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Until recently the potential scattering of a charged particle in a laser field received attention exclusively in atomic physics. The differential cross-section of laser-assisted electron-atom collisions for n emitted or absorbed photons is provided by a simple law which casts the result as a product between the field-free value and the square of the Bessel function of order n with its argument containing the effect of the laser in a non-perturbative way. From the experimental standpoint, laser-assisted electron-atom collisions are important because they allow the observation of multiphoton effects even at moderate laser intensities. The aim of this study is to calculate the nucleus-nucleus differential cross section in the field of a strong laser with wavelengths in the optical domain such that the low-frequency approximation is fulfilled. We investigate the dependence of the n-photon differential cross-section on the intensity, photon energy and shape of the pulse for a projectile/target combination at a fixed collision energy which exhibits a superposition of Fraunhofer and refractive behavior. We also discuss the role of the laser perturbation on the near and farside decomposition in the angular distribution, an issue never discussed before in the literature. We apply a standard optical model approach to explain the experimental differential cross-section of the elastic scattering of 4He on 58Ni at a laboratory energy E = 139 MeV and resolve the corresponding farside/nearside (F/N) decomposition in the field-free case. We give an example of reaction in which Fraunhofer diffraction and refractive rainbow hump effects are easily recognized in the elastic angular distribution. Next, we apply the Kroll-Watson theorem, in order to determine the n -photon contributions to the cross-section for continuous-wave (cw) and modulated pulses. In the elastic scattering of heavy ions in a radiation field of low intensity, the amplitude drops by orders of magnitude with respect to the unperturbed case once the exchange of photons is initiated. For intensities approaching $I=10^{17}$ W/cm2 multiphoton effects become important. In the case of short laser pulses we conclude that the strength of n-photon contribution increases with the pulse duration.

The asymptotic normalization coefficient (ANC) for a nuclear system specifies the normalization of the tail of the nuclear overlap function. ANCs may be determined experimentally by measuring peripheral nuclear reactions. They may be used to calculate the astrophysical S-factors for radiative capture reactions at stellar energies and to determine the halo structure of loosely bound nuclei. A brief introduction to ANCs is given and applications to the 7Be(p,γ)8B and 11C(p,γ)12N reactions and the halo structure of 8B are described.

We give a description of the binary cold fission process of 252Cf within the stationary scattering formalism. The decay of the dinuclear system (quasi-molecule) consists in the tunnelling of a metastable state from an internal region, where the nucleus–nucleus potential makes a quasi-molecular pocket due to the interplay of repulsive and attractive nuclear forces and the Coulomb force, to the asymptotic region which is governed solely by the Coulomb repulsion. As a transverse internal motion, we suppose angular oscillations of the fragments up to the scission point. In the external region these vibrations transform into rotations. The nuclear interaction is given by a double-folding procedure using M3Y forces plus a repulsive contact potential. For the experimental Q-value we find several resonant states of the binary system, depending on the repulsive strength. We predict a strong dependence of decay widths upon the internal structure of the considered resonant state. Therefore the measured yields of the two fragments with given angular momenta in coincidence are able to provide more insight into the internal molecular dynamics of the decaying dinuclear system.

Peripheral transfer reactions can be used to determine asymptotic normalization coefficients (ANCs). These coefficients, which specify the normalization of the tail of the nuclear overlap function, determine S-factors for direct capture reactions at astrophysical energies. A variety of proton transfer reactions involving both stable and radioactive beams have been used to measure ANCs. Tests have demonstrated that ANCs determined from proton transfer reactions can be used to calculate astrophysical direct capture rates to within 9%. The 10B(7Be, 8B)9Be and 14N(7Be, 8B)13C reactions have been used to measure the ANC appropriate for determining the 7Be(p,γ)8B rate, and the 14N(11C, 12N)13C reaction has been used to measure the ANC required to calculate the 11C(p,γ)12N rate.

A study of interaction of neutron rich oxygen isotopes $^{17,18}$O with light targets has been undertaken in order to determine the optical potentials needed for the transfer reaction $^{13}$C($^{17}$O,$^{18}$O)$^{12}$C. Optical potentials in both incoming and outgoing channels have been determined in a single experiment. This transfer reaction was used to infer the direct capture rate to the $^{17}$F(p,$\gamma$)$^{18}$Ne which is essential to estimate the production of $^{18}$F at stellar energies in ONe novae. The success of the asymptotic normalization coefficient (ANC) as indirect method for astrophysics is guaranteed if the reaction mechanism is peripheral and the DWBA cross section calculations are warranted and stable against OMP used. We demonstrate the stability of the ANC method and OMP results using good quality elastic and inelastic scattering data with stable beams before extending the procedures to rare ion beams. The peripherality of our reaction is inferred from a semiclassical decomposition of the total scattering amplitude into barrier and internal barrier components. Comparison between elastic scattering of $^{17}$O, $^{18}$O and $^{16}$O projectiles is made.

