Resonant and Direct Components In the 3He.D, P.4 He Reaction at Low Energies

Nuclear reactions of interest in astrophysics often proceed both by resonant and direct reaction mechanisms. To decouple these processes one should obtain as much information on reaction observables as possible. Polarization observables are particularly important in this context. The 3He (d,p) 4He reaction is dominated at deuteron energies below 1 MeV by a broad S-wave resonance in 5Li at Ed=0.430 MeV. However, recent measurements [1] have shown significant deviation from the expected S-wave resonant behavior. These discrepancies may be due to L.0 contributions to the reaction mechanism arising from direct transfer processes or tails of distant resonances. Additional experimental information as well as appropriate models are required to identify these processes and obtain information on the relative importance of direct and resonant mechanism. In this work new experimental results for the cross section nd Ayy tensor analyzing power observables of the 3He (d,p) 4He reaction at a scattering angle of u =0° are obtained. hese results, together with recent measurements of the polarization-transfer observable K yy (0°) at the same energies, allow the calculation of all the linearly independent lements of the scattering atrix at u =0°. Moreover the ew tensor observable measured, being very sensitive to the eaction process, provides an excellent tool to test a theoretical tudy of the mechanism of the reaction. In previous analyses, direct processes have been found to exist in transfer reactions at sub-Coulomb energies, as for example in (p,α) reactions where the outgoing particles have energies significantly above the Coulomb barrier. Other studies of the same reaction at energies near low-energy resonances suggested the need for including direct processes. This work describes a similar high Q value reaction, constituting the first attempt for a systematic modeling of low energy nuclear reactions by including both resonant processes and direct mechanisms from a potential model. We start by describing the experimental setup and procedures in Sec. II. The data analysis and the calculation of the observables are also explained in Sec. II. In the third section the linearly independent scattering matrix amplitudes are calculated.

The experiment was performed in the 61-cm-diameter scattering chamber using the FN Tandem accelerator.

The Ayy analyzing power at u =0° was measured with a polarized deuteron beam incident on a 3He gas cell target. The setup is shown schematically in Fig. 1. The gas target was 2.54 cm diameter cell with a 6.3 mm Havar-foil cylindrical window. This cell was filled with 3He gas and the pressure (1 atm for runs at Ed=0.52 MeV and 2 atm for runs at Ed=0.89 and 1.49 MeV) monitored to be constant during the experiment. The polarized deuteron beam was obtained from the atomic beam polarized ion source a three polarization state method with fast state switching [8]. During the measurements the beam current on target ranged from 100 nA to 200 nA, depending on the energy. Three silicon detectors were positioned inside the chamber, a central detector (labeled C) at u =0° and the others at 10° left (L), and right (R), from the 0° detector. Consecutive runs at the deuteron energies of interest were intercalated with runs at Ed=4 MeV to determine the tensor beam polarization pzz. The beam current was integrated from the gas cell and a tantalum foil in front of the 0° detector. Calculations with were performed to obtain the beam energies corresponding to the mean reaction energies at the center of the gas cell. This procedure was also used for the self-supported targets described later in Sec. II B. For the determination of the analyzing power, Ayy (0°), the normalized yield Yi for a detector in the ith polarization state is determined by normalizing the number of reaction counts collected in that detector and state to the charge collected. These yields also include a correction for dead time in the data acquisition system. A value of i=0 is used to represent the unpolarized state. The analyzing power is calculated using where the subscript C denotes the central detector, and pzz i is the beam polarization in the ith polarized state. The beam polarization was calculated from the 4 MeV runs using where L and R denote the left and right detectors, respectively, and Ayys10°d=0.818±0.004 is the value obtained. During the experiment, the on target beam polarizations were determined to be stable for both polarization states. The average of the magnitudes of the two polarizations was 75%. The final values, given in Table I, are the averages of both spin states. The cross section at u =0° was measured in inverse kinematics with a 3He beam incident on a deuterated carbon target. The setup is shown schematically in Fig. 2. The self-supported deuterated carbon targets were produced using the plasma-assisted chemical vapor deposition. technique with deuterated methane gas. These targets have been shown to be stable and to have a slow decrease of deuterium thickness. To normalize the results to the p-d elastic cross section, the 3He runs were intercalated with proton runs for the same value of the magnetic field in the analyzing magnet. The proton beam was obtained from the direct extraction negative ion source. Typical beam currents on target were 40 nA for the proton beam and 70 nA for the 3He beam. Three detectors were positioned inside the chamber, two fixed detectors (monitors) at 45° and 55° (detectors 2 and 3, respectively), and a central detector (detector 1), positioned at u =0° for the 3He beam and sliding to 30° when running with the proton beam. In this way, one avoids radiation damage of the detector during the proton runs and is able to avoid solid angle corrections. During the 3He runs beam current integration was performed from the target and a tantalum foil in front of detector 1. During the proton runs the current was measured from the target and a Havar foil that slid rigidly with the central detector and was located at 0°. The differential cross section at 0° for the 3He (d, p) a reaction, α(0°), is determined using where Q' and Q are the collected charges obtained during 3He runs and proton runs, respectively, and Nα and Np are the dead-time-corrected integrals of the counts in the a peak and proton elastic peak, respectively. The subscripts denote the detectors, as shown in Fig. 2, and m refers to the detector used for p-d elastic scattering. The elastic p-d cross section. For Ed=1.49 MeV, one can use detector 1 for p-d elastic yields; thus m=1, θm=30°, and the ratio of solid angles in Eq. (3) vanishes. However, for the lower energy the scattered particles are absorbed by the foil in front of detector 1. The ratio of solid angles is then obtained from the proton runs at Ep=1.68 MeV using The angles in Eqs. (3) and (4) are laboratory angles. The final values, given in Table I, are the average of the values obtained from normalizing to different detectors.

