The energy dependence of fusion in the 9Be+28Si system

The angular distributions of the energy spectra of the light charged particles (p, d and α) from the ⁹Be + ²⁸Si reaction have been measured in the energy range 12 ≦ E_lab ≦ 30 MeV. The particle evaporation spectra and the angular distributions were analyzed with a spin dependent statistical model. Angular distributions of ⁹Be ions elastically scattered on ²⁸Si have been measured at the energies 12 MeV, 17 MeV, 23 MeV and 30 MeV and were analysed, together with previously measured cross sections, with the optical model. The fusion cut-off angular momentum l_fus(E), the fusion cross section σ_fus(E) and the ratio σ_fus/σ_R^OM(E) were deduced. The excitation function for fusion was analyzed with the Glas and Mosel model. The parameters obtained from the fusion excitation function were compared with the corresponding ones from the ⁹Be + ²⁸Si optical-model interaction potential.     

A study of the states of 30Si with the 28Si(t,p)30Si and 29Si(d,p)30Si reactions

The excitation energies of the levels in ³⁰Si have been measured up to an excitation of 9.46 MeV with the ²⁸Si(t, p)³⁰Si reaction at a triton energy of 6.0 MeV. Angular distributions have been measured of proton groups from the ²⁸Si(t, p)³⁰Si and ²⁹Si(d, p)³⁰Si reactions in a multi-angle magnetic spectrograph. Triton bombarding energies of 10.5 and 12.1 MeV were used and the deuteron incident energy was 10.0 MeV. States in ³⁰Si up to an excitation of 8 MeV were observed. Spins and parities of several states have been assigned using an empirical method for the (t, p) results and using a DWBA analysis for the (d, p) distributions. Spectroscopic factors for twelve states were obtained from the latter analysis. Two of these disagree with theoretical predictions. The state previously reported at an excitation of 6.63 MeV in ³⁰Si was observed to be formed by a strong L = 0 transition in the (t, p) reaction and also by a strong l = 1 transition in the (d, p) reaction. We deduce that there are two closely spaced states at about this excitation, one having a spin and parity of 0⁺ and the other 0^?, 1^? or 2^?.     

Coupled-channel fusion and inelastic scattering calculations for 18O + 44Ca and 12C + 48Ti

Fusion and inelastic scattering coupled-channel calculations are carried out for the systems ¹⁸O + ⁴⁴Ca and ¹²C + ⁴⁸Ti. Comparison between ¹²C + ⁴⁸Ti and ³²S + ²⁴Mg sub-barrier fusion cross-section enhancement is made using simple analytical expressions. The distribution of the angular momentum absorbed by the compound nucleus is discussed in a quantum-mechanical coupled-channel model.     

Transfer reactions induced by 16O on 29, 30Si

Angular distributions for one- and two-nucleon transfer reactions induced by ¹⁶O on ^{29, 30}Si and for the elastic scattering of ¹⁶O on ^{28, 29, 30}Si have been measured at 73.5 MeV bombarding energy. The results are analyzed with the DWBA code BRUNHILD that includes recoil effects. Spectroscopic factors extracted for all observed transitions in one-nucleon transfer reactions agree well with those derived from light panicle reactions. The effects of recoil on the Spectroscopic factors for transitions to final states with different spins are discussed. The transitions from smooth to oscillating angular distributions are examined. It is found that the shape of the angular distributions depends on both the matching conditions of the reaction and the localization of the S-matrix amplitudes in L-spacef.     

Alpha-heavy-ion angular correlations from 28Si + 12C

Alpha particles have been measured in coincidence with heavy recoil nuclei from the ²⁸Si + ¹²C reaction. At E_lab = 87 MeV angular correlations for alphas between 15° and 55° and heavy ions at angles ?9°, ?12° and ?15° have been taken. An excitation function of coincidence events with θ_α = 30° and θ_HI = ?12° has been measured for 84 MeV < E_lab < 91.5 MeV. The results are well described by a statistical-model calculation for compound nucleus decay. No evidence is found for additional processes.     

