Analyzing power measurements for the 13C(p,d)12C reaction at 200 and 400 MeV

Cross sections and analyzing powers for the ¹³C($\text{p}$,d) reaction have been measured at 200 and 400 MeV to the 0⁺, ground state and 2⁺, 4.44 MeV state of ¹²C. While the cross sections are rather structureless, DWBA calculations in exact finite range account well for both the magnitude and shape of the angular distributions. On the other hand, the measured analyzing powers are in serious disagreement with the DWBA calculations.     

Three-nucleon transfer on 12C: The 12C(α, p)15N reaction at 96.8 MeV

Angular distributions of protons from the ¹²C(α, p)¹⁵N reaction have been measured over the angular range from 10–70° at an α-particle bombarding energy of 96.8 MeV. Well defined particle groups are observed up to an excitation energy of 18 MeV in ¹⁵N. The relatively small number of states excited implies a selectivity both in the reaction mechanism and in structure effects. DWBA calculations using a semi-microscopic three-nucleon form factor have been performed using several different sets of wave functions. Good agreement in the ratio σ_exp/σ_th is obtained for most states using the ¹⁵N wave functions of de Meijer. The strongest state in the (α, p) spectrum is observed at 15.397 MeV in ¹⁵N and DWBA calculations give good agreement for a $\text{13}\text{2}{}^{\mathrm{+}}$ assignment. This state has been observed only in other three-nucleon transfer reactions involving heavy ions. The recent discovery of a $\text{9}\text{2}{}^{\mathrm{+}}$ state at 10.693 MeV in a p+¹⁴C resonance measurement is supported by our analysis.     

Study of 20Ne(3He,n)22Mg at 3He energies between 2.6 and 4.0 MeV

The ²⁰Ne(³He, n) reaction leading to the ground state of ²²Mg has been investigated in the ³He⁺ energy range of 2.6 to 4.0 MeV. Angular distributions were determined with a neutron time-of-flight spectrometer at average incident energies (lab) of 3.27, 3.69, and 4.01 MeV between 0° and 120° (lab). Excitation functions for the energy region were measured at 0° and 80° (lab). The observed differential cross sections are explained by coherent contributions from direct interaction and compound-nucleus formation. A spectroscopic factor was extracted for the DWBA calculation from the absolute cross-section measurements and found to be $\text{? = 0.43±0.21}$. Resonances in the compound-nucleus formation were found at 3.00 and 3.33 MeV (c.m.) with widths of 0.28 and 0.21 MeV and spins of $\text{5}\text{2}{}^{\mathrm{+}}\text{and}\text{1}\text{2}{}^{\mathrm{?}}$, respectively.     

Optical-model analysis of 7Li + 25Mg and 7Li + 27Al elastic scattering at 89 MeV

The elastic scattering angular distributions for ⁷Li + ²⁵Mg and ⁷Li + ²⁷Al were measured at $\text{E(}{}^7\text{Li}\text{) = 89}\text{MeV}$ over angular ranges of 8–55° c.m. and 8–64° c.m. Previously published measurements for ^{24, 26}Mg at 89 MeV and ²⁴Mg at 34 MeV are reanalyzed. The cross sections were analysed using a 6-parameter phenomenological Saxon-Woods potential. No discrete ambiguities were found but the usual continuous ambiguities exist. The data were also analysed with double folded real potentials generated using the M3Y effective interaction. The folded potential must be multiplied by about 0.6 to fit the data. The extent to which ⁷Li optical-model potentials are determined and suggestions for further work on the normalization of the folded potential are discussed.     

The structure of 26Mg investigated with the (d,p) reaction

Angular distributions have been measured for the ²⁵Mg(d, p)²⁶Mg reaction at 13 MeV leading to excited states between E_x = 0 and 8 MeV. Experimental cross sections are compared with DWBA calculations and extended shell-model calculations in the full sd shell. Spin and parity restrictions are obtained for several levels in the region E_x = 6?;8 MeV. Spectroseopic factors for transitions to the lowest four positive-parity states of each spin are well reproduced by the shell-model calculations; however, in mixed configurations the largest component is systematically underestimated by the shell model. Only 60% of the strength for $\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ transfer is observed.     

