The (6Li, 6He) spin-isospin-flip reaction

A formulation of the (⁶Li, ⁶He) spin-isospin-flip scattering problem is presented. The method is applicable to quasielastic collisions between⁶Li described in pureLS coupling scheme and any target nucleus which can be described in a shell model or an adiabatic deformed-nucleus model picture. The effective interaction responsible for the (⁶Li, ⁶He) reaction involves an integration of the (σ₁ · σ₂) (ρ₁ · ρ₂) compo nent of the central part and the (τ₁· τ₂) tensor part of the nucleon-nucleon interaction over the internal wave function of the projectile. The ⁴⁸Ca(⁶Li,⁶He)⁴⁸Sc reaction populating the ($\text{πf}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{νf}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$) multiplet in ⁴⁸Sc is analysed. It that the tensor force makes some contribution to the transitions to high spin states.     

Nucleon-exchange type charge-exchange process and the spin-forbidden (6Li, 6He) transitions

The second order DWBA formalism for the nucleon pick-up and stripping type two-step process is presented for the cases of exact finite-range interaction, no-recoil approximation and zero-range approximation. The several first-order “spin-forbidden” charge-exchange (⁶Li, ⁶He) transitions are investigated by such direct nucleon-exchange mechanisms. They are the analog transitions: ${}^{26}\text{Mg}\text{(0}{}^{\mathrm{+}}\text{) →}{}^{26}\text{Al}\text{(0.226}\text{MeV}\text{0}{}^{\mathrm{+}}\text{)}$ and ${}^{42}\text{Ca}\text{(0}{}^{\mathrm{+}}\text{→}{}^{42}\text{Sc}\text{(}\text{g.s.}\text{0}{}^{\mathrm{+}}\text{)}$, and the natural parity state excitations: ${}^{48}\text{Ca}\text{(0}{}^{\mathrm{+}}\text{) →}{}^{48}\text{Sc(g.s.}\text{6}{}^{\mathrm{+}}$ and 0.253 MeV 4⁺). The spin-flip mechanisms using a spin-independent force through the direct nucleon-exchange process are discussed. This type of two-step approach can provide a satisfactory interpretation for these transitions. It may also indicate a strong nucleon-exchange type charge-exchange mechanism for allowed transitions.     

12C(7Li,t)16O and stellar helium fusion

The reaction ¹²C(⁷Li, t)¹⁶O has been studied at $\text{E(}{}^7\text{Li}\text{) = 34}\text{MeV}$ with the LASL tandem accelerator and QDDD magnetic spectrometer. Angular distributions to levels with E_x < 11 MeV have been obtained from 0° to 90°, including 0°. The results have been analyzed with finite-range distorted-wave Born approximation theory. The α-particle spectroscopic factors and reduced widths obtained are compared with those calculated with group theory (SU(3)) and other models. The analysis of data for the 7.1 and 9.6 MeV J^π = 1^? levels, which are of great importance in stellar helium buring, yields a ratio, R, of dimensionless reduced α-widths $\text{θ}{}^2{}_{\mathrm{<mtext>a</mtext>}}\text{(7.1}\text{MeV}\text{)}\text{θ}{}^2{}_{\mathrm{<mtext>a</mtext>}}\text{(9.6}\text{MeV}\text{)}\text{= 0.35b ± 0.13}$. The observed line width of the 9.6 MeV level (Γ_c.m. = 390 ± 60 keV) is less than the accepted value (Γ_c.m. = 510 ± 60 keV) and implies θ²_a(9.6 MeV) ≈ 0.6. These results as well as data for the 6.92 MeV J^π = 2⁺ and 10.35 MeV J^π = 4⁺ “α-cluster” states indicate 0.09 < θ²_a(7.1 MeV) < 0.33 with a mean value θ²_a(7.1 MeV) = 0.14 ± 0.04. The implication for stellar helium burning is discussed.     

