The (18O,16O) reaction on even tin isotopes

The two-neutron transfer reaction^ASn(¹⁸O,¹⁶O)^A+2Sn has been measured for the isotopes A=112, 116, 118, 120, 122 and 124 at bombarding energies of 57 and 60 MeV together with the elastic scattering. Angular distributions have been analysed for the transitions to the ground state and to the first excited 2⁺ state. The observed ground state transition is strongly enhanced. The theoretical DWBA analysis is performed with a finite range 2n-transfer form factor including recoil correction. The calculated cross section reproduces the observed systematic change over all isotopes. The absolute cross sections are normalized by a factor of 4.7 and 7.5, depending on the two different sets of 2n-wave functions used in the analysis. The results confirm the prediction of the pairing model that the transition strengths of a neutron pair between the ground states of even tin isotopes are the same.     

Nuclear-level densities around Z = 50 from neutron evaporation spectra in (p, n) reactions

Neutron excitation functions, spectra, and angular distributions in the (p, n) reactions on the isotopes ¹¹⁶Sn, ¹¹⁸Sn, ¹²²Sn, and ¹²⁴Sn were measured in the proton-energy range 7–11 MeV. The measurements were performed by the time-of-flight method with the aid of a fast-neutron spectrometer at the EGP-15 pulsed tandem accelerator of the Institute of Physics and Power Engineering (Obninsk). A high resolution (about 0.6 ns/m) and a high stability of the time-of-flight spectrometer made it possible to identify reliably low-lying levels along with the continuous section of the neutron spectra. The data obtained in this way were analyzed on the basis of the statistical equilibrium and preequilibrium models of nuclear reactions. The respective calculations were performed with the aid of the precise Hauser-Feshbach formalism of statistical theory. The nuclear-level densities in the isotopes ¹¹⁶Sb, ¹¹⁸Sb, ¹²²Sb, and ¹²⁴Sb were determined, along with their energy dependences and model parameters. In the excitation-energy range 0–2 MeV, the energy dependence of the nuclear-level densities exhibits a structure that is associated with the shell inhomogeneities of the spectrum of single-particle states near filled shells. The isotopic dependence of the nuclear-level density is discovered and explained. It is also shown that the data obtained here for the nuclear-level density differ markedly from the predictions of model systematics of nuclear-level densities.     

A global optical-model analysis of neutron elastic scattering data

Differential cross sections for neutron elastic scattering in the energy range 7–26 MeV from ⁴⁰Ca, ⁹⁰Zr, ⁹²Mo, ^{116, 124}Sn and ²⁰⁸Pb are analyzed in terms of a global optical-model potential. A smooth variation of the real radius parameters with mass number is investigated. Otherwise, optical-model geometrical parameters are kept fixed at values obtained by averaging individual best fits. The energy and isospin dependences of potential strengths and volume integrals per nucleon are presented.     

A microscopic calculation of inelastic electron scattering to the first 2+ state in some even tin isotopes

We present a calculation of the inelastic electron scattering form factors to the first excited 2⁺ state in the even ^{116, 120, 124}Sn isotopes in the plane wave Born approximation. The states of the even tin isotopes are described in terms of one particle parentage coefficients, which have been obtained self-consistently for the pairing-plus-quadrupole model. The experimentally observed structure of the cross section is well reproduced but the magnitude of the cross section shows the need for a DWBA analysis.     

Neutron inelastic scattering to octupole states in single-closed-shell nuclei

Differential cross sections for the excitation of the first octupole-vibrational state in the closed- neutron-shell nuclides ⁸⁸Sr and ⁹⁰Zr and in the closed-proton shell-nuclei ^{116, 118, 120, 124}Sn by 11 MeV neutrons are presented. The distorted-wave Born approximation is used to obtain deformation lengths, σ(3^?), for each state. Results are compared with earlier measurements of inelastic proton scattering to the same states. Although limited resolution in the neutron time- of-flight spectrometer complicates the interpretation of the Sn data, the overall conclusion that σ_nn′(3^?) ≈ σ_pp′(3^?) is supported by all of the measurements.     

Reaction spectroscopy with even tin isotopes

The two-particle transfer reactions ^{116, 118}Sn(t, p) and the inelastic scattering of 55 MeV protons from ¹¹⁶Sn and 16 MeV protons from ^{116, 118, 120}Sn are analysed for various transitions to collective and non-collective states in the final nucleus using DWBA. Form factors have been calculated with wave functions containing two-quasiparticle excitations of neutrons in open and closed shells as well as 1p-1h transitions from closed proton shells. In the inelastic scattering, generally a Serber-type Gaussian effective interaction was inserted. The results are compared with those obtained on the assumption of two-quasiparticle excitations in a restricted configuration space only. For both types of reaction, reasonable agreement with experimental data is obtained for the angular distribution. In the (t, p) reaction the measured and calculated relative cross sections agree within a factor of two. For the inelastic scattering, apart from relative cross sections the mass dependence of the collective excitations and the influence of four-quasiparticle excitations have been examined. The transition to the collective 2⁺ level in ¹¹⁶Sn was calculated with the proton component of the wave function corrected according to electromagnetic measurements. From inelastic scattering it follows that the transitions to negative-parity states especially are not described satisfactorily by the wave functions used. Cross sections for unobserved higher excited levels have been estimated.     

