Pion-exchange contributions to the nuclear charge,current, and Hamiltonian operators

Using a Foldy-Wouthuysen reduction procedure and the time-dependent perturbation theory, we have calculated the one-pion-exchange contribution to the nuclear charge and current densities to order $\text{(}\text{v}\text{c}\text{)}{}^2$. At the same time a renormalization scheme defines the pion-exchange potential including nonstatic and three-body correction terms of order $\text{(}\text{v}\text{c}\text{)}{}^2$. The requirements of relativity are investigated, and it is found that the retardation effect in the potential and charge density plays a critical role. The covariance conditions for the potential, charge, and current densities are shown to be satisfied to the order we have calculated. Finally, the deuteron case is discussed in detail. Throughout the calculation the role of the equivalence theorem is stressed.     

Muon capture in deuterium with realistic potentials

The transition rates for muon capture in deuterium are calculated using the Reid soft-core deuteron, and ¹S₀ and ${}^3\text{P}{}_{\mathrm{J}}\text{(J = 0, 1, 2)}$ neutron-neutron wave functions. The validity of the closure approximation and of the Omnés-Muskhelishvili method is studied. The off-shell effects admissible in a class of phase-shift-equivalent potentials by present experimental data are evaluated.     

Double spectator poles and quasi-free inelastic scattering in the 6Li + 6Li → 2α + 2d reaction

We have searched for double spectator pole events in the reaction ${}^6\text{Li}\text{+}{}^6\text{Li}\text{→ 2α + 2}\text{d}$, such that the deuteron from the projectile goes forward with the beam velocity while α or d from the target remains at rest. Triple coincidence studies of the reaction show such events, but with the 0° deuteron energy spectrum peaked at slightly higher velocities. Similar effects are seen in d-⁶Li double coincidence spectra from the single breakup reaction ${}^6\text{Li}\text{→}{}^6\text{Li}\text{+ α +}\text{d}$. Quasi-free inelastic scattering, where the d from the projectile receives no momentum transfer while the α excites the target to its first excited state, is also shown to be an important mechanism.     

The 12+ state of 3H and 3He below the break-up threshold: (II). Gammel-Brueckner potential

Results for the $\text{J}{}^{\mathrm{\pi }}\text{=}\text{1}\text{2}{}^{\mathrm{+}}$ state of ³H and ³He using the Gammel-Brueckner (GB) nucleon-nucleon potential are presented. Comparison is made with the predictions of the Hamada-Johnston (HJ) potential for bound-state properties and N-d scattering. Whilst the GB potential gives an ³He binding energy at ?7.75 MeV which is close to experiment, the Coulomb energy still remains low. The minimum in the electron scattering charge form factor is in worse agreement with experiment than HJ whilst the secondary maximum shows insufficient enhancement over the HJ results. The N-d doublet scattering length is closer to experiment than the results for HJ but there still appears to be a discrepancy with experiment. These results partially support the suggestion that a two-nucleon potential of HJ type with a larger hard-core radius than HJ, but fitted to a smaller deuteron D-state probability, may give a reasonable representation of the three-nucleon data apart from the Coulomb energy. Evidence now appears strong from this latter parameter for a small charge asymmetry in the two-nucleon potential.     

Exact finite range CCBA results for the reaction 24Mg(d,p)25Mg at 14 and 15 MeV

The differential cross-sections for the ${}^{24}\text{Mg(d, p)}{}^{25}\text{Mg}\text{5}\text{2}{}^{\mathrm{+}}\text{(}\text{g.s.}\text{)}$ reactions at E_d = 15 Mev and $\text{7}\text{2}{}^{\mathrm{+}}\text{(1.61}\text{MeV state}\text{)}$ reaction at E_d = 14 and 15 MeV have been calculated using the full finite range CCBA code OUKID. It is shown that finite range effects are very important for these light ion reactions and that the deuteron D-state makes a negligible contribution at these energies.     

Polarization in n-d scattering at 14.2 MeV

The angular distribution of the analyzing power in ${}^2\text{H(}\text{n}\text{,}\text{n}{}^2\text{H}$ elastic scattering has been measured at a neutron energy of 14.2 MeV in the angular range 50° to 152° c.m. Neutrons with a polarization of approximately 0.5 were obtained from the ${}^3\text{H(}\text{d}\text{n}\text{)}{}^4\text{He}$ reaction at a deuteron energy of 140 keV and lab emission angle of 82°. The ${}^3\text{H(}\text{d}\text{n}\text{)}{}^4\text{He}$ reaction was induced by vector polarized douterons obtained from a source of polarized ions. The latter was of a conventional “atomic beam” type. The results show good agreement with the data on the charge symmetric $\text{p}\text{+}\text{d}$ process at a proton energy of 14.5 MeV. Comparison is also made with the theoretical calculations of Doleschall and of Pieper and a good agreement is found.     

