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.     

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.     

Feasibility Study of D(3H,3He)nn Experiment Searching for nn Ground State

Possibility of existence of nn ground state was discussed in 2011 by H. Witala and W. Glöckle based on anomalous enhancement of nn QFS (Quasi-Free Scattering) cross section in nd breakup at E _n = 26 MeV reported in 2002. To search for the nn ground state, we have made a feasibility study of D(³H,³He)nn and D(n, p)nn experiments. ³H and n secondary beams are produced respectively by D(d,³H)p and D(d, n)³He reactions at forward angle, and are injected on a CD₂ foil target. If an nn ground state exists, a single peak is observed in the ³He and p energy spectra. We conclude that these experiments are feasible.     

Experimental Study of Photon Induced Reactions on 3He and 4He at Low Energies

Data are reported for the photodisintegration cross section of the reaction ³He(??, p)²H at ten energies between 7.0 and 16.0?MeV. Very preliminary data are presented for the reaction ⁴He(??, p)³H between 22.0 and 29.5?MeV in 0.5?MeV energy steps, and for the reaction ⁴He(??, n)³He at three energies around 28.0?MeV. High-pressure He/Xe gas scintillators served as target and detector. Our data are in better agreement with recent theoretical calculations than the majority of the existing data for all three reactions, but differ significantly from recent data taken with a mono-energetic photon beam and a time-projection chamber.     

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.     

Die2H+d-Reaktion bei niedrigen Energien

It is shown that in the angular distributions of the²H(d, p)³H (using polarized and unpolarized deuterons) and likewise in the neutron polarization of the mirror reaction²H(d, n)³He the resonance found atE _d ≈105 keV can be understood as a threshold resonance. From the experimental dataJ)^π=2⁽⁺⁾,T=0 is derived for spin, parity and isospin of the resonance. Additionally it is found, that the resonant part of the reaction has a small coupling matrix element, linking the²H+d channel with the³H+p and³He+n channels.     

Spectroscopy of 7He and superheavy hydrogen isotope 5H

The neutron-transfer reaction d(⁶He, p)⁷He is investigated. The data obtained show that, in the range between 1 and 7 MeV above its ground-state resonance, ⁷He does not have well-pronounced narrow excited states with a single-particle structure. A resonance state of ⁵H with an energy of 2 MeV above the n+n+³H decay threshold is obtained for the first time by making use of the reaction p(⁶He, ²He)⁵H.     

Indirect Study of the 2H(d,p)3H and 2H(d,n)3He Reactions at Astrophysical Energies via the Trojan Horse Method

The ²H(d,p)³H and ²H(d,n)³He reactions have been indirectly studied by means of the Trojan Horse Method applied to the quasi-free ²H(³He, p³H)¹H?²H(³He, n³He)¹H reaction at 18?MeV of beam energy. This is the first experiment where the spectator (here ¹H) has been detected in coincidence with the charged participant, avoiding the limitations of standard neutron detectors. The d ? d relative energy has been measured from 1.5?MeV down to 2?keV, at center of mass angles from 40° to 170°. Indirect angular distributions are compared with the direct behaviour in the overlapping regions.     

Winkelverteilung der Kernphotoreaktion3He (γ,p)2H

The angular distribution of the photonuclear reaction³He(γ,p)²H was measured with an exitation energyE _x=16 to 27 MeV using a 32.5 MeV betatron. In agreement with a theoretical calculation of Böschet al. we found for the coefficients of the distributionf(θ)=b (a/b+sin²θ(1+β·cosθ+γ·cos²θ)) the values:a/b≦0.14; β=0.77 (+0.14; ?0.07); γ≦0.30. This was the first attempt to use spark chambers as a detection device for photonuclear reactions in the low energy range. We found it to be a promising new facility.     

The d + d reactions at low energies II. Comparison of angular distributions of outgoing nucleon polarizations for the charge symmetric reactions2H(d,p)3H and2H(d,n)3He

Precision measurement of the angular distribution of polarized protons from the²H(d,p)³H reaction at about 1 MeV is compared with experimental polarization data from the mirror reaction²H(d,n)³He at the same entrance and exit channel energies. In both comparisons, differences in polarizations of outgoing nucleons from the d + d charge symmetric reactions were found to be larger than experimental uncertainties.     

