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Notes: Abstract We have performed Monte Carlo calculations to estimate the exact energies of model problems for4He and theL=0,1, and 2 states of6Li. Using a Feynman path-integral expression for the imaginary-time evolution operator, we recast the ground state energy as a sum over histories, which are then sampled stochastically. Use of a trial wave function dramatically improves the efficiency of the Monte Carlo method. For a state-independent Malfliet-Tjon potential, together with the Coulomb interaction, we find a ground state energy of −28.00+0.20 MeV for4He, and a degeneracy of theL=0,1, and 2 states in6Li at about −59.65+-0.50 MeV. Density distributions for these nuclei are also calculated.

Notes: Abstract In the framework of a potential model we have calculated the various bremsstrahlung cross sections into the5Li ground state, includingM 1 andE 2 γ-transitions leading from the high energy wing of the5Li ground state resonance into states belonging to the same resonance at lower energy (intrastate transition). Our calculation supports the hypothesis of Schmalbrock et al. [1] that intrastate transitions ofM 1 andE 2 multipolarity exist. While we find a maximum cross section of roughly 1.4 nb for theE 2 transition, we predict the cross sections forM 1 intrastate transition to be less than 3·10−5nb. An experimental observation of the intrastate γ-ray emission appears to be very difficult due to the dominance of competing resonant (M 1) and direct (E 1) capture processes. Schmalbrock et al. have suggested to deduce magnetic dipole and electric quadrupole moments of resonant states from the measurements of the respectiveM 1 andE 2 intrastate transitions. We will show that theM 1 intrastate cross sections do not yield the appropriate information to determine the magnetic dipole moment. We will also discuss thatE 2 intrastate transitions do not seem to be a suited tool to find the quadrupole moment of an unstable state.

Notes: Abstract The two presently available measurements of the low-energy3H(α, γ)7Li reaction differ from each other by roughly 30% in total magnitude as well as in their determination of the branching ratios for the transition into the two final7Li bound states. Studying the3H(α, γ)7Li reaction in the framework of the microscopic Resonating Group Method we were able to reproduce both experimental total cross sections using different effective nucleon-nucleon interactions. However, none of the effective forces yields branching ratios compatible with the data measured by the Toronto-Münster-collaboration.

Notes: Abstract StrongB(E1) transitions have been recently observed between states in the18O nucleus which follow roughly the energy sequence of a dimolecular α+14C rotator. These findings have been interpreted by Gai et al. as evidence for a molecular dipole degree of freedom being present in the18O nucleus. However, this idea was contradicted by the results of a microscopic multichannel calculation performed by Descouvemont and Baye which was based on elastic α+14C and inelastic α+14C(2+) many-body cluster wave functions. We have improved this study by performing a microscopic multichannel calculation including additionally an+17O many-body fragmentation in order to enlarge our model space by those shell model components which dominate the structure of the (positive parity)18O ground state band. Like Descouvemont and Baye we find a positive parity α+14C molecular band in18O and, additionally, a rather strong collectivity in the lowest 1−, 3− and 5− states in18O. However, since the internal structure is different within these states, the calculated states should not be interpreted as a negative parity α+14C molecular band. In this perspective, the microscopic multichannel calculations do not support the hypothesis of a molecular dipole degree of freedom being present in the18O nucleus.

Notes: Abstract We have studied theD(α, γ)6Li reaction at stellar energies within a potential model. Our calculation improves previous investigations as we explicitely take into account the internal quadrupole moment of the deuteron and ad-state component in the6Li ground state. We reproduce the experimental data for energiesE〈3 MeV. We find, however, that our improvements represent only minor corrections.

Notes: Abstract We have studied the14N(p, γ)15O reaction leading into thej π=1/2+ resonance atE cm =260 keV in the proton channel. Our calculation is based on a potential model for nuclear bremsstrahlung allowing both fragments to have non-vanishing spins. Our study reproduces consistently the total width of the final resonance as well as the capture cross sections into this state thereby not confirming a contradiction between these two experimental data sets as discussed recently.

