Analytic proton-nucleus scattering amplitudes

Analytic expressions for the elastic nucleon-nucleus amplitudes F(q) and G(q) are derived. They are based on analytic approximations of the nuclear profile functions in the Glauber formulation. Our amplitudes are sums of terms with a familiar structure, black-sphere Bessel functions multiplied by form factors accounting for the diffuseness of the nuclear surface. Their accuracy is tested with the Woods-Saxon density and found to be excellent for momentum transfers q? 5fm^?1.     

Hidden relation between reflection amplitudes and thermodynamic Bethe ansatz

In this paper we compute the scaling functions of the effective central charges for various quantum integrable models in a deep ultraviolet region R → 0 using two independent methods. One is based on the “reflection amplitudes” of the (super-)Liouville field theory where the scaling functions are given by the conjugate momentum to the zero-modes. The conjugate momentum is quantized for the sinh-Gordon, the Bullough-Dodd, and the super sinh-Gordon models where the quantization conditions depend on the size R of the system and the reflection amplitudes. The other method is to solve the standard thermodynamic Bethe ansatz (TBA) equations for the integrable models in a perturbative series of 1/(const. - In R). The constant factor which is not fixed in the lowest order computations can be identified only when we compare the higher order corrections with the quantization conditions. Numerical TBA analysis shows a perfect match for the scaling functions obtained by the first method. Our results show that these two methods are complementary to each other. While the reflection amplitudes are confirmed by the numerical TBA analysis, the analytic structures of the TBA equations become clear only when the reflection amplitudes are introduced.     

Meson properties in an extended non-local NJL model

We consider a non-local version of the NJL model, based on a separable quark-quark interaction. The interaction is extended to include terms that bind vector and axial-vector mesons. The non-locality means that no further regulator is required. Moreover the model is able to confine the quarks by generating a quark propagator without poles at real energies. Working in the ladder approximation, we calculate amplitudes in Euclidean space and discuss features of their continuation to Minkowski energies. Conserved currents are constructed and we demonstrate their consistency with various Ward identities. Various meson masses are calculated, along with their strong and electromagnetic decay amplitudes. We also calculate the electromagnetic form factor of the pion, as well as form factors associated with the processes γγ^* → π⁰ and ω → π⁰γ^*. The results are found to lead to a satisfactory phenomenology and lend some dynamical support to the idea of vector-meson dominance.     

High resolution proton inelastic scattering from 50Cr

Resonances in the ⁵⁰Cr(p, p′γ) reaction were investigated with the TUNL high resolution system. All previously observed p-wave resonances between Ep = 2.00 and 3.03 MeV were studied. Measurement of the p' and the γ-ray angular distributions provides sufficient information to determine unambiguously the J-value of the resonance and the magnitude and relative phase of the inelastic decay amplitudes. Expressions are given for the appropriate angular distributions and for the transformation between the channel spin and the total angular momentum representation. Experimental results are presented for 24 p-wave resonances in ⁵¹Mn including decay amplitudes and relative phases for $\text{16}\text{3}\text{2}{}^{\mathrm{?}}$ resonances. Six resonances formerly assigned $\text{1}\text{2}{}^{\mathrm{?}}$ are reassigned $\text{3}\text{2}{}^{\mathrm{?}}$. Inelastic spectroscopic factors were determined for two analogue states. Proton strength functions were evaluated from both the elastic and inelastic data.     

Amplitudes of multichannel scattering on a two-dimensional potential barrier with constant height

The immersing method is applied to solve the N-channel scattering problem for concrete potential. In particular, we consider the particle scattering on a two-dimensional potential barrier, which is constant in the scattering direction and arbitrary in the cross-section direction. For this case the scattering amplitudes t _m and r _m (1,2, m= ...,N) are determined. A transition from the obtained formulas to the case of ?-potential is performed. For this case transmission amplitudes t _m and reflection amplitudes r _m are obtained. It is also shown that the product of transmission and reflection amplitudes along the channel m does not depend on the scattering channel.     

Two-channel separable potential model for the low-energy hyperon-nucleon interaction

A two-channel separable potential model is given such that the T-matrix is given in the form of a N/D matrix. This model is used to examine the relationships between the three different definitions for a resonance in the two-channel problem, particularly for a ³S₁ Λp resonance. In order to obtain a phenomenological hyperon-nucleon (YN) scattering T-matrix in the present model, a least-squares fit is performed to the existing available data for the $\text{I =}\text{1}\text{2}\text{YN}$ scattering cross sections and angular distributions at low energies using the s- and p-wave N/D solutions which carry sixteen independent parameters. Several solution sets of potential parameters are found, for which we can obtain good fits to the Λp → Λp, Σ^?p → Λn and ΣN → ΣN data, particularly to the cross-section data for these processes. The p-wave contributions are estimated, and particularly the possibility of p-wave YN resonances is pointed out for the solutions for which we do not assume a ³₁ Λp resonance.     

