Reciprocal space-time and momentum-space singularities in the narrow resonance approximation

A general scheme is proposed which makes explicit the relationship between the singularities of off-shell amplitudes in position-space and momentum-space in the narrow resonnace approximation. In some ways this may be viewed as a duality scheme for amplitudes involving external quarks, in which narrow resonances in certain channels build the Fourier transform of power singularities in x² (x^μ being a position vector). This scheme is made precise by dual string off-shell amplitudes. As well as highlighting possible connections between the general dual framework and the structure of confined field theories we are able to pinpoint certain grave shortcomings of present dual models.     

Duality,string model and two forward leading particle effect

The dual or string model implies that, in high-energy multiproduction, there are generally, in each hemisphere, two leading particles. Inclusive two-particle spectra from K^?p, π⁺p and π^?p reactions are analyzed with this idea in mind, as well as exclusive data on K^?p → K^?p 2π⁺2π^?. The results agree with the qualitative predictions for this effect. The conventional multiperipheral approach is compared. Theoretical improvements are suggested in the duality framework. Experiments using hyperon beams are proposed to see the effect more clearly.     

The 18O(p, α)15N reaction at stellar energies

The ¹⁸O(p, α)¹⁵N reaction has been investigated in the energy range E_p = 72–935 keV. The three known resonances above E_p = 620 keV have been confirmed and four new resonances have been found below E_p = 340 keV. All observed resonances correspond to known compound states in ¹⁹F. Information on resonance energies, total widths and ωγ values is reported. The low-energy resonances are superimposed on a non-resonant reaction yield, which varies smoothly with beam energy and which exhibits pronounced α-particle angular distributions asymmetric around 90°. The explanation of these data requires either interferring amplitudes of broad resonances with differing parities or a direct (p, α) reaction mechanism. The investigated energy range corresponds to the important temperature range of T = (0.05–2.5) × 10⁹ K. The energy averaged astrophysical reaction rates are compared with predictions.     

Electric-magnetic duality in non-abelian gauge theories

The duality transformation of the vacuum expectation value of the operator which creates magnetic vortices (the 't Hooft loop operator in the Higgs phase), is performed in the radial gauge (x_uA_u^a(x) = 0). It is found that in the weak coupling region (small g) of a pure Yang-Mills theory the dual operator creates electric vortices whose strength is $\text{1}\text{g}$. The theory is self-dual in this region, and the effective coupling of the dual Lagrangian is $\text{1}\text{g}$. (It is self-dual also in the extreme strong coupling region.) Thus the above duality transformation reduces to electric-magnetic duality where the electric field in the 't Hooft loop operators transforms into a magnetic field in the dual operator. In a spontaneously broken gauge theory these results are valid only within the region where the vortices (or the monopoles) are concentrated, or in directions of the algebra space of unbroken symmetry, as self-duality holds only for this subset of fields. Noting that the 't Hooft loop operator project into the subspace of these field configurations we find that it is an electric-magnetic duality for the spontaneously broken theory as well. In the strong coupling region a strong coupling expansion in powers $\text{1}\text{g}$ is suggested.     

Duality for the reggeon-reggeon amplitude: A study through quasi-three-body reactions

We consider reactions of the type ab→cdR in the double-Regge region. The cross sections are proportional to the reggeon-reggeon forward amplitude in the resonance region. Using semi-local duality the cross sections can be written in terms of the relevant triple-Regge couplings which are already known from reggeon-particle scattering, i.e. from analysing data on reactions of the type ab→cR. We compare the predictions of pp→pp (?, f) π^?p→π^?p (?, f) with data at 12, 24 and 205 GeV/c and find encouraging results. We suggest a series of cross sections, the measurement of which will provide a definite test of the duality hypothesis for reggeon-reggeon scattering.     

