Unnatural parity states in nuclei and pion condensation

This is a systematic study to assess a lower limit on the threshold density for pion condensation on the basis of empirical nuclear data. It turns out that the isovector unnatural parity states in ⁴He, ¹⁶O and ⁴⁰Ca, and quantities related to them are best suited for a quantitative test. Assuming for the interactions parameters in the nucleon-hole and Δ-isobar-hole channels g′: = g′_NN = g′_NΔ = g′_ΔΔ, a value g′ = 0.7±0.1 is obtained from the measured energy shifts of unnatural parity states. Taking also into account results by Oset and Rho who obtain g′_ΔΔ = 0.6?0.7 from the observed quenching of Gamov-Teller matrix elements of (A±1) nuclei around ¹⁶O and ⁴⁰Ca, one finds the onset of pion condensation in nuclear matter at densities considerably larger than twice normal nuclear density, if at all. We discuss the work of Migdal et al. who prefer the assumption g′_NΔ = g′_ΔΔ = 0 and obtain lower critical densities. Also the question of (pre)critical behaviour in finite nuclei is investigated in terms of a quantitative example. It is found that a genuine signal for proximity to pion condensation would be the appearance of a strongly collective spin-isospin mode which has, however, not been observed experimentally so far.     

A partial wave analysis of the (3π)0 system from the charge exchange reaction π+n→π+π−πop AT 4 GeV/c

From a partial wave analysis of the (3π)^o state in the charge exchange reaction π⁺n→π⁺π^?π^op, we observe strong unnatural parity as well as natural parity production. The observed strong unnatural parity states are identified with well-established resonances. The unnatural parity production is consistent with Reggeized Deck model predictions, with the exception of the I = 1, JP = 1⁺ state. Here there is no evidence for A₁ production at ～1.1 GeV, but the data could support resonance production at higher masses.     

Global-vector representation of the angular motion of few-particle systems II

The angular motion of a few-body system is described with global vectors which depend on the positions of the particles. The previous study using a single global vector is extended to make it possible to describe both natural and unnatural parity states. Numerical examples include three- and four-nucleon systems interacting via nucleon-nucleon potentials of AV8 type and a 3α system with a nonlocal αα potential. The results using the explicitly correlated Gaussian basis with the global vectors are shown to be in good agreement with those of other methods. A unique role of the unnatural parity component, caused by the tensor force, is clarified in the 0^? ₁ state of ⁴He. The two-particle correlation function is calculated in the coordinate and momentum spaces to show different characteristics of the interactions employed.     

The screening of the particle-hole interaction to all orders

Starting from Brueckner's G-matrix the effects of the induced interactions on the particle-hole interaction in nuclear matter are investigated to all orders. Although an iterative solution of the non-linear integral equations, which have to be solved, leads to divergent contributions, it can be shown that the renormalization effects summed to all orders are finite. The complete momentum dependence of the particle-hole interaction is treated which in the Landau limit results in less attractive F₀ and more repulsive G′₀ parameters. For finite ph momenta these features are maintained implying that the collectivity in the pion spin-isospin channel is screened also when the renormalization is considered to all orders.     

A comparison of πππ, Kππ, πKKKK system produced in the reactions meson +p→3 mesons + p

A comparison is made of the low-mass three-meson systems (πππ), (Kππ), $\text{(π}\text{K}\text{K}\text{)}$ and $\text{(}\text{K}\text{K}\text{K}\text{)}$ diffractively produced in the reaction meson + proton → three mesons + proton. Several striking similarities and a few important differences are observed: (i) the reactions are consistent with the assumption that the three mesons decay entirely into a 0^? meson and a 0⁺, 1^? or 2⁺ resonance; (ii) the three-meson mass spectra have a peak ≈ 250 MeV above the effective threshold M_eff of the dominant decay mode and then fall off approximately as (mass)^?3;(iii) the average spin 〈J〉 = 0.55 + 1.1 Q_eff, where Q_eff = M - M_eff; (iv) the average orbital angular momentum 〈l〉 increases according to 〈l〉 = 0.75 Q_eff; (v) the three-meson states are produced dominantly in unnatural spin-parity states and no evidence for their being resonant is found; (vi) the only natural spin-parity states found are the well-established 2⁺ resonances A₂ and K¹ (1420); they have similar properties to the non-resonant unnatural parity states except for a dip at t = 0 in the dσ/dt distributions; (vii) both the unnatural and natural spin-parity states are produced mostly by an exchange of natural parity; (viii) there is evidence for two types of production mechanism with different polarization properties, one approximately conserving helicity in the t-channel and the other in the s-channel.     

Direct and sequential processes in the 16O(7Li, 7Be)16N reaction

Calculations are presented for the ¹⁶O(⁷Li, ⁷Be)¹⁶N charge exchange reaction. For the direct reaction, the tensor interaction leads to form factors with large spin and angular momentum transfer which are important for the unnatural parity states. The (⁷Li, ⁶Li)(⁶Li,⁷Be) sequential process exhibits a strong J-dependence and is the dominant contribution to the natural parity states.     

