Relativistic corrections to electron scattering by the deuteron and triton

Relativistic corrections to electron-deuteron and electron-³He scattering have been calculated. the deuteron corrections agree substantially with the results of Gross and the ³He corrections are approximately equal in magnitude to those of Cocho and Flores.     

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.     

Preliminary results of the study of the d(d,n)3He reaction in the astrophysical energy range with the use of a Hall plasma accelerator

The possibility of using a plasma accelerator based on a pulsed Hall ion source to study the characteristics of pd, dd, d³He, ³He, and⁴He reactions in the astrophysical energy range (2–12 keV) has been considered. The preliminary experimental data on measurement of the astrophysical S factor for the dd reaction (dd → ³He + n (2.5 MeV)) at average deuteron collision energies E _col = 4.5 and 4.95 keV and the deuteron beam energy spread FWHM = 18% are reported. The found value of the S factor is in agreement with the results of the experiments carried out by us previously using linear plasma in the inverse Z-pinch configuration.     

Deutron transfer in the 3He(3He,p)5Li reaction

Evidence supporting the transfer of deuteron cluster in the reaction ³He(³He, $\text{p}$)⁵Li is presented. This entails a selection of total angular momentum in a two-nucleon transfer reaction.     

Maximal acceleration corrections to the Lamb shift of hydrogen,deuterium and He+

The maximal acceleration corrections to the Lamb shift of one-electron atoms are calculated in a nonrelativistic approximation. They are compatible with experimental results, are in particularly good agreement with the 2S2P Lamb shift in hydrogen and reduce by ∼ 50% the experiment-theory discrepancy for the 2S2P shift in He⁺.     

Pionic fusion study of the halo nucleus 6He, the reaction d+4He→6He+π + at CELSIUS

The halo nucleus ⁶He has been studied in a pionic fusion experiment at the CELSIUS storage ring facility in Uppsala. The ⁶He nuclei were produced in reactions with a deuteron beam incident on a ⁴He jet target 0.9–5.4 MeV above threshold in the center-of-mass frame. The ⁶He ions were detected in a ΔE-E solid-state detector telescope inserted into the CELSIUS ring. The aim of the experiment was to investigate, in particular, the high-momentum part of the halo wave function by measuring the total and differential cross sections of the reaction d+⁴He→⁶He+π ⁺.     

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.     

Inelastic electron-deuteron scattering with final-state interactions

Measurements of the cross sectiond ² σ/dΩ dE′ for the inelastic electron-deuteron scattering processe+d→e+n+p have been used to determine the electromagnetic structure of the neutron. The effects on the theoretical cross section of the structure of the deuteron and of interactions between the outgoing nucleons are examined in detail. We start with the relativistic invariant expressions of the one-nucleon exchange diagram including deuteron structure to obtain the interaction Hamiltonian. For the disintegration near the quasi-elastic peak thed-n-p vertex function can be represented by nonrelativistic deuteron wave functions. The final state interaction is calculated from phenomenological nucleon-nucleon potentials. The rescattering corrections are found to lead to a decrease in the peak value of the cross section between ?6% and ?2% depending on the electron momentum transfer q² which has been varied between 2.5f ^?2 and 40f ^?2. These corrections are largest for smallq ²<5f ^?2. Furthermore the results show that the influence of our insufficient knowledge of the deuteron structure on the cross section is small.     

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 tensor analyzing power Azz AT θ = 0° for the He( , p)He reaction

The tensor analyzing power f_zz has been measured for the ³He( , p)⁴He reaction at 0 = 0° over an incident deuteron energy range E_d = 6.6–15.8 MeV in steps of 0.5 MeV. The present results agree with and extend the previous measurements of Grüebler et al. The present results indicate that this reaction is a very good tensor analyzer for polarized deuteron beams with energies up to 15.8 MeV.     

Vector analyzing power in the 4He(d,p) reaction at 10–11 MeV

The vector analyzing power in the ${}^4\text{He}\text{(}\text{d}\text{,}\text{p}\text{)}$ reaction at 10–11 MeV deuteron energy is analyzed by using a semi-phenomenological method. The values for the free parameters are determined by an analysis of the ⁴He(d, αp)n reaction at 9 MeV deuteron energy. An excellent fit to the experimental data for the vector analyzing power as well as the absolute differential cross sections is obtained.     

Statistical mechanics of dilute mixtures of 3He in superfluid 4He

A statistical mechanical theory of the dilute mixtures of ³He and ⁴He is presented. It is shown that the ground state energy is proportional to the ³He density. The chemical potential expressed in terms of the sound velocity assumes the form which has been suggested phenomenologically. From the chemical potential, the effective ³He⁴He interaction and osmotic pressure are derived. The effective mass of ³He is also calculated as a function of potential parameters.     

Deuteron structure and diffractive deuteron-nucleus interaction

A nonrelativistic deuteron wave function involving the D-wave state and having a correct asymptotic behavior is constructed on the basis of the experimentally measured deuteron charge form factor G _C(q) and deuteron structure function A(q). The differential cross section for elastic deuteron-nucleus scattering is calculated by using this wave function and is found to agree with experimental data at an energy of 110 MeV. Integrated cross sections for various processes involving deuteron-nucleus interactions are also calculated. The distribution in the emission angle of the center of mass of the neutron-proton system produced in the diffractive dissociation of 110-MeV deuterons in the field of ²⁰⁸Pb nuclei is obtained.     

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.     

