(3He, 2n) excitation functions for some light nuclei

Excitation functions have been measured for the reaction ⁹Be(³He, 2n)¹⁰C over the range $\text{E(}{}^3\text{He}\text{) = 10–41}\text{MeV}$ and for the reaction ²⁷Al(³He, 2n)²⁸P over the range $\text{E(}{}^3\text{He}\text{) = 14–41}$ MeV by detecting β-delayed γ-rays. An excitation function has also been measured for the reaction ²⁴Mg(³He, 2n)²⁵Si over the range $\text{E(}{}^3\text{He}\text{) = 21–43}\text{MeV}$ by detecting β-delayed protons.     

Elastic scattering of vector polarized 6Li

Vector polarized ⁶Li nuclei have been elastically scattered on ${}^{12}\text{C(E = 20, 22.8}\text{MeV}\text{)}$ and on ¹⁶O, ²⁸Si, ⁵⁸Ni (E = 22.8 MeV). For the lighter nuclei surprisingly large asymmetries have been observed. The order of magnitude of the polarization effects observed can be understood within a folding model for the ⁶Li spin-orbit potential.     

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.     

A microscopic DWBA analysis of (6Li, 6He) reactions

The spin-isospin flip (⁶Li, ⁶He) reaction has been studied. The experiment was performed with a 34 MeV ⁶Li beam incident upon ^{25, 26}Mg and ²⁷Al targets. Angular distributions associated with the lowest $\text{5}\text{2}{}^{\mathrm{+}}\text{,}\text{1}\text{2}{}^{\mathrm{+}}\text{,}\text{7}\text{2}{}^{\mathrm{+}}{}^{25}\text{Al}\text{, 5}{}^{\mathrm{+}}\text{, 3}{}^{\mathrm{+}}\text{, 1}{}^{\mathrm{+}}{}^{26}\text{Al and}\text{5}\text{2}{}^{\mathrm{+}}{}^{27}\text{Si}$ states were measured. Microscopic DWBA calculations were performed using Yukawa central and r². Yukawa (r² · Y) tensor (μ = 1.0 fm^?1) potentials averaged over the ⁶Li(⁶He) cluster model wave functions. Knock-on (KO) exchange corrections corresponding to the central interaction are included using the local-energy approximation (LEA) method. The conclusion is that the quasi-elastic process is of major importance in the (⁶Li, ⁶He) transition studied in this work.     

The 6Li-induced three-nucleon transfer reaction on 40Ca

Analog (fp)³ states preferentially excited in the ${}^{40}\text{Ca}\text{(}{}^6\text{Li,t}\text{)}{}^{43}\text{Ti}$ and the ${}^{40}\text{Ca}\text{(}{}^6\text{Li}\text{, τ)}{}^{43}\text{Sc}$ reactions have been identified in the mass 43 mirror nuclei. A simple zero-range DWBA calculation made with a cluster form factor gives good agreement with the measured angular distributions, but spectroscopic strengths deduced for mirror levels do not agree. The 3p-0h states are excited with a rather uniform cross section not strongly correlated with spins.     

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.     

Coherent pion production in 3He3He collisions

A model is proposed to describe the near-threshold production of pions in the ${}^3\text{He}\text{(}{}^3\text{He}\text{, π}{}^{\mathrm{+}}\text{)}{}^6\text{Li}$ reaction. Taking experimental data on the ${}^3\text{He}\text{(p, π}{}^{\mathrm{+}}\text{)}{}^4$He process as input the cross sections for the first three levels of ⁶Li are reproduced semi-quantitatively.     

On the 18O positive-parity rotational band

Deuteron-alpha angular correlations have been measured for the reaction ${}^{14}\text{C}\text{(}{}^6\text{Li,d}\text{)}{}^{18}\text{O}{}^1\text{→α}{}_0\text{+}{}^{14}\text{C at}\text{E(}{}^6\text{Li}\text{)=34}\text{MeV}$ and θ_d^lab=10°. Transitions involving the 11.69 MeV (6⁺) and the 17.6±0.2 MeV ¹⁸O states have been analyzed. Spin and parity are confirmed for the known 11.69 MeV (6⁺) state and assigned to be 8⁺ for the 17.6 MeV level. This last is suggested to be the fifth member of the positive-parity ¹⁸O rotational band built on the 3.63 MeV (0⁺) level.     

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.     

Anomalous 3He scattering in the Ca region

Elastic ³He scattering on ⁴⁰Ar, ³⁹K, ⁴¹K, ⁴⁰Ca and ⁴²Ca was investigated at $\text{E(}{}^3\text{He) = 28}\text{MeV}$. A comparison of the scattering on neighbouring nuclei shows differences in backward angle cross sections up to one order of magnitude. This variation is clearly outside the domain of the standard optical model. This anomalous backward angle scattering is discussed in connection with similar anomalies observed in elastic α-particle scattering.     

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.     

Double spectator poles and quasi-free inelastic scattering in the 6Li + 6Li → 2α + 2d reaction

We have searched for double spectator pole events in the reaction ${}^6\text{Li}\text{+}{}^6\text{Li}\text{→ 2α + 2}\text{d}$, such that the deuteron from the projectile goes forward with the beam velocity while α or d from the target remains at rest. Triple coincidence studies of the reaction show such events, but with the 0° deuteron energy spectrum peaked at slightly higher velocities. Similar effects are seen in d-⁶Li double coincidence spectra from the single breakup reaction ${}^6\text{Li}\text{→}{}^6\text{Li}\text{+ α +}\text{d}$. Quasi-free inelastic scattering, where the d from the projectile receives no momentum transfer while the α excites the target to its first excited state, is also shown to be an important mechanism.     

