Excitation function of giant resonances as doorway states in the 12C(p, p′)12C1 reaction between 19 and 23 MeV

Differential cross section and analyzing power angular distributions for the elastic scattering and inelastic scattering to the 2⁺ state at 4.44 MeV and the 1⁺ state at 12.7 MeV have been measured at incident proton energies varying from 19.15 to 23.34 MeV in 200 keV steps. Elastic scattering data are analyzed using an averaged optical model. Coupled-channel calculations reproduce roughly the 2⁺ data. The rapid variation of the data concerning the 1⁺ state is explained by virtual excitation of giant resonances. For each value of the incident energy, the coupling strength for each resonance is found by fitting the experimental angular distributions. The analysis assuming a weak coupling in the compound system gave a satisfactory fit to the cross section but a poor reproduction of the analyzing power. The assumption of a strong coupling in the ¹³N system allowed a good fit of all data. The angular distributions are dominated by the E1 resonance, whose $\text{1}\text{2}{}^{\mathrm{+}}$ component exhausting more than 37 % of the energy weighted sum rule, explains the isotropy of the cross section below 22 MeV. A $\text{7}\text{2}{}^{\mathrm{+}}$ resonance (15 % EWSR) is located at 19.9 MeV. The $\text{5}\text{2}{}^{\mathrm{?}}$ resonance with its maxima at 20.2 and 21.4 MeV, exhausts about 18 % of the sum rule, which is in good agreement with the results of previous works.     

201 MeV proton excitation of giant resonances in 208Pb: Macroscopic and microscopic analysis

The region of the giant resonances in ²⁰⁸Pb has been investigated by inelastic scattering of 201 MeV protons. To test the analysis, angular distributions were measured for the low-lying 3^?, 5^?, 2⁺ and 4⁺ collective states. The giant isoscalar quadrupole resonance (ISGQR) is split into two structures, one at 9.0 MeV with a full width at half-maximum Γ = 1.0 MeV, the other one at 10.6 MeV (Γ = 2.0 MeV), with fine structures at 8.9, 9.3, 10.1, 10.6 and 11 MeV. A macroscopic analysis using the distorted-wave Born approximation (DWBA) leads for the low-lying collective levels, as well as for the ISGQR, to transition probabilities too small by a factor of two, compared with those obtained in other reactions. Microscopic analysis using the distorted-wave impulse approximation (DWIA), with three different sets of random phase approximation (RPA) transition densities, is in very good agreement with the data. At forward angles, in the 12 to 16 MeV excitation energy region, a strong resonance at 13.5 MeV (Γ = 3.6 MeV) is accounted for by the Coulomb excitation of the isovector giant dipole resonance (IVGDR); at larger angles the results are compatible with the excitation of the isoscalar monopole resonance (ISGMR) located at 13.9 MeV (Γ = 2.6 MeV).A resonance located at 21.5 MeV (Γ = 5.7 MeV) appears as the superposition of an isovector quadrupole resonance (IVGQR) excited by Coulomb interaction and a resonance of multipolarity L = 1 ΔT = 0 (ISGDR “squeezing mode”).     

Electroexcitation of 208Pb,distribution of electric dipole and quadrupole strength and fragmentation of the isoscalar quadrupole giant resonance

Low momentum transfer, high-resolution inelastic electron scattering on ²⁰⁸Pb has been used to study the distribution of E1 and E2 strength in the region of excitation energy E_x = 8?12MeV. The E1 and E2 strength is very fragmented and the EWSR strength amounts to (10⁺⁷_?6)% and (29⁺¹¹_?8)% in the investigated energy region, respectively. The E2 strength found is less than most current theoretical predictions but agrees qualitatively with a 1p - 1h +2p - 2h model calculation presented in this paper. The E2 strength is also smaller than what is known from hadron scattering and the shape of the strength distribution is also markedly different in electron and hadron scattering.     

Three-jet distributions ine + e − annihilation: Electromagnetic and weak production

Hard gluon bremsstrahlung off quarks ine ⁺ e ^? annihilation is expected to produce three-jet events. The angular distributions of the jets are calculated for electromagnetic and weak production in the high energy region (Z resonance decay included). Numerical estimates are presented for the vectoraxialvector interference terms within the Weinberg-Salam theory. We discuss (i) angular correlations between jets, (ii) semiinclusive pion distributions and (iii) we comment on angular asymmetries of leptons originating from heavy quark decays.     

A study of the reaction K−p→Λπ+π− at c.m. energies in the range 1.65 to 1.72 GeV

Results are presented of a study of the reaction K^?p→Λπ⁺π^? in the c.m. energy region of 1.65 to 1.72 GeV. Dalitz plots indicate that the reaction proceeds primarily through the intermediate states Σ^?(1385)π⁺ and Σ^?(1385)π⁺, but the resonance bands intersect inside the kinematic ellipse and a simple quasi-two-body interpretation is not possible. Legendre coefficients are presented for the angular distributions of the Λπ⁺ and Λπ^? sub-systems in the overall c.m. frame. Analogous coefficients as suggested by Deler and Valladas, which describe the angular distribution of the final three-body state are also presented.     