Final-state interactions with inelastic effects in non-leptonic hyperon decays

A recent work by Reid and Trofimenkoff seemed to indicate that a satisfactory model using current algebra, PCAC and the soft-pion limit can be formulated to obtain the s- and p-wave amplitudes of the non-leptonic decays of Λ and Σ, as well as the $\text{ΔI =}\text{1}\text{2}$rule if final state interactions are included. We demonstrate in this paper that by including inelastic effects in the final-state interactions (that is without the usual approximation of elastic unitarity) the results bring us back full circle. The disagreement between theory and experiment for the p-wave amplitudes still persists and no significant suppression of the $\text{I =}\text{3}\text{2}$ state for the final particles can be predicted.     

Average neutron resonance parameters and radiative capture cross sectins for the isotopes of molybdenum

The neutron capture cross sections of the stable molybdenum isotopes have been measured with high energy resolution (ΔE/E ? 0.2 %), between 3 and 90 keV neutron energy, at the 40 m station of ORELA. Average resonance parameters are extracted for s- and p-wave resonances. The s-wave neutron strength function is close to 0.5 × 10^?4 for all isotopes, but the p-wave strength function exhibits a well defined peak near At~ 95.Both s- and p-wave radiative widths decrease markedly as further neutrons are added to the closed shell. The p-wave radiative widths are generally greater than the s-wave widths showing the presence of non-statistical γ-decay mechanisms.Valence neutron theory fails to explain the magnitude of the p- to s-wave radiative width disparity and doorway state processes are invoked. In particular, the data for ⁹⁸Mo appear to violate the usual valence theory, since the correlations between radiative and neutron strengths are small. Further, the radiative widths are smaller than can be explained on the valence model. An explanation for the loss of valence strength is advanced.Interpolated resonance parameters allow an estimate for the unknown cross section for ⁹⁹Mo(n, γ).     

Scattering of massive open strings in pure spinor

In Park (2008) [4], it was proposed that the D-brane geometry could be produced by open string quantum effects. In an effort to verify the proposal, we consider scattering amplitudes involving massive open superstrings. The main goal of this paper is to set the ground for two-loop “renormalization” of an oriented open superstring on a D-brane and to strengthen our skill in the pure spinor formulation of a superstring, an effective tool for multi-loop string diagrams. We start by reviewing scattering amplitudes of massless states in the 2D component method of the NSR formulation. A few examples of massive string scattering are worked out. The NSR results are then reproduced in the pure spinor formulation. We compute the amplitudes using the unintegrated form of the massive vertex operator constructed by Berkovits and Chandia (2002) [15]. We point out that it may be possible to discover new Riemann type identities involving Jacobi ?-functions by comparing a NSR computation and the corresponding pure spinor computation.     

A remark on quantum gravity

We discuss the structure of Dyson-Schwinger equations in quantum gravity and conclude in particular that all relevant skeletons are of first order in the loop number. There is an accompanying sub-Hopf algebra on gravity amplitudes equivalent to identities between n-graviton scattering amplitudes which generalize the Slavnov-Taylor identities. These identities map the infinite number of charges and finite numbers of skeletons in gravity to an infinite number of skeletons and a finite number of charges needing renormalization. Our analysis suggests that gravity, regarded as a probability conserving but perturbatively non-renormalizable theory, is renormalizable after all, thanks to the structure of its Dyson-Schwinger equations.     

Magnetooptical properties of a ferromagnetic superlattice

Transmission and reflection of a normally incident wave from a magnetic superlattice consisting of 2N ferromagnetic layers with alternating orientation of the magnetization vector are considered. The characteristic matrix of a superlattice relating wave amplitudes at the entrance to the system and at the exit from it is calculated in the closed form and Jones matrices determining all the basic magnetooptical characteristics of the structure (transmission and reflection coefficients, the degree of polarization of transmitted and reflected waves, and so on) are constructed. A significant dependence of these characteristics on the number of layers is demonstrated.     

Vector boson pair production in e−e− collisions with polarized beams

The W-boson pair production in e⁻e⁻ collisions with polarized beams is investigated. The helicity amplitudes are derived for general couplings and the conditions for a good high-energy behaviour of the cross-section are given. The results are applied to the heavy vector boson production in the context of the left-right symmetric model. The Ward identities and the equivalence theorem are also discussed.     

