Proton-neutron correlation in the deuteron breakup at 56 MeV and prior-form DWBA analysis

Proton-neutron angular correlations in the ¹²C, ⁵¹V and ¹¹⁸Sn(d, pn) reactions have been measured at 56 MeV to investigate the deuteron breakup process. The elastic breakup which leaves the target nucleus in its ground state dominates the coincident spectra. The elastic breakup cross sections are estimated to be 36–48% of the inclusive breakup yields at 15° or 17.5°. In the angular correlations the protons are emitted predominantly on the side of the beam opposite to the neutrons. The experimental data have been analyzed using the prior-form DWBA. For both nuclear and Coulomb breakup, sufficient convergence of the calculations is obtained by including the pn angular momenta up to l = 2. For the nuclear breakup calculations, the l = 0 and 2 contributions dominate the cross sections. For the Coulomb breakup the l = 1 contribution is predominant. In the calculations the effect of the Coulomb breakup is seen at forward angles of the angular correlation. The DWBA calculations reproduce fairly well the coincident energy spectra and the angular correlations in the angular region where the protons are emitted on the side of the beam opposite to the neutrons. On the other hand the calculations overestimate the break-up cross sections by a factor of 2 to 10 in the angular region where the protons are emitted on the same side of the beam as the neutrons. The distributions of deuteron c.m. angular momenta that contribute to the breakup amplitude are examined to obtain information on the region of space in which the breakup reactions takes place.     

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.     

A study of the 2H(d,p)3H AND 2H(d,n)3He reactions and the excited state of 4He at 23.9 MeV

The relative differential cross sections have been measured for the ²H(d, p)³H and the ²H(d, n)³He reactions from 300 keV to 700 keV in 50 keV steps. Angular distributions of all charged particles from the reactions were taken from 20° to 160° in the laboratory system. Energy-dependent asymmetry coefficients from the expansion of the centre-of-mass angular distributions in terms of even powers of cos θ were obtained as were the branching ratios between the two reaction modes. The different energy dependences of the moments of the two cross sections were used to test the need for the existence of a recently reported T = 0 state in ⁴He.     

A study of the (α, t) reaction on 19F, 27Al, 51V and 59Co

The angular distributions of tritons from the (α, t) reaction on ¹⁹F, ²⁷Al, ⁵¹V and ⁵⁹Co nuclei corresponding to the (0⁺) ground states and (2⁺) excited states in the final nuclei have been measured in the angular range between 15° and 170° at α-particle energies of 25 MeV. For reactions on ²⁷Al and ⁵¹V nuclei, the differential excitation functions have also been obtained at different angles of outgoing tritons at E_α from 20 to 25 MeV. The experimental angular distributions are analysed by the DWBA approximation on the assumption of a nucleon stripping mechanism. The analyses of the present results and the data obtained earlier for the (α, t) reaction on the 1 p shell nuclei, A ? 30, reveal that the distinguishing feature of the reaction under study is the presence of backward angle peaks in the reaction cross section, which appear to be associated with exchange processes. For the (α, t) reaction on the heavier nuclei (A > 30), the dominant mechanism is nucleon stripping.     

Study on the 208Pb(α, 6He)206Pb reaction at Eα = 109 MeV

The ²⁰⁸Pb(α, ⁶He)²⁰⁶Pb reaction induced by 109 MeV α particles has been studied with 70 keV energy resolution. Twenty-five transitions up to 6.2 MeV in excitation energy have been analyzed. The shapes of the angular distributions are reproduced well by the zero-range distorted-wave Born approximation (DWBA) calculations. The spin and parity of the level at 6.10 MeV are proposed to be 9⁻. It is interpreted as a weakly-coupled state of the collective 3⁻ state and the two-hole 6⁺ shell-model state.The energy dependence of the total cross sections of the (α, ⁶He) and (p, t) reactions has been studied systematically by using our present data and other data from the literatures. It reveals that there exists an empirical rule which allows one to compare quantitatively the ratios of the transition strengths of both reactions. The transition strength of the (α,⁶He) reaction is found to be about 35 times smaller than that of the (p, t) reaction for the transitions to the natural parity states, while it is about 15 times smaller for the transition to the unnatural parity 3⁺ state. These small transition strengths are explained by the fact that this reaction occurs at the surface region of the nucleus.     