The 56Fe(α, γ)60Ni reaction at excitation energies in the region of the giant dipole resonance

Excitation functions for the ⁵⁶Fe(α, γ₀)⁶⁰Ni and ⁵⁶Fe(α, γ₁)⁶⁰Ni reactions have been measured at 90° to the beam direction over the bombarding energy range 8.0–17.6 MeV. Gamma-ray angular distributions were measured at ten bombarding energies. Excitation functions for the ⁵⁹Co(p, γ₀)⁶⁰Ni and ⁵⁹Co(p, γ₁)⁶⁰Ni reactions were measured over the range E_x = 16.58–16.92 MeV and compared with the (α, γ) data. The angular distribution data indicate that the (α, γ₀) and (α,γ₁) reactions proceed through 1^?, and 1^? and 3^? states, respectively. The (α, γ) excitation functions are discussed with respect to isospin splitting of the ⁶⁰Ni giant dipole resonance. The fine structure observed in the excitation functions is shown to be most probably due to Ericson fluctuations. The gross (α, γ) cross sections are shown to be in reasonable agreement with the results of calculations made using the theory of Hauser and Feshbach assuming excitation of the giant dipole resonance.     

Investigation of giant E3 resonances by (N, γ) reactions

Effects related to the presence of giant E3 resonances are investigated by nucleon radiative capture according to the direct-semidirect model. The γ-ray angular distributions from the ²⁰⁸Pb(N, γ₀) reactions are calculated in the energy region above the giant dipole resonance and the influence of the E1–E3 and E2–E3 interferences is discussed. The results provide indications of an appreciable effect on the 90° photon emission when a collective isovector E3 excitation is present.     

Elastic π± scattering on 4He, 16C, 16O and 40Ca

A calculation of π⁺ and π^? elastic scattering in the resonance region by four spin-zero nuclei is presented. A non-static first order optical potential which includes binding corrections and short range correlations is used. The comparison with the experimental data shows rather good agreement at and above the resonance but elastic scattering at lower energies is largely overestimated. The calculated angular distributions are more sensitive to the variations of the rms radius than to variations of the surface thickness of the nucleus.     

Positive parity giant multipole resonances in16O

Distributions of the (J =0⁺, 1⁺, 2⁺, 3⁺, 4⁺) isoscalar and isovector strength in¹⁶O have been calculated in then particle —n hole (n=0, 1, 2) shell model. The isoscalar quadrupole giant resonance comes out fragmentated over eight peaks which exhaust 33% of the EWSR betweenE ^*=17 and 25 MeV. This result agrees nicely with the recent³He and alpha inelastic scattering experiments. Giant monopole isoscalar (isovector) resonance appears to exhaust more than 50% of the EWSR nearE ^*=30 MeV (E ^*=40 MeV). Several collective states of other multipolarities are predicted either near to 30 MeV or between 50 and 60 MeV. The ground state correlations of the 2p2h type give rise to a considerable strength redistributions as compared with the case of the closed shell ground state.On leave fromInstitute of Nuclear Physics, Czechosl. Acad. Sci., 250 68 e, Czechoslovakia.     

The energy dependence of 18O(π+, π−)18Ne(gs)

Eight angular distributions measured for ¹⁸(π⁺, π^?)¹⁸Ne(gs) across the Δ₃₃ resonance show the details of the energy dependence of the reaction. At higher energies, the maximum is at q ? 0.85 fm^?1, in agreement with simple sequential scattering models, but a lower energies it is at q ? 0.5 fm^?1, with the transition occuring over a narrow energy range.     

Formalism and applications of electrofission and photofission fragment angular distributions

A formalism for the joint analysis of angular distributions of electro- and photofission fragments is presented, utilizing the vitual-photon spectrum technique in DWBA. This formalism is applied to the study of angular distributions for the electrofission of ²³⁸U, measured near the fission barrier, to obtain information about the low-lying levels (J^π, K) of the transition nucleus. The (2⁺, 0), (1^?, 0), and (1^?, 1) levels, previously detected in photofission experiments, were confirmed. Evidences of a significant contributions of (1⁺, 1), (2⁺, 1)and (2⁺, 2) levels are also presented.     