Investigation of fast neutron interaction with235U

The angular distribution of neutrons emitted by elastic, inelastic and fission processes on²³⁵U were measured at the incident neutron energies of 1.5, 1.9, 2.3, 4.0, 4.5, 5.0 and 5.5 MeV using nanosecond time-of-flight technique. The differential elastic scattering cross sections and their angular distributions at all the seven energies are presented. The total elastic scattering cross sections, angle and energy integrated cross sections for the inelastically scattered neutrons in energy bands of 200 keV, fission cross sections and the angular distributions of fission neutrons were extracted at 1.5, 1.9 and 2.3 MeV incident neutron energies. The energy distributions of the prompt fission neutrons and of the inelastically scattered neutrons are given at the incoming neutron energies of 1.5, 1.9 and 2.3 MeV; and the average fission neutron energies and the inelastic neutron evaporation temperatures were also evaluated at these energies.     

Charge-exchange pigmy resonances of tin isotopes

Charge-exchange states, the so-called “pigmy” resonances, which are below the giant Gamow–Teller resonance, have been studied in the self-consistent theory of finite Fermi systems. Microscopic numerical calculations and semiclassical calculations are presented for nine tin isotopes with the mass numbers A =112, 114, 116, 117, 118, 119, 120, 122, and 124, for which experimental data exist. These data have been obtained in the Sn(³He,t)Sb charge-exchange reaction at the energy E(³He) = 200 MeV. The comparison of calculations with experimental data on the energies of charge-exchange resonances gives the standard deviation δE < 0.40 MeV for microscopic numerical calculations and δE < 0.55 MeV for calculations by semiclassical formulas, which are comparable with experimental errors. The strength function for the ¹¹⁸Sn isotope has been calculated. It has been shown that the calculated resonance energies are close to the experimental values; the calculated and experimental relations between heights of pygmy resonance peaks are also close to each other.     

Comparative analysis of cross sections of residual nuclei on separated tin isotopes at a beam energy of protons and deuterons 3.65 GeV/nucleon

The cross sections of residual nuclei in the separated tin isotopes (¹¹²Sn, ¹¹⁸Sn, ¹²⁰Sn, and ¹²⁴Sn), irradiated with proton and deuteron beams with energy 3.65 GeV/nucleon, are investigated. Parametrization by ten parametric semi-empirical formula was conducted with the aim of determining the total cross sections and analyzing the measurement results. The dependence of total inelastic cross sections on the mass number of the target and the structure of the incoming particle was investigated via the comparison of the obtained data.     

Differential cross section and polarization for 2.63 MeV neutrons scattered from 12C

The differential cross section and polarization of 2.63 MeV neutrons scattered from ¹²C have been measured at eight angles between 17° and 118° in the laboratory system. By simultaneously fitting the cross section and polarization data, a set of scattering phase shifts was obtained. The values of the resulting d-wave phase shifts were larger than those of other existing sets of phase shifts in the energy region. A subsequent R-function analysis, reflecting these larger d-wave phase shifts, gave excellent fits to other experimental data below 3 MeV neutron energy region. The influence of narrow states at 7.50 and 7.55 MeV excitation energy in ¹³C is discussed.     

Cross sections for 197Au(n, γ)198Au and 115In(n, γ)116mIn in the neutron energy region 2.0–7.7 MeV

The cross sections for the reactions ¹⁹⁷Au(n, γ)¹⁹⁸Au and ¹¹⁵In(n, γ)^116mIn have been measured with the activation method in the neutron energy region 2.0–7.7 MeV. The influence of background neutrons on the results was studied in considerable detail. The main problems are caused by low-energy neutrons produced by charged-particle reactions in the target material and secondary neutrons from nonelastic reactions in the sample and surrounding materials.The measured capture cross sections are generally lower than previous results and the deviation tends to increase with increasing neutron energy. The data are also compared with calculations based on the compound-nucleus model and quite good agreement is obtained.     

Measurement of (n,p) cross sections on isotopes of Cd,Sn and Te for 14 MeV neutrons

For several isotopes of Cd, Sn and Te, cross sections for the (n, p) process have been measured by activation relative to ²⁷Al(n, α)²⁴Na. As target materials, natural Cd, Sn and TeO₂ of high purity have been used. Measurements were carried out by γ-detection using a Ge(Li) detector. For measuring short-lived activities, a pneumatic tube system was used. The neutron energy was 14.6±0.2 MeV for all activations. The results obtained for the total (n, p) cross sections show decreasing values with increasing number of neutrons for a given proton number. This trend obviously follows the behaviour of the difference of the proton and neutron separation energies, determining the competition between proton and neutron emission.     