The $^{14}\mathrm{C}$ + $n\ensuremath{\leftrightarrow}^{15}\mathrm{C}$ system has been used as a test case in the evaluation of a new method to determine spectroscopic factors that uses the asymptotic normalization coefficient (ANC). The method proved to be unsuccessful for this case. As part of this experimental program, the ANCs for the ${}^{15}$C ground state and first excited state were determined using a heavy-ion neutron transfer reaction as well as the inverse kinematics ($d$,$p$) reaction, measured at the Texas A Cyclotron Institute. The values ${C}_{2s1/2}^{2}=1.88\ifmmode\pm\else\textpm\fi{}0.18$ fm${}^{\ensuremath{-}1}$ for the ground state and ${C}_{1d5/2}^{2}=4.25\ifmmode\pm\else\textpm\fi{}0.38\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ fm${}^{\ensuremath{-}1}$ for the first excited state (${E}_{\text{exc}}=740$ keV) were obtained. The ANCs were used to evaluate the astrophysical direct neutron capture rate on $^{14}\mathrm{C}$, which was then compared with the most recent direct measurement and found to be in good agreement. A study of the $^{15}\mathrm{C}$ SF via its mirror nucleus $^{15}\mathrm{F}$ and a new insight into deuteron stripping theory are also presented.

The asymptotic normalization coefficients of the bound states ${J}^{\ensuremath{\pi}}=({0}_{1}^{+},{2}_{1}^{+},{4}_{1}^{+},{2}_{2}^{+})$ in $^{18}\text{O}$ are extracted from the peripheral neutron transfer reaction $^{13}\text{C}$$(^{17}\text{O}$$,^{18}\text{O}$$)^{12}\text{C}$. They are then converted to their mirror states in $^{18}\text{Ne}$, which are further used to evaluate the astrophysical $S$ factor for the proton capture reaction $^{17}\text{F}$($p$,$\ensuremath{\gamma}$)$^{18}\text{Ne}$. The elastic-scattering cross sections have been measured in both incoming and outgoing channels in order to extract the optical potentials needed for distorted-wave-Born-approximation calculations. The $S$ factor is found to be ${S}_{1\ensuremath{-}17}(0)=2.17\ifmmode\pm\else\textpm\fi{}0.37$ keV b. The contribution of the direct capture rate to this reaction is estimated, and its consequences on the production of $^{18}\text{F}$ at stellar energies in ONe novae are discussed.

The indirect method of determining astrophysical nuclear reaction rates is discussed. The overall normalization of the astrophysical S-factor for such reactions may be determined from one quantity, the asymptotic normalization coefficient of the overlap function of the bound state wave functions for the initial and final channels.These coefficients can be found also from peripheral transfer reactions whose amplitudes are determined by the same overlap function as the amplitudes of the corresponding astrophysical radiative capture processes.The experimental test of this approach and the last results of S 17 measurements are presented.

The {sup 13}C({sup 14}N,{sup 13}C){sup 14}N proton exchange reaction has been measured at an incident energy of 162 MeV. Angular distributions were obtained for proton transfer to the ground and low-lying excited states in {sup 14}N. Elastic scattering of {sup 14}N on {sup 13}C also was measured out to the rainbow angle region in order to find reliable optical model potentials. Asymptotic normalization coefficients for the system {sup 13}C+p{r_arrow}thinsp{sup 14}N have been found for the ground state and the excited states at 2.313, 3.948, 5.106, and 5.834 MeV in {sup 14}N. These asymptotic normalization coefficients will be used in a determination of the {ital S} factor for {sup 7}Be(p,{gamma}){sup 8}B at solar energies from a measurement of the proton transfer reaction {sup 14}N({sup 7}Be,{sup 8}B){sup 13}C. {copyright} {ital 1998} {ital The American Physical Society}

A new phenomenon is studied: the cold (neutronless) ternary α-accompanied fragmentation of 252Cf. The corresponding isotopic yields were calculated as the ratio of the penetrability of a given fragmentation over the sum of penetrabilities of all possible (neutronless) α-ternary fragmentations. No preformation factors were considered. We considered that close to the scission configuration the nucleons of the alpha particle form a small neck. At a given value of the neck radius a double scission takes place and a third light fragment is formed between the two heavier fragments. The corresponding barriers between the light and heavy fragment and between the alpha particle and the two heavier fragments were evaluated by using a double folding potential generated by M3Y nucleon-nucleon forces and realistic fragment ground state deformations. The relative calculated isotopic yields greater than 2 × 10-3 have been observed experimentally for the partners with known spectra. We predict that fragmentations with unknown light partners 105,106Zr, 109,110Mo and 114Ru to be identified in the present data.