The reaction 14C(3He,n)16O and the coexistence model of 16O

The reaction ¹⁴C(³He, n)¹⁶O has been measured at a ³He bombarding energy of 25.4 MeV. The zero-degree differential cross section for the excitation of the three low lying 0⁺T = 0 states, at energies 0.0, 6.05 and 12.05 MeV are, respectively, 1.33 ± 0.10, 0.49 ± 0.10, and 0.50 ± 0.10 mb/sr These measured cross sections are in rough agreement with single-step zero-range DWBA calculations using an empirically determined ¹⁴C ground state wave function and in which the Brown and Green coexistence-model wave functions are used to describe the ¹⁶O 0⁺ states. The angular distribution of the transition to the ground state is measured between 0° and 32°.     

The (α, α), (α, α′) and (α, 3He) reactions on 12C at 139 MeV

The nucleus ¹²C was bombarded with 139 MeV α-particles to study the characteristics of the elastic, inelastic, and (α, ³He) reactions. An optical model analysis of the elastic data yielded a unique family of Woods-Saxon potential parameters with central real well depth V ≈ 108 MeV, and volume integral $\text{J}\text{4A}\text{≈ 353}\text{MeV}\text{·}\text{fm}{}^3$. By comparing the present results with those of other studies above 100 MeV, we find that the real part of the α-nucleus interaction decreases with increasing energy; the fractional decrease with energy is roughly one-half that observed for proton potentials. Using the optical potential parameters derived from the elastic scattering, first-order DWBA calculations with complex first-derivative form factors reproduced the inelastic scattering data to the 4.44 MeV (2⁺) and 9.64 MeV (3^?) states of ¹²C. For the 0⁺ state at 7.65 MeV it was necessary to employ a real, second-derivative form factor to fit the data. The deformation lengths β_lR_m and deformations β_l obtained in this and other experiments are summarized and compared. DWBA calculations using microscopic model form factors were also performed for the 2⁺ and 3^? states using the wave functions of Gillet and Vinh Mau. These reproduced the shapes and relative magnitudes of the differential cross sections. We also fit the shape of the 0⁺ differential cross section using a microscopic form factor which contains a node, which is similar to that occurring in the collective model second-derivative form factor. In the ($\text{α,}{}^3\text{He}$) reaction the differential cross sections to the ground state ($\text{1}\text{2}{}^{\mathrm{?}}$) and the 3.85 MeV ($\text{5}\text{2}{}^{\mathrm{+}}$) state in ¹³C could not be reproduced by zero-range local DWBA stripping calculations; it was necessary to employ finite-range and non-local corrections in the local-energy approximation. This DWBA analysis is notable in that unambiguous optical potentials were available for both entrance and exit channels. The ground state spectroscopic factor is in agreement with the prediction of Cohen and Kurath, while the relative spectroscopic factors agree fairly well with the rather few existing measurements of this kind.     

The (p,t) reaction on 12C, 54Fe and 208Pb at 80 MeV

Angular distributions have been measured for the low-lying levels of the residual nuclei for the ¹²C, ⁵⁴Fe and ²⁰⁸Pb(p, t) reactions at E_p = 80 MeV. The shapes of these angular distributions are generally well reproduced by the zero-range distorted-wave Born approximation (DWBA). Enhancement factors extracted from the data show that the DWBA predicts relative strengths consistent with those observed at lower bombarding energies. However, the overall empirical DWBA normalization at E_p = 80 MeV is observed to be $\text{1}\text{12}$ ($\text{1}\text{4}$) of that required at 40 MeV for ²⁰⁸Pb (⁵⁴Fe).     

