Effects of electron screening on the 3He(d,p)4He low-energy cross sections

The reaction ³He(d, p)⁴He has been investigated for E_CM = 5.9−41.6 keV with the use of D projectiles and ³He atomic gas target nuclides as well as with ³He projectiles and D₂ molecular gas target nuclides. These studies show for the first time the effects of electron screening on low-energy fusion cross sections, i.e. a nearly exponential enhancement of the cross sections compared to the case of bare nuclei. The enhancement is about a factor 2 smaller for the case d(³He, p)⁴He due to the molecular nature of the D₂ target nuclides.     

Large-space cluster model calculations for the 3He(3He,2p)4He and 3H(3H,2n)4He reactions

The ³He(³He,2p)⁴He and ³H(³H,2n)su4He reactions are studied in a microscopic cluster model. We search for resonances in the ³He+³He and ⁴He + p + p channels using methods that treat the two- and three-body resonance asymptotics correctly. Our results show that the existence of a low-energy resonance or virtual state, which could influence the ⁷Be and ⁸B solar neutrino fluxes, is rather unlikely. Our calculated ³He(³He,2p)⁴He and ³H(³H,2n)⁴He cross sections are in a good general agreement with the experimental data.     

Microscopic study of the low-energy3He(3He, 2p)4He and3H(3H, 2n)4He fusion cross sections

We have calculated the³He(³He, 2p)⁴He and³H(³H, 2n)⁴He reaction cross sections at low energies within the microscopic multichannel resonating group method. For both reactions, we find good agreement with experiment. For the³H(³H, 2n)⁴He reaction, our calculated energy dependence reproduces that of each individual low-energy experimental data set, except for a normalization constant. Using this fact, we derive at a low-energy³H(³H, 2n)⁴He rate by taking the averaged mean of these fits.This work has been supported in part by the National Science Foundation, Grants PHY86-04197 and PHY88-17296.     

The differential cross section and polarization quantities in the 4He(d,p)n4He and 2H(α, n)p4He reactions

The differential cross section and the polarization quantities (T₁₁, T₂₀, T₂₁, T₂₂, P_γ') in the deuteron breakup reaction by an α-particle are calculated in the framework of the recently developed three-body model. All values are discussed under the incomplete kinematical condition. All polarization quantities are caused by the difference of the potential between $\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and $\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ waves of the N-α interaction. Results of the calculation are compared with the available measurement of (i) the differential cross section and the deuteron vector analysing power in the ⁴He($\text{d}$, p)n⁴He reaction and (ii) the differential cross section and neutron polarization in the ²H(α, $\text{n}$)p⁴He reaction. The agreement with experiment is very satisfactory in each case. Among the tensor analysing powers of the deuteron the absolute value of T₂₀ is very large. Observables at the FSI peak corresponding to ⁵He_g.s. are discussed systematically in the energy region of 5.4–20 MeV of the incident deuteron in the ⁴He(d, p)n⁴He reaction. Although the differential cross section is not sensitive to the energy of the three-body resonance, the polarization quantities T₁₁, T₂₀, P_γ' are quite sensitive to it.     

Theoretical Study of the 4He(γ, p)3H and 4He(γ, n)3He Reactions

Ab initio calculation of the total cross section for the reactions ⁴He(γ, p)³H and ⁴He(γ, n)³He is presented, using state-of-the-art nuclear forces. The Lorentz integral transform (LIT) method is applied, which allows exact treatment of the final state interaction (FSI). The dynamic equations are solved using the effective interaction hyperspherical harmonics method. In this calculation of the cross sections the three-nucleon force is fully taken into account, except in the source term of the LIT equation for the FSI transition matrix element.     

On electron screening effects in the low-energy 3He(d,p)4He data

We have calculated the screening effects of the two electrons in the atomic ³He gas target on the low-energy³He(d, p)⁴He data. The nuclear degrees of freedom have been described within the microscopic multi-channel Resonating Group Method, while the two electrons have been treated in Born-Oppenheimer approximation deriving the exact screening potential within the Path Integral Monte Carlo method. Our model underestimates the observed screening effects implying the need to consider the coupling of nuclear and electronic degrees of freedom.     