Gamma-gamma energy correlations and moment of inertia in light Xe isotopes

High-spin properties of even ^118–122Xe isotopes have been studied in experiments when a 118 MeV ¹²C beam impinged on ¹¹⁴Cd and ¹¹⁶Cd targets. The γ-rays emitted following the reactions were detected by six NaI(Tl) counters. The coincidence events from the counters were sorted into a two-dimensional matrices, from which the energy-correlation spectra were extracted. From the energy correlation spectra the quantities of the collective moment of inertia $\text{I}$⁽²⁾ are deduced and compared with data obtained for the same nuclei in previous experiments, as well as with results from theoretical studies.     

Analysis of elastic scattering of 0.8 GeV polarized protons from 116Sn and 124Sn

Differential cross section and analyzing power data for elastic scattering of 0.8 GeV polarized protons from ¹¹⁶Sn and ¹²⁴Sn are analyzed in terms of a spin-dependent Kerman-McManus-Thaler formalism. Neutron matter densities and rms radii are deduced with careful attention to sources of error, and found to be in good agreement with Hartree-Fock predictions.     

Possible resonance structure in the elastic scattering of neutrons by Y near En = 1 MeV

The total cross section as well as the differential cross section and polarization in the elastic scattering of 0.8–1.4 MeV neutrons by Y have been measured with neutron beams of energy spread less than 20 keV. Rather weak structure with widths ≈ 50 keV was observed at a few energies within this range. The data were analyzed by use of a model in which the scattering process is described in terms of resonance amplitudes superimposed on an optical-potential background. Although not completely definitive, this analysis indicates the existence of three intermediate-width resonances (two 1^? and one 1⁺) at neutron energies between ≈ 1.0 and 1.2 MeV. The properties of the 1^? resonances suggest that these are the parent states of the proposed T_> components of the El giant resonance observed near 21 MeV excitation energy in ⁹⁰Zr produced in the ⁸⁹Y(p,γ₀) reaction. The resolved resonance structure in this energy region is in reasonable agreement with a recent calculation of the energies and widths of negative-parity states in ⁹⁰Y.     

GDR excitation by isoscalar probes: a means to determine the neutron-skin thickness

Inelastic scattering of α-particles can excite the isovector giant dipole resonance (GDR) via the Coulomb interaction. In spite of their isoscalar nature α-particles can also excite the GDR via the nuclear interaction due to the difference in the radii of the neutron and proton density distributions. The absolute cross section to excite the GDR in inelastic α-scattering is therefore a measure of this radial difference, the so-called neutron-skin thickness. Furthermore, since the GDR strength distribution has a centroid energy which depends on the nuclear radius, these studies, when performed in deformed nuclei, can measure the neutron-skin thickness along both the short and the long axes independently. Results of an experiment performed at KVI atE _α=120 MeV and small scattering angles, including 0°, to determine the neutron-skin thickness in²⁰⁸Pb,¹¹⁶Sn,¹²⁴Sn, and the deformed¹⁵⁰Nd are discussed and compared to earlier measurements and theoretical predictions. Future improvements in the experimental set-up are also discussed.     

Elastic scattering of35Cl from27Al,58, 62Ni,116, 120, 124Sn and141Pr

Elastic scattering angular distributions for³⁵Cl from²⁷Al,^{58, 62}Ni,^{116, 120, 124}Sn and¹⁴¹Pr have been measured at energies between 100 and 170 MeV. Optical model analyses have been performed to determine reaction cross sections, strong absorption radii and grazing angular momenta. The results are compared with the corresponding quantities extracted by means of the Fresnel scattering model. Near the interaction barrier the quarter point method yields reaction cross sections systematically smaller than the optical model results. The interaction radii, however, do not show significant differences or energy dependencies. These radii are compared with trend formulae for interaction radii, and comparisons with fusion radii are made.     

Neutron scattering from 208Pb

Elastic scattering of 7, 9, 11, 20 and 26 MeV neutrons from ²⁰⁸Pb has been measured with the Ohio University Tandem Van de Graaff accelerator. Standard pulsed beam time-of-flight techniques were employed. Measurements of the incident flux at 0° were used to normalize the differential cross sections. The measured cross sections were corrected for dead time, detector efficiency, flux attenuation, multiple scattering, finite geometry, neutron source anisotropy and compound elastic contribution. Relative uncertainties are estimated to be between 5%–10% and the uncertainty in the normalization is estimated to be less than 5 %. The data were used to obtain neutron optical potential parameters. A comparison with proton optical parameters is presented, and the (p, n) quasi-elastic cross section is calculated and compared with available data. Deformation parameters for the 3^? state (Q = ?2.615 MeV) and 5ā (Q = ?3.198 MeV) in ²⁰⁸Pb were obtained at incident energies of 11 and 26 MeV.     

Isovector deformation parameters and core polarization

Analysis of measurements of elastic and inelastic neutron scattering cross sections on ^{116,118,120,122,124}Sn are reported. The isovector and isoscalar quadrupole deformation parameters β₁ and β₀ are obtained in a set of isotopes from a comparison with published parameters from (p, p′) measureements. The relation β₁ > β₀ anticipated from shell model arguments is verified, and its value of about 2 is roughly the same magnitude predicted by the schematic model of core polarization by valence neutrons.