Optical-model analysis of 7Li + 25Mg and 7Li + 27Al elastic scattering at 89 MeV

The elastic scattering angular distributions for ⁷Li + ²⁵Mg and ⁷Li + ²⁷Al were measured at $\text{E(}{}^7\text{Li}\text{) = 89}\text{MeV}$ over angular ranges of 8–55° c.m. and 8–64° c.m. Previously published measurements for ^{24, 26}Mg at 89 MeV and ²⁴Mg at 34 MeV are reanalyzed. The cross sections were analysed using a 6-parameter phenomenological Saxon-Woods potential. No discrete ambiguities were found but the usual continuous ambiguities exist. The data were also analysed with double folded real potentials generated using the M3Y effective interaction. The folded potential must be multiplied by about 0.6 to fit the data. The extent to which ⁷Li optical-model potentials are determined and suggestions for further work on the normalization of the folded potential are discussed.     

Interaction dans l'état final n-p dans les réactions 2H(d,pn)2H, 4He(d,pn)4He, 6Li(d,pn)6Li et 3He(d,pn)3He

Three-body break-up in n-p final-state interaction regions has been investigated through the reactions ${}^2\text{H}\text{+}\text{d}\text{→}\text{p}\text{+}\text{n}\text{+ [su2}\text{H}\text{,}{}^4\text{He}\text{+}\text{d}\text{→}\text{p}\text{+}\text{n}\text{+}{}^4\text{He}\text{,}{}^6\text{Li}\text{+}\text{d}\text{→}\text{p}{}^3\text{He}\text{+}\text{d}\text{→}\text{p}\text{+}\text{n}\text{+}{}^3\text{He}$. In all cases, the proton and the neutron were detected at the same angle in a kinematically complete experiment for a deuteron bombarding energy of 27.5 MeV. Helium and deuterium gas targets in a small gas cell cooled with liquid nitrogen were used. No indication of any possible contribution from the (isospin-forbidden) ¹S₀ p-n final-state interaction was observed in the first three reactions. For the ³He + d reaction, the data shown pronounced enhancements due to the p-n final-state interaction. In the forward regions the observed peaks are broader than the predictions of final-state interaction models.     

A microscopical DWBA description of the charge-exchange reactions (7Li, 7Be)

The charge-exchange reaction (⁷Li, ⁷Be is described in the frame of a microscopical DWBA with central effective forces. The transition density for ⁷Li-⁷Be is calculated in two ways: with a one-particle model and with a cluster model, taking full account of recoil effects. The formalism is used for the cases of (⁷Li, ⁷Be reactions with ⁶Li and ⁴⁰Ca. Further cross sections for reactions on ¹²C and ¹⁶O with $\text{E(}{}^7\text{Li) = 78 MeV}$ and excitation energies around 4.5 and 6.2 MeV, respectively, are compared to new data obtained at the Kurchatov Institute. Here particle-hole states in an oscillator model were used to characterize the heavy system. Angular distributions are well reproduced, but absolute cross sections are 6–7 times too small. This indicates that the assumption of a direct one-step process is correct, but that tensor forces should be included as a component of the effective nucleon-nucleon force.     

The (7Li, 8Li) reaction to the (h92)−1 state in 207Pb

Relative differential cross sections for the reaction ²⁰⁸ P(⁷Li, ⁸Li) leading to the predominantly single-hole states in ²⁰⁷Pb have been analysed using the DWBA to determine the rms radius of the 1h_{$\text{9}\text{2}$} neutron orbital in ²⁰⁸Pb by comparison with known sizes of the 3p_{$\text{1}\text{2}$} and 2f_{$\text{7}\text{2}$} orbits. The experiment was performed at a beam energy of 52 MeV. The insensitivity of the technique to unknown input parameters to the DWBA analysis is demonstrated and a value of 5.94±0.11 fm for the rms radius of the 1h_{$\text{9}\text{2}$} orbit obtained assuming 70% of the hole strength is concentrated on the $\text{9}\text{2}{}^{\mathrm{?}}$, 3.41 MeV state in ²⁰⁷Pb. Effects due to fragmentation of the different hole strengths are examined and a value of 6.00 ± 0.11 fm is extracted as the best value for the rms radius of the neutron excess in ²⁰⁸Pb. The relevance of these data to mean-field calculations of nuclei is discussed.     