Vector analysing power and cross section for 90Zr(d, p)91Zr at 11 and 12 MeV

Angular distributions of the vector analysing power and the cross section were measured for ⁹⁰Zr($\text{d}$, p)⁹¹Zr. Measurements were made on two transitions at a deuteron energy of 11 MeV and on 20 transitions at 12 MeV. The observed j-dependence of the vector analysing power provided unambiguous spin assignments for most final states. Measurements of the cross section and vector analysing power were also made for deuteron elastic scattering at 11 MeV in order to determine the potential parameters for DWBA calculations. The DWBA predictions are in good agreement with the measured (d, p) cross sections and in qualitative agreement with the analysing powers. Enriched targets.     

Microscopic interpretation of the (<Emphasis Type="Italic">t</Emphasis>, <Superscript>3</Superscript>He) reaction at 130 MeV on <Superscript>90</Superscript>Zr and isovector monopole strength

The 130-MeV primary tritium beam of the AGOR facility with an intensity of up to 10⁸ pps and the Big Bite Spectrometer experimental setup have been used to study the (t, ³He) reaction between 0° and 5° lab angles on ¹²C and ⁹⁰Zr targets. The standard ray-tracing procedure has allowed us to obtain excitation-energy spectra up to 30 MeV in six angular bins for each residual nucleus, with an average energy resolution of 350 keV. We have used the DWBA reaction mechanism model to reproduce those spectra and their angular distributions. In this approximation, the form factor was treated as a folding of an effective projectile-nucleon interaction with a transition density. The effective projectile-nucleon interaction has been adjusted to reproduce the 0° cross section of the 1⁺ ground state of ¹²B populated in the ¹²C(t, ³He) reaction. We have employed RPA wave functions of excited states to construct the form factors. This DWBA+RPA analysis is used to compare calculated and experimental cross sections directly and to discuss the giant resonance excitations in the ⁹⁰Y nucleus. In this talk, we give some details on this analysis. We show that there are important contributions of L = 2 transitions in the observed cross sections for the 1⁺ final states that explain the previous difficulties in clearly identifying the monopole strength distributions. We then have a better indication of where the L = 0 part is located with this reaction and its microscopic analysis. The text was submitted by the author in English.     

The 18O(18O, 16O)20O reaction at 52 MeV

The structure of the ²⁰O nucleus was studied by the ¹⁸O(¹⁸O, ¹⁶O)²⁰O reaction at E_1ab = 52 MeV. Angular distributions for the transitions to the lowest four states in ²⁰O were obtained and analyzed with finite-range DWBA calculations. Optical potential sets were used which fit the experimental elastic scattering differential cross sections over almost the whole angular range. The two L = 0 transitions to the ground state and the 4.45 MeV state of ²⁰O populated by the ¹⁸O(¹⁸O, ¹⁶O) reaction were analyzed with exact finite-range DWBA calculations using microscopic form factors. These calculations underestimate the absolute cross sections by a factor of 11. The relative strength of the two L = 0 transitions is well reproduced in the ¹⁸O(¹⁸O, ¹⁶O) reaction. However, DWBA calculations for the ¹⁸O(t, p)²⁰O reaction overestimated the relative cross sections for the excited 0⁺ state by a factor of 6. Several model wave functions were tested for the ground-state transition. It was found that the absolute cross sections of the (¹⁸O, ¹⁶O) reaction are very sensitive to the mixing of shell-model configurations. The angular distribution shapes are also slightly dependent on the mixing.     

Inelastic processes and form factor effects in the 162, 164Dy(3He,d) reactions at 46.5 MeV

The 162, 164Dy(³He, d) reactions at E_3He = 46.5 MeV are analyzed using the coupled channels Born approximation (CCBA) and improved form factors derived from a deformed Woods-Saxon potential. The latter are generated using the coupled channels procedure of Rost. The transitions considered populate the $\text{7}\text{2}$^?[523], $\text{1}\text{2}$⁺[411], $\text{3}\text{2}$⁺[411], $\text{1}\text{2}$^?[541] and $\text{5}\text{2}$⁺ orbitals in ^{163, 165}Ho. Indirect processes induced by inelastic scattering are found to have an influence on the cross sections comparable to that deduced for neutron transfer reactions on rare earth nuclei at lower energies. Considered alone, these can alter the cross sections even of strong transitions by a factor of two and of weaker ones by an order of magnitude. For the weaker transitions equally large changes can result when the improved form factors, rather than conventional spherical Woods-Saxon functions, are used in the calculations. In the examples considered these two effects tend to cancel, often, but not always, resulting in predicted cross sections similar in magnitude to the results of conventional DWBA calculations made with spherical Woods-Saxon form factors. The CCBA angular distributions are generally similar in shape to DWBA predictions, which usually give good fits to the experimental angular distributions over the 0–35° range of the data. Compared with DWBA predictions which use (he same optical parameters, but spherical Woods-Saxon form factors, the CCBA with deformed Woods-Saxon form factors is in better overall agreement with the experimental cross-section magnitudes. However there are a number of cases in which the CCBA, although usually predicting larger cross sections than the DWBA, still underestimates the experimental cross sections by nearly factor of two. These cases all occur in the $\text{71}\text{2}$^?[541] band or in the strongly Coriolis mixed $\text{1}\text{2}$⁺[411] and $\text{3}\text{2}$⁺[411] bands, and include the majority of transitions populating these orbitals. Since both nuclear structure and reaction mechanism effects are interwoven m the calculations, further data would be most useful in probing the origin of the discrepancy.     

