The boundary condition approach to nucleon-nucleon potentials and the calculation of the T- and K-matrices

It has been shown that the off-shell T- and K-matrices can be obtained by means of boundary conditions imposed upon the off-shell wave function only. When there is a potential outside the boundary condition radius the method proposed permits to deduce in a rather simple way a renormalized Lippmann-Schwinger equation. The S-components of the T- and K-matrices are considered in detail using a potential of the exponential type in the exterior region. For such types of potentials a rather effective method for factorizing the K-matrix is given. Parameter fits to the ¹S₀ and ³S₁ phases are presented.     

Solutions of the integral equations for four identical particles

Using the separable representation of the scattering amplitudes for the subsystems 3 + 1 and 2 + 2, the integral equations for four identical particles with a separable two-particle interaction are reduced to a set of single variable integral equations. By solving the equations obtained, the binding energies and wave functions of the low-lying 0⁺ states of the system of four identical bosons, as well as the scattering length of a particle scattered by three bound particles, are calculated. The solution of the set of integral equations, describing the bound state of four nucleons, is performed, approximating the space wave function by a symmetric one, and the binding energy and wave function of the nucleus ⁴He are calculated.     

Measured lifetimes of states in 197Au and a critical comparison with the weak-coupling core-excitation model

The lifetimes of five excited states in ¹⁹⁷Au up to an excitation energy of 885 keV were measured by the recoil-distance method (RDM). These levels were populated by Coulomb excitation using both 90 MeV ²⁰Ne and 120 MeV ³⁵Cl ion beams. The experimentally determined spectroscopy of the low-lying levels $\text{3}\text{2}{}^{\mathrm{+}}$ (ground state) and $\text{1}\text{2}{}^{\mathrm{+}}$, $\text{3}\text{2}{}_2{}^{\mathrm{+}}$, $\text{5}\text{2}{}^{\mathrm{+}}$, and $\text{7}\text{2}{}^{\mathrm{+}}$ at 77.3, 268.8, 278.9, and 547.5 keV excitation energy, respectively, has been critically compared with the detailed predictions of the de-Shalit weak-coupling core-excitation model. When the model is taken to represent the case of a $\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ proton hole coupled to a ¹⁹⁸Hg core, the model parameters obtained are in accord with the criteria implicit for weak core coupling and, at the same time, are in remarkably good agreement with virtually all measured E2 and M1 transition rates.     

Energy spectra of single neutrons and charged particles emitted following the absorption of stopped negative pions in 4He

Energy spectra have been measured of single neutrons, protons and deuterons emitted following the capture at rest of negative pions in ⁴He. The neutron energy spectrum has been measured with an energy resolution of 4% at 90 MeV. The absolute number of stopped pions has been measured.     

A coordinate-space study of kowalski's three-term separable approximation for the fully off-shell two-nucleon T-matrix

Using elementary coordinate-space methods, we show that a three-term separable approximate fully off-shell T-matrix proposed by Kowalski can be reduced to a simpler expression. This T-matrix incorporates off-shell unitarity exactly, is exact half off the energy shell, and is free from the spurious poles that arise in the Noyes approximation. However, numerical tests employing the wave-function model of Picker, Redish, and Stephenson show that for realistic ¹S_o interactions, the Noyes approximation is more accurate than Kowalski's approximation except near the spurious pole at 250 MeV. We give a plausible explanation of this result.     

The energy dependence of fusion in the 9Be+28Si system

The angular distributions of the energy spectra of the light charged particles (p, d and α) from the ⁹Be + ²⁸Si reaction have been measured in the energy range 12 ≦ E_lab ≦ 30 MeV. The particle evaporation spectra and the angular distributions were analyzed with a spin dependent statistical model. Angular distributions of ⁹Be ions elastically scattered on ²⁸Si have been measured at the energies 12 MeV, 17 MeV, 23 MeV and 30 MeV and were analysed, together with previously measured cross sections, with the optical model. The fusion cut-off angular momentum l_fus(E), the fusion cross section σ_fus(E) and the ratio σ_fus/σ_R^OM(E) were deduced. The excitation function for fusion was analyzed with the Glas and Mosel model. The parameters obtained from the fusion excitation function were compared with the corresponding ones from the ⁹Be + ²⁸Si optical-model interaction potential.     

Formation of covalent nuclear molecules in the 13C + 12C system

Angular distribution's of the elastic scattering of ¹³C on ¹²C and the inelastic scattering leading to the lowest-lying $\text{1}\text{2}{}^{\mathrm{+}}$ and $\text{5}\text{2}{}^{\mathrm{+}}$ states in ¹³C have been measured at energies close to the Coulomb barrier. Analyses carried out in the framework of a complete coupled-reaction-channel theory show that extremely polarized single-particle molecular orbits (hybridization) are formed during the scattering process which give rise to a multiple-step interaction of the valence nucleon, i.e. the formation of a covalent nuclear molecule.     

