Local-potential approximation for the Brueckner G matrix and problem of optimally choosing model subspace

The validity of the local-potential approximation, which was proposed previously for the singlet-pairing problem in semi-infinite nuclear matter, is investigated in the Bethe-Goldstone equation for the Brueckner G matrix. For this purpose, use is made of the method developed earlier for solving this equation for a planar slab of nuclear matter in the case of a separable form of NN interaction. The ¹ S ₀ singlet and the ³ S ₁+³ D ₁ triplet channel are considered. The complete two-particle Hilbert space is split into a model and the complementary subspace that are separated by an energy E ₀. The two-particle propagator is calculated precisely in the first subspace, and the local-potential approximation is used in the second subspace. With an eye to subsequently employing the G matrix to calculate the Landau-Migdal amplitude, the total two-particle energy is fixed at E=2μ, where μ is the chemical potential of the system under consideration. Specific numerical calculations are performed at μ=?8 MeV. The applicability of the local-potential approximation is investigated versus the cutoff energy E ₀. It is shown that, in either channel being considered, the accuracy of the local-potential approximation is rather high for E ₀≥10 MeV.     

Dependence of nuclear Z factor on the chemical potential

A simple microscopic formula is derived for the renormalization factor Z of Green’s function on the basis of the self-consistency relation of many-body theory and the Brueckner method. This formula involves the derivative of the Brueckner G matrix with respect to energy. Based on the analysis of the properties of the G matrix for a slab of nuclear matter, the G matrix is approximately replaced by the off-mass-shell T matrix taken for free NN scattering at a negative energy E equal to the doubled chemical potential μ of the nucleus under consideration. The Z factor thus calculated depends strongly on μ and decreases with |μ|. This effect is important for analyzing the properties of atomic nuclei near the drip line, where μ is zero.     

Effective theory of NN interactions in a separable representation

We consider the effective field theory of the NN system in a separable representation. The pionic part of the effective potential is included nonperturbatively and approximated by a separable potential. The use of a separable representation allows for the explicit solution of the Lippmann-Schwinger equation and a consistent renormalization procedure. The phase shifts in the ¹ S ₀ channel are calculated to subleading order.     

Infinite-Cutoff Renormalization of the Chiral Nucleon–Nucleon Interaction up to N3LO

Naively, the “best” method of renormalization is the one where a momentum cutoff is taken to infinity while maintaining stable results due to a cutoff-dependent adjustment of counterterms. We have applied this renormalization method in the non-perturbative calculation of phase-shifts for nucleon–nucleon (NN) scattering using chiral NN potentials up to next-to-next-to-next-to-leading order (N³LO). For lower partial waves, we find that there is either no convergence with increasing order or, if convergence occurs, the results do not always converge to the empirical values. For higher partial waves, we always observe convergence to the empirical phase shifts (except for the ³G₅ state). Furthermore, no matter what the order is, one can use only one or no counterterm per partial wave, creating a rather erratic scheme of power counting that does not allow for a systematic order-by-order improvement of the predictions. The conclusion is that infinite-cutoff renormalization is inappropriate for chiral NN interactions, which should not come as a surprise, since the chiral effective field theory (chiral EFT), these interactions are based upon, is designed for momenta below the chiral-symmetry breaking scale of about 1 GeV. Therefore, this value for the hard scale should also be perceived as the appropriate upper limit for the momentum cutoff.     

Correlations of pions and kaons as a measure for delayed expansion due to the QCD phase transition

We study pion and kaon correlations in ultra-relativistic heavy ion collisions in a hydrodynamical model with transverse cylindrical and boost-invariant longitudinal symmetry. As a function of the initial energy density ε₀, the ratioR _out/R _side of the inverse widths of the two-particle correlation function in out- and side-direction reflects the behaviour of the lifetime of the system. The ratio shows an enhancement in the case of a delayed expansion caused by the QCD phase transition. We discuss how this time-delay signal depends on the average transverse momentum of the pair, and show that it appears particularly strong for pairs with large average transverse momentum,K _⊥～1 GeV and for initial energy densities ε₀ ? 10 ? 20 GeVfm^?3 GeVfm^?3, corresponding to nuclear collisions at RHIC.     

The Reid93 Potential Triton in the Unitary Pole Approximation

The Reid93 potential provides a representation of the nucleon–nucleon (NN) scattering data that rivals that of a partial wave analysis. We present here a unitary pole approximation (UPA) for this contemporary NN potential that provides a rank one separable potential for which the wave function of the deuteron (³S₁-³D₁) and singlet anti-bound (¹S₀) state are exactly those of the original potential. Our motivation is to use this UPA potential to investigate the sensitivity of the electric dipole moment for the deuteron and ³H and ³He to the ground state nuclear wave function. We compare the Reid93 results with those for the original Reid (Reid68) potential to illustrate the accuracy of the bound state properties.     