Fusion and neutron-transfer cross sections for 13C + 10B and 13C + 11B reactions at subbarrier energies

The cross sections for the ¹⁰B(¹³C, ¹²C)¹¹B neutron-transfer reaction, leading to the ¹¹B 4.45 and 6.74 MeV and ¹²C 4.44 MeV excited states, and for ¹³C + ¹⁰B fusion have been measured by the characteristic and total γ-ray yield methods, respectively, over the energy (c.m.) interval 2.4–5.8 MeV. For ¹³C + ¹¹B, with no transfer reactions present, the fusion cross sections have been measured between E_c.m. = 2.3 and 6.4 MeV. The fusion cross sections for ¹³C + ¹⁰B and ¹³C + ¹¹B are found to be almost equal and slightly enhanced with respect to those for ¹²C + ¹⁰B and ¹²C + ¹¹B.     

The 26Mg(14N, 10B)30Si and 26Mg(14N, 11B)29Si reactions

Reactions induced by ¹⁴N on ²⁶Mg at bombarding energies of 60–95 MeV have been studied. Angular distributions for states populated in ²⁹Si by the (¹⁴N, ¹¹B) reaction and in ³⁰Si by the (¹⁴N, ¹⁰B) reaction have been compared with Hauser-Feshbach and DWBA calculations to determine the reaction mechanism and to deduce spectroscopic information. The cross sections for the states populated in ²⁹Si and ³⁰Si are in poor agreement with statistical model calculations, indicating a non-compound nucleus mechanism.     

Yrast cascade in 60Ni

Yrast levels of ⁶⁰Ni were investigated via the study of in-beam γ-rays induced by 15–25 MeV α-partictes on ⁵⁸Ni, 26–48 MeV ¹²C ions on ⁵⁰Cr and 30–60 MeV ¹⁶O ions on ⁴⁶Ti. The compound nucleus formed by these target-projectile combinations is ⁶²Zn, and its decay by two-proton emission populates yrast levels of ⁶⁰Ni. The ordering and decay modes of the yrast levels were determined from the analyses of in-beam γ-ray angular distribution and γ-γ coincidence measurements. The new levels established are at 4.262, 5.345 and 6.807 MeV. These together with the known 2₁⁺ (1.332 MeV) and 4₁⁺(2.505 MeV) levels constitute the yrast cascade. The spin assignments based on the present study are 6, 7, 9 for the 4.262, 5.345 and 6.807 MeV levels, respectively. The excitation functions for the yrast γ-rays from the ⁵⁰Cr(¹²C, 2p)⁶⁰Ni reaction show peaks near 33 MeV incident energy.     

Cross-section measurements and thermonuclear reaction rates for 46Ti(p, γ)47V, 47Ti(p, γ)48V, 47Ti(p,n)47V and 48Ti(p, γ)49V

The yield of γ-rays from the reaction ⁴⁶Ti(p, γ)⁴⁷V has been measured as a function of bombarding energy over the range 0.72–3.00 MeV, from ⁴⁷Ti(p, γ)⁴⁸V over the range 0.74–3.50 MeV, and from ⁴⁸Ti(p, γ)⁴⁹V over the range 0.72–4.40 MeV. The yields of γ-rays following (p, p') reactions on all three targets were also measured and (p, p') cross sections were deduced for the first excited state proton groups for ⁴⁶Ti and ⁴⁸Ti and for the first ten proton groups for ⁴⁷Ti. The yield of neutrons from the reaction ⁴⁷Ti(p, n)⁴⁷V has been measured over the range from threshold to 4.40 MeV. All these data are compared with statistical-model calculations, and good agreement is achieved. Thermonuclear reaction rates for the (p, γ) and (p, n) reactions are calculated for the temperature range 5 × 10⁸–10¹⁰ K which includes the range of temperatures of interest in nucleosysnthesis 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.     

