IWB analysis of scattering and fusion cross sections for the 12C+12C, 13C+16O and 16O+16O reactions for energies near and below the Coulomb barrier

Calculations are presented of the elastic scattering and fusion cross sections for the astrophysically interesting reactions ¹²C+¹²C, ¹²C+¹⁶O and ¹⁶O+¹⁶O. The calculations are performed using the incoming wave boundary condition (IWB) and a real ion-ion interaction potential. The results are compared with the available experimental data for the energy region near and below the Coulomb barrier. With values of two adjustable potential parameters (the radial position of the l = 0 barrier and the diffuseness) determined by fitting elastic scattering data, good agreement is obtained for the average energy dependence of the ¹²C+¹²C and ¹²C+¹⁶O fusion cross sections. In the case of ¹⁶O+¹⁶O, both the calculated absolute magnitude and the energy dependence of the fusion cross section are inconsistent with the data and this discrepancy is discussed.     

Direct neutron scattering from 182W and 184W

Differential elastic and inelastic neutron scattering cross sections for ¹⁸²W and ¹⁸⁴W have been measured at incident energies 4.87 and 6.00 MeV. Cross sections for the first (0⁺, 2⁺, 4⁺, 6⁺), second (0⁺, 2⁺), and some higher excitations are presented. Angular distributions exhibit direct reaction characteristics, suggesting that compound cross sections for these states are small. This is supported by statistical-model calculations. Coupled-channel calculations of cross sections are made using a phenomenological deformed optical potential. Quadrupole and hexadecapole deformations have been searched to optimize fits. The necessity of introducing a β₆ deformation is investigated. Electric multipole transition matrix elements, used in the coupled-channel analysis, are obtained from the rotation-vibration model and the dynamic-deformation theory.     

Elastic and inelastic scattering of 18O by 16O and 18O

Angular distributions have been measured for the elastic and inelastic scattering of ¹⁸O by ¹⁶O and ¹⁸O at laboratory bombarding energies of 42 and 52 MeV. The inelastic scattering data are analyzed in terms of collective excitations using a coupled channel approach. Deformation parameters are obtained for the strongly excited states. The relationship between the strength of inelastic scattering and the amount of structure in the elastic scattering distributions is discussed.     

Energy levels of O between 10.0 and 17.1 MeV excitation

A phase-shift analysis has been performed on ¹²C(α, α₀)¹²C cross sections which were measured over a broad angular range from 4.0 to 13.3 MeV in 15 to 50 keV increments. In addition to confirming the presence and determining the J, π, Γ, Γ_α, of the levels at 10.36, 11.50, 11.60, 12.47, 13.10, 13.11, 13.13, 13.25, 13.89, 14.07, 14.6, 14.82, 14.87, 15.47 and 16.30 MeV excitation in the ¹⁶O compound system, the results include the observation of a new 0⁺ level at 15.17 MeV. Definite J^π values of 4⁺, 5⁻ and 3⁻ have been assigned for the levels at 14.6, 14.82 and 15.47 MeV respectively. Refined level parameters are given for the 0⁺ (14.07 MeV) and 6⁺ (14.87 MeV) levels.     

The particle-hole spectra of 16O and 16N as observed in pick-up reactions from 17O

The reactions ¹⁷O(d, t) ¹⁶O and ¹⁷O(d, τ)¹⁶N have been investigated at E_d = 52 MeV. Energy spectra of tritons and τ-particles have been measured simultaneously up to excitation energies of 22 MeV in ¹⁶O and 10 MeV in ¹⁶N, respectively. Spectroscopic factors have been obtained by a DWBA analysis of the measured angular distributions. From the comparison of the t- and τ-spectra analog (T = 1) states in ¹⁶O could be identified and the distribution of T = 0 and T = 1 spectroscopic strengths could be deduced. Nearly the total $\text{1}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and $\text{1}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ hole strengths have been found and the $\text{1}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{1}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{and}\text{1}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{1}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$ particle-hole multiplets could be located both for T = 0 and T = 1. The average residual interactions in both shell-model configurations turned out to be strikingly different.     

Study of the 182W(t,p)184W reaction at 20 MeV

The ¹⁸²W(t, p)¹⁸⁴W reaction has been studied at 20 MeV. The outgoing protons were detected in an Elbek broad range magnetic spectrograph. Absolute cross sections and angular distributions were measured. Evidence for inelastic effects in the reaction mechanism was observed for the first excited 2⁺ state, the 3^? level at 1221 keV and the 5⁺ state at 1295 keV. The 0⁺ level at 1002 keV was populated with ≈ 2% the ground state cross section. A 4⁺ level at 1536 keV was observed with ≈ 50% the ground state cross section. Calculations of the absolute (t, p) cross sections to this and other states with known structure resulted in excellent agreement with the measured values.     