The phenomenon of cold (neutronless) alpha ternary fission in spontaneous fission of {sup 252}Cf was experimentally observed by triple gamma coincidence technique with Gammasphere with 72 gamma-ray detectors. Correlated pairs of {sub 36}Kr-{sub 60}Nd, {sub 38}Sr-{sub 58}Ce, {sub 40}Zr-{sub 56}Ba, {sub 42}Mo-{sub 54}Xe, {sub 44}Ru-{sub 52}Te, and {sub 46}Pd-{sub 50}Sn were observed to be associated with {alpha} ternary fission of {sup 252}Cf. Yields of cold {alpha} ternary fission were extracted. {copyright} {ital 1998} {ital The American Physical Society}

The differential cross sections for the reactions 9 Be( 10 B, 9 Be) 10 B at an incident 10B energy of 100 MeV and 16 O( 3 He,d) 17 F ∗ (0.495 MeV , 1 2 + ) at an incident 3He energy of 29.75 MeV were measured. By normalizing the theoretical DWBA proton exchange cross sections to the experimental ones, the asymptotic normalization coefficients (ANC's) for the virtual decays 10 B → 9 Be+p and 17 F ∗ (0.495 MeV ) → 16 O+p have been found. These ANC's are used to calculate the S(0)-factors for the direct radiative captures 9 Be + p → 10 B + γ and 16 O + p → 17 F ∗ (0.495 MeV ) + γ .

A new type of decay corresponding to the neutronless $^{10}$Be-accompanied fragmentation of $^{252}$Cf is studied. We employ a cluster model similar to the model used for the description of cluster radioactivity. No preformation factors were considered. The ternary relative isotopic yields were calculated as the ratio of the penetrability of a given ternary fragmentation over the sum of penetrabilities of all possible ternary neutronless fragmentations. The corresponding barriers between the light and heavy fragment and between the $^{10}$Be cluster and the two heavier fragments were computed with the help of a double folding potential generated by M3Y-$NN$ effective interaction and realistic fragment ground state deformations. Also, we studied the influence of the fragment excitation energies on the yields, by including the level densities and the $\beta$-stretching of the fragments. The new phenomenon could be experimentally observed by the triple gamma coincidence technique between the fragments and $^{10}$Be.

Experimental integral isotopic yields for the spontaneous cold (neutron-less) binary and α-ternary fission of252Cf were obtained by using triple γ-γ-γ coincidence technique at Gammasphere facility. For the first time10Be- and14C-ternary fission isotopic yields were also measured. The results are interpreted within simple cluster model with binary and ternary potential barriers generated by M3Y effective interaction and ground-state deformation.

The phenomenon of cold (neutronless) binary and ternary fission in spontaneous fission of252 Cf was experimentally observed by triple gamma coincidence technique with Gammasphere with 72 gamma-ray detectors. Many correlated pairs for both binary and ternary (4He,10Be) fission were observed in the spontaneous fission of252 Cf. Yields of cold ternary and cold binary fission were extracted. These results are compared with the theoretical calculations using M3Y nucleon-nucleon potential and WKB approximation for barrier penetration.

The differential cross sections for the reactions ${}^{9}\mathrm{Be}{(}^{10}\mathrm{B}{,}^{10}\mathrm{B}{)}^{9}\mathrm{Be}$ and ${}^{9}\mathrm{Be}{(}^{10}\mathrm{B}{,}^{9}\mathrm{Be}{)}^{10}\mathrm{B}$ have been measured at an incident energy of 100 MeV. The elastic scattering data have been used to determine the optical model parameters for the ${}^{9}\mathrm{Be}{+}^{10}\mathrm{B}$ system at this energy. These parameters are then used in distorted-wave Born approximation (DWBA) calculations to predict the cross sections of the ${}^{9}\mathrm{Be}{(}^{10}\mathrm{B}{,}^{9}\mathrm{Be}{)}^{10}\mathrm{B}$ proton exchange reaction, populating the ground and low-lying states in ${}^{10}\mathrm{B}$. By normalizing the theoretical DWBA proton exchange cross sections to the experimental ones, the asymptotic normalization coefficients (ANC's), defining the normalization of the tail of the ${}^{10}\mathrm{B}$ bound state wave functions in the two-particle channel ${}^{9}\mathrm{Be}+p$, have been found. The ANC for the virtual decay ${}^{10}\mathrm{B}(\mathrm{g}.\mathrm{s}.){\ensuremath{\rightarrow}}^{9}\mathrm{Be}+p$ will be used in an analysis of the ${}^{10}\mathrm{B}{(}^{7}\mathrm{Be}{,}^{8}\mathrm{B}{)}^{9}\mathrm{Be}$ reaction to extract the ANC's for ${}^{8}\mathrm{B}{\ensuremath{\rightarrow}}^{7}\mathrm{Be}+p$. These ANC's determine the normalization of the ${}^{7}\mathrm{Be}(p,\ensuremath{\gamma}{)}^{8}\mathrm{B}$ radiative capture cross section at very low energies, which is crucially important for nuclear astrophysics.

The isotopic yields for the spontaneous cold ternary alpha-accompanied fission of were calculated using a double folding potential generated by Coulomb plus M3Y nucleon - nucleon forces and realistic fragment ground state deformations. The penetrabilities through the ternary fragmentation barrier were obtained within the one-dimensional WKB approximation.

We calculate the relative isotopic yields and partial half-lives of the most frequent splittings in the spontaneous cold fission of , described as a heavy cluster radioactivity. A double-folding potential and M3Y nucleon - nucleon forces are used to obtain the potential barrier between the final fragments. The penetrabilities through this barrier are estimated within the one-dimensional WKB approximation. Realistic fragment ground-state deformations are used for the calculations.