E1 polarization in coulomb excitation of 7Li

Coulomb excitation of the 0.478 MeV $\text{J}{}^{\mathrm{\pi }}\text{=}\text{1}\text{2}{}^{\mathrm{?}}$ state of ⁷Li has been studied by a partiele-γ coincidence technique. From the dependence of the excitation probabilities on bombarding energy and scattering angle a sizeable interference contribution from E1 excitation of continuum states has been determined. General expressions for the size of the E1 polarization effect in Coulomb excitation are given and the observed magnitudes in ^6,7Li are compared with schematic model calculations.     

12C(6Li,d)16O and16O(6Li,d)20Ne at E(6Li) = 42 MeV

Spectra up to 25 MeV excitation in ¹⁶O have been obtained from ¹²C(⁶Li, d) at 42 MeV bombarding energy. Angular distributions have been measured for ten states, including two J^π = 1^? states of astrophysical interest, and appear to be mostly direct α-transfer. In addition, data for ¹⁶(⁶Li, d)²⁰Ne(g.s.) and ²⁰Ne¹(2⁺) have been obtained. Excitation energies and widths have been extracted for states in ¹⁶O, including several states at E_x > 15 MeV. Alpha spectroscopic factors, S_α, and reduced α-widths, γ²_α and θ²_α have been deduced for levels in ¹⁶O and ²⁰Ne and compared with theoretical predictions. The J^π = 1^? levels in ¹⁶O at 7.12 and 9.6 MeV excitation appear to have comparable S_α and γ²_α values, viz. $\text{γ}{}^2{}_{\mathrm{\alpha }}\text{(7.12 MeV)}\text{γ}{}^2{}_{\mathrm{\alpha }}\text{(9.6}\text{MeV}\text{) = 0.6}{}^{\mathrm{+1.7}}{}_{\mathrm{?0.3}}$. Both states have apparent S_α and γ²_α values smaller than that for the J^π = 2⁺ “α-cluster” state at 6.9 MeV however. Furthermore, the observed line shape for the J^α = 1^?, 9.6 MeV level indicates Γ_c.m. = 400 ± 50 keV, which is substantially less than the accepted width for this level Γ_c.m. = 510±60 keV). The possible implications of these results for stellar helium burning calculations are discussed.     

Two-step processes in the 40Ca(α, 3He)41Ca reaction

The ⁴⁰Ca(α, ³He) reaction has been studied at 36 MeV incident energy. About fifty levels have been observed up to 7.1 MeV excitation energy and angular distributions were measured from 6–60° using a split-pole spectrometer. A local zero-range DWBA analysis has been carried out, and the deduced l-assignments and spectroscopic factors are compared with those obtained from previous neutron stripping experiments. Core-excited states in ⁴¹Ca with a [3^? ? f_7,2], [2⁺ ? f_7,2] and [5^? ? f_7,2] component previously observed in inelastic scattering experiments, are selectively excited by the (α, ³He) reaction. Their angular distributions are compared with coupled-reaction-channel calculations, assuming a pure two-step reaction mechanism. The agreement between theory and experiment may be considered as rather satisfactory for a number of levels. In particular the $\text{1}\text{2}{}^{\mathrm{+}}\text{and}\text{3}\text{2}{}^{\mathrm{+}}$ levels and the high-spin states with $\text{J}{}^{\mathrm{\pi }}\text{=}\text{9}\text{2}{}^{\mathrm{?}}\text{,}\text{11}\text{2}{}^{\mathrm{+}}\text{,}\text{15}\text{2}{}^{\mathrm{+}}\text{and}\text{17}\text{2}{}^{\mathrm{+}}$ are successfully described within the framework of the weak-coupling model.     