Nucleon charge form factors and chiral quark models

Calculations of the proton and neutron charge form factors G_E^p,n(q²) are presented, based on chiral bag as well as confining Dirac potential models with chiral pion-quark coupling. Special emphasis is placed on a detailed treatment of the charged pion cloud contribution to the nucleon current. The role of a finite extension of the pion-quark vertex in truncating the summation over intermediate quark bag states is studied. Quark core radii (including recoil corrections) are constrained by a simultaneous calculation of the nucleon axial form factor. The proton charge form factor is well reproduced for $\text{|q}{}^2\text{|}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{? 0.7}\text{GeV}$ with quark core rms radii between 0.5–0.6 fm. About $\text{1}\text{3}$ of the proton charge is carried by the pion cloud in this model. The neutron charge form factor is obtained with the correct sign and overall q² dependence but needs further refinements, probably at the level of the isoscalar form factor.     

Spin assignments in 59Ni from the 58Ni(d, p)59Ni reaction

Angular distributions of the vector analyzing power and the absolute cross section were measured for the ⁵⁸Ni(d, p)⁵⁹Ni reaction at a deuteron energy of 10 MeV. The observed j-dependence of the vector analyzing power allowed unambiguous spin assignments for the following states in ⁵⁹Ni with excitation energies in $\text{MeV}\text{: 0.0,}\text{3}\text{2}{}^{\mathrm{?}}\text{; 0.341,}\text{5}\text{2}{}^{\mathrm{?}}$; $\text{0.465,}\text{1}\text{2}{}^{\mathrm{?}}\text{; 0.879,}\text{3}\text{2}{}^{\mathrm{?}}$; $\text{1.303,}\text{1}\text{2}{}^{\mathrm{?}}\text{; 1.686,}\text{5}\text{2}{}^{\mathrm{?}}\text{; 3.454,}\text{3}\text{2}{}^{\mathrm{?}}\text{; 3.858,}\text{3}\text{2}{}^{\mathrm{?}}\text{; 4.495,}\text{5}\text{2}{}^{\mathrm{+}}$. The data are well reproduced by DWBA calculations employing deuteron and proton optical model parameters obtained from analyses of elastic scattering cross sections and polarizations. A tentative spin assignment of $\text{9}\text{2}{}^{\mathrm{+}}$ is made for the level at 3.061 MeV. A $\text{5}\text{2}{}^{\mathrm{+}}$ assignment to the level at 3.538 MeV is suggested on the basis of the empirical behavior of the j-dependence of the vector analyzing power for l = 2 transitions. Measurements of the vector analyzing power for the four low-lying ⁵⁹Ni states formed by l = 1 transfer were made for angles from 2.5° to 15° using a magnetic spectrograph. A very strong j-dependence was observed for these far-forward-angle measurements in agreement with DWBA predictions.     

The 7Li(d, n0)8Be reaction with polarized 800 keV deuterons

The analysing power of the ${}^7\text{Li}\text{(}\text{d}\text{, n}{}_0\text{)}{}^8\text{Be}$ reaction for vector and tensor polarization of an 800 keV deuteron beam, as well as the relative cross section for the unpolarized beam were measured at 7 to 9 angles between 0° and 160°, using a thick target. Analysis in terms of (l, s, J^π) matrix elements shows that two intermediate states with $\text{J}{}^{\mathrm{\pi }}\text{=}\text{3}\text{2}{}^{\mathrm{+}}$ and $\text{J}{}^{\mathrm{\pi }}\text{=}\text{5}\text{2}{}^{\mathrm{?}}$ present, strongly interfering with each other. Assignments to known ⁹Be levels and to threshold resonances as suggested by Hackenbroich and Seligman are briefly discussed. The magnitude of the vector analysing power makes the reaction interesting as a monitor for the vector polarization of low-energy deuteron beams.     

Shell model calculations of inelastic electron scattering from 51V and effective charges

Form factors for inelastic electron scattering for the excitation of the $\text{3}\text{2}{}^{\mathrm{?}}$, $\text{5}\text{2}{}^{\mathrm{?}}$, $\text{9}\text{2}{}^{\mathrm{?}}$, $\text{11}\text{2}{}^{\mathrm{?}}$ and $\text{15}\text{2}{}^{\mathrm{?}}$ members of the ($\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{)}{}^3$ configuration in ⁵¹V are studied by considering the effect of configuration mixing in the shell model. The inclusion of the highly excited configurations which does not contribute to the γ-transitions is shown to give rise to significant modifications of the form factors in large momentum transfer regions. Under the assumption of the static central potential as the residual interactions between protons, good agreement with the experimental data on form factors is obtained by the ordinary force as well as smaller effective charges than the bare charge for higher multipole transitions.     

