Electron screening effect in the reactions He(d, p)He and d(He, p)He

The cross section of the reactions ³He(d, p)⁴He and d(³He, p)⁴He has been measured at the center-of-mass energies E=5 to 60 keV and 10 to 40 keV, respectively. The experiments were performed to determine the magnitude of the electron screening effect leading to the respective electron-screening potential energy U_e=219±7 and 109±9 eV, which are both significantly higher than the respective values from atomic physics models, U_e=120 and 65 eV.     

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.     

Cross-section measurements for the reaction B(p, He)Be

Cross sections have been measured for the transitions to the ground state and first excited state of ⁸Be and to the two 2⁺ levels at 16.63 MeV and 16.93 MeV excitation in the reaction ¹⁰B(p, ³He) at E_p = 49.5 MeV. The angular distributions of the cross section were compared with DWBA predictions.     

The (He, t) reaction at intermediate energies : Spin-isospin multipole transitions

Data for the (³He, t) reaction at 900 MeV and 2 GeV on the targets ²⁶Mg, ⁴⁰Ca, ⁴⁸Ca, ⁵⁴Fe, ⁹⁰Zr and ²⁰⁸Pb are presented. A multipole decomposition for the data at 900 MeV has been made and the different distributions have been analysed. From the L = 0 cross section the Gamow-Teller strength distributions are extracted and compared with (p, n) data. The L = 1 and 2 distributions are analysed in a schematic model which describes the general systematics fairly well. The spectra at 2 GeV and Θ = 4° show for all targets a well-developed quasi-elastic peak. The A-dependence of the cross section is analysed in a simple model.     

Pion-transfer (n, d) and (d, He) reactions leading to deeply bound pionic atoms

Theoretical studies are given on the (n, d) and (d, ³He) reactions leading to deeply bound pionic atoms in heavy nuclei of configuration [(nl)_π·j_n⁻¹]J. The cross sections for various pionic and neutron-hole configurations in the case of a ²⁰⁸Pb target are calculated at incident energies 300–1000 MeV/u by using the effective number approach and the eikonal approximation for distortion. The effective number with a pion in the 1s or 2p state and a neutron hole in the orbit peaks around the same incident energy (T_n = 600 MeV) as the elementary cross section n+n→d+π⁻, where the momentum transfer matches the angular-momentum transfer of L = 5–7. The DWIA cross section for (n,d) producing a pion in the 1s or 2p orbit at T_n = 600 MeV is found to be around 42 or 75 μb/sr, respectively. At T_n = 350 MeV, where the momentum transfer is small, quasi-substitutional states of configurations and are preferentially populated with (n, d) cross sections of 95 and 190 μb/sr, respectively. The (d, ³He) cross sections are estimated to be an order of magnitude smaller than the (n, d) cross sections. Thus, the (n, d) and (d, ³He) reactions are found to be suited for the production of deeply bound pionic atoms.     

Inelastic electron scattering from He

The spectra of electrons scattered inelastically from ⁴He have been measured at incident energies from 150 MeV to 400 MeV for scattering angles from 38° to 90°. Through the use of a liquid ⁴He target, a high momentum resolution (≈0.25%) was obtained, and the 20 MeV 0⁺ state of the -particle was observed for the first time in electron scattering. The excitation energy and the total width of this state were determined and are in good agreement with the results from other experimental methods. It was found that the total disintegration cross section appears be smaller than 2(σ_p+σ_n) by more than an order of magnitude at the lowest q²(≈ 0.33 fm⁻²). In earlier work the assumption of a total cross section of 2(σ_p+σ_n) was found to be quite accurate for higher q². As a new result, the partial radiative width for the 0⁺ state is determined to be Γ_rad = 1.1±0.3 meV.     

Polarization of neutrons from the reaction H(d, n)He

The angular dependence of the polarization of neutrons from the reaction ³H(d, n)⁴He was measured at deuteron energies of 3.35, 4.35 and 5.35 MeV for reaction angles up to 165° lab. Polarization values were derived from the left-right asymmetry in n- scattering.     