Absolute residue cross sections for 46–50Ti + 13C reactions at 36, 46 and 56 MeV

Absolute cross sections for nuclei produced in the reactions ^46–50Ti + ¹³C at 36, 46 and 56 MeV (lab) were measured. Complete identification in mass and atomic number for the evaporation residues was obtained by means of in-beam γ-ray spectroscopy techniques. In the entire energy range, an overall satisfactory account of the observed product nuclei is given by the predictions of the fusion-evaporation model. Direct channels like inelastic scattering and n-transfer appear to be noticeable and contribute ~ 15 % to the total cross section.     

Determination of angular momenta in the incomplete-fusion channels of the reactions Ta+22Ne and Ir+12C

By using the γ-ray-multiplicity technique, experiments were carried out to determine the input angular momenta lⁱⁿ corresponding to the heavy-ion induced incomplete-fusion reactions involving the emission of fast charged particles. The α-particle and Li-nuclei emission channels were investigated in the reaction ¹⁸¹Ta + ²²Ne at the average Ne-ion energy of 155 MeV and for the α-particle emission channel in the reaction ^natIr+¹²C at E = 100 MeV. The separation of the reaction channels was carried out using an X-ray spectrometer. The angular distributions of the fission fragments were measured in the reaction ¹⁸¹Ta(²²Ne, αf). The data obtained indicate that input angular momenta are equal to about 60 ? and 50 ? for the channels of Li emission and α-emission, respectively, being practically independent of the particle energy. For the α-emission channel the lⁱⁿ values are the same for both reactions within experimental errors. The lifetime of the system of interacting target and projectile nuclei, prior to the emission of an α-particle, has been estimated to be equal to 10^?20s.     

Investigation of states in 30P via the 30Si(3He,t)30P reaction at 30 MeV

The ³⁰Si(³⁰He, t)³⁰P reaction has been measured for about 100 levels in ³⁰P with E_x < 8.8 MeV. Little selectivity in the population of states has been observed. For 75 levels angular distributions have been analysed using a “fingerprint method” by determining the L-value from a comparison in shape with transitions to states with known J^π. For possible mixed L-transitions a dominance of the higher L-value is observed for almost all cases. Coulomb displacement energy calculations utilizing shell-model wave functions have been used to identify T = 1 states.     

Masses and level schemes of 33Si and 34Si

The mass excesses of ³³Si and ³⁴Si have been measured using the ³⁶S(¹¹B, ^{14, 13}N)^{33, 34}Si; reactions. Values of $\text{?20.550 ± 0.030}\text{MeV}\text{(}{}^{33}\text{Si) and ?20.017 ± 0.025}\text{MeV}\text{(}{}^{34}\text{Si)}$ were obtained. In addition, an excited state of ³⁴Si was observed at 5.33 ± 0.05 MeV, and excited levels of ³³Si were observed at 1.06 ± 0.02 and 4.32 ± 0.03 MeV. These results are compared with recent shell-model calculations.     

Spectroscopy of A = 16 from 13C(6Li,t)16O

The ¹³C(⁶Li, t)¹⁶O reaction has been studied at 34 MeV. Selective population of narrow states is observed up to 21 MeV excitation in ¹⁶O. This reaction populates strongly both unnatural-and natural-parity states that have little or no ¹²C + α₀ width. The measured angular distributions are compared with Hauser-Feshbach and finite-range DWBA calculations. Reasonable agreement with the DWBA calculations is found for most of the states strongly populated. The widths of the narrow states populated in the 16–20 MeV excitation region are presented. Comparison of the present data with that from medium-energy inelastic scattering and other multiparticle transfer reactions is made.     

