On the Present Status of the Problem of Charge Dependence and Charge Asymmetry of the Nucleon-Nucleon Force

The charge dependence of the nucleon-nucleon force can be derived from the low-energy scattering parameters. The p-p and n-p parameters were measured in direct scattering experiments. The n-n parameters a_nn = (-16.70 ± 0.38) fm and r_nn = (2.78 ± 0.13) fm have been determined from few particle reactions. The difference of the scattering lengths (a_nn - a_nn) ≈ 7 fm demonstrates the violation of the charge independence. Information on the charge symmetry is still doubtful due to the inaccuracy of the charge correction for the p-p parameters. Whereas the n-n and the charge corrected p-p parameters known at present yield a weaker n-n force than the p-p force, the opposite result follows from the binding energy difference for ³He and ³H and the meson theory of the nuclear forces.     

The 3H(t, α)2n reaction at 40 keV

The two-dimensional energy spectrum of the α-particle and the neutron of the ³H(t, α)2n reaction was measured with a small single-gap accelerator at 90 keV. The mean energy of the ³H ions initiating the reaction was estimated to be about 40 keV, i.e. small against the Q-value of 11.3 Me V. It was found that the n-α interaction plays a strong part in the reaction so that no unambiguous determination of a_n-n, the n-n scattering length, was possible. The addition of an n-α final-state interaction to the n-n Jost-function enhancement factor in the analysis greatly improves the agreement with the experimental results, but it was not possible to distinguish between various forms of the n-α enhancement factors nor between different combinations of the n-α and the n-n interactions. The failure to obtain a well established n-n interaction peak is attributed to the absence of a direct reaction mechanism.     

The n-n S-wave scattering length from the neutron spectra of the reaction π− +d → 2n+γ

We present a measurement of the neutron-neutron S-wave scattering length, a_nn, from an analysis of the neutron energy and angular spectra for the reaction d(π^?, γ)2n. This reaction provides the unique advantage that while all three final-state particles are experimentally detectable, only the neutrons are strongly interacting. The data are analyzed using the treatment of this reaction given by Bander, taking the effects of experimental resolution into account with Monte Carlo techniques. Two independent analyses of 4200 events yield a_nn = ?16.7 ±1.3 fm assuming r_nn = 2.65 fm. This value is in good agreement with calculations of a_nn which assume charge symmetry of the nuclear components of p-p and n-n interactions.     

Particle mixing and charge asymmetric nuclear forces

The charge asymmetric effect of ?ω and πη electromagnetic mixing on the ¹S₀ NN potential is reviewed. It is found that the ?ω contribution dominates and leads to an n-n potential which is more attractive than the p-p potential. The shift in the scattering lengths is then calculated to be |a_nn|?|a_pp| ≈ 0.9 fm and the shift in effective ranges is r_nn?r_pp ≈ ?0.02 fm.     

Investigation of the reaction 2H(n,np) at θn = 0°

The differential cross section of the ²H(n, np) reaction was measured at θ_n = 0°. Because of the applied special geometry the experimental data extend over a large fraction of the phase space, including several final state interaction regions as well as regions far from the dominance of quasi-two-body processes. The experiment was analysed with an exact three-body calculation using s-wave separable potentials (CEE). The analysis of the n-n and n-p final state interaction peaks gave a_nn = ?16.3 ± 1.6 fm for the n-n ¹S₀ scattering length and r_nn = 3.15 ± 0.7 fm for the effective range. Remarkable deviations from the calculated cross sections-were found in regions where no strong final state interaction was present.     

Baryon asymmetry,stable proton and n-n̄ oscillations in superstring models

The violation of baryon number is discussed in the context of a gauge model inspired by the E₈ × E₈ superstring theory. Lepton number is an accidental unbroken symmetry of the model. The proton, as a consequence, is essentially stable. The model yields an acceptable value (∼10⁻¹⁰) for the baryon asymmetry in the universe. It also predicts n-n̄ oscillations at a rate which may be amenable to ongoing experimental searches.     

