Resonant and Direct Components In the 3He.D,P.4 He Reaction at Low Energies
by Dharmesh Khare*,
- Published in Journal of Advances in Science and Technology, E-ISSN: 2230-9659
Volume 1, Issue No. 1, Feb 2011, Pages 0 - 0 (0)
Published by: Ignited Minds Journals
ABSTRACT
Newexperimental results for the cross section and Ayy tensor analyzingpower observables of the 3He (d, p)4 He reaction at a scattering angle of u =0° are presented for Ed=0.52, 0.89, and 1.49 MeV, and alllinearly independent scattering amplitudes at this angle are calculated. Ahybrid R matrix+potential model is used to fit these results and other 3He(d, p) 4He reaction data for Ed,1 MeV. Thisanalysis indicates significant direct process contributions to the reactionmechanism.
KEYWORD
resonant, direct components, 3He.D,P.4 He reaction, low energies, experimental results, cross section, Ayy tensor, analyzing power observables, scattering angle, linearly independent scattering amplitudes, hybrid R matrix+potential model, fit, reaction data, direct process contributions, reaction mechanism
. INTRODUCTION
uclear reactions of interest in astrophysics often proceed both by resonant and direct reaction echanisms. To decouple these processes one should obtain as much information on reaction bservables as possible. Polarization observables are particularly important in this context. The He (d,p) 4He reaction is dominated at deuteron energies below 1 MeV by a broad -wave resonance in 5Li at Ed=0.430 MeV. However, recent measurements [1] have shown ignificant deviation from the expected S-wave resonant behavior. These discrepancies may be ue to L.0 contributions to the reaction mechanism arising from direct transfer processes or tails of istant resonances. Additional experimental information as well as appropriate models are equired to identify these processes and obtain information on the relative importance of direct and esonant mechanism. n this work new experimental results for the cross section nd Ayy tensor analyzing power bservables of the 3He (d,p) 4He reaction at a scattering angle of u =0° are obtained. hese results, ogether with recent measurements of he polarization-transfer observable K yy (0°) at the same energies, allow the calculation of all the inearly independent lements of the scattering atrix at =0°. Moreover the ew tensor observable measured, being very sensitive to the eaction process, rovides an excellent tool to test a theoretical tudy of the mechanism of the reaction. n previous analyses, direct processes have been found to exist in transfer reactions at sub- oulomb energies, as for example in (p,α) reactions where the outgoing particles have energies ignificantly above the Coulomb barrier. Other studies of the same reaction at energies near low- nergy resonances suggested the need for including direct processes. This work describes a similar igh Q value reaction, constituting the first attempt for a systematic modeling of low energy uclear reactions by including both resonant processes and direct mechanisms from a potential odel. We start by describing the experimental setup and procedures in Sec. II. The data analysis nd the calculation of the observables are also explained in Sec. II. In the third section the linearly ndependent scattering matrix amplitudes are calculated.
I. EXPERIMENT
he experiment was performed in the 61-cm-diameter scattering chamber using the FN Tandem ccelerator.
. Ayy measurement
he Ayy analyzing power at u =0° was measured with a polarized deuteron beam incident on a 3He as cell target. The setup is shown schematically in Fig. 1. he gas target was 2.54 cm diameter cell with a 6.3 mm Havar-foil cylindrical window. This cell as filled with 3He gas and the pressure (1 atm for runs at Ed=0.52 MeV and 2 atm for runs at d=0.89 and 1.49 MeV) monitored to be constant during the experiment. he polarized deuteron beam was obtained from the atomic beam polarized ion source a three olarization state method with fast state switching [8]. During the measurements the beam current n target ranged from 100 nA to 200 nA, depending on the energy. Three silicon detectors were ositioned inside the chamber, a central detector (labeled C) at u =0° and the others at 10° left (L), nd right (R), from the 0° detector. Consecutive runs at the deuteron energies of interest were ntercalated with runs at Ed=4 MeV to determine the tensor beam polarization pzz. he beam current was integrated from the gas cell and a tantalum foil in front of the 0° detector. alculations with were performed to obtain the beam energies corresponding to the mean reaction nergies at the center of the gas cell. This procedure was also used for the self-supported targets escribed later in Sec. II B. or the determination of the analyzing power, Ayy (0°), the normalized yield Yi for a detector in the th polarization state is determined by normalizing the number of reaction counts collected in that etector and state to the charge collected. These yields also include a correction for dead time in he data acquisition system. A value of i=0 is used to represent the unpolarized state. The nalyzing power is calculated using here the subscript C denotes the central detector, and pzz is the beam polarization in the ith olarized state. The beam polarization was calculated from the 4 MeV runs using here L and R denote the left and right detectors, respectively, and Ayys10°d=0.818±0.004 is the alue obtained. During the experiment, the on target beam polarizations were determined to be table for both polarization states. The average of the magnitudes of the two polarizations was 5%. The final values, given in Table I, are the averages of both spin states.