The isotopic yields for the spontaneous cold fission of $^{252}\mathrm{Cf}$ are predicted by using a double-folding potential and the M3Y nucleon-nucleon forces. The penetrabilities through this barrier are obtained within the one-dimensional WKB approximation. Realistic fragment ground-state deformations are used for the calculations. The results are in good agreement with zero neutron channel yields extracted from \ensuremath{\gamma}-\ensuremath{\gamma}-\ensuremath{\gamma} coincidence studies in the spontaneous fission of $^{252}\mathrm{Cf}$ recorded with the early implementation Gammasphere. The double fine structure in such cold fragmentations has been experimentally observed for the first time. \textcopyright{} 1996 The American Physical Society.

Background: To understand explosive hydrogen burning in stars and to explore various explosive scenarios such as type I x-ray bursts (XRBs), reliable reaction rates are needed. The cross sections for radiative proton capture on near-dripline nuclei are necessary for the determination of the reaction rates, but cannot be measured directly.Purpose: To determine the reaction rate for the radiative proton capture reaction ${}^{23}\mathrm{Al}{(p,\ensuremath{\gamma})}^{24}\mathrm{Si}$ using indirect methods and, as a consequence, evaluate if sequential $2p$ capture on ${}^{22}$Mg seed nuclei is significant at high temperatures.Method: Nonresonant radiative proton capture on ${}^{23}$Al is investigated using the one-proton breakup of ${}^{24}$Si at 61 MeV/nucleon and the asymptotic normalization coefficient (ANC) for ${}^{24}{\mathrm{Si}}_{\mathrm{gs}}\ensuremath{\rightarrow}{}^{23}\mathrm{Al}+p$ is deduced.Results: From the ANC, the nonresonant component of the astrophysical $S$-factor for the ${}^{23}\mathrm{Al}{(p,\ensuremath{\gamma})}^{24}\mathrm{Si}$ reaction is determined and, using other new experimental data the resonant component is re-evaluated.Conclusions: The ${}^{23}\mathrm{Al}{(p,\ensuremath{\gamma})}^{24}\mathrm{Si}$ reaction is of interest for type I XRB nucleosynthesis and its reaction rate can affect both the ${}^{22}$Na abundance and the total energy output. New determinations of the rates for the ${}^{22}\mathrm{Mg}{(p,\ensuremath{\gamma})}^{23}\mathrm{Al}{(p,\ensuremath{\gamma})}^{24}\mathrm{Si}$ reaction chain are provided here and we point to the need that they be included in XRB scenarios.

We present a complete analysis of ${\phantom{\rule{0.16em}{0ex}}}^{6}\mathrm{Li}+{}^{16}\mathrm{O}$ elastic scattering at 4 and 5 MeV/nucleon. Using either traditional Woods-Saxon or a range of semimicroscopic folding form factors we find that the data require deep, highly transparent potentials. Physically relevant solutions are selected according to the dispersion relation. The intermediate angle structures and the oscillatory increase of the cross section at large angles are interpreted either as a pre-rainbow oscillation resulting from the interference of the barrier and internal barrier far-side scattering subamplitudes or, equally well, as a resonant diffraction arising from two Regge poles located in peripheral waves. Both semiclassical and Regge pole approaches allow a dynamical separation of the resonant component of the $S$ matrix.

The fusion reaction ${}^{40}$Ca + ${}^{40}$Ca was very recently reinvestigated by the Legnaro group and cross sections down to $\ensuremath{\mu}$b were measured. In the present work this reaction is analyzed within the coupled-channel formalism including ${2}^{+}$, ${3}^{\ensuremath{-}}$, and ${5}^{\ensuremath{-}}$ phonon states. The heavy-ion entrance channel potential is calculated within the double-folding prescription and comprises a direct local term and a local equivalent of the nonlocal knock-on exchange component. The single-particle densities entering the folding integrals are prescribed according to the density matrix expansion. Coupling potentials are calculated from the $G$-matrix Michigan three-range Yukawa-type semirealistic nucleon-nucleon interaction (M3Y) as well as one modern parametrization of the density-dependent Gogny effective interaction. Realistic deformation parameters are used. The best fit to the data is not pointing to a possible maximum in the astrophysical $S$-factor as in a previous study on sub-barrier fusion involving ${}^{48}$Ca projectiles.

