Structure of 13C from an R-matrix analysis of 12C + n scattering and reaction cross sections

Differential cross sections for ¹²C + n elastic and inelastic scattering and for the ²C(n, α) ⁹Be reaction, together with high resolution total cross-section data were analyzed by means of a multilevel multichannel R-matrix program to determineJ, π, and γ_λc for states in ¹³C up to E_x = 13.5MeV. Good overall fits to the data were obtained throughout this large energy range. Spin and parity assignments for thirteen states above E_x = 9.5MeV for which there had been either no previous J^π assignments or only tentative assignments have been made in this study. The present results are in good agreement with previous analyses and model calculations.     

P-Matrix analysis of the dibaryon1 D 2 resonance

We study the relation between intermediate energy nucleon-nucleon scattering and the eigenstates of the bag model using theP-matrix formalism. Data of existing phase-shift analyses are employed to calculate theP-matrix for the coupled¹ D ₂(pp) and⁵ S ₂(NΔ) channels in the energy region above the Δ-isobar production threshold. TheP-matrix calculated for the equivalent hadronic bag radiib=1.4?1.5 fm is shown to have a pole in the mass range 2.31–2.34 GeV in agreement with the MIT bag model prediction of theI=1,J ^P =2⁺ 6-quark state with the mass 2.34 GeV. The hadronic shift of this state is shown to be ≈200 MeV; the dibaryon pole of theS-matrix is located at the energy 2.15–2.17 GeV with the width ≈100–200 MeV.     

Analyses of electron and proton scattering to low-excitation isoscalar states in 20Ne, 24Mg and 28Si

The excitation of low-lying isoscalar 2⁺ and 4⁺ states in ²⁰Ne, ²⁴Mg and ²⁸Si by electron and proton scattering is studied. Large basis models of nuclear structure are used to determine both the electromagnetic and hadronic transition densities. The analyses of the longitudinal form factors obtained from electron scattering show that little or no effective charges are required with these nuclear structure models. Proton inelastic scattering to these states then is analysed to test effective forces based upon the Paris and Hamada-Johnston interactions. At intermediate energies (155 MeV) density-dependent t-matrices from both potentials were used with fits to data giving a clear preference for that based upon the Paris interaction. For lower energies only the Hamada-Johnston t-matrix is available and comparison of analyses of 24 and 49 MeV data made using this (complex) t-matrix with those in which the (real) Paris G-matrix is used as the effective force show a clear preference for the t-matrix. This is particularly the case with analyses of polarization data and suggests that the use of the G-matrix as an effective force in nuclear reaction calculations is inadequate even at low energies.     

Two-pion spectra for the reaction π− p → π0π0 n at a pion momentum of 38 GeV/c and combined analysis of GAMS, Crystal Barrel, and BNL data

We perform a K-matrix analysis of IJ ^PC =00⁺⁺, 10⁺⁺, 02⁺⁺, and 12⁺⁺ meson partial waves using GAMS data on π^? p → π⁰π⁰ n, ηηn, ηη'n that are supplemented with BNL data on π^? p → K $\bar K$ n and Crystal Barrel data on p $\bar p$ (at rest) → π⁰π⁰π⁰, π⁰ηη, π⁰π⁰η. The positions of the amplitude poles (physical resonances) are determined, together with the positions of the K-matrix poles (bare states) and the values of barestate couplings to two-meson channels. The nonet classification of the bare states found in the present analysis is discussed.     

Observation of a spin 4 neutral meson with 2 GeV mass decaying in π° π°

The invariant mass spectrum of neutral meson states from π^?p interactions at 40 GeV/c incident momentum has been investigated in a high statistics experiment performed at the 70 GeV IHEP accelerator. To detect the high energy photons coming from the produced neutral states, a hodoscope spectrometer with a computer on-line was used. A clear structure on the mass spectrum of dipions produced in the reaction π^?p→π°π°n is observed at 2 GeV. The decay angular distributions show in this mass region the variation with mass typical of a state with a spin J = 4. The mass of the observed meson is found to be M = (2020±30)MeV and the estimate of the full width is (180±60) MeV.     

