, p) reactions, but none of these is readily explainable by theory.     

The study of the width for intermediate resonances in the 27Al(d,p)28Al, 27Al(d, α)25Mg, 31P(d,p)32P and 31(d, α)29Si reactions

The protons and α-particles from the reactions ²⁷Al(d, p)²⁸Al(d, α)²⁵Mg, ³¹P(d, p)³²P and ³¹P(d, α)²⁹Si were measured and analyzed with the channel cross correlation function and auto-correlation function to determine the correlating numbers N_d and average width 〈Γ_μ〉. With these values, the theoretical intermediate widths were calculated to be 119 ± 30 keV in the ²⁹Si nucleus and 249 ± 46 keV in the ³³S nucleus, which were in good agreement, within the errors, with the present experimental results of 185 ± 37 keV in ²⁹Si and 204 ± 24 keV in ³³S.     

Interaction dans l'état final n-p dans les réactions 2H(d,pn)2H, 4He(d,pn)4He, 6Li(d,pn)6Li et 3He(d,pn)3He

Three-body break-up in n-p final-state interaction regions has been investigated through the reactions ${}^2\text{H}\text{+}\text{d}\text{→}\text{p}\text{+}\text{n}\text{+ [su2}\text{H}\text{,}{}^4\text{He}\text{+}\text{d}\text{→}\text{p}\text{+}\text{n}\text{+}{}^4\text{He}\text{,}{}^6\text{Li}\text{+}\text{d}\text{→}\text{p}{}^3\text{He}\text{+}\text{d}\text{→}\text{p}\text{+}\text{n}\text{+}{}^3\text{He}$. In all cases, the proton and the neutron were detected at the same angle in a kinematically complete experiment for a deuteron bombarding energy of 27.5 MeV. Helium and deuterium gas targets in a small gas cell cooled with liquid nitrogen were used. No indication of any possible contribution from the (isospin-forbidden) ¹S₀ p-n final-state interaction was observed in the first three reactions. For the ³He + d reaction, the data shown pronounced enhancements due to the p-n final-state interaction. In the forward regions the observed peaks are broader than the predictions of final-state interaction models.