Recent fusion reaction data for the systems ${}^{36}\mathrm{S}+{}^{48}\mathrm{Ca}$, ${}^{48}\mathrm{Ca}+{}^{48}\mathrm{Ca}$, and ${}^{96}\mathrm{Zr}+{}^{48}\mathrm{Ca}$ are analyzed within the coupled-channel formalism. The heavy-ion entrance channel potential is calculated employing an improved double-folding prescription. The nonlocal kernel arising from the knock-on exchange component of the effective $N\ensuremath{-}N$ interaction is localized within the lowest order of the Perey-Saxon approach, including full recoil. The single-particle densities entering the folding integrals are prescribed according to the density matrix expansion method. The investigation is more elaborated because each case is tested with four different types of $N\ensuremath{-}N$ effective forces: The two standard parametrizations of the density-independent M3Y force (Reid and Paris) and two parametrizations of the density-dependent Gogny force (D1S and D1N). A consistent description of all three reactions is achieved by keeping fixed the nuclear structure input for $^{48}\mathrm{Ca}$. The inclusion of 2${}^{+}$ and 3${}^{\ensuremath{-}}$ phonon states in the coupled-channel calculation, within an energy excitation window identical for all three reactions explains better the hindrance in extreme sub-barrier fusion cross sections. The interactions providing the best fit to the data are not pointing to a possible maximum in the astrophysical $S$ factor, thereby confirming the conclusion reached by the Legnaro group for these cases.

Double folding α – α potentials based on the density dependent n – n Gogny interactions are constrained to reproduce the l = 0 resonance in 8 Be . Shallow potentials are obtained by successive supersymmetric transformations which eliminate the l = 0 Pauli forbidden states. Implication for the EOS of cold α-matter are discussed.

The production of $^{22}\mathrm{Na}$ in ONe novae can be influenced by the $^{22}\mathrm{Mg}$$(p,\ensuremath{\gamma})$$^{23}\mathrm{Al}$ reaction. To investigate this reaction rate at stellar energies, we have determined the asymptotic normalization coefficient (ANC) for $^{22}\mathrm{Mg}$$+p\ensuremath{\rightarrow}$$^{23}\mathrm{Al}$ through measurements of the ANCs in the mirror nuclear system $^{22}\mathrm{Ne}$$+n\ensuremath{\rightarrow}$$^{23}\mathrm{Ne}$. The peripheral neutron-transfer reactions $^{13}\mathrm{C}$($^{12}\mathrm{C}$,$^{13}\mathrm{C}$)$^{12}\mathrm{C}$ and $^{13}\mathrm{C}$($^{22}\mathrm{Ne}$,$^{23}\mathrm{Ne}$)$^{12}\mathrm{C}$ were studied. The identical entrance and exit channels of the first reaction make it possible to extract independently the ground-state ANC in $^{13}\mathrm{C}$. Our experiment gives ${C}_{{p}_{1/2}}^{2}$($^{13}\mathrm{C}$)$=2.24\ifmmode\pm\else\textpm\fi{}0.11$ fm${}^{\ensuremath{-}1}$, which agrees with the value obtained from several previous measurements. The weighted average for all the obtained ${C}_{{p}_{1/2}}^{2}$ is $2.31\ifmmode\pm\else\textpm\fi{}0.08$ fm${}^{\ensuremath{-}1}$. This value is adopted to be used in obtaining the ANCs in $^{23}\mathrm{Ne}$. The differential cross sections for the reaction $^{13}\mathrm{C}$($^{22}\mathrm{Ne}$,$^{23}\mathrm{Ne}$)$^{12}\mathrm{C}$ leading to the ${J}^{\ensuremath{\pi}}=5/{2}^{+}$ and $1/{2}^{+}$ states in $^{23}\mathrm{Ne}$ have been measured at 12 MeV/u. Optical model parameters for use in the DWBA calculations were obtained from measurements of the elastic scatterings $^{22}\mathrm{Ne}+^{13}\mathrm{C}$ and $^{22}\mathrm{Ne}+^{12}\mathrm{C}$. The extracted ANC for the ground state in $^{23}\mathrm{Ne}$, ${C}_{{d}_{5/2}}^{2}=0.86\ifmmode\pm\else\textpm\fi{}0.08\ifmmode\pm\else\textpm\fi{}0.12$ fm${}^{\ensuremath{-}1}$, is converted to its corresponding value in $^{23}\mathrm{Al}$ using mirror symmetry to give ${C}_{{d}_{5/2}}^{2}$($^{23}\mathrm{Al}$)$=(4.63\ifmmode\pm\else\textpm\fi{}0.77)\ifmmode\times\else\texttimes\fi{}{10}^{3}$ fm${}^{\ensuremath{-}1}$. The astrophysical $S$ factor $S(0)$ for the $^{22}\mathrm{Mg}$($p,\ensuremath{\gamma}$) reaction was determined to be $0.96\ifmmode\pm\else\textpm\fi{}0.11$ keV b. The consequences for nuclear astrophysics are discussed.

Within the variational approach of Bose liquids we analyze the g.s. energy of charge neutral alpha matter at $T$=0. As a prerequisite for such calculation we take from the literature or propose new $\alp-\alp$ potentials that are particularly suitable for this task, i.e. posses a repulsive core and/or reproduce the low energy scattering data and the resonance properties of the $\alp-\alp$ system. The alpha matter EOS is then obtained with the HNC method using Pandharipande-Bethe correlation derived variationally in the lowest order expansion of the energy functional or a simple gaussian function with a healing range determined by the normalization of the radial distribution function in the lowest order. We show that saturation is achieved only via repulsive and shallow potentials that are not consistent with the scattering and resonance constraints.