Peripheral model approach to the process of radiative proton capture by tritium

Within the framework of the direct reaction peripheral model the differential cross section for the reaction ${}^3\text{H}\text{(}\text{p}\text{, γ)}{}^4\text{He at}\text{E}{}_{\mathrm{<mtext>p</mtext>}}\text{= 156}\text{MeV}$ is calculated. The theoretical angular distribution is in good agreement with the experimental one and the obtained value of the coupling constant of the nuclear vertex ³H + p → ⁴He is close to the results of previous works.     

Angular correlation experiments in the reactions 2H(α, nα)p and 2H(α, pα)n and comparison with the Faddeev theory and the resonating group method

At the Hamburg Isochronous Cyclotron angular correlation experiments were carried out in the reactions ²H(α, nα)p and ²H(α, pα)n, in order to determine the tensor polarization of the ground-state resonances ${}^5\text{Li}\text{(}\text{3}\text{2}{}^{\mathrm{?}}\text{)}$ and ${}^5\text{He}\text{(}\text{3}\text{2}{}^{\mathrm{?}}\text{)}$, respectively. We find that the observables for the two mirror reactions ${}^2\text{H}\text{(α,}\text{n}\text{)}{}^5\text{Li}\text{and}{}^2\text{H}\text{(α,}\text{p}\text{)}{}^5\text{He}$ are charge-dependent. This result is interpreted as evidence for a violation of charge symmetry.In the whole phase-space region absolute break-up cross sections are generally well reproduced by the Faddeev theory. On the other hand, we find that the resonating group method which has up to now been mainly applied to two-body reactions can also provide valuable information for break-up reactions. The predictions of Hackenbroich, Schütte and coworkers are in quite good agreement with the measured tensor polarization of ⁵He and ⁵Li and the corresponding angular correlation functions.     

Strong coupled-channels effects in the 9Be(α, t)10B reaction

Differential cross sections were measured for the reactions ${}^9\text{Be}\text{(α, α')}{}^9\text{Be}\text{,}{}^9\text{Be}\text{(α,}\text{t}\text{)}{}^{10}\text{B and}{}^9\text{Be}\text{(α,}{}^3\text{He}\text{)}{}^{10}\text{B at}\text{E}{}_{\mathrm{\alpha }}\text{= 65}\text{MeV}$ for angles ranging from θ_lab = 6° to 48°. Optical-model analysis was performed for elastic α-scattering from ⁹Be at E_α = 48, 65 and 104 MeV, and DWBA and CC calculations were done for the inelastic α-scattering at E_α = 65 MeV. DWBA calculations for the ⁹Be(α, ³He) reactions do not fit the transfer data so well and extracted spectroscopic factors are in disagreement with those of Cohen and Kurath and with values obtained from other reactions. Full CRC calculations assuming a band structure for the low-lying states of ¹⁰B and employing a modified set of Cohen and Kurath spectroscopic factors yield globally better fits both in shape and in absolute cross section for differential cross sections to low-lying states in ¹⁰B obtained in ⁹Be(α, t)¹⁰B at $\text{E}{}_{\mathrm{\alpha }}\text{= 65}\text{MeV and}{}^9\text{Be}\text{(}{}^3\text{He, d}\text{)}{}^{10}\text{B at}\text{E}{}_{\mathrm{<mtext>d</mtext>}}\text{= 17}\text{MeV}$. In general, strong coupled-channel effects mainly affecting the distorted waves are observed both in entrance and exit channels.     

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.     

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.     

7Li + 54Fe Single-nucleon stripping reactions at E = 48 MeV

Angular distributions have been measured for the ⁵⁴Fe(⁷Li, ⁶Li/⁶He)⁵⁵Fe, ⁵⁵Co reactions at $\text{E(}{}^7\text{Li) = 48}\text{MeV}$. Exact finite-range DWBA calculations for both reactions, employing Woods-Saxon real and imaginary potentials to generate the distorted waves, reproduce the shape of the f-state angular distributions but not the rate of fall-off with increasing angle for p-states. Using real potentials constructed by double-folding a microscopic nucleon-nucleon potential with a Woods-Saxon shaped imaginary potential to generate the distorted waves did not change the calculations. The forward angle (⁷Li, ⁶He) data allowed the $\text{2}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ states in ⁵⁵Co to be located and the determination of the single-particle centroid energies. The ⁵⁵Co spectroscopic factors are in good agreement with those from the (d, n) reaction but are generally 25 % lower than those from average (³He, d) results. The ⁵⁵Fe spectroscopic factors are in good agreement with (d, p) results.     

A useful spectroscopic tool: The (7Li, 6He) reaction

Angular distribution measurements for the reactions ²⁴Mg(⁷Li, ⁶He)²⁵ Al and ⁵²Cr(⁷Li, ⁶He)⁵³ Mn at$\text{E(}{}^7\text{Li) = 34}$ MeV show that for angles less than 15°, the shapes of the measured angular distributions allow $\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ or $\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$, and $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ or $\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ final-state configurations to be distinguished when compared with finite-range DWBA calculations.