Evolution of molecular states studied in collisions of ions with laser excited atoms by a crossed beam experiment

Differential scattering cross sections in the energy rangeE _CM=25–50 eV have been measured in a crossed beam machine for the scattering of Na⁺ by laser excited Na(3² P _3/2). The superelastically scattered ions resulting from the collisional deexcitation process 3² P _3/2-² S _1/2 are sharply peaked at a constant reduced scattering angle of 180eV degrees. Through the choice of either linearly or circularly polarized light, one can selectively excite the magnetic sublevels of the Na atoms. This ability to align or orient the Na^* allows us to discuss in considerable detail both the transition from the space-fixed (atomic) to the body-fixed (molecular) system and the dynamics in the merging region of the two frames. We find that the symmetry axis of the excited electron charge cloud is locked to the internuclear axis and hence to the body-fixed reference frame at an internuclear separation of about 35 a.u. A pronounced asymmetry of the scattering from atoms excited with LHC or RHC polarized light is discussed in terms of simple models.     

Charge symmetry breaking interactions and coulomb energy differences

A detailed study of the possibility that the long standing discrepancies between theory and experiment in the values of Coulomb displacement energies have their origin in the charge asymmetry of the nuclear force is presented. A review of the present status of the theory of Coulomb displacement energies of mirror states is given. We have constructed a phenomenological charge asymmetric potential that can remove the Coulomb energy discrepancies for several mirror nuclei yet having only minimal effect on the ¹S₀ nucleon-nucleon scattering length. The form of this potential is however not compatible with the contributions due to charge asymmetric meson exchange processes that have been considered in the literature. We assume that these meson exchange effects can be reasonably described, up to strength factors, by a sum of one-pion, one-scalar-meson (σ) and one-vector-meson exchange potentials. The need for some additional type of charge asymmetric effect, e.g. three-body forces, is pointed out.     

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.     

Elastic scattering of electrons by nuclei of half-integer spin and discrete symmetries

Analytical expression is obtained for the right-left asymmetry A _RL ^(3/2) for the process of elastic scattering of the longitudinally polarized electrons by nuclei with spin 3/2, described in the framework of Rarita-Schwinger formalism by invariant form factors of electromagnetic and weak vertex functions. It is shown, that this asymmetry directly depends on the nuclear anapole form factors G ₁ ⁽ⁿ⁾, and structurally is equivalent to asymmetry A _RL ^(1/2), which arises in electron scattering by proton.     

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.     

Determination of low-energy parameters of neutron-neutron scattering from an analysis of the binding-energy difference between the 3H and 3He mirror nuclei

A relation between quantities that characterize the breaking of the charge symmetry of nuclear forces in systems of two and three nucleons is found on the basis of an analysis of the binding-energy difference between the ³H and ³He mirror nuclei. For the neutron-neutron scattering length and effective range, the values of a _nn = ?18.38(55) fm and r _nn = 2.84(4) fm, respectively, were obtained by using purely nuclear parameters of proton-proton scattering in the ¹ S ₀ state. The calculated values agree with present-day experimental results.     

Orbital correlations in doped manganites

We review our recent X-ray scattering studies of charge and orbital order in doped manganites, with specific emphasis on the role of orbital correlations in Pr_1-xCa_xMnO₃. For x=0.25, we find an orbital structure indistinguishable from the undoped structure and long-range orbital order at low temperatures. For dopings 0.3≤x≤0.5, we find scattering consistent with a charge and orbitally ordered CE-type structure. While in each case the charge order peaks are resolution limited, the orbital order exhibits only short-range correlations. We report the doping dependence of the correlation length and discuss the connection between the orbital correlations and the finite magnetic correlation length observed on the Mn³⁺ sublattice with neutron-scattering techniques. The physical origin of these domains, which appear to be isotropic, remains unclear. We find that weak orbital correlations persist well above the phase transition, with a correlation length of 1–2 lattice constants at high temperatures. Significantly, we observe similar correlations at high temperatures in La_0.7Ca_0.3MnO₃, which does not have an orbitally ordered ground state, and we conclude that such correlations are robust to variations in the relative strength of the electron–phonon coupling. Received: 22 May 2001 / Accepted: 4 July 2001 / Published online: 5 October 2001     

Charge symmetry as an off-shell constraint on the nuclear force for finite range transformations

An upper bound on the variation of the Coulomb subtracted pp scattering length in the ¹S₀ state is obtained for arbitrary unitary and Baker transformations of finite range. It is shown that this variation is always less than the experimental error in the nn scattering length, if the range of the transformation is less than about 1 fm, implying that Sauer's charge symmetry constraint is then automatically fulfilled. This also means that the charge symmetry principle is most relevant for the intermediate range of the nuclear force. We also discuss the zero-energy off-shell parameters which are actually constrained by charge symmetry and a knowledge of the outer part of the interaction.     