Duality and symmetry tests for multiparticle production models

Two-body absorptive parts generated by unitarity from multi-Regge particle production models are tested with respect to duality and symmetry structure (suppression of exotics and exchange degeneracy in output). A multi-Regge model with production of only stable particles generates exotic and non-exotic outputs of equal strength; resonances (clusters) are needed to pass these symmetry tests. Two complementary approaches are used, explicit S-matrix models and duality diagrams; the connection between dynamical assumptions and different duality diagram rules is discussed. C-parity plays a crucial role; using C-conserving duality diagrams we show that standard manipulations lead to a topological pomeron which has secondary terms; one, with C_t = ?1, cancels the topological ω₁ meson, another one, with C_t = +1, cancels the topological ?₁ meson.     

Gaussian Multiplicative Chaos and KPZ Duality

This paper is concerned with the construction of atomic Gaussian multiplicative chaos and the KPZ formula in Liouville quantum gravity. On the first hand, we construct purely atomic random measures corresponding to values of the parameter γ ² beyond the transition phase (i.e. γ ² > 2d) and check the duality relation with sub-critical Gaussian multiplicative chaos. On the other hand, we give a simplified proof of the classical KPZ formula as well as the dual KPZ formula for atomic Gaussian multiplicative chaos. In particular, this framework allows to construct singular Liouville measures and to understand the duality relation in Liouville quantum gravity.     

Investigation of 38Ar levels by 37Cl+p reactions: (I). Yield curves,excitation energies and branching ratios

Yield measurements have been performed on the reactions ³⁷Cl(p, p₀)³⁷Cl, ³⁷Cl(p, α₀)³⁴S (E_p = 1.17–1.70 MeV) and ³⁷Cl(p, n₀)³⁷Ar, ³⁷Cl(p.γ)³⁸Ar (E_p = 0.64–2.92 MeV); detailed investigations are restricted to resonances below E_p = 1.79 MeV. Resonance energies, strengths and (some) widths are reported for 12, 26 and 247 resonances in the reactions (p, p₀), (p, n₀) and (p, γ), respectively.Simultaneous (p, α₀) and (p, γ) yield measurements over selected E_p intervals in the E_p = 0.88–1.64 MeV range established the existence of 42 resonances decaying by both γ and α₀ emission. Analysis of the γ-ray spectra of 100 ³⁷Cl(p, γ)³⁸Ar resonances leads to precision excitation energies (ΔE_x = 0.1–2 keV) of 57 bound states (E_x < 8 MeV) and branching ratios of the resonances and of 50 bound states.     

Resonance production and clustering effects in reactions K−p → Λ0 + pions at an incident beam momentum 8.25 GeV/c

We have estimated cross sections for the production of resonances in the reactions K^?p → Λ⁰ + pions. The data have also been analysed by a method which examines event-to-event fluctuations. Within the framework of the simple parametrization of resonance production assumed, the contribution from the resonances is insufficient to explain the observed fluctuations in the longitudinal emission of the final-state particles. These features are well reproduced by an independent cluster emission model.     

(p, γ) Resonance strengths in the s-d shell

The strengths of selected resonances in the range E_p = 0.5–2.0 MeV in the (p, γ) reactions on Mg, ³⁰Si, ³⁴S, ³⁷C1, ³⁹K and ⁴⁰Ca have been found relative to the E_p = 632 and 992 keV resonances in ²⁷Al(p, γ)²⁸Si by relative yield measurements. Targets were made from mixtures or chemical compounds such that each contained at least two of the isotopes of interest and their chemical composition was determined by Rutherford back-scattering of α-particles. Absolute measurements were conducted on the selected resonances in ²⁷A1(p, γ)²⁸Si and ³⁰Si(p, γ)³¹P by semi-thick target and thin target techniques with the target thickness, needed for the latter technique, found by Rutherford back-scattering of protons. Absolute strengths for all of the resonances treated, together with one from each of ²³Na, ³¹P and ³⁵Cl, reported in a previous paper, were deduced by normalizing to the absolute measurements on the Al(p, γ)²⁸Si resonances.     