High resolution investigation of 91Mo and 92Mo via (p,d) and (p,t) reactions on 90Mo

The (p, d) and (p, t) reactions on ⁹²Mo have been studied at a proton energy of 28.0 MeV. Using an Enge split-pole spectrograph, resolutions of 11–15 keV for the detected deuterons and tritons were obtained. A total of 87 levels up to 4.9 MeV in ⁹¹Mo and 25 levels up to 4.0 MeV in ⁹⁰Mo were found, several of which were previously unknown. By comparing the measured angular distributions with DWBA calculations l-values and spectroscopic factors were determined. The results are compared with data from previous experiments on ⁹¹Mo and ⁹⁰Mo, with experiments on other N = 49 and 48 nuclei, and with theoretical calculations.     

A study of the odd isotopes of copper using the 58, 60, 62, 64Ni(τ, d) 59, 61, 63, 65Cu and 48Ca(τ, d)49Sc reactions

Experimental measurements are reported for the ^{58, 60, 62, 64}Ni(τ, d) ^{59, 61, 63, 65}Cu and ⁴⁸Ca(τ, d)⁴⁹Sc reactions and for the elastic scattering of ³He particles from ^{58, 60, 62, 64}Ni and ⁴⁸Ca targets at an incident energy of 18 MeV. The (τ, d) angular distributions cover the angular range from approximately θ_c.m. = 5° to 90° and the elastic scattering angular distributions range from θ_c.m. = 12° to 172°. In the (τ, d) reactions several weakly excited states, not previously seen in stripping reactions, have been identified and assignments of the transferred angular momentum made. The ⁴⁸Ca(τ, d)⁴⁹Sc reaction data are used in conjunction with the theoretical sum rules of MacFarlane and French to determine the normalization factors to be used with DWBA calculations for different sets of optical potentials. These normalization factors are used to extract spectroscopic strengths and centroid energies from the Ni(τ, d)Cu data which are compared with published model calculations for the odd copper isotopes. It is concluded that these calculations invariably fail to give a consistent picture of the odd copper isotopes mainly due to the use of centroid energies as variable parameters in the model calculations.     

Single-particle and core-excited states in 49Sc: (II). The 48Ca(α, t)49Sc reaction

The ⁴⁸Ca(α, t)⁴⁹Sc reaction has been studied at 36 MeV incident energy. About eighty levels have been observed up to 7.5 MeV excitation energy and angular distributions were measured from 6° to 58°, using a split-pole spectrometer. A local zero-range DWBA analysis has been carried out, and the deduced l-assignments and spectroscopic factors are compared with those obtained from the (³He, d) reaction. In the other hand, a large number of angular distributions cannot be reproduced by the DWBA calculations; they have been compared with the results of coupled-reaction-channel calculations, assuming two-step excitation of weak coupling states with a [${}^{48}\text{Ca}{}^1\text{?}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$] structure. Good agreement between experimental angular distributions and two-step predictions is obtained for several ⁴⁹Sc levels, suggesting spin and parity assignments. Moreover, as rather large cross sections are predicted for two-step excitations, it is concluded that, generally, these processes cannot be neglected in the analysis of (α, t) reactions.     

7Li(α,n)10B differential cross-section measurements from threshold to Eα = 5.1 MeV

Differential cross sections for the ⁷Li(α, n)¹⁰B reaction have been measured at lab angles of 0°, 20°, 31°, 50°, 60°, 70°, 80°, 90°, 100° and 114° for α-particle energies between 4.385 and 5.1 MeV. A thick natural lithium target was bombarded with a 5.2 MeV, nanosecond-pulsed ⁴He⁺ beam and neutron velocity spectra at each angle were measured by time-of-flight techniques. These data have been converted to cross sections at 10 keV intervals in α-particle energy. Angular distributions have been fitted with a series of Legendre polynomials. Angle-integrated cross sections, the 0° excitation function, and angular distributions are compared to past measurements and R-matrix calculations.     