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.     

s- and p-wave neutron spectroscopy. Xe. Intermediate structure in 90Y and the generalized R-matrix theory

The resonance structure observed in the ⁸⁹Y(n, n)⁸⁹Y total cross section measurements in the range of 0.3 to 1.2 MeV incident energy was investigated using the generalized R-matrix theory of nuclear reactions and the doorway interpretation of intermediate structure. The energies and wave functions of the doorway resonances were calculated in a 2-particle and 3p-1h basis of the shell model. The model space and the parameters of the model calculation chosen were consistent with other shell model calculations in the mass-90 region. Several strong p-wave doorways with J^π = 0⁺, 1⁺, and 2⁺ were predicted by the model in the energy range studied. This is due to proximity of p-wave giant resonance. The escape widths Γ^↑ and the spreading widths Γ^↓ for these states were evaluated using the model wave functions and the R-matrix formalism. The calculated energy dependence of the total cross section shows that most of the predicted doorways are in general agreement with the observed anamolies with similar relative strength. More significantly, the underlying p-wave gross structure representing a grand average is of very similar shape in both theory and experiment. As expected in the mass 90-region, the s- and d-wave doorways contribute less significantly to the calculated resonance structure.     

Can spin-flip quadrupole resonances be observed?

Shell model calculations ofJ=2⁺,S=0 andS=1 states indicate that the spin flip quadrupole strength is much more fragmented than itsS=0 analog, at least in light nuclei. A sum rule technique is then used to study the coexistence betweenS=0 andS=1 states; it illustrates why theS=0 strength is fairly immune to changes in the noncentral part of the nuclear interaction. In¹⁶O, someE2 spin flip strength is predicted to lie in the 40 MeV region where it could be located by inelastic electron and pion scattering experiments.     

Thermal spectrum in leaky cavities: A string model

A leaky cavity is an example of a dissipative quantum system. The thermal spectrum of such a system can be expressed exactly in terms of a generalized density of states π^c(ω) for the cavity. The latter is evaluated for a string model; compared to the zero leakage limit, each δ-function is replaced by a pair of poles in the ω-plane, related to the poles of the S-matrix.     

<Emphasis Type="Italic">T</Emphasis>-invariance conditions for sequential multistep statistical nuclear reactions

A generalized version of the R-matrix theory is used to determine the amplitudes of sequential n-step statistical nuclear reactions. T-invariance conditions for these amplitudes are analyzed. Within the scope of the unified theory, integral formulas are constructed for the decay amplitudes of the intermediate states of compound nuclei via the matrix elements QHP of the system Hamiltonian H, where Q and P operators perform projections onto resonance and energy-continuous states of the system, respectively.     

Time-dependent mean field S-matrix theory

By using the path integral approach to many-body systems, we formulate a time-dependent mean field S-matrix theory of nuclear reactions. Many-body channel eigenstates are constructed by using projection techniques. In this way the S-matrix between the channel eigenstates is expressed as a superposition of S-matrix elements between wave-packet-like states localized in space and time. A field operator representation of the interaction picture S-matrix is derived which enables one to apply the path integral approach. Applying the stationary phase approximation to the path integral representation of the interaction picture S-matrix between the localized states an asymptotically constant time-dependent mean field approximation to this S-matrix is obtained. Finally, the S-matrix between the projected channel eigenstates is obtained by evaluating the integral, arising from the projections, over the space-time positions of the localized states in the stationary phase approximation. The stationary phase conditions select those localized states from the projected channel states for which the mean field values of energy and momentum coincide with their corresponding channel eigenvalues.     

The structure of 32S I. Spectroscopy of highly-excited states

Assignments of I, π, T are made to 30 levels in ³²S between 7.35 and 11.76 MeV excitation energy, making the spectroscopy of the T= 0 states rather complete up to 10 MeV and that of the T = 1 states up to 12 MeV. A reassessment of existing data in the light of the new results clarifies the spectrum of I ^π = 1⁺, T = 1 states up to 15 MeV excitation energy. High-spin states (I = 52 - 7) below 10 MeV excitation energy have been investigated by n t γ angular-correlation measurements with the ²⁹Si(α, nγ) reaction at E _α 14.4 MeV. Five g-wave resonances of the ³¹P(p, γ) reaction, leading to the formation of I _π + 4⁺, 5⁺ states in ³²S, have been identified between 10 and 12 MeV excitation energy. The spectrum of T = 1 states between 10.7 and 12 MeV, has been investigated by measurements of γ-ray angular distributions on resonances of the ³¹P(p, γ) reaction and by measurements of resonance strengths. Several ³²S levels between 7.35 and 8.75 MeV excitation energy were studied as final states in resonance decays. Finally a search was performed for I ^π = 0⁺ resonances of the ²⁸Si(α, γ) reaction.     