Measurement of the Baryon-exchange reactions K−p→Λη, K−p→Λπ0 at 6 GeV/c and the value of the ηNN coupling constant

In order to determine the ηNN coupling constant we have measured the two reactions K^?p→Λη and K^?p→Λπ⁰ with a magnetic wire chamber spectrometer which contained a gamma counter for the γγ decays of π⁰ and η. The Λ polarization and the differential cross sections are given. The latter have quite different u dependences. Their ratio is interpreted, in terms of a nucleon-Regge exchange model, as the effect of a small ηNN coupling constant for which we obtain G_ηNN² = G_πNN² · (0.26 ± 0.10) as allowed by SU(3). The large value given by Heisenberg's non-linear field theory, G_ηNN² = G_πNN² · 0.9, is excluded by this measurement if the characteristic u dependence of the Λπ⁰ channel is attributed to N_α Regge exchange.     

A pion-nucleus optical potential containing effects of genuine pion absorption and emission

We derive in two ways a lowest-order optical potential $\text{V}$_πA using the projectile and a pair of target nucleons as the basic interacting unit. The first derivation—a heuristic one—uses a multiple-scattering theory, while the second employs a field theory where pions can be absorbed and emitted as well as scattered. The lowest-order terms of $\text{V}$_πA contain the two-particle ground state density and the πNN → πNN scattering matrix. In the same field-theoretical model one analyzes the latter in standard multiple-scattering contributions and genuine absorption corrections. The form of these corrections and their relation to often ad hoc assumed forms is discussed.     

The Triton from the Reid93 Potential in the UPA

The unitary pole approximation (UPA) provides an effective means to construct a rank one separable potential for calculations in which one requires a simple representation of the deuteron and/or triton ground-state wave function. By construction the deuteron wave function and the ¹S₀ anti-bound state wave function of the original potential are reproduced. We report results for the corresponding triton ground state. We choose to utilize the realistic Reid93 potential for this purpose. The Reid93 potential, generated by the Nijmegen group, is a Reid-like, partial-wave local potential that produces a χ² representation of the nucleon–nucleon (NN) scattering data that is as precise as an NN partial-wave analysis. Results for properties of ²H and ³H from the UPA are compared with those for the original potential. To further illustrate the precision of the method, results for properties of the deuteron and triton from the UPA are also compared with those for the original Reid68 potential.     

The intrinsic transverse momentum of Drell-Yan pairs

A soft gluon summation technique is used in conjunction with a singular infrared behaviour of the QCD coupling constant to compute the moments of transverse momentum <Q _⊥ ² > and <Q _⊥ ⁴ > of lepton pairs produced in hadron-hadron scattering. Remarkably, it is found that an α _s which produces asymptotically linear Regge trajectories, gives the best account of <Q _⊥ ² > for lepton pairs produced through valence quarks (and antiquarks), with no need of any intrinsic transverse momentum. Factorization of the cross section into its longitudinal and transverse momentum part is not assumed for the derivation of the mean values.     

The Rank-One Separable Interaction Kernel for Nucleons with Scalar Propagator

In the paper the covariant kernel of the nucleon-nucleon interaction of particles with scalar propagators is analyzed. The Bethe–Salpeter equation for the T matrix is considered in the rank-one separable kernel. The parameters of the kernel for the specific partial-wave channels explicitly connect with the observables low energy scattering parameters and phase shifts, deuteron binding energy. Covariant separable kernels for the partial-wave channels with total angular momentum J = 0 (¹S₀, ³P₀) and J =1 (³S₁ ? ³D₁, ¹P₁, ³P₁) are constructed.     

Fluctuations and defects in the spiral state of magnetic superconductors

We want to point out three properties of a magnetic superconductor: (i) The absence of true long-range order in the spiral state leads to the structure functions behaving like (q₆ ? q₀)^η?2 and (q²_⊥)^η?2 for q_⊥=0 and q₆=0, respectively, where q₀ is the preferred momentum. The indices η are measured via Bragg-like neutron scattering. (ii) The state is perforated by line-like defects. (iii) Above some critical temperature the defect lines proliferate, thereby destroying the spiral quasi-order.     

Inclusive single-particle distributions in π±p reactions at 8 and 16 GeV/c

Invariant single-particle cross sections for pion and proton production in π^±p interactions at 8 and 16 GeV/c are presented in terms of integrated distributions as functions of x, reduced rapidity ζ and p_⊥², and also in terms of double differential cross sections E d²σ/(dx dp_⊥²) and dζ dp_⊥²). A comparison of π^± and π^? induced reactions is made and the energy dependence is discussed. It is shown that the single-particle structure function cannot be factorized in its dependece on transverse and longitudinal momentum. For the beam-unlike pion, there is an indication for factorizability in terms of rapidity and transverse momentum in a small central region.     

Transverse momentum of hadrons produced in ν and ν interactions on an isoscalar target in BEBC

The average transverse momentum squared, 〈p_⊥²〉, of hadrons is studied as a function of W² and of Q² for ν and $\text{ν}$ interactions on an isoscalar target. An increase of 〈p_⊥²〉 with W² is observed for the hadrons emitted forward in the hadronic c.m.s. The p_⊥ dependence of the fragmentation function is found to factorise from the structure function at fixed W, but does not factorise at fixed Q². Unlike the case of forward-going particles, the 〈p_⊥²〉 of hadrons going backward in the c.m.s. shows no strong dependence on W².     