Two-amplitude model of pion DCX applied to the 18O angular distribution and excitation function

An earlier model developed to fit the DCX excitation function of ¹⁸O has been extended to account for the $\text{T}{}_{\mathrm{\pi }}\text{= 164}\text{MeV}{}^{18}\text{O DCX}$ angular distribution in terms of that for ¹⁶O and a double-isobaric-analog transition.     

Enhancement of two-proton transfer in N = 82 nuclei: A study of 1p, 2p and (2p+2n) transfer reactions induced by 16O on 140Ce, 142Nd and 144Sm near the Coulomb barrier

One-proton, two-proton, and α-particle transfer have been studied on nuclei with closed neutron shell N = 82 using ¹⁶O beams of 63 to 66.5 MeV incident energy. Transfer probabilities defined in a semiclassical model are derived for the different reaction channels. For this purpose the Q-value and angular dependence of the cross section are discussed. The two-proton transfer to the ground states shows an enhancement by a factor 20–25 compared to other nuclei, showing the effect of the proton pairing in these nuclei (they correspond to equivalent neutron configurations in ^{108, 110, 112}Sn). The total transfer probability follows a common trend for all three target nuclei as a function of energy above the Coulomb barrier for the proton and two-proton transfer, respectively, but not for the four-nucleon transfer.     

Elastic and inelastic scattering of 16O and 12C by 24Mg near the Coulomb barrier

Angular distributions for ¹⁶O + ²⁴Mg and ¹²C + ²⁴Mg elastic and inelastic (2⁺, 1.37 MeV state in ²⁴Mg) scattering have been measured at energies spanning the Coulomb barrier. Apart from the structure typical of strong destructive Coulomb-nuclear interference, the data exhibit some additional specific features. Coupled channel calculations were performed, along with DWBA calculations to analyse the data using fixed coupling strengths deduced from the results of Coulomb excitation work. The importance of higher-order effects such as reorientation, is demonstrated.     

An experimental study of He elastic,inelastic and charge-exchange scattering from Li

A target of ⁶Li was bombarded with the ³He beam from the University of Illinois cyclotron. Differential cross sections for the elastic scattering, the inelastic scattering to the first two excited states of ⁶Li, and the (³He, t) charge-exchange reaction to the ground state of ⁶Be were determined over angular ranges of approximately 20° to 115° (c.m.) at ³He energies of 24.6 MeV and 27.0 MeV. (The weak inelastic transition to the 3.56 MeV state of ⁶Li, ordinarily obscured by a background of three-body break-up, was observed by requiring a coincidence at most angles between the scattered ³He and the ⁶Li recoil.) The ratio of the integrated charge-exchange cross section between 55° and 115° to the integrated inelastic cross section for this transition (both with ΔT = 1) is somewhat less than expected from isospin considerations (i.e., about 1.6 instead of 2.0).     

9Be + 12C, 9Be + 16O,9Be + 19F reactions at energies below the barrier

The ¹⁶O + ⁹Be reactions have been studied from E_c.m. = 2.0 MeV to 5.1 MeV, an energy near the top of the Coulomb barrier. The cross section for the neutron transfer reaction ⁹Be(¹⁶O,¹⁷O¹ (0.87 MeV))⁸Be has been measured over this range by detecting the prompt 0.87 MeV γ-rays. The total fusion cross section has been determined from E_c.m. = 2.8 to 5.1 MeV by observing individual γ-ray transitions in the evaporation residues with a Ge(Li) detector, and then summing the separate yields. Direct processes are found to dominate the reaction yield below E_c.m. = 4 MeV. A comparison of the energy dependence of the fusion cross section for this reaction and the ¹²C + ¹³C reaction, which proceeds via the formation of the same compound nucleus, ²⁵Mg, reveals differences at sub-barrier energies. Optical model and incoming-wave boundary condition calculations are presented. Data have also been obtained for the near optimum Q-value neutron-transfer reactions ⁹Be(¹²C, ¹³C¹)⁸Be and ⁹Be(¹⁹F, ²⁰F)⁸Be, and these are discussed in terms of a simple model of sub-barrier direct reactions.     