Measurements of interaction cross sections and radii of He isotopes

Secondary beams of ³He, ⁴He, ⁶He, and ⁸He were produced through the projectile fragmentation of an 800 MeV/nucleon ¹¹B primary beam. Interaction cross sections (σ_I) of all He isotopes of 790 MeV/nucleon on Be, C, and Al targets were measured by a transmission-type experiment. The interaction nuclear radii of He isotopes R_I(He) = (σ_I/π)^1/2 − R _I(T) where R_I(T) is the radius of the target nucleus, have been deduced to be R_I(³He) = 1.59 ± 0.06 fm, R_I(⁴He) = 1.40 ± 0.05 fm, R_I(⁶He) = 2.21 ± 0.06 fm, and R_I(⁸He) = 2.52 ± 0.06 fm.     

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.     

Polarization of protons from the Be(d, p)Be reaction

The polarization of protons from the ⁹Be(d, p)¹⁰Be reaction has been measured for deuteron energies between 1 and 6 MeV. Angular distributions of the polarization for the ground state proton group (Q=4.59 MeV) have been measured for laboratory angles 10° and 135° at 2.5, 4.0 and 5.5 MeV. The polarization at a laboratory angle of 30° was measured in 0.2 MeV steps between 1 and 6 MeV. In addition the polarization of protons leaving ¹⁰Be in its first excited state (Q=1.22 MeV) was measured between 10° and 90° for a deuteron bombarding energy of 5.5 MeV. Measurements were made by conventional double-scattering techniques using elastic scattering from helium at 45° as the analyser. The results show a strong energy dependence contrary to what one might expect on the basis of the lack of structure in the cross section. The maximum polarization observed at each energy is about 0.35.     

Spin-dependent reaction mechanism in Ti(d, p)Ti from proton-γ correlation

The γ-decays of the states in ⁴⁷Ti at 157 keV and 1547 keV have been studied following the ⁴⁶Ti(d, p)⁴⁷Ti reaction at 5.0 MeV incident energy. Protons were detected at 0° with a semiconductor detector. The angular correlations of the γ-rays with the reaction protons were measured. The E2/M1 mixing ratios of the γ-decays and the population ratios of the to the substates were deduced. From the non-zero population of the substate it was concluded that a spin-flip mechanism exists in the ⁴⁶Ti(d, p)⁴⁷Ti stripping reaction.     

π Meson interaction on He at 120, 145 and 165 MeV

The total cross sections and the differential cross sections of π⁺-⁴He elastic and inelastic reactions at E_π=120, 145 and 165 MeV have been measured using a 38 cm diffusion cloud chamber in a magnetic field exposed to the Frascati Laboratories' pion beam. Total π⁺ track lengths of (2141 ± 10) × 10³ cm, (3435 ± 10) × 10³ cm and (2413 ± 10) × 10³ cm were measured at the three considered energies, respectively. The elastic cross-section data are in good agreement with the results of the Dubna-Torino collaboration. The total inelastic cross sections have been obtained taking into account the contributions from all the inelastic channels. The analysis of the various inelastic processes has allowed us to distinguish five main reaction mechanisms, which compare reasonably with the existing data and with the models for pion-light-nuclei interactions.     

Pionic K X-rays in liquid He

Energies and lorentzian widths of pionic K X-ray transitions have been measured in liquid ³He with improved accuracy. The strong interaction on the π³He 1s level is found to be attractive and to produce an increase in the K transition energies of 34 ± 4 eV; the measured lorentzian width is 36 ±7 eV. Measured values are also presented for K X-ray energies in liquid π⁴He and μ⁴He, the lorentzian width of the 1s level in π⁴He, and relative intensities of K X-ray transitions in π³He, π⁴He and μ⁴He. The measurements are compared with those of others and with recent theoretical calculations.     

A study of the S levels and the analogue levels of P by the P(He, d)S reaction

The ³¹P(³He, d)³²S reaction has been studied with high resolution at 12 MeV bombarding energy. A detailed level scheme for ³²S has been determined up to an excitation energy of 9.5 MeV revealing several previously unobserved states. The l_p values and absolute spectroscopic factors extracted from a DWBA analysis of the experimental deuteron angular distributions have provided information on the wave functions for the T = 0 states as well as for the T = 1 isobaric analogue states of ³²P. A comparison between the present data and those of previous experiments is made, and the results are discussed in terms of existing theoretical work in this mass region. Information on Coulomb displacement and symmetry energies is also extracted.     

