A study of the Ca(d, p)Ca reaction (I). The single-particle states

The reaction ⁴⁰Ca(d, p)⁴¹Ca has been studied with a resolution 30 keV. Excitation functions for the first three strong states have been measured in the energy interval 9.80 to 12.12 MeV. Cross section fluctuations are found to be entirely within statistics, i.e. < 5 %, and it is concluded that σ_CN(θ)/(2J_f+1) < 5 μb/sr. Differential cross sections have been measured for elastic scattering, and the (d, p) transitions to the ground state and the strong single-particle states at E^* = 1.949, 2.471, 3.623 and 3.954 MeV at E_d = 12.00 MeV and, over a limited angular range, at E_d = 11.00 MeV. The angular distributions have been analysed by the DWBA method and spectroscopic factors have been determined. It is suggested that the 3.623 MeV state may be the third state predicted by Gerace and Green rather than as assigned by earlier studies.     

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.     

Unconventional Medium Effect in K+-and π+-Nucleus Scattering

The ratios of total cross section of K⁺-nucleus to K⁺-deuterium at 400 MeV/c≤pk≤800 MeV/c for ⁶Li, ¹²C, ²⁸Si, ⁴⁰Ca and the differential cross section of π⁺-¹²C scattering at p_π= 800 MeV/c are calculated by taking into account the unconventional medium effect.An enhancement of both the K⁺-and π⁺-nucleus scattering cross sections is obtained.     

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.     

Photoproduction of positive pions from hydrogen with PHOENICS at ELSA

The differential cross section of the reaction γp→π⁺n has been measured with the PHOENICS detector at ELSA in Bonn. For the first time this cross section has been determined simultaneously over a large range of photon energies (E_γ = 220−900 MeV) and pion angles (Θ^c.m._pi = 35°−135°) with a tagged photon facility. The experimental set-up allowed a considerable kinematic overdetermination of the investigated reaction. Accordingly, the background contributions have been suppressed to below 1%. The measured differential cross section is in good agreement with existing data. The comparison with different model calculations is presented.     

Pionic excitation of giant resonances in Y

Inelastic scattering of π⁺ and π⁻ exhibits strongly excited giant resonance structures. Besides the giant quadrupole resonance centered around 14 MeV, structures are observed at 16.8 MeV which can be fitted with a mixing of L=0 and L=1, and around 25 MeV (E_x = 110A^−1/3).     

Proton polarization observables for the elastic and inelastic scattering of 500 MeV protons from Ca and Pb

Measurements for the elastic and inelastic scattering of 500 MeV protons from ⁴⁰Ca and ²⁰⁸Pb at small momentum transfers are reported. The induced proton polarization P and the spin rotation parameter Q were measured for the elastic scattering. The spin rotation parameters D_SS′, D_SL′, D_LL′, d_LS′ and the induced polarization P were measured for transitions to the 3⁻(3.37 MeV) and 5⁻(4.48 MeV) states in ⁴⁰Ca and the 3⁻(2.61 MeV) state in ²⁰⁸Pb. Comparisons of the data with the theoretical calculations were carried out in the framework of nonrelativistic and relativistic approaches. We extracted the spin-up and spin-down channels for the elastic scattering cross sections and found that predictions of the relativistic and nonrelativistic approaches agree well with the spin-up channel data and differ considerably in the spin-down channel.     

Proximity scattering in the sequential decay Ca(d, n)Sc3.46(p)Ca

In a nuclear two-stage reaction proceeding through excited states of an unstable intermediate system, rescattering can occur between two of the three outgoing particles as a special type of final-state interaction (“proximity scattering”). The probability for proximity scattering increases with a decreasing lifetime of the intermediate state. Correlations between protons and neutrons from the reaction ⁴⁰Ca(d, np)⁴⁰Ca were measured at a bombarding energy of 5.80 MeV and a neutron emission angle of 70°. The results are compared with a quantal calculation of the cross section for this process. A width Γ = 50±20 keV for the excited state at 3.46 MeV in ⁴¹Sc has been deduced from this comparison. Apparent discrepancies between the Γ-values obtained by this method and by a classical prediction for the proximity scattering probability are discussed.     

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.     