The (p, t) and (p, τ) reactions on O at 39.8 MeV

Differential cross sections have been measured at forward angles for (p, t) and (p, τ) transitions from ¹⁷O to the ⁻ ground states and lowest-energy ⁻ states in the ¹⁵O and ¹⁵N mirror nuclei. The data are compared with DWBA calculations using simple single-particle and single-hole wave functions. When the (p, t) and (p, τ) transitions are considered separately, the calculated and experimental ratios of the ⁻ integrated cross sections to the ⁻ integrated cross sections agree to within 30 %; however, the ratios of (p, τ) cross sections to the mirror state (p, t) cross sections are calculated to be about twice as large as actually measured. This experimentally observed reduction of the (p, τ) cross section relative to the (p, t) cross section can possibly be attributed to interference between the S = 0 and S = 1 components of the (p, τ) transitions.     

Elastic and inelastic scattering of 22 MeV protons from natural even-even Zn and Ge isotopes: (II). Spectroscopy of the 68,70Zn and comparison between structure of low-lying states of Zn and Ge

The (p, p′) inelastic scattering on ⁶⁸Zn and ⁷⁰Zn has been measured at 22 MeV incident energy with an overall energy resolution of 14 keV for ⁶⁸Zn and 24 keV for ⁷⁰Zn using a tandem Van de Graaff and a split-pole magnetic spectrometer. Differential cross sections were obtained for levels up to 4.9 and 4.4 MeV excitation energy for ⁶⁸Zn and ⁷⁰Zn respectively. Experimental cross sections are compared with DWBA calculations, asymmetric rotor model, harmonic and anharmonic vibrational models coupled-channels calculations. Spin and parity assignments have been deduced for both isotopes. Results for ⁶⁴Zn, ⁶⁶Zn, ⁶⁸Zn and ⁷⁰Zn are discussed. Comparison between the deformation lengths deduced from these measurements and those derived from similar analysis using other projectiles, for the natural even-even Zn and Ge nuclei, are made; also, comparison between the structure of low-lying states of these nuclei are made.     

Fast neutron radiative capture in silicon

Using the²⁸Si(n, γ)²⁹Si reaction, transitions to the ground state and first excited state in²⁹Si have been studied in the neutron energy range 3–14 MeV with improved neutron energy resolution (of about 100 keV). The 90° cross sections show considerable structure in the entire neutron energy range. Comparison with theoretical calculations shows that compound-nucleus and direct-semidirect processes account for the non-resonant part (smoothly varying part) of the cross section. A microscopic model is, however, required to describe the resonance structure. Continuum shell-model calculations have proven to be a very promising means towards a better understanding of the capture process in, and below, the giant resonance region in light nuclei. The angular distributions of gamma rays in the neutron energy range 8–14 MeV indicate that the capture reaction is mainly of direct character and that the effect of interference between the electric dipole and isoscalar quadrupole resonance is weak.     

Effects of inelastic multistep processes on (p,t) reactions in a transition region between rare-earth nuclei and double-magic 208Pb

Effects of inelastic multistep processes on (p, t) reactions in a transition region between well-deformed rare-earth nuclei and the double-magic ²⁰⁸Pb have been investigated by the ¹⁸⁸Os(p, t) ¹⁸⁶0s, ^{194, 196}Pt(p, t)^{192, 194}Pt and ^{200, 202}Hg(p, t)^{198, 200}Hg reactions at E_p = 51.9 MeV. The observed ground 0⁺, first excited 2⁺ and 4⁺ angular distributions together with those for the ^{206, 208}pb(p, t)^{204, 206}pb reactions have been compared with CCBA and DWBA calculations, using transfer form factors based on the Nilsson, vibrational and shell models. It is found that the inelastic multistep processes play a very important role in reproducing both the shapes and magnitudes of the observed first excited 2⁺ angular distributions, contrasting to small contributions in the ground-state 0⁺ transitions. The effects of the inelastic multistep processes on the first excited 4⁺ transitions are also considered to be important.     

High-resolution investigation of the 112Sn(p,p')112Sn reaction

The ¹¹²Sn(p, p') reaction was studied at proton energies of 20.51 and 25.0 MeV. The outgoing protons were momentum analysed with an Enge split-pole spectrograph and recorded with position-sensitive solid-state detectors with a total resolution between 10 and 15 keV. Excitation energies and angular distributions for states below 5.5 MeV excitation energy were obtained. The angular distributions were compared with macroscopic DWBA calculations in order to extract L-values and deformation parameters. Coupled-channels calculations were performed to investigate two-phonon excitations and the mixing between one- and two-phonon states. The results of the present experiment are compared with previous experimental results and with number-projected BCS calculations. The results for some of the excited states were compared with similar results for the other even Sn isotopes.