Spectroscopic study of 15N states with the reaction 14C(d,n)

Energy and angular distributions of neutrons from the reaction ¹⁴C(d, n)¹⁵N have been measured at 6.5 MeV deuteron energy. The DWBA analysis yielded l-values and absolute spectroscopic factors for fifteen states in ¹⁵N below 10 MeV excitation energy. For the 9.23 MeV level J^π is determined to be $\text{3}\text{2}$⁺ or $\text{5}\text{2}$⁺, for the 9.93 MeV level the data suggest $\text{J}{}^{\mathrm{\pi }}\text{=}\text{1}\text{2}{}^{\mathrm{+}}$. The spectroscopic factors are in qualitative agreement with pure jj coupling and in semi-quantitative agreement with shell-model calculations.     

Fusion cross section for 13C + 13C at low energies

The energy dependence of the fusion cross section has been measured over the range E_c.m. = 3.05–6.88 MeV by detecting the γ-rays from residual nuclei in a 4π geometry. Analyzing the 1.37 MeV photopeak, originating from ${}^{24}\text{Mg}\text{1.37}\text{MeV}\text{→}\text{g.s. transition}$, the cross sections for ²⁴Mg+2n channel were also deduced. The measured fusion cross sections have been compared with those for ¹²C + ¹²C and ¹²C + ¹³C systems and found to be significantly different. For ¹³C+¹³C the fusion cross sections agree with the standard optical-model prediction down to the lowest measured energies, while for ¹²C + ¹²C and ¹²C + ¹³C they are, at the lowest energies, too low. It is suggested that the unpaired valence nucleons facilitate fusion at energies well below the Coulomb barrier.     

Electrofission of 24Mg

The electron induced fission of ²⁴Mg leading to the ground states of two carbon nuclei has been studied using 25 to 45 MeV electrons. The observed sin²2θ angular distribution of the carbon nuclei indicates the dominance of E2 virtual photon absorption. The yield of ground state carbon nuclei is observed to decrease with increasing excitation energy in ²⁴Mg above 24 MeV.     

Study of low-lying levels in 47Ca with the 48Ca(d, t)47Ca reaction

Angular distributions of cross sections [α(θ)] and vector analyzing powers [iT₁₁(γ)] have been measured for seven low-lying states or groups of states excited by the ⁴⁸Ca($\text{d}$, t)⁴⁷Ca reaction with 13.5 MeV deuterons and analyzed by the DWBA. On the basis of comparison of vector analyzing powers with DWBA calculations, spin-parity assignments have been made or confirmed for several states. Spectroscopic factors have been extracted. Angular distributions for weak states at 3.30 and 3.57 MeV excitation in ⁴⁷Ca could not be reproduced by DWBA calculations. Investigations of compound nucleus and multi-step contributions to the cross sections and analyzing powers for these states have been made by means of Hauser-Feshbach and CCBA calculations. Optical model parameters were obtained from analysis of 13.5 MeV deuteron elastic scattering cross sections and analyzing powers.     

Spin assignments from the 142Nd(7Li, 6He)143Pm and 144Sm(7Li, 6He)145Eu reactions at 52 MeV

Angular distributions have been measured for transitions to low-lying states in ¹⁴³Pm and ¹⁴⁵Eu populated by the ¹⁴²Nd(⁷Li, ⁶He)¹⁴³ and the ¹⁴⁴Sm(⁷Li, ⁶He)¹⁴⁵Eu reactions at $\text{E(}{}^7\text{Li}\text{) = 52}$ MeV. Elastic scattering of ⁷Li at 52 MeV on ¹⁴²Nd and ¹⁴⁴Sm, and ⁶Li at 46 MeV on ¹⁴²Nd and at 45 MeV on ¹⁴⁴Sm, were measured. Optical-model parameters extracted from fits to the scattering data were used in a finite-range DWBA analysis of the angular distributions for levels below 1.40 MeV excitation energy in ¹⁴³Pm and 1.84 MeV in ¹⁴⁵Eu. The reaction cross sections forward of 6° c.m. allow unambiguous distinction to be made between 2d_{$\text{5}\text{2}$} and 2d_{$\text{3}\text{2}$} final states. Final-state spins have been assigned to d-states in ¹⁴³Pm at 1.40 MeV($\text{3}\text{2}$⁺)and in ¹⁴⁵Eu at 1.042 MeV ($\text{3}\text{2}$⁺). Existing assignments to other levels in both residual nuclei have been confirmed.     