The nature of three-pion enhancements in the minimal K-matrix model

The square of the magnitude of the inverse Fredholm determinant associated with the minimal K-matrix integral equations describing three-pion to three-pion scattering was calculated as a function of three-pion mass ¢M from threshold to 1900 MeV for the 0 ≦ I ≦ 2, 0 ≦ J ≦ 2 channels of the three-pion system. The input for these equations consisted of the on-shell π-π t-matrices t₀⁰, t₀², t₁¹, and t₀² obtained from phenomenological phase-shift analyses. For the minimal K-matrix model, the only structure in the natural parity states is an enhancement of kinematical origin at 1284 MeV in the ω-channel. Spurious enhancements appear in all the unnatural parity states considered at roughly 1150 MeV corresponding to the ρπ → ρπ Peierls singularity. In the I = 1 unnatural parity channels, broad enhancements at $\text{1450}\text{MeV}\text{≦ ¢M ≦ 1675}\text{MeV}$ occur. These correspond to the ρπ → fπ fit generalized Peierls singularity.     

Possibilities of revealing collective pion degrees of freedomin nuclei by means of quasielastic pion knockout by high-energy electrons

The kinematics of quasielastic pion knockout by longitudinal virtual photons in the electroproduction process is presented. The possibility of directly investigating pion momentum distributions in specific channels owing to pole-amplitude dominance is considered. It is shown that, taking into account the final-state interaction of the knock-on pion and the nucleus involved, one can reveal the existence of a pion condensate in nuclei, since the momentum distribution of collective pions has a pronounced maximum at a momentum in excess of 0.3 GeV/c and since the excitation spectrum of the final recoil nucleus is concentrated in the low-energy region E* ≈ K ²/(2AM _N ) ≤ 1 MeV. The picture of pion knockout from meson clouds of individual nucleons is totally different. The analogous rho-mesonmomentum distributions for the process ρ + γT* → π are also presented.     

Pion-nucleus inelastic scattering and charge exchange

Using a separable fixed scatterer pion-nucleon interaction and the distorted wave impulse approximation we have made predictions for medium energy pion inelastic scattering from ¹⁶O and (π^?, π⁰) charge exchange from ⁴⁸Ca. An optical potential based on the pion-nucleon interaction adopted in this work has been shown previously to provide good fits to pion-nucleus elastic scattering. After a discussion of the basic formulae, we present results of calculations for pion inelastic scattering from ¹⁶O for initial pion lab kinetic energies of 70 and 180 MeV. Because of the strong energy dependence of the pion-nucleon interaction there are qualitative differences between the predictions for the nuclear response in the momentum transfer, energy loss plane for T_π^lab = 70 and 180 MeV. At these energies, states not prominently excited by other probes are predicted to be observable. In particular, J^π = 3^? and 4^?, T = 0 states appear prominently in the excitation spectrum region at large momentum transfer. A comparison of π^? and π⁺ scattering showing the effects of the Coulomb interaction is presented. The predictions for pion single-charge exchange on ⁴⁸Ca indicate that this interaction would be useful for studying the location of the T_> states arising from the splitting of the giant dipole resonance in T ≠ 0 nuclei.     

Isovector kaon form factor in the dispersion theory and S-wave π K-scattering lengths

A one-dimensional integral representation for isovector kaon form factor is constructed within the dispersion theory in terms of the pion form factor and the backwardπK-scattering amplitude. The normalization condition for isovector kaon form factor at zero momentum transfer gives a sum rule for theπK-scattering amplitude, with the use of which difference between thes-waveπK-scattering lengths in triplet and singlet isospin states is estimated to bea ₀ ^3/2 - a ₀ ^1/2 ≈μ ^{? 1} whereμ is the pion mass. In agreement with the vector-meson-dominance model, deviations of the isovector kaon form factor from half of the pion form factor are found to be small.     

Two new Regge trajectories in the Neveu-Schwarz model

The existence of two new families of Regge trajectories at the tree diagram level of the Neveu-Schwarz dual pion model is pointed out. They both have odd G-parity but are of opposite naturality. The highest lying new trajectory is related to the usual unnatural parity pion trajectory $\text{α}{}_{\mathrm{\pi }}\text{by}\text{β}{}_{\mathrm{\pi }}\text{=}\text{1}\text{2}\text{α}{}_{\mathrm{\pi }}\text{+}\text{1}\text{2}$. It factorizes and has positive signature. The parent of the new natural parity trajectories is related to the usual trajectory α_ω by $\text{β}{}_{\mathrm{\omega }}\text{=}\text{1}\text{2}\text{α}{}_{\mathrm{\omega }}$.     

Interferometrical signature of mixed phase in A+A collisions

We have calculated the pion rapidity distribution, the transversal momentum spectrum and the pion correlator in outward, sideward and longitudinal directions for S+S collisions at high energy. We used a two-temperature model that allows us to explain the abundance of pions at smallp _T and highp _T . The first source, which is at high temperature, is in a quark-gluon-hadron mixed phase radiating pions due to a deflagration shock wave on the background of longitudinal expansion. The second source consists of the unburnt part of the matter in hadronic phase. The interferometrical analysis at differentp _T gives a signature for two expanding sources separated in time and allows the measurement of the lifetime and other parameters of each of them.     