The reaction 14C(3He,n)16O and the coexistence model of 16O

The reaction ¹⁴C(³He, n)¹⁶O has been measured at a ³He bombarding energy of 25.4 MeV. The zero-degree differential cross section for the excitation of the three low lying 0⁺T = 0 states, at energies 0.0, 6.05 and 12.05 MeV are, respectively, 1.33 ± 0.10, 0.49 ± 0.10, and 0.50 ± 0.10 mb/sr These measured cross sections are in rough agreement with single-step zero-range DWBA calculations using an empirically determined ¹⁴C ground state wave function and in which the Brown and Green coexistence-model wave functions are used to describe the ¹⁶O 0⁺ states. The angular distribution of the transition to the ground state is measured between 0° and 32°.     

An orthonormalization method: Theory and application to the j-j coupling of fermions in a single j-shell

An orthonormalization method suitable to deal with an overcomplete and non-orthogonal set of vectors is derived. It is then used to obtain the orthonormal set of states connected with the angular momentum coupling of N fermions in a single j-shell.     

Non-energy-weighted sum rule analysis of one nucleon transfer data on 41Ca, 43Ca, 45Se, 49Ti and 51V and the validity of the shell model

Spin-dependent sum rules for spectroscopic factors have been fitted to experimental data for the transfer of f_{$\text{7}\text{2}$} nucleons. The fits give the error in absolute normalizations in terms of the percentage error, σ, in relative spectroscopic factors, and evidence is presented that standard distorted wave Born approximation analyses of light-ion induced reactions give σ < 10%. The sum rule analyses then imply f_{$\text{7}\text{2}$} occupancies m agreement with simple shell-model expectations to an accuracy of about 10%. The f_{$\text{7}\text{2}$} occupancy deduced for ⁵¹V is completely inconsistent with the results of a Hartree-Fock-Bogolyubov calculation.     

Measurements of the spin correlation parameters Axx and Ayy for p-p scattering at 46.9 MeV

The A_xx and A_yy spin correlation coefficients of proton-proton scattering have been measured at E_lab = 46.9 MeV and θ_c.m. = 90° with the same experimental techniques already used at Saclay from 11 to 26 MeV and at Grenoble at 37.2 MeV. For A_xx the deviation from the predictions of the energy-dependent phase-shifts analysis of Livermore is significant (≈ 3.7 standard deviations) but not as large as for the 47.5 MeV Tokyo measurement. For A_yy the agreement is very good.     

Search for E2 strength in electrofission of 238U and 232Th

We have measured the cross-section ratio σ^?/σ⁺ for the electron and positron induced fission of uranium and thorium in the energy range 10–40 MeV with detectors at 90° and in a 2π geometry. The observed periodic structure is discussed with respect to E2 admixtures and an anisotropy of the angular distribution, after the onset of each higher chance fission threshold, as well as with respect to the shape of the photofission cross section.     

On the decay of the photo resonance in 14N and 14C nuclei

The decay of the photo resonances in ¹⁴N and ¹⁴C nuclei is analyzed in terms of the shell model with intermediate coupling. Cross sections and branching ratios of nucleon channels are compared with experimental data. Successive decay branches are estimated.     

Decay of the ground state and the 292+ isomer in 217Ac and g-factor measurements from perturbed α-particle angular distributions

The nucleus ²¹⁷Ac was studied using the ²⁰⁵Tl(¹⁶O, 4n), ²⁰⁶Pb(¹⁵N, 4n) and ²⁰⁹Bi(¹²C, 4n) reactions. The mesurements included αγ, γγ, α-ce and ce-ce coincidence experiments as well as γ-ray and α-particle perturbed angular distribution studies. Results are $\text{g(}{}^{\mathrm{217g}}\text{Ac}\text{) = + 0.85(1)}$ and $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(}{}^{\mathrm{<mtext>217</mtext><mtext>g</mtext>}}\text{Ac}\text{) = 69(4)}\text{ns}$, the shortest known α-decay of a ground state. ^217mAc decays mainly by a γ-cascade, but also by α-emission to the single-particle states $\text{π}\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{,}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{,}\text{i}{}_{\mathrm{<mtext>f</mtext><mtext>13</mtext><mtext>2</mtext>}}$ of ²¹³Fr. Spins and parities of levels to the $\text{29}\text{2}$⁺ isomer at 2013 keV with $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 740(40)}\text{ns}$ and g = + 0.347(5) are determined. The level scheme of ²¹⁷Ac and the α-decay of N = 128 isotones are discussed.     

Search for γ-rays emitted in the formation of a fission isomer

A search for γ-rays preceding isomeric fission in the reaction²³⁸U(α, 2n)^240mPu yielded negative results. Upper limits are given for the number of unconverted photons per isomer formed.     

