Radiative pion capture in 12C and 16O

Radiative pion capture in ¹²C and ¹⁶O is investigated. An effective interaction Hamiltonian based upon the CGLN theory is employed. Capture rates in ¹²C and ¹⁶O from Is and 2p pionic orbits are calculated by using the nuclear model of Kamimura, Ikeda and Arima for the odd parity states of ¹²C, and that of Walker with strong ground state correlations, for the odd parity states of ¹⁶O. The results are compared with those of the 1p-1h nuclear model under the Tamm-Dancoff and random phase approximations of Gillet and Vinh Mau. Detailed examinations are made for the transitions to low-lying states with 1⁺ and 2⁺ for ¹²C and with 1^?, 2^? and 3^? for ¹⁶O by using the Cohen-Kurath and the Walker models, respectively. The results are in good agreement with the recent experimental data from Berkeley.     

Microscopic analysis of the 12C(α, γ)16O reaction

Electric transition probabilities in the ¹⁶O spectrum, and the ¹²C(α, γ_o,3¹⁶O capture cross sections are calculated with antisymmetric wave functions by the generator coordinate method. The influence of bound states on radiative capture is shown to be automatically included in the model. The reduced α-widths of the ¹⁶O bound states are discussed, and compared with previous theoretical and experimental estimates. The microscopic E2 capture cross sections to the O⁺₁ and 2₁⁺ states yield an astrophysical S-factor of 0.09 MeV · b at 0.3 MeV. An attempt to treat the El multipolarity by relaxing the long-wavelength approximation leads to a large underestimation of the γ-widths. Adopting the experimental γ- width and the theoretical reduced α-width of the 1₁^? state provides s_E1 = 0.30 MeV · b at 0.3 MeV.     

Charged pion photoproduction from 10B and 13C

Positive and negative pion photoproduction cross sections from ¹⁰B and ¹³C leading to the ground state of the residual nucleus have been calculated in the plane-wave and distorted-wave impulse approximations. The results are compared with experiment and with other theoretical calculations. While a large discrepancy is observed between experiment and theory in the case of negative pion photoproduction from ¹³C, fair agreement is obtained between experiment and the plane-wave calculations in all other reactions. It is found that in all reactions studied, except in the case of positive pion production from ¹³C, the inclusion of the pion-wave distortions moves the theory away from the experimental points. It is also found that the photopion differential-cross-section calculations show a sensitivity to the nuclear wave function different from that predicted by the electron scattering form-factor calculations.     

No pre-critical enhancement observed in 13C(π+, γ)13N(g.s.) at q ≅ 2mπ

The cross section and angular distribution for the reaction ¹³C(π⁺, γ)¹³N(g.s.) have been measured from 37 to 85° in the laboratory, at a pion energy of 115.5 MeV. The observed cross section ranges from 320 to 660 $\text{nb}\text{sr}$. These results do not show the large magnitude and wide-angle peaking expected if pre-critical effects due to nascent pion condensation were present. In addition, the observed cross section is less than one-half of the predictions of available theoretical calculations which do not include the pre-critical effect. Data on the reaction ¹H(π^?, γ)n at T_π = 116.6 MeV were also obtained for calibration purposes. These data agree with expectations based on knowledge of the inverse reaction and previous measurements.     

T = 1 excitation mechanism in pion induced reactions on 12C

The cross sections for the reactions π^± → π^±, π⁰ on ¹²C with excitation of the T = 1 states are calculated for the N₃₃¹ energy region. The Chew-Low amplitude for pion-nucleon scattering is used in the framework of impulse approximation which has been supported by recent calculation of pion scattering with excitation of definite nuclear states.     

Inclusive neutron and proton energy spectra following the negative pion absorption at rest in 12C

The results of a measurement of the inclusive energy spectra of the neutrons and protons emitted following the absorption at rest of negative pions on ¹²C are presented. The spectra have been measured with the time-of-flight method with an overall resolution of 650 psec. From the neutron spectrum the rate of 1.7 × 10^?2 neutrons per stopped pion has been deduced for the single-neutron emission reaction ¹²C(π^?, n)¹¹ B. Comparisons are made with calculated spectra and other experimental spectra.     