Observation of πo mesons with large transverse momentum in high-energy proton-proton collisions

Invariant cross-sections are presented for the inclusive reaction p + p → π^o + anything, Measurements of large transverse momentum π^o's (2.5 GeV/c<p_⊥<9 GeV/c) were made near 90° at the CERN ISR at five centre-of-mass energies (√s = 23.5, 30.6, 44.8, 52.7 and 62.4 GeV. At large p_⊥, the invariant cross-sections are seem to vary with s and p_⊥, in good agreement with a fit of the form Ap_⊥^?nF(p_⊥/√s), with n≈8 and F(p_⊥/√s)≈exp(?26p_⊥/√s).     

Simple microscopic model for the scalar-isoscalar component of the Landau-Migdal amplitude

A simple microscopic model is proposed that describes the coordinate dependence of the zeroth harmonic f ₀(r) of the scalar-isoscalar component of the Landau-Migdal amplitude. In the theory of finite Fermi systems due to Migdal, such a dependence was introduced phenomenologically. The model presented in this study is based on a previous analysis of the Brueckner G matrix for a planar slab of nuclear matter; it expresses the function f ₀(r) in terms of the off-mass-shell T matrix for free nucleon-nucleon scattering. The result involves the T matrix taken at the negative energy value equal to the doubled chemical potential μ of the nucleus being considered. The amplitude f ₀(r) found in this way is substituted into the condition that, in the theory of finite Fermi systems, ensures consistency of the self-energy operator, effective quasiparticle interaction, and the density distribution. The calculated isoscalar component of the mean nuclear field V(r) agrees fairly well with a phenomenological nuclear potential. Owing to a strong E dependence of the T matrix at low energies, the potential-well depth V(0) depends sharply on μ, increasing as |μ| is reduced. This effect must additionally stabilize nuclei near the nucleon drip line, where μ vanishes.     

The nucleon axial form factor and the pion-nucleon vertex function

The nucleon axial current and related form factors are investigated in a model of relativistic quarks confined by a scalar potential of the formM(r)=c r ⁿ , with special emphasis on center-of-mass corrections and pionic effects. Pionic contributions to the axial form factorG _A (q ²) from af _π?_μφ term with constantf _π are demonstrated to vanish. The pion-nucleon form factorG _πNN (q ²) is derived and turns out to be longer ranged thanG _A (q ²). The induced pseudo-scalar form factorG _p (q ²) is shown to be connected toG _πNN (q ²) by the standard PCAC relation, contributions from the quark core toG _p (q ²) being negligibly small.     

3He Transverse Electron Scattering Response Function with �� Degrees of Freedom

A calculation of the ³He transverse (e, e??) inclusive response function, R _T , which includes ?? degrees of freedom is performed using the Lorentz integral transform method. The resulting coupled equations are treated in impulse approximation, where the NNN and NN?? channels are solved separately. R _T is calculated for the breakup threshold region at a momentum transfer of q?=?862 MeV/c.     

Electromagnetic form factors of nucleons in a relativistic square-root potential model of independent quarks

The nucleon electromagnetic form factorsG _E ^P (q²),G _M ^P (q²) and the axial-vector form factor G_A(q²) are studied in a relativistic model of independent quarks confined by an equally mixed scalar-vector square root potentialV _q(r)=1/2(1+γ ⁰)(ar ^1/2+ν ₀) taking into account the appropriate centre-of-mass corrections. The respective root-mean-square radii associated withG _E ^P (q²) and G _A (q²) come out as [〈r ²〉 _E ^P ]^1/2=0.86 fm and 〈r _A ² 〉^1/2=0.88 fm. Restoration of chiral symmetry in this model is discussed to derive the pion-nucleon form factorG _πNN(q²) and consequently the pion-nucleon coupling constant is obtained asg _πNN(q²)=12.81 as compared tog _πNN(q²)_exp⋍13.     

Production of pion and muon pairs in e±e− colliding beams. Extension of the equivalent photon approximation

The reactions e^?e^?→e^?e^?π⁺π^?(μ⁺μ^?) are considered here in the situation where only pions (muons) are recorded and k_⊥ (total transverse momentum of the pair) is not too small (roughly speaking m_e²?k_⊥²?m_π²); this domain gives the main contribution to the cross section. In this paper the differential cross sections have been obtained to an accuracy of (Ink_⊥²/me²)^?1k_⊥/m_π. The amplitudes with one scalar photon have to be taken into account in this approximation. Also the charge asymmetry appears due to the interference of the two-photon and bremsstrahlung diagrams. It is shown what information on amplitudes of the reaction γγ→π⁺π^? and on the pion electromagnetic form factor can be obtained from an experiment in the given set-up.