Large transient magnetic fields for rare-earth ions recoiling in gadolinium and g-factors of high-spin states in 156, 158, 160Gd

We have determined the transient magnetic field for Coulomb-excited rare-earth nuclei recoiling with velocities in the range between 0.7ν₀ and 6ν₀ into ferromagnetic gadolinium cooled to a temperature T = 80 K. Measured and calculated g-factors in ¹⁶⁹Tm have been used as calibration standards. The transient field is found at first to increase with increasing recoil velocity, and then to level off, approaching a nearly constant value of 5.5 kT at ν = 6ν₀. At the higher velocities (3ν₀ < ν < 6ν₀) the transient fields for ¹⁶⁹Tm recoils in gadolinium are a factor of 1.42 ± 0.12 larger than those in iron, whereas the densities of polarized electrons are the same in both ferromagnets. This result demonstrates that an explanation of the transient field must take into account the atomic structure of the host (and probably also that of the recoil). The transient field is too large to be described only in a statistical picture in which inner-shell (ns) vancancies are filled by capture of polarized (4f) electrons. Possible mechanisms may involve either polarization transfer from the outer shells by spin-flip interactions, or direct vacancy polarization by diabatic molecular orbitals.The transient field calibration has been corroborated making use of known g-factors of low-spin states in ^{156, 158, 160}Gd populated by Coulomb excitation of thick Gd single crystals. For the high-spin states in these nuclei, the g-factors are found to decrease slightly, with the ratio $\text{g(10}{}^{\mathrm{+}}\text{)}\text{g(2}{}^{\mathrm{+}}$) reduced to 0.89±0.12, 0.83±0.11, and 0.93±0.13, respectively. Similar decreases have been observed previously for other N = 90?96 nuclei.     

High spin states in the ground and β-bands of 156Dy and the band-crossing interpretation of back bending

High spin states have been identified in ¹⁵⁶Dy using (HI, xn) reactions and γ-γ coincidence techniques. The ground state band does not show any “phase change” or “back bending” behaviour up to spin 18⁺. However a second sequence, based on the β-vibrational band, does show back bending at spin 12⁺. The two sequences intersect just below spin 16⁺ with the 16⁺, 18⁺ and 20⁺ members of the β-band sequence becoming yrast levels. Branching ratios have been obtained for transitions above and below the bend at spin 12⁺. The data are discussed in terms of a simple band-crossing model of back bending.     

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.     

The (γ, p0) reactions in the giant dipole resonance region of 51V and 52Cr nuclei

The differential cross sections at 90° for the ⁵¹V(e, p₀)⁵⁰Ti and ⁵²Cr(e, p₀ + p₁)⁵¹V reactions have been measured over the giant dipole resonance region. These cross sections were used to obtain the differential cross sections of the ⁵¹V(γ, p₀)⁵⁰Ti and ⁵²Cr(γ, p₀ + p₁)⁵¹V reactions. The results show two peaks that appear at the same energies as the main peaks of the (γ, n) and (γ, p) cross section for both nuclei. The angular distributions of protons from the (e, p) reaction have also been measured at several points of the incident electron energy. The coefficients A₂ obtained by fitting with a series of Legendre polynomials, W(θ) = 1 + A₁P₁(cos θ)+A₂P₂(cos θ), varies with excitation energy. These results are discussed in terms of the direct-semidirect process considering isospin effects in the giant dipole resonance.     

High-spin states in 24Mg and upper limits for particle spectroscopy of high spins by heavy-ion compound reactions

High-spin states in ²⁴Mg have been investigated by the reaction ¹⁰B(¹⁶O, d)²⁴Mg up to $\text{E}{}^1\text{≈ 24}\text{MeV}$. High-spin states with $\text{I ≧ 9}$ have been identified at $\text{E}{}^1\text{= 19.20, 20.26, 20.8, 21.6, 23.1,}\text{and}\text{23.5}\text{MeV}$. The 10⁺ yrast state in ²⁴Mg is probably located at 20.26 MeV. The upper limits with respect to spin and excitation energy of the applicability of heavy-ion compound reactions for particle spectroscopy of high-spin states are discussed. The main limitations result from the increasing continuum and from a decrease of the high-spin selectivity when the final spins approach the critical angular momentum for compound-nucleus formation. It will be shown that the difficulty in the analysis of the experiments arising from the decreasing probability of finding isolated yrast states at high excitation energies, i.e. from the increasing level density, can be overcome in such experiments. The decrease in the high-spin selectivity of the total cross section is compensated for spins up to J_max by the fact that the shape of the angular distributions depends on the final spin for states with I ～ J_max. This is caused by the decreasing alignment of the final nucleus with decreasing values of |I ? J_max| and can be used for high-spin spectroscopy.