Coulomb dissociation of 9Li and the rate of the 8Li(n,g)9Li reaction
P. Banerjee, R. Chatterjee, R. Shyam
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13 pages Revtex, 2 figures, title and abstract changed on referee's suggestions, figures modified and discussions extended, results remain the same; version to appear in Phys. Rev. C
We calculate the Coulomb dissociation of 9Li on Pb and U targets at 28.5 MeV/A beam energy within a finite range distorted wave Born approximation formalism of the breakup reactions. Invoking the principle of detailed balance, these cross sections are used to determine the excitation function and subsequently the rate of the radiative capture reaction 8Li(n,g)9Li at astrophysical energies. Our method is free from the uncertainties associated with the multipole strength distributions of the 9Li nucleus. The rate of this reaction at a temperature of 10^9K is found to be about 2900 cm^3 mole^{-1} s^{-1}.
A short status report on Coulomb dissociation, an indirect method for nuclear astrophysics is given. An analytically solvable approach to study electromagnetic excitation in ^{11}Be, the archetype of a halo nucleus, is proposed.
We have measured the Coulomb dissociation of 8B into 7Be and proton at 254 MeV/nucleon using a large-acceptance focusing spectrometer. The astrophysical S17 factor for the 7Be(p,gamma)8B reaction at E{c.m.} = 0.25-2.78 MeV is deduced yielding S17(0)=20.6 \pm 1.2 (exp.) \pm 1.0 (theo.) eV-b. This result agrees with the presently adopted zero-energy S17 factor obtained in direct-reaction measurements and with the results of other Coulomb-dissociation studies performed at 46.5 and 51.2 MeV/nucleon.
In their recent study Neelam, Shubhchintak, and Chatterjee have claimed that "it would certainly be useful to perform a Coulomb dissociation experiment to find the low energy capture cross section for the reaction" $^{15}$N(n,$γ$)$^{16}$N. However, it is obvious that a Coulomb dissociation experiment cannot constrain this capture cross section because the dominating branchings of the capture reaction lead to excited states in $^{16}$N which do not contribute in a Coulomb dissociation experiment. An estimate of the total $^{15}$N(n,$γ$)$^{16}$N cross section from Coulomb dissociation of $^{16}$…
Coulomb Dissociation provides an alternative method for determining the radiative capture cross sections at astrophysically relevant low relative energies. For the breakup of $^8$B on $^{58}$Ni, we calculate the total Coulomb Dissociation cross section and the angular distribution for E1, E2 and M1. Our calculations are performed first within the standard first order semiclassical theory of Coulomb Excitation, including the correct three body kinematics, and later including the projectile-target nuclear interactions.
We study the Coulomb dissociation of the 19C nucleus in an effective field theory that uses the 18C core and the neutron as effective degrees of freedom and exploits the separation of scales in this halo system. We extract the effective-range parameters and the separation energy of the halo neutron from the experimental data taken at RIKEN by Nakamura et al. We obtain a value of (575 +/- 55(stat.) +/- 20(EFT)) keV for the one-neutron separation energy of 19C, and (7.75 +/- 0.35(stat.) +/- 0.3(EFT)) fm for the 18C-neutron scattering length. The width of the longitudinal momentum distribution pr…
The much needed nuclear input to the Standard Solar Model, $S_{17}(0)$, has now been measured with high precision ($\pm$5% or better) by different groups and good agreement is found, even when very different methods are employed. We review the decade long research program to measure the cross section of the $^7Be(p,γ)^8B$ reaction using the Coulomb dissociation method, including the pioneering RIKEN1 experiment carried out during March 1992, followed by RIKEN2, GSI1, GSI2 and an MSU experiment. Our RIKEN and GSI data allow us to rule out the much tooted large E2 contribution to the Coulomb dis…
Detection in zero degree calorimeters of the correlated forward-backward Coulomb or nuclear dissociation of two colliding nuclei is presented as a practical luminosity monitor in heavy ion colliders. Complementary predictions are given for total correlated Coulomb plus nuclear dissociation and for correlated forward-backward single neutrons from the giant dipole peak.