A precise measurement of the spin-dependent neutron scattering length of 3He

The poor knowledge of the spin-dependent neutron scattering length of ³He has until now handicapped nuclear four body theory and the interpretation of excitations in the quantum liquid. We have measured, for the first time directly, the real part of the bound incoherent neutron scattering length, b_i′ of ³He. A neutron spin echo spectrometer was used to detect pseudomagnetic precession of polarised neutrons passing through polarised ³He gas. Any absolute calibrations of sample and beam parameters were avoided using simple transmission measurements with non-polarised neutrons. The only a priory information required was the spin-dependent neutron absorption cross section of ³He. The result is b_i′ = -2.365(20) fm, which reduces the prior uncertainty by a factor 30. The corresponding new value of the bound incoherent scattering cross section is σ_i = 1.532(12) barn. Including the known value of the coherent neutron scattering length, we obtain new values for the real parts of the free triplet and singlet neutron scattering lengths, a_-′ = 7.370(58) fm and a₊′ = 3.278(53) fm.     

Electrically weak asymmetry in the elastic scattering of electrons by nuclei with multipole moments

The differential elastic-scattering cross section of longitudinally polarized electrons by nuclei of arbitrary spin and isospin is calculated in the Born approximation, taking into account the interference of electromagnetic interaction and the interaction of weak neutral currents. For a nucleus of spin J 3/2, explicit expressions are obtained for the interference terms in terms of the electromagnetic multipole form factors F_C, f_Q, f_M1 and f_M3. Using the example of the³He,¹¹B,¹⁹F and⁴⁰Ca nuclei, the behavior of electrically weak asymmetry of the cross section is investigated in detail in the framework of three gauge models. It is shown that the asymmetry of a_Rl is 10^–5 for E - 100 MeV, and is sensitive to the nuclear structure: By taking into account the contributions not only of the charge and magnetic-dipole scattering but also of the quadrupole and octupole scattering, one can obtain additional information on the structure of weak electron-nucleus interaction.This paper was presented at a conference on Investigations of Spin Phenomena in High-Energy Physics held at Protvino, November 23–26, 1982.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 79–84, April, 1984.     

BaTiO3和Ce:BaTiO3单晶的高温喇曼散射研究

从室温至180℃测量了BaTiO₃和Ce:BaTiO₃单晶的偏振喇曼谱,在X(ZZ)Y几何配置下发现了三条频率分别为986,1204和1480cm^-1的新谱线.根据喇曼散射截面的温度依赖关系,确认这些新谱线对应二阶喇曼散射,而A₁(TO)谱中位于275和514cm^-1处的非对称宽峰则属于一阶喇曼散射.在此基础上,对立方相BaTiO₃的喇曼谱和结构相变机制进行了讨论.通过比较B     

The K<Superscript>-</Superscript>α scattering length and the reaction dd↦αK<Superscript>+</Superscript>K<Superscript>-</Superscript>

We present predictions for the K^-α scattering length obtained within the framework of the multiple-scattering approach. Evaluating the pole position of the K^-α scattering amplitude within the zero-range approximation, we find a loosely bound K^-α state with a binding energy of E_R = - 2,..., - 7 MeV and a width Γ_R = 11,..., 18 MeV. We propose to measure the K^-α scattering length through the final-state interaction between the α and K^--meson produced in the reaction dd↦αK⁺K^-. It is found that the K^-α invariant-mass distribution from this reaction at energies near the threshold provides a new tool to determine the s-wave K^-α scattering length.     

An experimental investigation of the decays K± → π0π0π±: The slope parameter and its charge asymmetry

The slope parameter and its charge asymmetry have been measured for the τ′ decay mode of the charged K mesons. No charge asymmetry in the parameter is observed to the precision level of 1.25%, indicating the absence of CP violating transitions. The result for the slope parameter is consistent with previous measurements and taken with other results on K_π³ decay modes supports the conclusion that the $\text{ΔI =}\text{1}\text{2}$ rule is not exact.