The heavy‐ion potential is calculated semi‐microscopically within the double folding method with various effective n—n interactions (Gogny, M3Y) and applied to fusion reactions relevant for the carbon and oxygen burning cycles in highly evolved stars. Reaction rates at temperatures relevant for such stellar processes are estimated and upon comparison with traditional and modern extrapolation formulas conclusions are drawn regarding the importance of the employed n—n interactions on the corresponding burning cycle.

The folded Michigan — 3–Yukawa (M3Y) potential is used for the first time for calculating the WKB penetration probabilities, with deformation effects of the emitted clusters also included for the first time. For the clusters to be spheres, our calculations of the (empirical) performation probabilities P0 show that, depending rather sensitively on the choice of nuclear potential, P0 decreases with mass Ac of the emitted cluster, as is the case for other two model calculations of Blendowske–Walliser and Malik–Gupta. The deformation effects of the emitted clusters are shown to reduce the performation probabilities by an order of magnitude 103, which invalidates the simple straight line formula between — log 10 P0 and Ac.

We present our investigations of double‐folding, heavy‐ion potentials and of the role played by nucleon‐nucleon interactions that incorporate medium effects in accordance with the saturation properties of nuclear matter. The dependence on the medium is included directly via a repulsive term in the heavy‐ion potential, and/or via a density dependent term as in the case of zero‐or finite‐range forces in mean‐field nuclear structure calculations. We illustrate this point with the coupled‐channels calculations we performed for systems that display a hindrance in fusion at deep sub‐barrier energies.

Excitation functions for total reaction cross sections, ${\ensuremath{\sigma}}_{R}$, were measured for the light, mainly proton-rich nuclei $^{6}\mathrm{Li}$, $^{7}\mathrm{Be}$, $^{10}\mathrm{B}$, $^{9,10,11}\mathrm{C}$, $^{12}\mathrm{N}$, $^{13,15}\mathrm{O}$, and $^{17}\mathrm{Ne}$ incident on a Si telescope at energies between 15 and 53 MeV/nucleon. The telescope served as target, energy degrader and detector. Proton-removal cross sections, ${\ensuremath{\sigma}}_{2p}$ for $^{17}\mathrm{Ne}$ and ${\ensuremath{\sigma}}_{p}$ for most of the other projectiles, were also measured. The strong absorption model reproduces the $A$-dependence of ${\ensuremath{\sigma}}_{R}$, but not the detailed structure. Glauber multiple scattering theory and the Jeukenne, Lejeune, and Mahaux (JLM) folding model provided improved descriptions of the measured ${\ensuremath{\sigma}}_{R}$ values. Rms radii, extracted from the measured ${\ensuremath{\sigma}}_{R}$ using the optical limit of Glauber theory, are in good agreement with those obtained from high energy data. One-proton removal reactions are described using an extended Glauber model, incorporating second order noneikonal corrections, realistic single particle densities, and spectroscopic factors from shell model calculations.

$^{13}\mathrm{N}(p,\ensuremath{\gamma})^{14}\mathrm{O}$ is one of the key reactions which trigger the onset of the hot CNO cycle. This transition occurs when the proton capture rate on $^{13}\mathrm{N}$ is faster, due to increasing stellar temperature $(\ensuremath{\geqslant}{10}^{8}\phantom{\rule{0.3em}{0ex}}\mathrm{K})$, than the $^{13}\mathrm{N}$ $\ensuremath{\beta}$-decay rate. The rate of this reaction is dominated by the resonant capture through the first excited state of $^{14}\mathrm{O}$ $({E}_{r}=0.528\phantom{\rule{0.3em}{0ex}}\text{MeV})$. However, through constructive interference, direct capture below the resonance makes a non-negligible contribution to the reaction rate. We have determined this direct contribution by measuring the asymptotic normalization coefficient for $^{14}\mathrm{O}\ensuremath{\rightarrow}^{13}\mathrm{N}+p$. In our experiment, an $11.8\phantom{\rule{0.3em}{0ex}}\text{MeV}∕\text{nucleon}$ $^{13}\mathrm{N}$ radioactive beam was used to study the $^{14}\mathrm{N}(^{13}\mathrm{N},^{14}\mathrm{O})^{13}\mathrm{C}$ peripheral transfer reaction, and the asymptotic normalization coefficient, ${({C}_{{p}_{1∕2}}^{^{14}\mathrm{O}})}^{2}=29.0\ifmmode\pm\else\textpm\fi{}4.3\phantom{\rule{0.3em}{0ex}}{\text{fm}}^{\ensuremath{-}1}$, was extracted from the measured cross section. The radiative capture cross section was estimated using an $R$-matrix approach with the measured asymptotic normalization coefficient and the latest resonance parameters. We find the $S$ factor for $^{13}\mathrm{N}(p,\ensuremath{\gamma})^{14}\mathrm{O}$ to be larger than previous estimates. Consequently, the transition from the cold to hot CNO cycle for novae would be controlled by the slowest proton capture reaction $^{14}\mathrm{N}(p,\ensuremath{\gamma})^{15}\mathrm{O}$.