B. Cross section measurement
he cross section at u =0° was measured in inverse kinematics with a 3He beam incident on a euterated carbon target. The setup is shown schematically in Fig. 2. The self-supported euterated carbon targets were produced using the plasma-assisted chemical vapor deposition. echnique with deuterated methane gas. These targets have been shown to be stable and to have a low decrease of deuterium thickness. o normalize the results to the p-d elastic cross section, the 3He runs were intercalated with proton uns for the same value of the magnetic field in the analyzing magnet. The proton beam was btained from the direct extraction negative ion source. Typical beam currents on target were 40 A for the proton beam and 70 nA for the 3He beam. hree 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 eam and sliding to 30° when running with the proton beam. In this way, one avoids radiation amage of the detector during the proton runs and is able to avoid solid angle corrections. uring the 3He runs beam current integration was performed from the target and a tantalum foil in ront of detector 1. During the proton runs the current was measured from the target and a Havar oil that slid rigidly with the central detector and was located at 0°. he differential cross section at 0° for the 3He (d, p) a reaction, α(0°), is determined using here Q' and Q are the collected charges btained during 3He runs and proton runs, espectively, and Nα and Np are the dead-time-corrected integrals of the counts in the a peak and
roton elastic peak, respectively. The subscripts denote the detectors, as shown in Fig. 2, and m
efers to the detector used for p-d elastic scattering. The elastic p-d cross section. or Ed=1.49 MeV, one can use detector 1 for p-d elastic yields; thus m=1, θm=30°, and the ratio f solid angles in Eq. (3) vanishes. However, for the lower energy the scattered particles are bsorbed by the foil in front of detector 1. The ratio of solid angles s then obtained from the proton runs at Ep=1.68 MeV using he angles in Eqs. (3) and (4) are laboratory angles. he final values, given in Table I, are the average of the values obtained from normalizing to ifferent detectors.
. Uncertainties
o estimate the systematic errors introduced in the analyzing power measurement by the ncertainties in the reaction energies and gas leaking effects in the target calculations were erformed. The systematic errors in the Ayy values associated with the uncertainties in the reaction nergies are 2.2%,2.1%, and 0.9% for Ed=0.52, 0.89, and 1.49 MeV, respectively. Furthermore, it as found that 5% uncertainty in the gas pressure during a run corresponds to a 0.5% systematic rror in the values of Ayy obtained in this experiment. Also, the systematic error in the value of yy (10°) obtained corresponds to a 0.5% systematic error in the values of Ayy. The systematic rror associated with the angular acceptance introduced by the collimators was found to be egligible (less than 0.1%). Detector position, energy loss in the target, and beam motion effects ere found to be the main sources of systematic uncertainties involved in the determination of the ross section. The errors in the detector angles were determined, through the peak positions, to be ccurate within 0.25°. Based on angular dependence data the systematic errors associated with the ositions of the detectors were found to be 0.9% and 1.1% for Ed=0.89 and 1.49 MeV, espectively, the upper limit to the systematic errors in the cross section values introduced by the ncertainties in the reaction energies is 2%. Horizontal 3 mm beam motion effects were found to ntroduce a 2.9% systematic uncertainty in the cross section value at Ed=0.89 MeV. The ystematic error in the cross section values associated with the angular acceptance introduced by he collimators was found to be negligible.
II. SCATTERING AMPLITUDES
he observables measured in a reaction can always be calculated from the scattering matrix. In ome cases, when the number of independent polarization observables is sufficient, experimental ata can be used to obtain information about the T matrix amplitudes. Due to the spin structure of he 3He (d, p)4He reaction 0.5+1 ---> 0.5+1 , the scattering matrix T has 6x2 complex elements. onservation of parity reduces the number of different amplitudes to six. For 0° scattering angle,
o preferential transverse direction is defined, so T must be invariant under rotations along the Z
xis (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 rbitrarily: onsequently, these amplitudes can be calculated from the three linearly independent observables yy, Ayy, and the cross section using n order to calculate the remaining scattering amplitudes necessary to describe the He (d, p) He eaction observables at all angles, and to determine the relative importance of direct and resonant echanisms, it is necessary to develop a model that extracts this information from the available xperimental data.
V. MODEL DESCRIPTION
ue to the dominant effect of the 1.5+ S-wave resonance at Ed=0.430 MeV on the 3He (d, p) 4He eaction observables for Ed<1 MeV, our theoretical model should be tested in this energy range. btained precise measurements of vector and tensor analyzing powers, and of total and ifferential cross sections at several energies in this range. In our analysis we will use these easurements, the 3He-d elastic cross section data and the new measurements presented in this ork. -matrix model to include the next excited state, the 1.5 state at Ed=2.62 MeV [18], as an R- atrix pole. The T2q and Kyy' are still well described, but the predictions for iT11, although nonzero, o not reproduce the data. This behavior indicates the strong sensitivity of this observable to other ontributions to the reaction mechanism. To account for these other mechanisms, we develop a odel that takes into consideration the direct component of the reaction through a potential escription. The scattering wave functions generated by the potential are expanded in an R-matrix asis and can therefore be added to the resonant contribution to calculate the scattering mplitudes. In this model, the 1.5+ and 1.5- resonant states are introduced through R-matrix poles, nd the other negative parity contributions to the reaction mechanism are obtained through a fitted otential. To improve the quality of the fits we also include 0.5+ and 1.5+ background poles at d=3 MeV.
. CONCLUSIONS
easurements of Ayy (0°) and α (0°) of the 3He (d, p)4He reaction were taken at Ed=0.52, 0.89, and .49 MeV, complementing the existing Kyy'(0°) data at those energies. These measurements allow, or the first time, the determination of all linearly independent scattering matrix elements at 0°. hese and previous results at Ed<1 MeV were described using a hybrid model that accounts for oth resonant and direct mechanisms by combining R-matrix poles and a potential description. We onclude that a consistent description of the different polarization observables, vector and tensor nalyzing powers, and spin transfer coefficients can be achieved by assuming that the reaction roceeds by a mixed mechanism where the dominant resonant component competes with a non- egligible direct component.
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