A study of reaction mechanisms for the Li(p, 2d)He reaction at 45 MeV

The first kinematically complete experiment involving a (p, 2d) reaction is reported. It is found that at 45 MeV bombarding energy a significant part of the ⁷Li(p, 2d)⁴He reaction cross section arises from contributions from sequential decay processes through excited states of ⁶Li. A new three-body break-up mechanism involving the quasi-free interaction of the proton with the bound triton is discussed.     

Isospin mixing in the electric-dipole He(γ, n) and He(γ, p) reactions

Possible isospin mixing of the J^π = 1⁻ excited states of ⁴He leading to sizable differences in the ⁴He(γ, n)³He and⁴He(γ, p)³H cross sections in the giant-resonance region is examined in a bound-state approximation. Results indicate that the general features of certain experimental data can be accounted for by the presence of Coulomb mixing of the (S = 1, T = 0) and (S = 1, T = 1) states in addition to the usual spin-orbit mixing of the (S = 0, T = 1) and (S = 1, T = 1) states.     

2H( 3He, t)2p reaction at 2 GeV

The exclusive ²H( ³He, t)2p reaction has been studied at 2 GeV for energy transfers up to 500 MeV and triton angles up to 3.4^°. The protons were measured in the large acceptance magnetic detector DIOGENE, in coincidence with the forward tritons detected in a dedicated magnetic arm. The energy transfer spectra extend well above the pion threshold. However, in the region of Δ excitation, the yield is less than 10% of the inclusive ²H( ³He, t) cross-section, which indicates the small contribution of the ΔN ↦ NN process. The angular distributions of the two protons in their center of mass have been analysed as a function of energy transfer and triton angle and a Legendre polynomial decomposition has been achieved. These data have been compared to a model based on a coupled-channel approach for describing the NN and NΔ systems. Received: 21 October 2002 / Accepted: 15 November 2002 / Published online: 11 March 2003 RID="a" ID="a"e-mail: ramstein@ipno.in2p3.fr RID="†" ID="†"Deceased. RID="†" ID="†"Deceased. RID="d" ID="d"Present adress: School of Engineering, J?nk?ping University, P.O. Box 1026, S-551 11 J?nk?ping, Sweden. Communicated by M. Gar?on     

Relativistic corrections to electron scattering by 2H, 3He,and 4He

Relativistic corrections to the scattering of electrons by a nonrelativistic nucleus are calculated, using the method of Close and Copley, and Krajcik and Foldy. Particular attention is paid to the deuteron, ³He and ⁴He. It is found that these corrections are substantially the same as those calculated by F. Gross for the deuteron. The corrections to ³He have the effect of moving the diffraction minimum, as calculated in a nonrelativistic model, outward by as much as 0.32 fm^?2. Smaller corrections are found for ⁴He.     

Formalism for the T(d,n)4He and 3He(d,p)4He reactions

The formalism required to describe the T(d, n)⁴He or ³He(d, p)⁴He reaction when all particles may be polarized is discussed. The relation among the various sets of spin-1 tensors is stated explicitly, so that the formulas applying to a particular experiment may be written easily in terms of any desired system.     

On the Li(p,pt)He reaction

Using a cluster model, the reaction ⁷Li(p, pt)⁴He has been analysed in the distorted-wave impulse approximation. All exchange terms arising from antisymmetrization of the target wave function have been calculated. When the correct asymptotic form for the intercluster wave function is used, the magnitude and shape of the measured angular correlation are reproduced both at 156 and 55 MeV. The analysis indicates that ⁷Li in its ground state is strongly clustered.     

The3He(d,p) α reaction at astrophysical energies

We have performed a microscopic study of the³He(d,p) α reaction at astrophysical energies within the framework of the Resonating Group Method adopting three different effective nucleon-nucleon interactions. The calculations suggest that the low-energy³He(d,p) α cross section is in good approximation given by the contribution arising from the 3/2⁺ resonant state atE _R =245 keV. In fact, the low-energy data can be better (and more physically) described by a single Breit-Wigner resonance parametrization than by a polynomial fit. Our fit to the³He(d,p) α cross section results in a noticeable reduction in the uncertainties of the resonance parameters of the 3/2⁺ resonant state as well as in a significantly improved extrapolation of the data to astrophysically important energies. On the basis of this extrapolation we were able to quantitatively deduce the enhancement of the low-energy cross section due to electron screening effects from the data of Krauss et al. and Engstler et al. These experimental enhancement factors were compared with various theoretical models which are all based on the Born-Oppenheimer approximation. As the models underestimate the observed enhancement we suggest that the theoretical study of electron screening effects requires a dynamical treatment.     