Correlation investigations of the low-energy 10He spectrum

The spectrum of low-lying states in the ¹⁰He nucleus is investigated for the two-neutron transfer reaction ³H(⁸He, p)¹⁰He. The secondary beam of ⁸He nuclei with the energy 21.5 MeV/nucleon and a cryogenic tritium target are used in the experiment. The ¹⁰He ground state is observed in the missing mass spectrum at the energy of 2.1 MeV (Γ ～ 2 MeV) above the decay threshold. Analysis of the angular correlations of the ¹⁰He decay products yields the spin and parity of two excited ¹⁰He states, J ^π = 1^? in the energy range from 4 to 6 MeV and J ^π = 2⁺ at energies above 6 MeV.     

The 18O(p, α)15N cross section at low energies

The ¹⁸O(p, α)¹⁵N reaction cross section has been measured over the energy range 661 keV > E_c.m > 223 keV. The S-function was extrapolated to energies of astrophysical interest using the R-matrix theory. The S-factor, S₀, is estimated to be 46 MeV · b which is a factor of 3 larger than the value used in a recent tabulation of nuclear reaction rates. The effects of broad levels near the proton threshold are discussed.     

s- and p-wave neutron spectroscopy Xf(i). Intermediate structure in the 28Si + n reaction: R-matrix interpretation of experimental data

A multilevel R-matrix analysis of Si neutron cross-section data measured at NBS has been performed up to about 4.5 MeV neutron energy. Only a small fraction of the p- and s-wave s.p. strength is observed, but both exhibit local concentrations of strength indicative of doorway structure around 1 and 0.2 MeV, respectively. Besides the well-known 180 keV, strong, $\text{1}\text{2}{}^{\mathrm{+}}$ resonance, the s-wave resonance structure is of moderate strength and widely distributed. The f- and d-wave assignments are not unambiguous, but J > 3/2 resonances show strong signs of intermediate structure for d-waves. A possible correlation between neutron and gamma decay channels and the connection between the states observed in (n, n), (d, p), (n, γ), and (γ, n) channels is discussed. A coreparticle doorway interpretation for s and p- waves is presented.     

The 12C(α, γ)16O reaction and stellar helium burning

The cross section for the reaction ¹²C(α, γ)¹⁶O has been measured for a range of c.m. energies extending from 1.41 MeV to 2.94 MeV, by using ¹²C targets of high isotopic purity, large NaI(T1) crystals, and the time-of-flight technique for the suppression of prompt neutron background and time-independent background. Gamma-ray angular distributions were measured at c.m. energies of 2.18, 2.42, 2.56 and 2.83 MeV. By means of theoretical fits, which include the coherent effects of the 1^? states of ¹⁶O at 7.12 MeV, 9.60 MeV, and those at higher energies, the electric-dipole portion of the cross section at astrophysically relevant energies has been determined. A three-level R-matrix parametrization of the data yields an S-factor at E_c.m. = 0.3 MeV, S(0.3 MeV) = 0.14^+0.14_?0.12 MeV · b. A “hybrid” R-matrix optical-m parameterization yields S(0.3 MeV) = 0.08^+0.05_?0.04 MeV · b. This S-factor is of crucial importance in determining the abundances of ¹²C and ¹⁶O at the end of helium burning in stars.     

Dynamics of pion double-charge-exchange reactions

The (π⁺, π^?) reactions leading to the double isobaric analog state are studied at pion energies 50 to 300 MeV, with¹⁴C as an example. Effects of nuclear structure, nuclear recoil, the reaction pathway and off-shell πN interactions are examined in detail. Our study reveals a very strong dependence of calculated cross sections on off-shell πN dynamics. Consequently, use of a self-consistent off-shell πN theory is essential to studying short-range nucleon-nucleon correlations from double-charge-exchange data. The present study further shows that reaction dynamics other than two successive pion single charge exchanges is needed to account for the experimental data.