Strengths of (p, γ) resonances in 33Cl, 35Cl and 28Si

Absolute strength measurements have been performed for the E_p = 580 and 588 keV ³²S(p,γ)³³Cl, E_p = 1214keV³⁴S(p,γ)³⁵Cl and E_p = 633 and 744 keV²⁷Al(p,γ)²⁸Si resonances with a Ge(Li) detector. Results are discussed with regard to the decay of isobaric analog resonances in ³⁵Cl and ³⁷Cl.     

Search for low-energy resonances in 21Ne(p, γ)22Na and 22Ne(p, γ)23Na

The reactions ²¹Ne(p, γ)²²Na and ²²Ne(p, γ)²³Na have been investigated at E_p(lab) = 70–355keV. Neon gas enriched to 91% in ²¹Ne and to 99% in ²²Ne was recirculated in a differentially pumped gas target system of the extended-static and quasi-point supersonic jet type. For ²¹Ne(p, γ)²²Na, new resonances were found at E_p = 126, 272, 291 and 352 keV. The 291 keV resonance corresponds to a new unbound state in ²²Na. Excitation energies, γ-ray decay schemes, resonance widths and strengths as well as J^π assignments are reported for all the resonances. Information on low-lying states in ²²Na is also obtained. Of the 9 expected resonances in ²²Ne(p, γ)²³Na none has been observed. Upper limits on their ωγy strengths are presented. The astrophysical as well as the nulcear structure aspects of the results are discussed.     

Study of inelastic proton amplitudes for a fragmented analogue state in45Sc

The relative sign of inelastic proton-channel amplitudes has been measured for 31 resonances in⁴⁵Sc. These resonances include the fragmented 3/2^? analogue state observed atE ^p=2.62MeV in the⁴⁴Ca(p, p) and⁴⁴Ca(p, p′) reactions. The analogue fine structure is analyzed for the elastic and two inelastic channels; the Robson asymmetry is displayed clearly in the inelastic channels. The relative sign of the mixing ratio remains the same for the 15 fine structure resonances of the analogue. The mixing ratios enable the determination of the amplitude correlation of the widths in the inelastic channels. The recently introduced “off-diagonal strength function” is constructed from these data and compared with the theory of analogue state broadening.     

Inclusive production cross sections of resonances in 32 GeV/c K+p interactions

The inclusive production of resonances is systematically studied in K⁺p interactions at 32 GeV/c. Total production cross sections are given for three baryon resonances, five vector and three 2⁺ tensor mesons. We also compare the central and fragmentation components of the total production cross sections with quark model predictions.     

Investigation of 28Si levels with the (α, γ) and (p, γ) reactions

Particle energies have been measured for resonances in the ²⁷Al(p, γ)²⁸Si and ²⁴Mg(α, γ)²⁸Si reactions with an accuracy of 0.5 × 10^?4 and 1 × 10^?4, respectively. The E_p = 991.88 ± 0.04 keV²⁷Al(p, γ)²⁸Si resonance served as calibration point. From these data the Q-value of the reaction ²⁷Al(p, α)²⁴Mg has been determined as 1600.14 ± 0.21 keV. Excitation energies of ²⁸Si levels have been measured with the ²⁷Al(p, γ)²⁸Si reaction; the reaction energy is Q = 11584.5 ± 0.4 keV.Of 33 resonances observed in the ²⁴Mg(α, γ)²⁸Si reaction (E_α = 1.5–3.8 MeV), energies, strengths and γ-ray decay have been measured; five of these resonances had not been reported previously. The γ-ray angular distribution measurements at three resonances yield the resonance J^π values and the mixing ratios of the strongest transitions involved in the decay. The 10.38 MeV level has J^π = 3⁺, T = 1. The arguments on which T-assignments can be based are critically reviewed. These arguments are used to assign T = 1 character to ¹⁹ states of ²⁸Si.     

Inelastic proton amplitudes forf-wave resonances in55Co

The measurement of inelastic proton channel amplitudes has been extended tof-wave resonances. Ten resonances were studied in the⁵⁴Fe(p, p′γ) reaction, All were established to haveJ ^π = 5/2^?, and inelastic decay amplitudes were determined for these resonances. Elastic and inelastic spectroscopic factors were determined for the 5/2^? analogue state atE _p =3.80 MeV.     