Longitudinal polarization transfer in the D(d,n)3He reaction at 0°

We have measured the longitudinal neutron polarization in the $\text{D(}\text{d}\text{,}\text{n}\text{)}{}^3\text{He}$ reaction, at θ=0°, for an incident longitudinally polarized deuteron beam. A deuteron energy range of 3.3–14.9 MeV was covered. The polarization transfer from the deuteron to the neutron is found to be large, and the reaction is potentially useful as a source of polarized neutrons.     

Pion charge radius from current algebra sum rule and short range correlation model

Starting from the Fubini-Dashen-Gell-Mann sum rule, we relate the slope of the pion electromagnetic form factor at t = 0 to the rotational properties of the photopion production amplitudes. When the pion's charge radius is calculated with a simple short range correlation model for the production amplitudes (diffractive processes being forbidden), the result is $\text{〈r}{}_{\mathrm{\pi }}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 0.8}\text{fm}$.     

On proton-deuteron backward elastic scattering at medium energies (II)

We examine rescattering corrections to the single nucleon exchange model of backward p-d elastic scattering and find them to be important at all energies. Using realistic deuteron wave functions we conclude that the rise at E_p (lab) ～ 400–600 MeV results from another mechanism, possibly the opening of the $\text{p}\text{+}\text{d}\text{→}\text{NNN}{}_{33}{}^1$ channel.     

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.     

Charge properties of the hadronic system in vp and νp interactions

Charge properties of the hadronic systems from νp and $\text{ν}\text{p}$ scattering in BEBC are studied in the framework of the quark-parto model (QPM). The average charges $\text{〈Q}{}_{\mathrm{<mtext>jet</mtext>}}\text{〈}{}^{\mathrm{<mtext>\nu </mtext>}}$ and $\text{〈Q}{}_{\mathrm{<mtext>jet</mtext>}}\text{〈}{}^{\mathrm{<mtext>\nu </mtext>}}$ of a quark jet and a d-qua jet, respectively, are determined according to two different methods. The difference $\text{〈Q}{}_{\mathrm{<mtext>jet</mtext>}}\text{〈}{}^{\mathrm{\nu }}\text{? 〈Q}{}_{\mathrm{<mtext>jet</mtext>}}\text{〈}{}^{\mathrm{<mtext>\nu </mtext>}}$ is in agreement with e QPM value of 1. Scaling of charge and energy flow in the angular variable λ is demonstrated. The ratios $\text{ΔQ}{}^{\mathrm{<mtext>\nu </mtext>}}\text{/ΔQ}{}^{\mathrm{\nu }}$ of charge flows in νp a $\text{ν}\text{p}$ scattering are in accord with the QPM in both hemispheres.     

Dynamical model for the ABC effect

We present a model for ABC production, which is experimentally observed in the missing mass spectrum of the reaction $\text{dp}\text{→}{}^3\text{He}\text{+ (}\text{MM}\text{)°}$. The reaction is assumed to be split in two successive steps, namely: (i) N₁p → d_i1 followed by (ii) $\text{N}{}_2\text{d}{}_{\mathrm{<mtext>i</mtext>}}\text{→}{}^3\text{He}\text{π}{}_2\text{,}\text{N}{}_1$ and N₂ being the two nucleons of the incident deuteron and d_i an intermediate deuteron. The total amplitude is factorized into the product of the two amplitudes of reactions (i) and (ii). We know that at low energy these two reactions are dominated by a Δ production. This implies that the total cross sections are given by Breit-Wigner type formulae and that the angular distributions are peaked in the backward and forward directions. The two main results are: (i) at given incident energy, the ABC effect results from the angular distribution of the two intermediate reactions; (ii) the energy dependence of the ABC is deduced from those of the intermediate processes. The resulting fits are generally excellent when the Fermi motion in the initial deuteron is taken into account.     

Dielectric susceptibility and correlation length of one-dimensional CDW in disordered systems. I. strong forward scattering

The dependence of dielectric susceptibility χ of one-dimensional charge, density wave, interacting with a lattice and with strong forward scattering impurities, on incommensurability parameter h has been found. At sufficiently large $\text{h}{}_{\mathrm{\chi }}\text{h}\text{?}{}^{\mathrm{4/3}}$.     

A study of the reactions d + p → τ + π0 and d + p → τ + η0

The reactions d + p → τ + π⁰ and d + p → τ + η⁰ were studied using the missing-mass method for incident deuteron momenta between 2.8 and $\text{3.8}\text{GeV}\text{c}$. The angular distributions show a peak in the forward direction ($\text{θ}{}_{\mathrm{\tau }}{}^1\text{= 0°}$) and are flat in the backward direction. The differential cross sections at $\text{θ}{}_{\mathrm{\tau }}{}^1\text{= 180°}$ for both reactions show a maximum for total center-of-mass energies near 3.46 GeV.