The (p, t) and (p, τ) reactions on O at 39.8 MeV

Differential cross sections have been measured at forward angles for (p, t) and (p, τ) transitions from ¹⁷O to the ⁻ ground states and lowest-energy ⁻ states in the ¹⁵O and ¹⁵N mirror nuclei. The data are compared with DWBA calculations using simple single-particle and single-hole wave functions. When the (p, t) and (p, τ) transitions are considered separately, the calculated and experimental ratios of the ⁻ integrated cross sections to the ⁻ integrated cross sections agree to within 30 %; however, the ratios of (p, τ) cross sections to the mirror state (p, t) cross sections are calculated to be about twice as large as actually measured. This experimentally observed reduction of the (p, τ) cross section relative to the (p, t) cross section can possibly be attributed to interference between the S = 0 and S = 1 components of the (p, τ) transitions.     

18O(p,p)18O and18O(p,p′)18O1for E = 6.1−16.6 MeV

Angular distributions of cross sections and analyzing powers have been measured for ¹⁸O(p, p)¹⁸O and ¹⁸O(p, p₁)¹⁸O¹(1.98 MeV) for proton energies between 6.1 and 16.6 MeV. The measurement were crarried out in 25 keV intervals between 6.1 and 8.0 MeV, and in 100 keV intervals between 8.0 and 16.6 MeV. Although the general appearance of the angular distributions changes quite smoothly with energy above about 8 MeV, structure is evident in the backangle excitation functions up to 14 MeV. A phase-shift analysis of the elastic scattering data yielded resonance parameters for 25 levels in ¹⁹F in the excitation enrgy region 13.8?21.4 MeV. A large fraction of these levels have odd parity, and the energies of the $\text{1}\text{2}{}^{\mathrm{?}}$ and $\text{3}\text{2}{}^{\mathrm{?}}$ levels coincide closely with peaks seen in the ¹⁹F photonuclear yield curves. A simple model involving proton single-particle states coupled to the 2₁^+; and 3₁^? levels of ¹⁸O is able to account for some features of the observed structure. The energy-averaged elastic and inelastic scattering data for E_p > 12 MeV agree reasonably well with the spherical optical model and the DWBA, respectively, as well as with coupled-channels calculations.     

Study of the Cl(He,p)Ar reaction

Angular distributions of protons from the ³⁵Cl(³He, p)³⁷Ar reaction have been measured at bombarding energies between 9 and 14 MeV. The 14 MeV data are compared with DWBA calculations based on various sets of shell-model wave functions.     

The elastic scattering of 33 MeV He particles from Ni,Cu and Zn

Differential cross sections have been measured for the elastic scattering of 33 MeV ³He particles from targets of ^58,60,62,64Ni,^63,65Cu and ^64,66,68Zn over the angular range 5° to 175°. The data have been analysed with the optical model, with particular emphasis on the investigation of the ambiguities in the real potential, the form of the imaginary potential and the use of a spin-orbit term.     

Circular polarization of neutron capture γ-rays from Mn,Ni, Ga and W

Capture γ-ray circular polarization measurements on the Mn(n, γ), Ni(n, γ), Ga(n, γ) and W(n, γ) reactions with polarized neutrons resulted in unambiguous spin assignments for 20 levels, 10 of which confirmed previous assignments. For another 20 levels the number of possible spin values has been reduced.     

Dispersion relations and low-energy elastic scattering of charged particles from nuclei: (II). Application to N-4He scattering

A “Coulomb-modified” dispersion relation is applied to low-energy p-⁴He forward elastic scattering. To check the validity of the modification, the results are compared with those deduced from n-⁴He elastic scattering. Completely analogous information is obtained for the two processes. The exchange of three bound nucleons is found to contribute strongly to N-⁴He forward scattering. The corresponding ⁴He-³H-p and ⁴He-³He-n coupling constants are evaluated as R_p = 3.8±0.3 and R_n = 3.0±0.3, respectively. These constants are related to the strength of the asymptotic wave function of nucleons in ⁴He and thus to the tail of the nucleon distribution. A comparison of R_p with the empirical proton distribution in ⁴He as deduced from e-⁴He elastic scattering shows excellent agreement. From R_p and R_n the effective ranges of the singlet ³H-p and ³He-n interactions in the ground state of ⁴He are determined to be equal, in accordance with charge symmetry, and to have a value of r_eff = 1.072±0.006 fm.     

Self-consistent center-of-mass correction and the charge form factor of He

The Hartree-Fock approximation is used for ⁴He in the case of Lipkin's Hamiltonian with several nuclear forces. The self-consistent solution practically coincides with the one obtained in the usual HF method applied to the intrinsic Hamiltonian; however, the center of mass is now in its ground state, and its motion is fairly separated in the ground state function of the nucleus. An unambiguous comparison between experimental and theoretical charge form factor is done. The discrepancies cannot be interpreted as due to spurious c.m. effects.