Existing experimental data for the breakup of $^{8}\mathrm{B}$ at energies from 30 to $1000\phantom{\rule{0.3em}{0ex}}\text{MeV}∕\text{nucleon}$ on light through heavy targets are analyzed in detail in terms of an extended Glauber model. The predictions of the model are in excellent agreement with independent reaction data (reaction cross sections and parallel momentum distributions for corelike fragments). Final-state interactions have been included in the Coulomb dissociation component. We extract asymptotic normalization coefficients (ANC) from which the astrophysical factor ${S}_{17}(0)$ for the key reaction for solar neutrino production, $^{7}\mathrm{Be}(p,\ensuremath{\gamma})^{8}\mathrm{B}$, can be evaluated. Glauber model calculations using different effective interactions give consistent, though slightly different results. The differences give a measure of the precision one can expect from the method. The unweighted average of all ANCs extracted leads to ${S}_{17}(0)=18.7\ifmmode\pm\else\textpm\fi{}1.9\phantom{\rule{0.3em}{0ex}}\text{eV}\phantom{\rule{0.3em}{0ex}}\mathrm{b}$. The results of this new analysis are compared with the earlier one. They are consistent with the values from most direct measurements and other indirect methods.

A study of the interaction of loosely bound nuclei 6,7Li at 9 and 19 AMeV with light targets has been undertaken. With the determination of unambiguous optical potentials in mind, elastic data for four projectile-target combinations and one neutron transfer reaction 13C(7Li,8Li)12C have been measured on a large angular range. The kinematical regime encompasses a region where the mean field (optical potential) has a marked variation with mass and energy, but turns out to be sufficiently surface transparent to allow strong refractive effects to be manifested in elastic scattering data at intermediate angles. The identified exotic feature, a "plateau" in the angular distributions at intermediate angles, is fully confirmed in four reaction channels and interpreted as a pre-rainbow oscillation resulting from the interference of the barrier and internal barrier farside scattering subamplitudes., Comment: 19 pages, 14 figures, 3 tables to submit to Phys. Rev. C

Asymptotic normalization coefficients (ANCs) for Li-8-->Li-7+n have been extracted from the neutron transfer reaction C-13(Li-7,Li-8)C-12 at 63 MeV. These are related to the ANCs in B-8-->Be-7 + p using charge symmetry. We extract ANCs for B-8 which are in very good agreement with those inferred from proton transfer and breakup experiments. We have also separated the contributions from the p(1/2) and p(3/2) components in the transfer. We find the astrophysical factor for the Be-7(p, gamma)B-8 reaction to be S-17( 0) = 17.6+/-1.7 eV b. This is the first time that the rate of a direct capture reaction of astrophysical interest has been determined through a measurement of the ANCs in the mirror system.

model calculations to extract the asymptotic normalization coefficient for the wave function of the last proton in the ground state of 9 C. The calculations are done first using folded potentials starting from two different effective nucleon-nucleon interactions and second in the optical limit using three nucleon-nucleon interactions, and the results are found to be consistent, with no new parameters adjusted. We find C 2 ( p3/2)1C 2 ( p1/2) 51.2260.13 fm 21 . From this result we obtain the astrophysical factor for the proton radiative capture reaction 8 B(p,g) 9 Ca sS 18(0)54666 eV b. The calculated energy dependence of the astrophysical S factor for the energy region Ec.m.5020.8 MeV and the reaction rates for T95021 are included. Radiative capture reactions are of crucial importance in nuclear astrophysics. The capture of charged particles on nu- clei, in particular of protons in basic processes like hydrogen burning in various stellar environments, is very much hin- dered by the Coulomb repulsion. This leads to very small cross sections and consequently to the well known experi- mental problems associated with direct determination of as- trophysical S factors at very low energies @1#. Moreover, with the large number of reaction chains found to be of impor- tance in nucleosynthesis calculations for different static and explosive burning scenarios @2-4 #, more data involving the capture on unstable nuclei becomes necessary. In many in- stances direct measurements involving unstable nuclei are very difficult or even impossible and indirect methods must be used. It has been known for a long time that transfer reactions can be used as indirect methods for nuclear astrophysics ~see, e.g., Refs. @5,1# and references therein! and various tech- niques have been used since. A few years ago another indi- rect approach based on measurements of peripheral transfer reactions was proposed @6,7#, and was subsequently used to determine the astrophysical factor S17(0) for the reaction 7 Be(p,g) 8 B using ( 7 Be, 8 B) transfer reactions. The method that is based on the observation that radiative capture of pro- tons is a very peripheral process at astrophysical energies, involves the extraction of nuclear quantities called asymptotic normalization coefficients ~ANC's ! from proton transfer reactions and these ANCs are then used to determine the astrophysical cross sections. The method works if the transfer reactions that have much higher cross sections than the capture reactions, are also peripheral. Using secondary beams available today, such experiments can be done in a matter of days @ 8-1 2#. More recently we have shown @13# that one-nucleon-removal reactions offer an alternative and complementary technique for extracting ANCs that is par- ticularly well adapted to rare isotopes produced using frag- mentation. In the breakup of loosely bound nuclei at inter- mediate energies, the requirement of core survival in the final channel automatically selects core-target interactions that are highly peripheral, with the result that the wave function of the removed nucleon is probed at and beyond the core's nuclear surface. This is then very similar to the low-energy light ion transfer reactions, where the short mean free path of the ions in the optical potential leads to surface localization. In Ref. @13# 8 B breakup data at energies between 30 and 300 MeV/nucleon on a variety of targets were compared with calculations done using a Glauber model @14# to extract the same ANC as that obtained from transfer reactions at about 12 MeV/nucleon. We suggested that such experiments have the additional advantage of using beams of lesser quality, at higher energies, and therefore can be applied to nuclei farther away from the stability. Here we use a similar approach to analyze the breakup of