To estimate the systematic errors introduced in the analyzing power measurement by the uncertainties in the reaction energies and gas leaking effects in the target calculations were performed. The systematic errors in the Ayy values associated with the uncertainties in the reaction energies are 2.2%,2.1%, and 0.9% for Ed=0.52, 0.89, and 1.49 MeV, respectively. Furthermore, it was found that 5% uncertainty in the gas pressure during a run corresponds to a 0.5% systematic error in the values of Ayy obtained in this experiment. Also, the systematic error in the value of Ayy (10°) obtained corresponds to a 0.5% systematic error in the values of Ayy. The systematic error associated with the angular acceptance introduced by the collimators was found to be negligible (less than 0.1%). Detector position, energy loss in the target, and beam motion effects were found to be the main sources of systematic uncertainties involved in the determination of the cross section. The errors in the detector angles were determined, through the peak positions, to be accurate within 0.25°. Based on angular dependence data the systematic errors associated with the positions of the detectors were found to be 0.9% and 1.1% for Ed=0.89 and 1.49 MeV, respectively, the upper limit to the systematic errors in the cross section values introduced by the uncertainties in the reaction energies is 2%. Horizontal 3 mm beam motion effects were found to introduce a 2.9% systematic uncertainty in the cross section value at Ed=0.89 MeV. The systematic error in the cross section values associated with the angular acceptance introduced by the collimators was found to be negligible.

The observables measured in a reaction can always be calculated from the scattering matrix. In some cases, when the number of independent polarization observables is sufficient, experimental data can be used to obtain information about the T matrix amplitudes. Due to the spin structure of the 3He (d, p)4He reaction 0.5+1 ---> 0.5+1 , the scattering matrix T has 6x2 complex elements. Conservation of parity reduces the number of different amplitudes to six. For 0° scattering angle, no preferential transverse direction is defined, so T must be invariant under rotations along the Z axis (Madison frame). The scattering matrix is thus completely determined by two amplitudes [17]. These correspond to three real numbers since one relative phase factor can be chosen arbitrarily: Consequently, these amplitudes can be calculated from the three linearly independent observables Kyy, Ayy, and the cross section using In order to calculate the remaining scattering amplitudes necessary to describe the 3He (d, p) 4He reaction observables at all angles, and to determine the relative importance of direct and resonant mechanisms, it is necessary to develop a model that extracts this information from the available experimental data.

Due to the dominant effect of the 1.5+ S-wave resonance at Ed=0.430 MeV on the 3He (d, p) 4He reaction observables for Ed<1 MeV, our theoretical model should be tested in this energy range. Obtained precise measurements of vector and tensor analyzing powers, and of total and differential cross sections at several energies in this range. In our analysis we will use these measurements, the 3He-d elastic cross section data and the new measurements presented in this work. R-matrix model to include the next excited state, the 1.5- state at Ed=2.62 MeV [18], as an R-matrix pole. The T2q and Kyy' are still well described, but the predictions for iT11, although nonzero, do not reproduce the data. This behavior indicates the strong sensitivity of this observable to other contributions to the reaction mechanism. To account for these other mechanisms, we develop a model that takes into consideration the direct component of the reaction through a potential description. The scattering wave functions generated by the potential are expanded in an R-matrix basis and can therefore be added to the resonant contribution to calculate the scattering amplitudes. In this model, the 1.5+ and 1.5- resonant states are introduced through R-matrix poles, and the other negative parity contributions to the reaction mechanism are obtained through a fitted potential. To improve the quality of the fits we also include 0.5+ and 1.5+ background poles at Ed=3 MeV.

Measurements of Ayy (0°) and α (0°) of the 3He (d, p)4He reaction were taken at Ed=0.52, 0.89, and 1.49 MeV, complementing the existing Kyy'(0°) data at those energies. These measurements allow, for the first time, the determination of all linearly independent scattering matrix elements at 0°. These and previous results at Ed<1 MeV were described using a hybrid model that accounts for both resonant and direct mechanisms by combining R-matrix poles and a potential description. We conclude that a consistent description of the different polarization observables, vector and tensor analyzing powers, and spin transfer coefficients can be achieved by assuming that the reaction proceeds by a mixed mechanism where the dominant resonant component competes with a non-negligible direct component.

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