Elastic and inelastic scattering of 16O and 12C by 24Mg near the Coulomb barrier

Angular distributions for ¹⁶O + ²⁴Mg and ¹²C + ²⁴Mg elastic and inelastic (2⁺, 1.37 MeV state in ²⁴Mg) scattering have been measured at energies spanning the Coulomb barrier. Apart from the structure typical of strong destructive Coulomb-nuclear interference, the data exhibit some additional specific features. Coupled channel calculations were performed, along with DWBA calculations to analyse the data using fixed coupling strengths deduced from the results of Coulomb excitation work. The importance of higher-order effects such as reorientation, is demonstrated.     

The 24Mg(α, α')24Mg reaction; statistical analysis

The ²⁴Mg(α, α')²⁴Mg reaction to the 1.37 MeV state has been studied over an α-energy range of 9.625–13.825 MeV, in ≈40 keV steps, and over a 25°–160° angular interval. These cross sections have been analysed in terms of statistical theory and a number of deviations from its predictions are found. These deviations point to the importance of non-statistical processes, such as intermediate structure, to the α-scattering. The average compound nuclear width o₁ 62±7 keV is found for ²⁸Si over the 18–22 MeV excitation.     

The 54Fe(3He,t)54Co reaction at 70 MeV,Gamow-Teller strength

The ⁵⁴Fe(³He, t)⁵⁴Co reaction has been studied at 70 MeV with an energy resolution around 70 keV (FWHM). The triton spectra are characterized by sharp peaks up to 10 MeV excitation energy superimposed on a continuum. Most of the sharp peaks have a forward-peaked angular distribution and 38 peaks or groups of peaks are found to have an angular distribution corresponding to an angular momentum transfer of 2. Model considerations lead to the conclusion that most of these states are 1⁺ states. A shell-model calculation with parameters that account for the Gamow-Teller strength distribution in ⁴⁸Ca-⁴⁸Sc divides the β-strength in ⁵⁴Co in a ratio 5.7:6.8:1.3 for the T = 0, 1 and 2 states. A comparison is made with the 1⁺ spectrum in ⁵⁴Mn (T = 2 states) and a tentative assignment of T = 2 states in ⁵⁴Co is reached. The cross section has been calculated for the 0⁺, 1⁺ and 3⁺ states in ⁵⁴Co assuming a pure ($\text{π}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{ν}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$) configuration finite-range DWBA is used and the conclusions are that the (³He, α, t) and (³He, d, t) processes give significant contributions to the cross sections.     

Spectroscopic study of 55Co via the 54Fe(τ, d)55Co and 54Fe(τ, dp̃)54Fe reactions

The ⁵⁴Fe(τ, d)⁵⁵Co reaction has been studied at 25 MeV incident energy with a split-pole spectrometer. About one hundred levels have been observed in ⁵⁵Co up to 10 MeV excitation energy. Angular distributions have been measured and analyzed with DWBA and Gamow functions as form factors for unbound levels. The ⁵⁴Fe(τ,dp?)⁵⁴ reaction has been investigated at 24 MeV incident energy. The angular distributions of the emitted protons were measured in coincidence using method 2 of Litherland and Ferguson, with 0 detection of deuteron groups. Spins, population parameters, branching ratios and proton partial widths for the transitions to the ground and excited states of ⁵⁴Fe were determined from the analysis of the angular correlation data. The results of these two experiments provide a large number ofspectroscopic properties of unbound proton states and in particular of analog states of ⁵⁵Fe low-lying levels. The IAS of the $\text{3}\text{2}{}^{\mathrm{?}}$ ground state of ⁵⁵Fe is observed to be split between two individual levels. The amplitude of neutron coupling to the first 2⁺ excited state of ⁵⁴Fe is obtained for the $\text{lg}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ and $\text{2}\text{d}\text{5}\text{2}$ low-lying parent statfes in ⁵⁵Fe. summed spectroscopic factors and the centroid energies of the proton states in ⁵⁵Co are obtained. A comparison is made with previous (τ, d), (d, p) and (p, p) results.