Simultaneous measurements of the p+d→(A=3)+π reactions

A stack of annular detectors made of high-purity germanium was used to measure simultaneously pd → ³H π⁺ and pd → ³He π⁰ differential cross sections at beam momenta of 750 MeV/c, 800 MeV/c, and 850 MeV/c over a large angular range. The extracted total cross sections for the pd → ³He π⁰ reactions bridge a gap between near threshold data and those in the resonance region. The ratio of the cross sections for the two reaction channels taken at the same η=p^cm_π/m_π yields 2.11±0.08 indicating that a deviation from isospin symmetry is very small.     

Direct reactions to many-channel, many-level final states : (II). (d, p)n and (He, d)p

In an earlier paper, the cross section for a direct reaction to a generalised positive-energy final state, described by an R-matrix wave function, was derived. Here a distinction is emphasised between two classes of such a reaction, depending on whether it can or cannot decay back to the target state. A major contribution in the latter case can be via direct break-up. This is computed for the reaction ⁷Li(³He, d)⁸Be(p)⁷Li, treated by a stripping mechanism. The dependence of the cross section on the final-state (⁸Be) channel energy is discussed. The present work uses shell-model wave functions for R-matrix basis states, and this is shown to be appropriate and useful for direct reactions.     

Self energies of the pion and the Δ isobar from the He(e,e′π)H reaction

In a kinematically complete experiment at the Mainz microtron MAMI, pion angular distributions of the ³He(e,e′π⁺)³H reaction have been measured in the excitation region of the Δ resonance to determine the longitudinal (L), transverse (T), and the LT interference part of the differential cross section. The data are described only after introducing self-energy modifications of the pion and Δ-isobar propagators. Using Chiral Perturbation Theory (ChPT) to extrapolate the pion self energy as inferred from the measurement on the mass shell, we deduce a reduction of the π⁺ mass of MeV/c² in the neutron-rich nuclear medium at a density of fm⁻³. Our data are consistent with the Δ self energy determined from measurements of π⁰ photoproduction from ⁴He and heavier nuclei.     

Study of the structure of S and Ar

The ³⁷Cl(d, ³He)³⁶S and ³⁹K(d, ³He)³⁸ Ar reactions have been studied at a bombarding energy of 28.9 MeV. The results are compared with theoretical calculations for two or four holes in the sd-shell. The three-hole spectrum of ³⁷Cl is also briefly discussed. In the calculation for ³⁸Ar, additional states of a two-particle four-hole nature are included. In ³⁸Ar, the ground state and levels at 2.166 and 7.14 MeV are excited principally by l = 2 transfer, while transitions with appreciable l = 0 strength are observed to levels at 3.935, 4.569, 5.158 and 5.563 MeV. This fragmentation is quite well reproduced by the inclusion of the 2p-4h states. In particular the level at 3.935 MeV is largely of this type, a conclusion supported by both the spectroscopic factors and γ transition rates. The ³⁶S ground state and levels at 6.511 and 7.12 MeV in ³⁶S have angular distributions characteristic of l = 2. Three transitions with l = 0 strength are observed to levels at 3.295, 4.523 and 4.577 MeV in this nucleus. An additional level was identified at 7.71 MeV but the l-transfer could not be determined. The data are only qualitatively reproduced by the four-hole calculation, which while useful in making probable J^π assignments, suggests that core excitation is important here also.     

Studies on recoil proton tracks in NTA films with the T(d,n)He reaction

Recoil proton tracks in nuclear emulsion are counted by scanning them using strip, square or circular field of view of optical microscope. In this paper, the overestimate due to the edge effects in counting recoil proton tracks at different neutron energies produced from the T(d,n)⁴He reaction has been determined by measuring the true track density in NTA film. The overestimate has also been calculated using the measured value of the mean projected track length (L) in the film. The percentage of measured overestimates has been compared with those obtained by calculation and the results agree reasonably well. Fading effect in NTA film has been studied and found to be 22% more in the summer than in the winter season. A great reduction in fading rate could be achieved if the films are desiccated and sealed in highly pure dry nitrogen maintained at an over-pressure of 1000 Pa to reduce water vapour ingress. After the edge effect correction, the sensitivity of NTA film has been calculated from (1.72±0.08)×10⁻³ tracksn⁻¹ to (1.97±0.16)×10⁻³ tracksn⁻¹ in the neutron energy ranges from 15.91 to 18.88 MeV. The response was found to be from 0.24±0.02 trackscm⁻² permSv to 0.26±0.01 trackscm⁻² permSv in the same energy range.