Notes: Abstract We have performed a study of the14O(α, p)17 F reaction at stellar energies within the framework of the Generator Coordinate Method (GCM). Our calculation improves a previous study by enlargement of the model space. The mechanism of break-out from the hot CNO-cycle in novae and x-ray bursts, which subsequently leads to nucleosynthesis of elements up to the56Ni region by rapid proton capture, is still an important problem in nuclear astrophysics [1]. Besides the15O (α, γ)19Ne reaction, the14O(α, p)17F reaction is discussed as a possible candidate for this leakage process [1]. As14O and17F are both short-lived nuclei, the reaction rate cannot be measured with available techniques and still has to rely on theoretical estimates. For a wide range of temperatures (T ≤5 · 108K) the14O(α, p)17F reaction rate is dominated by a resonant contribution arising from the 2 3 + state at E=30 keV and by a non-resonant direct transfer reaction contribution [2,3]. As the coupling potentials of a transfer reaction are inevitably non-local, the latter cannot be derived at in simple phenomenological potential models. However, microscopic cluster models like the GCM, in which the diagonal and coupling potentials are derived on the basis of the involved nuclear constituents and by a reasonable interaction between them, are a suited tool to estimate both contributions to the14O(α, p)17F reaction rate [3]. We have therefore performed a GCM study of the14O(α, p)17F reaction at stellar energies improving a previous calculation [3] by enlarging the model space by an excited α+14O fragmentation as the inclusion of such an inelastic configuration has been shown to be important for the description of the analogue nucleus18O [4] and is therefore apriori expected to also improve the description of excited resonances in18Ne. Thus, in the present GCM study the model space is spanned by a superposition of antisymmetrizedα + 14O(0+),α + 14O(2+) and p +17F product states. The internal degrees of freedom of theα-cluster, the14O ground state (14O(0+)), the first excited 2+ state in14O (14O(2+)) and the17F ground state were all described by harmonic oscillator shell model states in jj-coupling. The relative wave functions between the various fragmentations have been determined from the coupled RGM-equations following along the lines of Ref. 3. The oscillator parameters for the cluster basis wave functions as well as parameters in the nucleon-nucleon interaction were adjusted to reproduce the correct energy splitting between the proton channel and theα-channel as well as the energy positions of the two18Ne states close to the a-threshold (the 2 3 + state and the 3 1 − state at −24 keV). Our calculated18Ne level spectrum is shown in Fig. 1. The calculated transfer cross section is shown in Fig. 2 in terms of the astrophysical S-factor. Up toE 〈 300 keV, it is dominated by the tail of the 2 3 + resonance, exceeding the contribution arising from the high-energy wing of the 31/− bound state by about one order of magnitude. In the energy regimeE ≈ 0.3 2.5 MeV the cross section is given by the contribution from the J=1 partial wave which can be separated into a non-resonant direct transfer part and its interference with the 1− resonance at E=3.6 MeV (not present in the previous study [3]). We find a constructive interference below the resonance energy. The 4+ resonance at 2.79 MeV yields an important contribution to the calculated S-factor atE =2.7–3 MeV. There are experimentally known resonances in theα + 14O channel atE 〉 1 MeV which are not present in our GCM study (see Fig. 1). The14O(α, p)17F reaction rate can be derived at following the procedure discussed in Ref. 3. Comparing the present results to those of Ref. 3 we find the following conclusions which are important for the14O(α, p)17 F rate at astrophysical energies: i) The resonant contribution arising from the 2 3 + state is smaller in the present calculation by about a factor of 3.6. This can be traced back to a smaller a-width of this state, while its proton-width Γ=9 keV remains uneffected by the inclusion of anα + 14O(2+) configuration (experimental value Γp=25±10 keV). We now find Γα=1.3 · 10−62 MeV which is in close agreement with the value deduced from the reduced a-width of its analogue-state in18OΓα=1.15 · 10−62 MeV, Ref. 2). The reduction in the calculated a-width is caused by a stronger configuration mixing between the 2 3 + state with the 2 2 + state at −1.49 MeV, whose energy splitting (and positions) agrees now exactly with experiment and is reduced by about 800 keV in comparison to the study of Ref. 3. ii) Separating the calculated J=1− partial cross section into resonant, direct and interference contributions we find a non-resonant direct transfer cross section very similar to the one calculated in Ref. 3. Thus, a modification of the direct transfer rate as recommended in Ref. 3 is not necessary, iii) Following the conclusions drawn in a microscopic study of the analogue nucleus18O [4], the 1− state at 3.6 MeV might correspond to the experimental 1 2 − level at 1.19 MeV. If this is so, the present study predicts a constructive interference between the 1 2 − state and the direct transfer contribution in the low energy regime. However, a study of the analogue nucleus18O, which we performed similar to the present one, favours an identification of the calculated 1− level with the 1 3 − state, iv) The spin assignment to the levels atE 〉 1 MeV still remains uncertain. Our calculation does not give evidence enough to rule out one of the spin assignments as given in the literature [2,3]. In particular, our study does not allow to undoubtedly identify the experimental state at Ex=7.06 MeV as the J*=4+ member of theα + 14O molecular band [3], although this assignment still seems to be more likely than an identification of the molecular 4+ state with the level at 6.30 MeV [2]. Although from a theoretical point of view the present approach is superior to previous studies [3,2] and should give a reasonable description of the 2 3 + state and of the direct transfer process, its description of the excited resonances is still unsatisfactory. Clearly, more experimental information is needed here. For the14O(α, p)17F rate as given in Ref. 3 the results of our improved calculation have the following consequences: For temperatures T9 〈 0.3, at which the rate is dominated by the contributions arising from the 2 3 + state and from the direct reaction process, it is lowered by about a factor of 3 due to the reduction of theα-width of the resonance. However, this change in the rate is rather unimportant, because the competing β+-decay of14O is much faster at the densities found in those astrophysical environment in which the14O(a, p)17F reaction is expected to take place. For higher temperatures, our study does not show a need to change the rate as recommended in Ref. 3. Thus, it supports the finding of Refs. 2,3 that at the high burning temperatures, as they are expected in type I x-ray bursts (1.5 · 109 K, [1]), the14O(α, p)17 F reaction seems to be much faster than the competing15O (α, γ)19Ne reaction [5] and provides therefore a path from the hot CNO-cycle to the rp-process.