Particle coupling to the octupole state in 89Sr from 88Sr(p,p')88Sr analog resonances and 88Sr(d,p)89Sr

A study has been made of the six most pronounced isobaric analog resonances in the ⁸⁸Sr(p, p')⁸⁸Sr (3^?) excitation function at E_p = 7.65, 7.80, 7.92, 8.78, 9.75, and 9.90 MeV. They are believed to have a simple structure in the parent nucleus ⁸⁹Sr consisting of the lowlying positive-parity, single-neutron spectrum of ⁸⁹Sr weakly coupled to the collective 3^? state in ⁸⁸Sr. A high-resolution ⁸⁸Sr(d, p)⁸⁹Sr experiment was performed to locate small 2f and 3p admixed fragments in ⁸⁹Sr which would allow these analog resonances their entrance widths. In addition, on-resonance ⁸⁸Sr(p, p')⁸⁸Sr (3^?) angular distributions were measured in order to determine the partial waves involved in the exit channel. Results are compared to a particlephonon coupling model, and overall selectivity, strengths, and angular distributions of the (p, p') analog resonances are consistent with the above interpretation.     

Application of off-shell R-matrix theory to the description of resonances observed in 15N(d,p)16N(unbound)

The off-energy-shell behavior of resonances in the ¹⁶N system as observed in the stripping reaction ¹⁵N(d, p)¹⁶N(unbound) is interpreted within the framework of off-shell R-matrix theory. Changes in the size and shape of the resonances in the nucleus ¹⁶N as a function of stripping angle are explained.     

Hydrogen burning of 24, 25, 26Mg in explosive carbon burning

The absolute resonance strengths of the ^24–26Mg(p, γ)^25–27Al reactions have been studied. The absolute values S_c.m.=1.03 ± 0.11, 2.3 ± 0.2 and 2.2 ± 0.2 eV for the frequently used standard resonances at E_p=823, 434 and 454 keV in the reactions ^24–26Mg(p, γ)^25–27Al, respectively, have been determined. In addition, absolute values for use as standards were determined for the 684 keV ²⁵Mg(p, γ)²⁶Al and 840 and 1966 keV ²⁶Mg(p, γ)²⁷Al resonances. New relative values were determined for the strengths of the if²⁵Mg(p, γ)²⁶Al resonances at ifE_{p = 0.3–1.7 MeV} and the ²⁶Mg(p, γ)²⁷Al resonances at E_p = 0.3–2.1 MeV. The resonance energies and total widths obtained in the present work are also given. The branching ratios and angular distributions of the γ-rays used in the absolute strength determinations were obtained in the same set-up as the absolute strength measurement. Using the revised resonance strengths, the astrophysical reaction rates of hydrogen burning of ^24–26Mg in explosive carbon burning in the stellar temperature region of T = (0.1–5.0) × 10⁹ K are compared with Hauser-Feshbach calculations. The present reaction rates are also discussed in the frame of the MgAl cycle.     

(γ, p) cross sections and isospin splitting of the giant dipole resonance in N = 50 nuclei

The differential (e, e'p) cross sections of ⁸⁸Sr, ⁸⁹Y, ⁹⁰Zr and ⁹²Mo have been measured at θ = 90°. The results are used to obtain the (γ, p) cross sections by correcting with the angular distribution data. The (γ, p) cross sections are compared with the (γ, n) cross sections. A resonance corresponding to the T_< GDR is found and another resonance is separated by fitting a Lorentz line with a width equal to that of the (γ, n) GDR. The ratios σ(γ, p)/σ(γ, n) and σ(γ, p₀)/σ(γ, p) show differences between the two resonances. The two GDR resonances are studied from the isospin splitting point of view. The sum rule and splitting energy of the (γ, p) GDR agree well with theory. However, when the sum of the (γ, p) and (γ, n) experimental data is taken, the results are too large to be explained by the T_> GDR.