Collision-induced dissociation of H 2 + ions into the fragmentations H+H(2p) and H++H(2p)

Using a photon-particle delayed coincidence method the energy distributions of H +H(2p) and H⁺+H(2p) fragment pairs have been measured arising from collisional dissociation of 10 keV H ₂ ⁺ ions incident on various target gases. H fragments in their 2p state are identified by the Lymanα radiation emitted. The distribution of H+H(2p) fragment pairs arising from dissociative charge exchange reveals a sharp increase below 0.2 eV in the center-of-mass frame of the H ₂ ⁺ ion. This is ascribed to predissociation of vibrational levels of higher H₂ Rydberg states close above then=2 dissociation limit by those H₂ Rydberg states which separate into H+H(2p) fragments. Only direct transitions into the continuum of theGK ¹ ∑ _g ⁺ state may compete. Some structure at 0.3–0.5 eV is attributed to the three statesI ¹ П _g,i ³ П _g, andh ³ bE _g ⁺ having potential barriers of this height. The distributions for H⁺+H(2p) have maxima at 3.4, 3.8, and 4.2 eV for a H₂, Ar, and He target, respectively, indicating that the 2pπ _u state as well as the 3dσ _g state ofH ₂ ⁺ is excited. The H+H(2p) process has a greater probability than the H⁺+H(2p) process for Ar and H₂ targets, though all electronic H₂ states under consideration are bound.     

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.     

The (p, 2p) reaction on 2H, 3He and 4He

The (p, 2p) cross sections on ²H, ³He and ⁴He were measured at 65, 85 and 100 MeV. The experimental data show rather strong energy and target mass dependence, particularly for ⁴He.     

Improved evaluation of the differential cross sections of the3H(d,n)4He reaction for deuteron energies between 3 and 7 MeV

For deuteron energies below 7 MeV, the evaluation of the differential cross sections of the³H(d,n)⁴He reaction was improved by including three associated⁴He particle excitation functions between 4 and 11 MeV. Above 7 MeV, the scale agrees within error limits with that of a previous evaluation, and no energy-dependent systematic deviations between measured and predicted values are observed. However, deviations of up to 20% from the Liskien and Paulsen evaluation are observed.     

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.     

Resonance states of hydrogen nuclei 4H and 5H obtained in transfer reactions with exotic beams

To investigate ⁵H resonance states with a better instrumental resolution, we utilized the two-neutron transfer reaction ³H(t, p)⁵H accomplished with the use of a cryogenic liquid-tritium target and 57.5-MeV triton beam. As a result of this study, a valuable fraction of protons detected at ? _lab=18°–32° in ptn coincidence events was attributed to the states of the ⁵H nucleus. Two resonance states situated at 1.8±0.1 and 2.7±0.1 MeV above the t + n + n decay threshold were obtained in the missing mass energy spectrum of the ⁵H nucleus. The peak located close to E5_H was clearly seen in the ⁵H spectrum obtained from the energy distributions of ³H nuclei emitted in the reaction ²H(⁶He, ⁵H)³He at ? _lab=17°–32°. The width (Γ_obs≤0.5 MeV) obtained for the two ⁵H resonance states is surprisingly small. A state of ⁴H with E _res=3.3 MeV and γ ²=2.3 MeV was obtained in the reaction ²H(t, p)⁴H from the spectra of protons leaving the target at ? _lab=18°–32° and detected in coincidence with neutrons emitted in the decay of ⁴H nuclei.     

Contributions of excited 6Li and 7Li nuclei to the production of 4He+2H and 4He+3H systems in 16O p collisions at a momentum of 3.25 GeV/c per nucleon

New experimental data on the cross sections for the yield of excited ⁶Li* and ⁷Li* nuclei and on their contributions to the production of ⁴He + ²H and ⁴He+³H light dinuclear systems in ¹⁶O _p collisions at a momentumof 3.25 A GeV/c per nucleon are presented.     

Electromagnetic contributions to proton- and neutron-4He scattering

A proper treatment of various electromagnetic contributions toN-⁴He scattering enables one to determinen(p)-⁴He observables fromp(n)-⁴He data. Several calculations ofn-⁴He observables considering different electromagnetic effects are presented. It is shown that the contribution of thep-⁴He Coulomb corrections ton-⁴He polarizations and differential cross sections dominates over other electromagnetic effects forθ _c.m.≧30°. For smaller scattering angles, neutron magnetic scattering is important and produces a divergingn-⁴He differential cross section atθ=0° and a large peak (Mott-Schwinger effect) in the polarization. The influence of thep- andn-⁴He vacuum polarizations on then-⁴He observables is found to be small.     

Microscopic study of the low-energy3H(d,n)4He reaction

We have studied the³H(d, n)⁴He reaction at low energies within a multi-channel resonating-group calculation based on many-bodyn+ andd+³H configurations and pseudo-states as well as on an effective nucleonnucleon interaction containing central, spin-orbit, and tensor components. The low-energy fusion cross section is excellently reproduced within our approach.Dedicated to Prof. Erich Schmid on the occasion of his 60th birthday     

Nondynamical calculation of polarization observables in the3H(d,n)4 He reaction below 1 MeV

The parametrization of cross-section, polarization, analysing powers, spin-correlation and polarization transfer observables in terms of (l, s, J) matrix elements is given for the³H(d, n)⁴He reaction at low energies. It is shown that a complete set of matrix elements can be obtained from these observables.