16O, 24, 26Mg, 28Si, 32S, 40Ca(α, 12C) and multi-α-cluster transfer reactions

The (α, ¹²C) reaction has been studied on a variety of nuclei, A = 16 to 40, at E_α = 90.3 MeV. The data indicate a rapid fall-off of cross sections with increasing target mass, approximately as A_t^{?5 ± 1}. This and other systematics are used to estimate cross sections for multi-α-cluster transfer reactions in heavy nuclei and suggest σ_T < 10^?34 cm² consistent with present experimental limits. The data for ²⁴Mg(α, ¹²C)¹⁶O has been studied in more detail and indicates a selective population of final states including ¹⁶O g.s., with oscillatory angular distributions in some instances. Finite-range distorted-wave Born approximation calculations for direct ⁸Be pickup have been performed utilizing cluster overlap amplitudes obtained with zero-order SU(3) wave functions. The calculations are in qualitative, and often quantitative, agreement with shapes and absolute magnitudes of the measured angular distributions although the cross sections for certain α-cluster states (2⁺, E_x ≈ 7 MeV; 4⁺, E_x ≈ 10.3 MeV) are greatly overestimated with this model. Other more complicated mechanisms, such as successive α-transfer, cannot be excluded. The systematics of the calculated ⁸Be cluster overlaps and the calculated and measured (α, ¹²C) cross sections are investigated, and implications for multi-α-cluster transfer reactions are discussed.     

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.     

Microscopic study of elastic 12C+16O scattering

The L=0 to 17 phase shifts are calculated microscopically for elastic ¹²C+¹⁶O scattering with a generator coordinate method. The experimental resonances are shown to belong to four different bands. Interpretations and spin assignments are suggested for several recently observed anomalies. A spin J=15 seems likely for the 22.8 MeV resonance. A missing J=13 resonance should be searched for between 17 and 18 MeV.     

Fission of muonic 232Th and 239Pu

The neutron emission is studied following the formation of muonic atoms of ²³²Th and ²³⁹Pu. Energy and time distributions are measured. Various processes which contribute to the measured spectra are considered. A collective resonance model of the muon capture is used to calculate the nuclear excitation function. The probability of the radiationless nuclear excitations and the influence of the presence of the bound atomic muon on the fission barrier are discussed. The existing data for the $\text{Γ}{}_{\mathrm{n}}\text{Γ}{}_{\mathrm{f}}$, are analysed. As a result of the analysis the rates of the prompt and delayed fission events (due to the radiationless mu-atomic transitions and the nuclear muon capture, respectively) are deduced from the experimental data to be 0.006/muon and 0.045/muon for ²³²Th and 0.10/muon and 0.49/muon for ²³⁹Pu, respectively. The increase of the fission barrier for muonic atoms is confirmed. The experimental neutron rates can be consistently explained only if it is assumed that in both nucleides the K_α radiationless transitions do not induce fission. The increase of the fission barrier for ²³⁹Pu is hence deduced to be not less than 1.2 MeV. The fate of the atomic muon after the nuclear fission is briefly discussed. Its influence on the interpretation of the present results is found to be small.     

The sub-Coulomb 12C + 12C resonances in a microscopic 12C+12C,α+20Ne, 8Be+16O cluster basis

The low-J resonances in the Coulomb barrier region of the ¹² C+¹²C system are investigated in the framework of a microscopic cluster model basis including ¹²C+¹²C, α+ ²⁰Ne, and su8 Be+ ¹⁶O fragment decompositions. Calculations are carried out in an orthogonality condition model approximation in which Pauli-forbidden components are properly excluded from the basis but in which the interaction among cluster fragments is approximated by a local potential, obtained from a gaussian NN interaction by a folding procedure leading to both spherical and Q · Q terms. Only minor adjustments of overall strength and fall-off parameters are introduced to gain a consistent picture of the low-energy spectrum in the separate rearrangement channels. The basis includes cluster relative motion excitations with oscillator quanta from 12 to 20 and is not quite rich enough to give a detailed quantitative comparison between theory and experiment. Predicted excitation energies are too high by ~ 3 MeV and predicted ¹²C partial widths are too small to indicate a well-developed surface-peaked molecular character; but it does appear possible to identify a 5 MeV region as the potential seat of the 0⁺, 2⁺, 4⁺ resonances. The number and approximate spacing of the resonance fine structure components are in agreement with experiment.     

Elastic scattering of π− from 12C at 29 MeV

We have measured the differential cross section for π^? elastically scattered from ${}^{12}\text{C at}\text{T}\text{?}{}_{\mathrm{\pi }}\text{=29}\text{MeV}$. The scattered π^? were detected with pion range telescopes. The measured angular distribution is compared with a momentum space optical potential calculation. Derived phase shifts are compared with those obtained from π⁺ data and from momentum and coordinate space calculations.     

Electron scattering and α-cluster description of 12C and 20Ne

The elastic and inelastic electron scattering form factors in the ground-state band of ¹²C and ²⁰Ne have been calculated using the Brink α-cluster model projected wave functions. From a systematic comparison with experiment it is concluded that usual central forces like the Brink-Boeker B1 force give an unrealistically large clustering while that obtained using density dependent interactions like the Skyrme S1 force is too low. For intermediate values of the clustering it is possible in ¹²C to reproduce simultaneously the elastic as well as the inelastic form factors to the 2₁⁺(4.44 MeV), 3₁^?(9.64 MeV) and 4₁⁺(14.08 MeV) states for not too large transfers. Noticeable discrepancies between calculated and experimental 2₁⁺ and 3₁^? inelastic form factors at transfers higher than 1.5 fm^?1 reveal inherent weaknesses of the α-cluster wave functions which are not corrected after inclusion of the θ-vibrations.     