Spin structure of the pion in a light-cone representation

The spin structure of the pion is discussed by transforming the wave function for the pion in the naive quark model into a light-cone representation. It is shown that there are higher helicity (λ ₁+λ ₂=±1) states in the full light-cone wave function for the pion besides the ordinary helicity (λ ₁+λ ₂=0) component wave functions as a consequence from the Melosh rotation relating spin states in light-front dynamics and those in instantform dynamics. Some low energy properties of the pion, such as the electromagnetic form factor, the charged mean square radius, and the weak decay constant, could be interrelated in this representation with reasonable parameters.     

The power of effective field theories in nuclei: The deuteron,NN scattering and electroweak processes

We show how effectively effective quantum field theories work in nuclear physics. Using the physically transparent cut-off regularization, we study the simplest nuclear systems of two nucleons for both bound and scattering states at a momentum scale much less than the pion mass. We consider all the static properties of the deuteron, the two-nucleon scattering phase-shifts, the n + p → d + γ process at thermal energy and the solar proton fusion process p + p → d + e⁺ + ν_e, and we demonstrate that these are all described with great accuracy in the expansion to the next-to-leading order. We explore how a “new” degree of freedom enters in an effective theory by turning on and off the role of the pion in the Lagrangian.     

A partial-wave analysis of the neutral 3π system produced in the reaction π−p → (π+π−π0) n at 12 and 15 GeV/c

Data on the charge-exchange reaction π^?p → (π⁺π^?π⁰)n have been taken at beam momenta of 12 and 15 GeV/c, using the CERN Omega Multiparticle Spectrometer. A partial-wave analysis has been made of the (3π)⁰ system. We observe both natural and unnatural spin-parity production. The natural parity states can be identified with established resonances. In addition a natural spin-parity enhancement is observed at a mass of about 2 GeV/c² with J^P = 4⁺ preferred. We have called this effect the A₂¹ (2030). The unnatural spin-parity production found is consistent with reggeized Deck model predictions. No unambiguous A₁ or A₃ production is observed.     

Self-similarity of pion production in AA collisions at RHIC

Experimental data on inclusive spectra of pions produced in heavy-ion collisions at RHIC are analyzed in the framework of z-scaling. The data indicate similarity as a characteristic feature of the mechanism of pion production at high energies. It is argued that this property includes structure of the colliding objects, interaction of their constituents, and character of the fragmentation process. A microscopic scenario of nucleus interactions at a constituent level in terms of momentum fractions is developed. The centrality dependence of the shape of the scaling function Ψ(z) and the fractal dimention ? _AA of the fragmentation process is studied. Energy losses of particles in the final state as a function of the collision energy, transverse momentum, and centrality are estimated. The scale dependence of the energy losses is discussed. A decreasing tendency of specific heat of the produced medium with the system size is established. The obtained results may be exploited to search for and study new physics phenomena in pion production in pp and AA collisions at high multiplicities.     

Higher moments of the pion multiplicity distribution in proton-proton interactions at 12 and 24 GeV/c

Results on higher moments of the pion multiplicity distribution are presented for pp interactions at 12 and 24 GeV/c incident lab momentum. A simple parametrization for the pion multiplicity distribution is established at 12 and 24 GeV/c and is then used to discuss the energy dependence of higher moments in a range from 4 to about 500 GeV/c incident lab momentum.     

Investigation of the deuteron spin structure at short nucleon-nucleon distances in the reaction of polarized-deuteron fragmentation to cumulative pions

Experimental results on the vector (A _y ) and tensor (A _yy ) analyzing powers in the fragmentation of 5- and 9-GeV/c polarized deuterons to high-momentum pions in the kinematical region corresponding to pion production on a strongly correlated nucleon pair (cumulative meson production) are presented. The angular and momentum dependences of A _yy are not described by calculations performed in the impulse approximation by using standard deuteron wave functions. An explanation for our data should be sought on the basis of models that treat the deuteron at short distances (deuteron-core region) as a multiquark state—for example, a 6q cluster, whose high orbital angular momentum (D wave) leads to the observed strong dependence of the reaction tensor analyzing power A( $\vec d$ , π)X on the pion transverse momentum.     

Production of f'(1520) in 8.25 GeV/c K−p interactions

We present results for the hypercharge exchange reaction K^?p→f' λ from a high statistics experiment at 8.25 GeV/c using the CERN 2m HBC. The total and differential cross sections have been measured; the polarisation of the Λ hyperon and the f' density matrix elements have been calculated as functions of momentum transfer. We also present detailed information on the relative strength of the natural and unnatural parity exchange contributions to the production mechanism.     

Production mechanism of ϱ0 and f mesons in πN→π+π−N reactions

The production of ?⁰ and f mesons in πN→π⁺π^?N reactions in the momentum range 4 to 17 GeV/c is investigated in a model-independent way by imposing in full the positivity of the density matrix. The results so obtained are used in order to determine the effective Regge trajectories for unnatural and natural parity exchanges and are compared to results obtained in different analyses.