Amplitudes of multichannel scattering on the barrier with a constant height in the scattering direction

The immersing method is applied to solve the N-channel scattering problem. In particular, we consider the particle scattering on a multidimensional potential barrier, which is constant in the scattering direction and arbitrary in the lateral direction. For this case the scattering amplitudes t _m and r _m (m = 1, 2, …, N) are determined. Transition from the obtained formulas to the case of thin potential is performed. For this case analytical expressions of transmission amplitudes t _m and reflection amplitudes r _m are obtained. We show that the product of transmission and reflection amplitudes in the channel m does not depend on the scattering channel. It is assumed that the scattering particle falls on the potential with the longitudinal wave vector k _l corresponding to the channel l.     

The absorptive pion-nucleus optical potential

We calculate s-wave and p-wave absorptive pion-nucleus optical potentials assuming that a pion is absorbed by a pair of nucleons. Employing a model which takes into account both a single nucleon absorption with nucleon-nucleon correlations and rescattering, we obtain simple analytic expressions for Im B₀ sid Im C₀ of the pion-nucleus optical potential. The off-shell effect on the s-wave pion absorption is examined and shown to be strongly modified by short range correlations. The result for the p-wave absorptive part Im C₀ clearly shows the importance of the tensor correlations. The enhanced nn emission after π^? absorption is shown to be related with a large p-wave πN scattering length a₃₃ via the tensor correlations.     

N-d elastic scattering and polarization calculations with tensor force and p-wave interaction

Three-body calculations for the n-d elastic scattering are preformed at E_n = 14.1 MeV with s and p-wave N-N interaction and tensor force. The tensor force is not able to reproduce even the order of magnitude of the elastic neutron polarization. It is also shown that the p-wave N-N interactions have an important effect on the neutron polarization.     

Effective range parameter ins-wave pion nucleon scattering

The effective range parameterb ^? for πN s-wave scattering is calculated from fixed-t dispersion relations, using experimental information for the imaginary parts. The result is compared with that of other calculations, based on Ward identities and phenomenological Lagrangians. It is pointed out that a direct determination ofb ^? from experimental data is not possible. Since the Δ-propagator is not unique, the Δ-exchange amplitudes are given for a one-parameter class of propagators (Appendix).     

A study of ππ → NN partial-wave amplitudes using hyperbolic dispersion relations

We investigate $\text{ππ →}\text{N}\text{N}$ partial-wave amplitudes, using a spin separation method based on hyperbolic dispersion relations. Partial-wave amplitudes with J ? 3 are dominant in the pseudophysical region between the ππ and $\text{N}\text{N}$ thresholds, but we find clear evidence for J = 4 and J = 5 contributions from regions near and above the $\text{N}\text{N}$ threshold. We isolate J = 2 and J = 3 partial waves and determine the couplings of f₀(1270) and g (1680). Knowing the high-spin contributions, we are able to eliminate thse and to study s- and p-waves. We find evidence for small p-wave contributions above the ?, having the same sign as the ? contributions. We develop methods for determining the I = J = 0 ππ scattering length a₀⁰ and find a₀⁰ = 0.30 ± 0.15.     

SU(6)对称性理论中的弱相互作用

本文提出了SU(6)对称性理论中的一个弱相互作用中间玻色子方案。基本假定是:(1)中间玻色子归为SU(6)群的不可约表示21;(2)弱流归为正规表示35;从而(3)s波及p波半弱相互作用分别归为表示21中的(3^*,1)部分及表示15中的(3^*,3)部分。则除了△I=1/2规则以外,由此得出的有效超子非轻子作用在s波(宇称破坏)振幅都分给出三个求和规则,在p波(宇称守恒)振幅部分给出一个求和规则,这些关系看来和实验符合得较好。     

Pion-nucleus interaction and the range of πN forces

We examine several definitions for the ranges r_πN of the pion-nucleon (πN) forces and conclude that 0.25 ≦ r_πN ≦ 0.5 fm. We investigate two consequences of the finite range of the p-wave πN interaction: the additional spatial extension of the p-wave π-nucleus optical potential and the quenching of the Lorentz-Lorenz effect. For 0.25 ≦ r_πN ≦ 0.5 fm (i) the additional extension of the p-wave optical potential gives negligible contributions to shifts and widths in π-mesic atoms and (ii) the Lorentz-Lorenz effect is largely quenched making nuclear correlations hard to detect by mesic atoms measurements.