The optical potential of halo and weakly bound nuclei has a long range part due to the coupling to breakup that damps the elastic scattering angular distributions at all angles for which the effect of the nuclear interaction is felt. In charge exchange reactions leading to a final state with a halo nucleus, the surface potential is responsible for a strong reduction in the absolute cross section. We show how the halo effect can be simply estimated semiclassically and related to the properties of the halo wave function. Assuming an exponential tail for the imaginary surface potential we show that the most important parameter is the diffusness $\alpha$ of the potential which is directly related to the decay length $\gamma_i$ of the initial wave function by $\alpha\approx(2\gamma_i)^{-1}$, Comment: 18 Latex pages, 1 table, 1 eps figures, 3 ps figures. accepted to Nucl. Phys. A

Peripheral transfer reactions can be used to determine asymptotic normalization coefficients (ANC). These coefficients, which provide the normalization of the tail of the overlap function, determine S-factors for direct capture reactions at astrophysical energies. A variety of proton transfer reactions have been used to measure ANCs. As a test of the technique, the 16 O(3He,d)17 F reaction has been used to determine ANCs for transitions to the ground and first excited states of 17 F. The S-factors for 16 O(p,γ)17 F calculated from these 17 F → 16 O +p ANCs are found to be in very good agreement with recent measurements. Following the same technique, the 10 B(7 Be,8 B)9 Be and 14 N(7 Be,8 B)13 C reactions have been used, along with optical model parameters for the radioactive beams that were obtained from a study of elastic scattering of loosely bound p-shell nuclei, to measure the ANC appropriate for determining 7 Be(p,γ)8 B. The results from the two transfer reactions provide an indirect determination of S 17(0). Recent measurements have been completed on the 14 N(11 C, 12 N)13 C reaction which will allow us to define the astrophysical S-factor for the 11 C(p,γ)12 N reaction.

We show that asymptotic normalization coefficients (ANC) can be extracted from one-nucleon breakup reactions of loosely bound nuclei at 30-300 MeV/nucleon. In particular, the breakup of 8B is described in terms of an extended Glauber model. The 8B ANC extracted from breakup data at several energies and on different targets, C(2)(tot) = 0.450+/-0.039 fm(-1), leads to the astrophysical factor S17(0) = 17.4+/-1.5 eV b for the key reaction for solar neutrino production 7Be(p, gamma)8B. The procedure described provides an indirect method to determine reaction rates of astrophysical interest with beams of loosely bound radioactive nuclei.

The experimental asymptotic normalization coefficient determined from peripheral transfer reactions is used to obtain the root-mean-square radius of the wave function for the loosely bound proton in ${}^{8}\mathrm{B}.$ It is shown that the asymptotic region contributes most and that matching of the interior wave function with the asymptotic part yields a nearly model-independent radius. We obtain $〈{r}^{2}{〉}^{1/2}=4.20\ifmmode\pm\else\textpm\fi{}0.22 \mathrm{fm}$ for the root-mean-square (rms) radius of the last proton, much larger than the rms radius of the ${}^{7}\mathrm{Be}$ core. This large value and the fact that the asymptotic part of the proton wave function contributes $85%$ to the rms radius are good sign that ${}^{8}\mathrm{B}$ is a halo nucleus.

Peripheral transfer reactions can be used to determine asymptotic normalization coefficients (ANC). These coefficients, which provide the normalization of the tail of the overlap function, determine S-factors for direct capture reactions at astrophysical energies. A variety of proton transfer reactions have been used to measure ANCs. As a test of the technique, the 16 O(3He,d)17 F reaction has been used to determine ANCs for transitions to the ground and first excited states of 17 F. The S-factors for 16 O(p,γ)17 F calculated from these 17 F → 16 O +p ANCs are found to be in very good agreement with recent measurements. Following the same technique, the 10 B(7 Be,8 B)9 Be and 14 N(7 Be,8 B)13 C reactions have been used, along with optical model parameters for the radioactive beams that were obtained from a study of elastic scattering of loosely bound p-shell nuclei, to measure the ANC appropriate for determining 7 Be(p,γ)8 B. The results from the two transfer reactions provide an indirect determination of S 17(0). Recent measurements have been completed on the 14 N(11 C, 12 N)13 C reaction which will allow us to define the astrophysical S-factor for the 11 C(p,γ)12 N reaction.