Alpha-deuteron structure of 6Li as predicted by a separable-potential three-body model

Schroedinger's equation with separable n-p (³S₁) and $\text{n}\text{-α (}{}^2\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{)}$ potentials solved to obtain a three-body model of the ⁶Li ground-state wave function. This model predicts the α-n-p binding energy of ⁶Li to be 4.67 MeV [Exp.: 4.53 MeV = 3.697 + 0.834 (Coulomb)], the asymptotic normalization constant of the d-α tail to be 2.39, and the amount of d+α component to be 65%. The ⁶Li→α+d vertex function is slightly more momentum dependent than present experiments suggest.     

A new 5.0 ns isomer in 144Eu

A new 9^? isomeric state having a 5.0 ns half-life has been observed in ¹⁴⁴Eu following the ¹⁴⁴Sm(α, p3n) reactions at 50 MeV. The new isomer most likely has a $\text{(π}\text{g}{}^{\mathrm{?1}}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{v}\text{h}{}^{\mathrm{?1}}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}\text{)}{}_9{}^{\mathrm{?}}$ configuration.     

Study of 20Ne(3He,n)22Mg at 3He energies between 2.6 and 4.0 MeV

The ²⁰Ne(³He, n) reaction leading to the ground state of ²²Mg has been investigated in the ³He⁺ energy range of 2.6 to 4.0 MeV. Angular distributions were determined with a neutron time-of-flight spectrometer at average incident energies (lab) of 3.27, 3.69, and 4.01 MeV between 0° and 120° (lab). Excitation functions for the energy region were measured at 0° and 80° (lab). The observed differential cross sections are explained by coherent contributions from direct interaction and compound-nucleus formation. A spectroscopic factor was extracted for the DWBA calculation from the absolute cross-section measurements and found to be $\text{? = 0.43±0.21}$. Resonances in the compound-nucleus formation were found at 3.00 and 3.33 MeV (c.m.) with widths of 0.28 and 0.21 MeV and spins of $\text{5}\text{2}{}^{\mathrm{+}}\text{and}\text{1}\text{2}{}^{\mathrm{?}}$, respectively.     

Effect of tensor force and one-nucleon exchange in the quasielastic (6Li, 6He) reaction

The effect of the tensor force and one-nucleon exchange is studied by applying the antisymmetrized DWBA method to the ${}^{48}\text{Ca(}{}^6\text{Li}\text{,}{}^6\text{He)}{}^{48}\text{Sc}\text{(π}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{ν}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{)}{}_{\mathrm{J}}$ reaction. The exchange effect increases the cross sections but does not change the angular shapes. In contrast to the tensor force with Gaussian shape, the TWOPEP tensor contribution is larger than that of the central force and dominates the reaction for large L-transfer.     

High-spin particle states in 151Sm studied with the (α, 3He) reaction

High-spin states have been located in ¹⁵¹Sm by means of the (α, ³He) reaction with 40 MeV α-particles. The scattered particles were momentum analyzed in a QMG/2 magnetic spectrometer and recorded in a position sensitive detector. Several high-spin states were observed in the energy range below 1.7 MeV excitation. The previously unknown strongly populated levels at 867 and 1480 keV can most likely be interpreted as $\text{13}\text{2}{}^{\mathrm{+}}$ states. Both the deduced nuclear structure factors and the energy location of these levels are in excellent agreement with a simple Coriolis coupling calculation.     