Scattering lengths of pionic 3He and 4He

Scattering lengths of pionic ³He and ⁴He and the charge exchange contribution to the 1s width of pionic ³He are calculated within the fixed scatterer approximation of the multiple scattering formalism. Particular attention is focussed on the nuclear physics part and on πN p-wave contributions. For the first time triple scattering and double-spin-flip contributions have been included. We find significant deviations from previous estimates and calculations. Good agreement is achieved with the experimental π^?3He scattering length, whereas in the case of ⁴He a repulsive dispersion contribution is clearly needed. We propose to use the measured 1s level shift of pionic ³He as a constraint to deduce a precise value of the isoscalar πN scattering length. Furthermore, we find that multiple scattering reduces the impulse approximation value for Γ_1s(π^?3He → π^{0 3}H) by more thsn 20 %. This result casts some doubt on impulse approximation calculations of radiative pion capture as well.     

Microscopic description of diffractive deuteron breakup by <Superscript>3</Superscript>He nuclei

A microscopic formalism for describing observed cross sections for deuteron breakup by threenucleon nuclei was developed on the basis of the diffraction nuclear model. A general formula that describes the amplitude for the reaction ²H(³He, ³Hep)n and which involves only one adjustable parameter was obtained by using expansions of the integrands involved in terms of a Gaussian basis. This formula was used to analyze experimental data on the exclusive cross sections for deuteron breakup by ³He nuclei at the projectile energy of 89.4MeV. The importance of employing, in calculations, a deuteron wave function that has a correct asymptotic behavior at large nucleon–nucleon distances was demonstrated.     

Observation of Andreev-Pushkarov vacancy clusters in phase-separated solid solutions of 4He in 3He

New features are observed for the pressure in a phase-separated dilute solid solution of ⁴He in ³He subjected to multiple temperature cycling within the phase-separation region. The results are explained within the framework of the hypothesis of A.F. Andreev and D.I. Pushkarov that the vacancies in a crystal without ideal periodicity are surrounded by clusters with a periodic structure. The equation for determining the radius of a cluster of pure ⁴He in a solution of ⁴He in ³He is refined. This hypothesis is shown to provide quantitative agreement between the calculated and experimental data under the assumption that the homogenization of the phase-separated solution is accompanied by the formation of metastable vacancies with a concentration of ～(4–5)×10^?5.     

A semirelativistic calculation of the deuteron electrodisintegration at the quasielastic peak

The cross section for inelastic electron deuteron scattering at the quasielastic peak is calculated in the laboratory system, using complete relativistic kinematics. The difference between the exact cross section formula andDurand's simple sum rule expression is found to be approximately 1.2% for 4-momentum transfers of 2.5 to 4f^?1 and the influence of the deuteron wave function on the final results to be smaller than 1% for reasonable deuteron models. Final state corrections are introduced through a simple correction term in the cross section formula.     

Real part of the optical potential for composite particles

The optical potential for a composite particle is most simply approximated by the sum of the optical potentials of the constituent nucleons. Restricting ourselves to the real parts of the potentials we use this model as a first approximation in a calculation of the potentials for d, ³He, α and ¹²C. We add corrections for (i) the energy dependence of the nucleon potentials, (ii) three-body terms, (iii) the Pauli principle. All corrections can be important and that for the Pauli principle can be very large. We obtain a good explanation of the following phenomena: (a) the deuteron potential is nearly the sum of the neutron and proton potentials, (b) the potential for ³He is about 20 % less than the sum of the potentials of the nucleons in the ³He projectile, (c) the volume integral of the potential for ³He falls at both high and low energies in the energy range 20–100 MeV, (d) shallow potentials with large radii are found for low energy (30 MeV) scattering of α-particles, (e) deeper potentials are found for higher energy α-particle scattering. We predict shallow potentials for ¹²C scattering from light targets but deeper potentials for heavier targets.     

Effective interactions in dilute mixtures of3He in4He

Nonlocal pseudopotentials which describe the effective interaction between³He quasiparticles, and between these quasiparticles and the background⁴He liquid, are obtained as a function of concentration and pressure by generalizing the Aldrich-Pines pseudopotentials for pure³He and⁴He to dilute mixtures. The hierarchy of physical effects which determine these pseudopotentials is established. Interaction-induced short-range correlations are the dominant physical feature; next in order of importance is the greater zero point motion associated with the replacement of a⁴He atom by a³He atom, while spin-induced Pauli principle correlations play a significantly smaller, albeit still important role. We find a consistent trend in the change of the effective direct quasiparticle interactions with increasing concentration, and show how the Aldrich-Pines pseudopotentials for pure³He quasiparticles represent a natural extension of our results for dilute mixtures. Our calculated nonlocal pseudopotential for³He quasiparticles is qualitatively similar to that proposed by Bardeen, Baym, and Pines; it changes sign at somewhat lower momentum transfers than the BBP result, varies little with concentration, and provides a physical basis for understanding the BBP result. The effective interaction between quasiparticles of parallel spin, here determined for the first time, is essentially repulsive in the very dilute limit; as the concentration increases, it becomes increasingly attractive at low momentum transfers, and resembles closely that between antiparallel spin quasiparticles at 5% concentration. The concentration-dependent transport properties calculated from these pseudopotentials (which involve only one phenomenological parameter) are in good agreement with experiment at saturated vapor pressure (SVP), 10 atm, and 20 atm. Maxima in the thermal conductivity and spin diffusion are predicted to occur at concetrations somewhat less than 4%. Because the effective quasiparticle interactions are somewhat more repulsive than those previously proposed, we find the transition of the³He quasiparticles to the superfluid state takes place at significantly lower temperatures than many previous estimates; our predicted maximum superfluid transition temperature is 2×10^–8 K (for a 0.6% mixture at 20 atm).