Notes: Abstract We have performed a microscopic study of the3He(d,p) α reaction at astrophysical energies within the framework of the Resonating Group Method adopting three different effective nucleon-nucleon interactions. The calculations suggest that the low-energy3He(d,p) α cross section is in good approximation given by the contribution arising from the 3/2+ resonant state atE R =245 keV. In fact, the low-energy data can be better (and more physically) described by a single Breit-Wigner resonance parametrization than by a polynomial fit. Our fit to the3He(d,p) α cross section results in a noticeable reduction in the uncertainties of the resonance parameters of the 3/2+ resonant state as well as in a significantly improved extrapolation of the data to astrophysically important energies. On the basis of this extrapolation we were able to quantitatively deduce the enhancement of the low-energy cross section due to electron screening effects from the data of Krauss et al. and Engstler et al. These experimental enhancement factors were compared with various theoretical models which are all based on the Born-Oppenheimer approximation. As the models underestimate the observed enhancement we suggest that the theoretical study of electron screening effects requires a dynamical treatment.

Notes: Abstract We have recalculated the fusion rates of the free deuterium molecule, ion and mesomolecule taking into account the shielding of the Coulomb barrier by the electrons and muon. Electron screening increases the rates by several orders of magnitude. The fusion of hydrogen nuclei is known to be the source of energy of stars occuring in their high-temperature, high-pressure interiors. In terrestrial conditions, one attempts currently to tap this source of nuclear fusion energy by alternative techniques, i.e. high-temperature plasmas or muon-catalyzed fusion. Very recently cold fusion in solids has achieved worldwide attention, since experimental evidence for increased hydrogenic fusion rates in palladium and titanium has been reported[1,2]. These reports have motivated us to reconsider the fusion probability of free hydrogen molecules, ions and mesomolecules, following closely the studies of Refs. [3,4,5]. Our aim however is to improve the previous estimates of the respective fusion rates by taking account of the screening effects of the electrons and muons on the nuclear Coulomb barrier which will turn out to be quite important. As in Ref. [5] we will restrict our numerical results to deuterium only.

Notes: Abstract We have studied resonant, intrastate and non-resonant bremsstrahlungγ-ray transitions leading to the 2+ state in8Be atE x=2.94 MeV. We find aγ-width of Γ γ =0.45 eV for the 4+ state in8Be, corresponding to anE 2 strength of 19 W.u. For the intrastateγ-ray transition within the 2+ resonance we predict a maximum cross section of 2.5 nb atE≈3.3 MeV. An experimental observation of this novel type ofγ-ray emission, however, appears to be difficult due to the dominance of competing resonant and direct capture processes.