The reaction3He(d,p)4He with a polarized target

The left-right asymmetry for the³He(d, p)⁴He reaction has been measured with a polarized³He target at a bombarding energy of 12 MeV. The experimental results are compared with proton polarization measurements for unpolarized target and beam. The construction of the optically pumped³He target is described. A special design has been chosen to overcome the difficulty that the target contamination caused by the bombarding particles destroys the polarization. The target can easily be purified without removing it from the experimental set-up.     

Study of Tensor Correlations in 4He via the 4He(p, dp)d and 4He(p, dp)pn Reactions

Tensor correlations in ⁴He were studied via the (p, dp) reaction at the incident energy of 392 MeV with a focus on spin configurations of correlated pn pairs in ⁴He at high relative momenta ${(P_{\rm rel}^{\rm cor})}$ . The preliminary results show that the correlated pn pair at ${P_{\rm rel}^{\rm cor} = 310 {\rm MeV/c}}$ predominantly has the channel spin S = 1, which is consistent with the characteristics of tensor correlations.     

Stability of 3He2 4He M and 3He3 4He M L = 0,1 Clusters

We have studied the stability of mixed ³He/⁴He clusters in L = 0 and L = 1 states by the diffusion Monte Carlo method, employing the Tang-Toennies-Yiu (TTY) He-He potential. The clusters ³He⁴He_M ( ) and ³He₂⁴He_M (L = 0, S = 0) are stable for M > 1, while to bind two ³He in a triplet state the minimum number of ⁴He is four. Considering clusters with three ³He, ³He₃⁴He₄ is the smallest stable system in the L = 1 state, while ³He₃⁴He₈ is the smallest stable system in the L = 0 state.     

Polarization in quasielastic (p,2p) scattering on a 4He nucleus at 1 GeV

The polarization of secondary protons from the (p, 2p) reaction induced by 1-GeV protons incident to a ⁴He nucleus was measured in a kinematically complete experiment. By using a two-arm magnetic spectrometer, two secondary protons from this reaction were recorded in coincidence at unequal scattering angles of Θ₁ = 18°?24.21° and Θ₂ = 53.22° over a broad range of the recoil-nucleus momentum K _B between 0 and 150 MeV/c. It was found that the measured polarization of either secondary proton is less than that observed in free elastic proton-proton scattering. The magnitude of this difference is determined by the mean binding energy of s-shell protons rather than by the effective nuclear density. The polarizations measured in inclusive quasielastic and elastic scattering of 1-GeV protons on ⁴He nuclei are presented for scattering angles in the range Θ₁ = 18° ? 24.21°.     

Angular distribution measurements of Li(p,α)He reaction at 140 keV proton energy using nuclear track detectors

Angular distributions of a ⁶Li(p,α) ³He reaction were measured at six angles for 140 keV proton energy using nuclear track detectors (NTDs). The measurements were carried out over 60°–160° lab. angles in 20° increments using a scattering chamber of 80° beam line of the 350 kV accelerator. A semiconductor silicon surface barrier (SSB) detector was placed at +160° and was used as a monitor. The results have shown that the CR-39 detector has excellent capabilities to distinguish 1.4–2.7 MeV α+ ³He particles from the ⁶Li(p,α) ³He reaction and 8–9.4 MeV α-particles from the ⁷Li(p,α) ⁴He reaction through their track diameters. However, it was not possible to distinguish between the 2.3 MeV ³He ions and the 1.7 MeV ⁴He ions from the ⁶Li(p,α) ³He reaction from their track diameter measurements, but it was possible to differentiate between the two, from the darker contrast of the ³He particles caused by its deeper tracks as compared to those of ⁴He.     

Study of the Cl(He,p)Ar reaction

Angular distributions of protons from the ³⁵Cl(³He, p)³⁷Ar reaction have been measured at bombarding energies between 9 and 14 MeV. The 14 MeV data are compared with DWBA calculations based on various sets of shell-model wave functions.