The (7Li, 6Li) reaction on 28Si and 40Ca at E(7Li) = 45 MeV

Angular distributions for the (⁷Li, ⁶Li) reaction on ²⁸Si and ⁴⁰Ca to ground and excited states of ²⁹Si and ⁴¹Ca have been measured at $\text{E(}{}^7\text{Li}\text{) = 45}\text{MeV}$. The shapes of the angular distributions are well described by exact finite-range DWBA calculations. To test the sensitivity of the calculated angular distributions to the exit channel potential, calculations were made using a strongly absorbing ⁷Li potential for both the entrance and exit channels. This calculation produced as good a fit to the shape of the angular distributions as did calculations with a ⁶Li potential in the exit channel, even though ⁷Li and ⁶Li elastic scattering on these target nuclei are not very similar. However, the magnitudes of the calculated cross sections are sensitive to the choice of potentials, and agreement with light-ion spectroscopic factors is obtained when the more weakly absorbing ⁶Li potentials are used. The spectroscopic factors obtained from the ⁴⁰Ca(⁷Li, ⁶Li) reaction study are in good agreement with the extensive light-ion results showing that the absolute magnitude of the reaction is correctly predicted by exact finite-range DWBA calculations that use optical parameters determined from elastic-scattering data.     

Study of 11B at high excitations with the 9Be(3He,p)11B and 9Be(α, d)11B reactions

The nucleus ¹¹B has been studied over the excitation energy range from 8.5 MeV to 21.5 MeV with the ⁹Be(³He, p)¹¹B / reaction at / E_{³He = 38 MeV}. The analogs of the parent states in ¹¹Be have been located at 12.56, 12.92, 14.40, 16.44, 17.69, 18.0, 19.15 and 21.27 MeV. A complementary measurement with the ⁹Be(α, d)¹¹B reaction at E_α = 48 MeV demonstrates that the 16.44, 17.69, 18.0 and 19.15 MeV resonances have rather pure isospin $\text{T}{}_{\mathrm{f}}\text{=}\text{3}\text{2}$. The 14.40 MeV state is a strongly isospin-mixed analog of the $\text{5}\text{2}{}^{\mathrm{+}}\text{1.78}\text{MeV}$ state in ¹¹Be. It is argued that spin S = 1 transfer is involved in the excitation of the 16.44 MeV state and its 3.887 MeV parent in ¹¹Be in a two-step stripping process. The $\text{T}{}_{\mathrm{f}}\text{=}\text{1}\text{2}$ states and the lowest three $\text{T}{}_{\mathrm{f}}\text{=}\text{3}\text{2}$ states are compared with the predictions of DWBA utilizing shell-model form factors. It is concluded that the $\text{T}{}_{\mathrm{f}}\text{=}\text{1}\text{2}$ strength is more strongly fragmented than is implied by the calculations of Teeters and Kurath.     

Pressure effects on the quadrupole coupling constant of 7Li in first stage lithium graphite

The pressure dependence of the experimental ⁷Li NMR spectra is reported for first stage lithium graphite (LiC₆) intercalation compound at temperatures T = 232 and 293 K. This experiment together with the presented point charge model calculation of the ⁷Li quadrupole coupling constant $\text{(}\text{e}{}^2\text{qQ}\text{h}\text{)}$ allows an unambiguous determination of the sign of e²qQ/h which is negative: $\text{e}{}^2\text{qQ}\text{h=-52 kHz}$ at p = 1 bar and T = 232 K. The averaged location of the electrons transferred from the Li intercalant to the graphite layers, as estimated in this study, is in excellent agreement with earlier theoretical energy-band calculations. The compressibility of LiC₆ in the c-direction is predicted to be k_c = 1.7 × 10^-12cm²dyn^-1, it agrees with estimates derived from the available phonon dispersion relations.     

Internal bremsstrahlung in the electron capture decay of 145Sm

Internal bremsstrahlung (IB) emitted in the non-unique first-forbidden electron capture decay of the $\text{7}\text{2}{}^{\mathrm{?}}$ ground state of ¹⁴⁵Sm to the $\text{7}\text{2}{}^{\mathrm{+}}\text{61}\text{keV}$ first excited level of ¹⁴⁵Pm has been studied. The total IB spectrum and the IB spectrum for captures proceeding via the 1s shell were measured for photons in the energy range of 100–580 keV and the spectra were normalized to the non-radiative capture rate. The experimental data agree with theoretical predictions.