Absorption cross sections for antiprotons on carbon, aluminum and copper at 485 and 597 MeV/c

Absorption cross sections for antiprotons on C, Al and Cu have been measured by a transmission method at 485 and 597 MeV/c. Nuclei are shown to be black to antiprotons at these momenta. Using the available data up to 280 GeV/c, the momentum dependence of the absorption cross sections is investigated. Empirically, a simple expression σ_abs = γ(p/p₀)^−β, with β and γ constants and p₀ = 1 GeV/c, gives a good account of the data in a remarkably wide momentum range, 0.5–280 GeV/c.     

Excitation of ΔL = 1 resonances in the (p,n) reaction on Zr, Sn, Ce and Pb at Ep = 41 MeV

A broad peak was systematically observed at about 10 MeV above the Gamow-Teller resonance in the ⁹⁰Zr, ¹²⁰Sn, ¹⁴⁰Ce, ²⁰⁸Pb (p,n) reactions at E_p = 41 MeV. The angular distribution shapes of these peaks support the interpretation that they they correspond to ΔL = 1 state. The data are compared with TDA-DWBA calculations.     

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.     

The (1f7/2) multiplet in Ca

The states of ⁴²Ca below 3.2 MeV excitation are studied by the ⁴¹Ca(d,p)⁴²Ca reaction at 12 MeV bombarding energy. The experimental spectroscopic factors are compared to predictions based on Gerace and Green's coexistence model.     

DWBA and CCBA analysis of selected transitions in the C(d,τ) B reaction at Ed = 80 MeV

Angular distribution of the reaction ¹²C(d,τ) ¹¹B leading to the 3/2⁻ ground state and the 4.44 MeV excited (5/2⁻ state ¹¹B have measured at E_d = 80 MeV up to about 70° and 40°, respectively. The inclusion of second-order processes in the framework of CCBA calculations gives a good reproduction of the 3/2⁻ as well as of the DWBA forbidden 3/2⁻ angular distribution. The strong dependence of the cross section on the sign of the deformation supports a positive β₂ value for ¹¹B.     

Cross sections and polarizations for protons scattered from Ca between 6.0 and 12.7 MeV

The energy dependence of cross sections and polarizations for protons scattered from ⁴⁸Ca has been measured in 50 keV steps from 6.0 to 12.7 MeV. Significant fluctuations are observed, especially in the polarization, over the entire energy range investigated. Angular distributions were measured at 8.0, 10.0 and 12.0 MeV. Results of an optical-model analysis are given.     

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.     

Sudden approximation for elastic scattering of composite projectiles at intermediate energies

Elastic scattering of deuterons by nuclei at intermediate energies is investigated by the sudden approximation. Scattering amplitudes of the deuteron are described in terms of those of the constituent nucleons. They consist of the amplitude of nucleon-nucleus single collision and that of double collision. The neglect of the latter explains similarity relations between the deuteron observables and the proton ones, which are found in experimental data. Cross sections and vector analyzing powers calculated with the single-collision terms successfully reproduce the measured ones for ¹⁶O, ⁴⁰Ca and ⁵⁸Ni targets in the energy region, E_d = 200 ˜ 700 MeV. Scattering of ⁶Li by ⁵⁸Ni is investigated in a similar way assuming the d + cluster model for ⁶Li.     

Calculations of particle and heavy ion interactions with space shielding materials using the SHIELD-HIT transport code

Spectra of secondary particles produced by nucleus–nucleus interactions and heavy-ion interactions in the extended targets of interest for space research were calculated using the Monte Carlo code SHIELD-HIT. This code simulates the interactions of hadrons and atomic nuclei of arbitrary charge and mass number (Z,A) with complex extended targets in a wide energy range, from 10 GeV/u down to 1 MeV/u, and to thermal energies in the case of neutrons. Inelastic nuclear reactions in SHIELD-HIT are simulated using the Russian models of nuclear reactions. The total reaction cross sections evaluated by these models are discussed for proton and carbon interactions with different nuclei in a wide energy range. Production of secondary neutrons and charged secondary particles from the thick targets of lead, water and PMMA irradiated by ⁴He, ¹²C and ²⁸Si ions of different energies was calculated and compared with the experimental data. The results obtained by SHIELD-HIT are in reasonable agreement with experiments and are promising for further applications in space research.     

Influence of intrinsic nucleon motion on energy spectra and angular distributions for O-induced reactions at 20 MeV/A

Energy spectra and angular distributions for peripheral reactions induced by ¹⁶O on ²⁰⁸Pb at 20 MeV/A can be explained in terms of the intrinsic nucleon motion of the excited projectile, in a manner similar to the interpretation of projectile fragmentation reactions at 2.1 GeV/A.