The isoscalar strength distribution in 24, 26Mg, 28Si and 40Ca obtained from inelastic alpha scattering at 120 Mev

The inelastic α-scattering reaction at E_α = 120 MeV with an energy resolution of 90–150 keV has been used to investigate isoscalar strength distributions in ^{24, 26}Mg, ²⁸Si and ⁴⁰Ca. For ^{24, 26}Mg and ²⁸Si the E2 strength between E_x = 14 and 27 MeV is strongly fragmented. In ⁴⁰Ca the E2 strength is mainly concentrated near $\text{E}{}_{\mathrm{<mtext>x</mtext>}}\text{~ 65 A}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}$ MeV, although here the onset of fragmentation can be observed. The sum rule strength for the different multipolarities was obtained by applying for each nucleus an L-dependent normalization procedure. In this way we observed in total in ^{24, 26}Mg, ²⁸Si and ⁴⁰Ca for excitation energies up to 27 MeV an amount of (61⁺⁸_?6), (50⁺⁹_?8), (38⁺⁸_?6) and (94 ± 14)%, respectively, of the isoscalar E2 energy weighted sum rule (EWSR) of which (36⁺⁷_?5), (28⁺⁸_?7), (24⁺⁷_?5) and (74 ± 12)% was found between E_x = 14 and 27 MeV. In addition isoscalar E0, E3 and E4 strength was observed in this excitation energy region. A detailed comparison has been made between the isoscalar quadrupole strength distribution observed in the ^{24, 26}Mg(α, α') reaction and the E2 strength excitation function obtained from radiative α-capture measurements. In the low excitation energy region coupled channel effects have been observed, especially for the excitation of the 3⁺ states. Moreover, a considerable percentage of the 1?ω isoscalar dipole and octupole strength has been observed for excitations below 14 MeV.     

Phase shift analysis of elastic proton scattering by12C

Angular distributions of the polarization and cross section in¹²C (p,p)¹²C were measured at 24 energies between 9.95 and 10.90 MeV. A phase shift analysis of the data was carried out. The results show four resonances in¹³N atE _x =11.40, 11.64, 11.67 and 11.82 MeV with spins 5/2⁺, 5/2^?, 3/2^? and 3/2⁺.     

Five-pion final state in pp annihilations at 0.70 to 1.1 GeV/c

Results are reported on the reaction $\text{p}\text{p}\text{→ π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{?}}\text{π}{}^0$ at six lab momenta spanning the region from 0.686 to 1.098 GeV/c. The cross section for this process drops from 20.3 ± 1.2 mb at 0.686 GeV/c to 13 1.0 mb at 1.098 GeV/c. Resonance production is determined by means of a model which includes Bose symmetrization, Breit-Wigner amplitudes and Bose-Einstein correlations for the like-charged pion pairs in the nonresonant part of the amplitude. The likelihood fit to the resonance channels yields about 0.8% ηππ, 12% ?^±πππ, 2% fπππ, 8% ωππ, 22% ?^±?⁰π, 13% ω?⁰ and 9% ωf with errors on the order of a few percent. Several percent A₁^±ππ and X(1440)π were also needed to obtain good fits. The ?⁰πππ and ?⁰?⁰π channels as well as A₂ππ and A₁⁰ππ are consistent with zero. Reasonable fits to the mass distributions are obtained. Production angular distributions are found to be essentially uniform. The angular correlations between pion pairs are approximately fit by the simple model of resonance production with Bose symmetrization.     

Near barrier fission channels (Jπ, K) in 238U for spins Jπ=0+, 1−, and 2+ from (e,e′f) angular correlation measurements

Complete in- and out-of-plane fission fragment angular correlations for ²³⁸U have been measured in (e, e′f) coincidence experiments for momentum transfers q_eff=0.20 and 0.28 fm⁻ and excitation energies ω=5.5–15 MeV. A combined analysis with previously extracted E1 and E2/E0 multipole strength distributions yields strength distributions for all 6 near barrier fission channels (J^π, K) = (0⁺, 0), (1⁻, 0), (1⁻, 1), (2⁺, 0), (2⁺, 1), and (2⁺, 2) up to ≈8 MeV. An estim ate of the respective fission barriers, deduced from the increase of the fission cross sections, is given.     

A lowP T parton fragmentation model with diffractive resonance production: Thepp→(π±,K ±)+X inclusive reactions

It is shown that carefully measured momemtum distributions in the inclusive reactionspp→C+X,C=π⁺, π^?,K ⁺,K ^? can be quantitatively understood in a parton fragmentation approach provided both diquark fragmentation as well as diffractive resonance production and decay are taken into a account.     

Excitation of high-spin unnatural parity states in 208Pb from the (p,p′) reaction at 135 MeV

Differential cross sections for the excitation of states at 6.42, 6.73 and 7.04 MeV in ²⁰⁸Pb by 135 MeV protons are reported. Both the excitation energies and the backward peaked angular distributions observed in this experiment and in a recent (e, e′) experiment strongly suggest that these states are predominantly one-particle-one-hole excitations with J^π = 12^?, 14^? and 12^?, respectively. The present (p, p′) data are interpreted using a distorted wave impluse approximation and the effect of configuration mixing between the two 12^? states is investigated.