12C(7Li,t)16O和20Ne(d,6Li)16O反应的研究

本文把用于处理重离子引起的单粒子转移反应的Goldfarb-Buttle方法推广到多粒子转移反应。计算了¹²C(⁷Li,t)¹⁶O和²⁰Ne(d,⁶Li)¹⁶O反应,用了¹⁶O的全相干波函数,考虑了某些反冲因素,并将结果与实验作了比较。     

Determination of the coupling constants 3Hdn, 3Hπ and 3He3Heπ from data on the differential cross sections OF n3H and n3He elastic scattering

A determination of the coupling constants ³Hdn, ³H³H_π and ³He³He_π from existing differential cross section data for n³H and n³He elastic scattering has been carried out. The method is based on the extrapolation of dσ/dΩ to the deuteron and pion poles, exploiting conformal mapping techniques. Calculations result in a value of the ³Hdn coupling constant which is ≈ 20% smaller than dispersion relation predictions. A comparison of the value obtained with predictions based on nuclear models allows one to discriminate between different potentials. The residue at the pion pole turns out to be too weak and the conclusion is drawn that it is impossible to determine the coupling constants ³H³H_π and ³He³Heπ on the basis of existing data.     

The (d, 6Li) reaction on 12C, 16O, 24Mg, 40Ca and 58Ni at 54.25 MeV

The (d, ⁶Li) reaction was studied at E_d = 54.25 MeV on the target nuclei ¹²C, ¹⁶O, ²⁴Mg, ⁴⁰Ca and ⁵⁸Ni. The data were analyzed with finite-range DWBA calculations. The absolute values of the α-cluster spectroscopic factors and the target mass dependence of the relative S_α were in agreement with those in the (p, pα) reaction at E_p = 100 and 157 MeV. The theoretical calculations of the relative S_α were in better agreement with the experimental data at higher energy than at the lower energies.     

The compound nucleus reaction 12C(11B, 2α) 15N

Energy spectra and differential cross sections of nitrogen products formed in the reaction 28 MeV ¹¹B + ¹²C have been measured using a ΔE?E counter telescope. The energy spectra are smooth and therefore indicate that the nitrogen products were formed by a compound nucleus mechanism, via the formation and decay of the compound nucleus ²³Na. The experimental results are compared with statistical model calculations and good agreement is obtained. This result provides further evidence for the importance of the compound nucleus mechanism in heavy ion reactions with light nuclei and also gives added validity to the statistical model for light compound systems.     

A study of the 14C(6Li, 6He)14N reaction at 93 MeV

The reaction ¹⁴C(⁶Li, ⁶He)¹⁴N was investigated with 93 MeV ⁶Li ions in an angular interval of 7–26°. Angular distributions were analysed for the four most intense groups of ⁶He nuclei, corresponding to transitions to the ground (1₁⁺) and the excited (1₂⁺, 2₁^?, 4₁^?) states of ¹⁴N. In the theoretical analysis a mechanism of the spin-isospin excitation was suggested in the DWBA frame with the finite range of interaction and recoil in the light system (⁶Li⁶He) taken into account. In the calculations both shell-model wave functions and transition densities obtained in the theory of finite Fermi systems (FFS) were used. From the comparison between theory and experiment the Landau-Migdal force constant g′ is estimated in order to obtain some information on the degree of nuclear proximity to the threshold of pion condensation.     

194Pt(12C, 12C′) reaction and the triaxial-rotor model

Elastic and inelastic scattering differential cross sections for the ¹⁹⁴Pt(¹²C, ¹²C′) reaction at a bombarding energy of 78 MeV have been measured. Data have been obtained for 0⁺, 2⁺, 4⁺, and 2^+′, states in ¹⁹⁴Pt. The data have been analyzed using a rigid asymmetric-rotor model in coupled-channels reaction calculations. It is found that satisfactory fits to all data can be obtained but only if the hexadecapole deformation is included in the asymmetric-rotor model.     

Investigation of the reaction 37Cl(n, γ)38Cl

With Ge(Li) detectors the γ-radiation following thermal-neutron capture in natural and in ³⁷Cl enriched targets was studied. A total of 79 γ-lines has been assigned to the ³⁷Cl(n, γ) reaction and 64 of these lines have been placed in a decay scheme of ³⁸Cl. The excitation energies of 24 bound states of ³⁸Cl have been determined with 0.09–1.2 keV errors. The neutron separation energy of ³⁸Cl is 6107.7 ± 0.4 keV. A strong correlation between reduced stripping widths and (n, γ) primary reduced widths was found for the l_n(d, p) = 1 states if, instead of the Weisskopf reduction factor E_γ^?3, a factor E_γ^?1.2 was used.