The interaction of 33 MeV polarised helions with 30Si

Distributions of cross sections and analysing powers have been measured over the range ～ 14°–100° c.m. for the $\text{(}{}^3\text{H}\text{,}{}^3\text{He), (}{}^3\text{H}\text{,}{}^4\text{He), (}{}^{\mathrm{<mtext>3</mtext><mtext>H</mtext>}}\text{,}{}^2\text{H)}$ reactions at 33.4 MeV incident e using a ～ 95 % enriched ³⁰Si target. Phenomenological optical-model analyses of the elastic-scattering data have been carried out. A DWBA analysis of the inelastic-scattering data for the 2.24 MeV (2⁺) and 5.49 MeV (3^?) states of ³⁰Si has yielded values of the deformation β₂ and β₃. The j-dependence of the analysing powers for the (³He, ⁴He) and (³He, ²H) reactions has identified the 6.71 MeV level of ²⁹Si as a $\text{5}\text{2}{}^{\mathrm{+}}$ state, and a level near 9.5 MeV in ³¹P as a possible $\text{7}\text{2}{}^{\mathrm{?}}$ state. Spectroscopic factors for ten states in ²⁹Si and seven states in ³¹P have been deduced and are compared with other work. The extent to which the data defines the ³He spin-orbit potential is discussed.     

Evidence for inelastic processes in the 24Mg(13C, 12C)25Mg reaction at elab = 30 MeV

The ²⁴Mg(¹³C, ¹²C)²⁵Mg reaction has been studied at 30 MeV using a magnetic spectrometer. Differential cross sections for transitions to several final states in ²⁵Mg have been measured and analysed using an exact finite range DWBA code. The DWBA predictions have fitted the bell-shaped distributions satisfactorily, yielding spectroscopic factors which are in reasonable agreement with those obtained using (d, p) reactions. The exceptions are the $\text{3}\text{2}$⁺ state at 0.97 MeV which displays a marked departure from the bell-shaped angular distribution obtained for the other $\text{3}\text{2}$⁺ state at 2.80 MeV, and the $\text{7}\text{2}$⁺ state at 1.61 MeV whose angular distribution has an unusual shape, displaying a deep minimum located at the grazing angle. A semiquantitative model has been used to suggest that the angular distribution for the 0.97 MeV state is evidence for the coupling of inelastic processes in this transition. In the case of the 1.61 MeV state it is suggested that the angular distribution shows the influence of indirect Coulomb excitation on the transfer cross sections.     

Microscopic study of the 12C + 16O system

An angular momentum projected microscopic calculation is performed for the ¹²C + ¹⁶O system with an effective nuclear force and the exact Coulomb interaction. The ¹²C wave function is projected on a 0⁺ state. Parametrizations of the Coulomb interaction between the nuclei are fitted. The L-projected energy curves present a quite complicated structure especially for the negative parity states. The role played by critical angular momenta is put into evidence. A generator coordinate calculation gives several bands of bound, quasibound and virtual states. Excellent agreement in energy and angular momentum is obtained with the 13.7 MeV (J = 9), 19.7 MeV (J = 14), 22.7 MeV (J = 15) and other resonances.     

The polarization of 3He elastically scattered from 27Al and 28Si at 21 MeV

The polarization of 21 MeV ³He elastically scattered from ²⁷Al and ²⁸Si has been measured in an angular range of θ_lab = 25°–55°. Differential cross-section data have been obtained out to angles of approximately 100°. The small values observed in the polarization distributions differ somewhat from optical-model predictions based on fits to the differential cross-section data and cannot be used to obtain significant information about the optical-model spin-orbit potential. It is concluded that statistically significant, non-zero ³He polarization measurements will not be possible using traditional double scattering techniques for ³He energies ≦ 27 MeV and targets of $\text{Z ≧ 13}$.     

The 20Ne(12C,p)31P, 20Ne(12C,d)30P and 20Ne(12C, α)28Si reactions in the region of the coulomb barrier

The excitation functions of the ²⁰Ne(¹²C, p)³¹P, ²⁰Ne(¹²C, d)³⁰P. and ²⁰Ne(¹²C, α)²⁸ Si reactions were measured at bombarding energies between 6.9 and 16.9 MeV (c.m.) by steps of 156 keV, at an average lab angle of 2.82°. The average coherence width of states in the compound nucleus, ³²S, populated in the reactions was deduced through the analysis of the fluctuations in the measured excitation functions. The result agrees with the average compound nucleus width predicted by the Hauser-Feshbach expression. The fluctuation analysis shows that these reactions proceed mainly through the formation of a compound nucleus. A cross correlation analysis revealed that the fluctuations in the different excitation functions are statistically independent and that there is no evidence of intermediate structure resonances.