Coulomb dissociation is an especially simple and important reaction mechanism. Since the perturbation due to the electric field of the (target) nucleus is exactly known, firm conclusions can be drawn from such measurements. Electromagnetic matrixelements and astrophysical S-factors for radiative capture processes can be extracted from experiments. We describe the basic elements of the theory of nonrelativistic and relativistic electromagnetic excitation with heavy ions. This is contrasted to electromagnetic excitation with leptons (electrons), with their small electric charge and the absence o…
Breakup reactions are generally quite complicated, they involve nuclear and electromagnetic forces including interference effects. Coulomb dissociation is an especially simple and important mechanism since the perturbation due to the electric field of the nucleus is exactly known. Therefore firm conclusions can be drawn from such measurements. Electromagnetic matrixelements, radiative capture cross-sections and astrophysical S-factors can be extracted from experiments. We describe the basic theory, give analytical results for higher order effects in the dissociation of neutron halo nuclei and …
A methodology for extracting neutron direct capture rates from Coulomb dissociation data is developed and applied to the Coulomb dissociation of 15C on 208Pb at 68 MeV/nucleon. Full Continuum Discretized Coupled Channel calculations are performed and an asymptotic normalization coefficient is determined from a fit to the breakup data. Direct neutron capture calculations using the extracted asymptotic normalization coefficient provide $(n,γ)$ cross sections consistent with direct measurements. Our results show that the Coulomb Dissociation data can be reliably used for extracting the cross sect…
In this work the semiclassical model of pure Coulomb excitation was applied to the breakup of 15,17,19C. The ground state wave functions were calculated in the particle-rotor model including core excitation. The importance of interference terms in the dipole strength arising after including core degrees of freedom is analyzed for each isotope. It is shown that Coulomb interference effects are important for the case of 17C.
A process, involving the 7Be core excitation in the Coulomb breakup of 8B into p + 7Be has been investigated. From the experimental results recently obtained in RIKEN we have derived the mixing amplitude of the | 7Be(1/2-) X (1p_{3/2}); 2+> configuration in the ground state of 8B. Implications on the evaluation of the S17 at stellar energies are discussed.
We investigate the Coulomb dissociation of 8B on 208Pb target at the beam energy of 250 MeV/nucleon, employing the cross sections for the radiative capture reaction 7Be(p,gamma)8B calculated within the Shell Model Embedded in the Continuum (SMEC) approach. In contrast to the situation at lower beam energies, the Coulomb breakup cross sections are found to be sensitive to the M1 transitions. Comparisons of SMEC and single-particle potential model predictions show that the Coulomb breakup cross sections at these high energies are sensitive to the structure model of 8B. Analysis of the preliminar…
We have calculated the E1 and E2 contributions to the low-energy B-8 + Pb-208 -> p + Be-7 + Pb-208 Coulomb dissociation cross sections using the kinematics of a recent experiment at RIKEN. Using a potential model description of the Be-7 (p,gamma) B-8 reaction, we find that the E2 contributions cannot a priori be ignored in the analysis of the data. Its inclusion reduces the extracted Be-7 (p,gamma) B-8 S-factor at solar energies by about 25%.
In an effort to better determine the 7Be(p,gamma)8B reaction rate, we have performed inclusive and exclusive measurements of the Coulomb dissociation of 8B. The former was a study of longitudinal momentum distributions of 7Be fragments emitted in the Coulomb breakup of intermediate energy 8B beams on Pb and Ag targets. Analysis of these data yielded the E2 contribution to the breakup cross section. In the exclusive measurement, we determined the cross section for the Coulomb breakup of 8B on Pb at low relative energies in order to infer the astrophysical S factor for the 7Be(p,gamma)8B reactio…
The recently observed large cross sections for the Coulomb dissociation of $^{31}$Ne nucleus indicate that this nucleus takes a halo structure in the ground state. We analyse these experimental data using the particle-rotor model, that takes into account the rotational excitation of the core nucleus $^{30}$Ne. We show that the experimental data can be well reproduced when the quadrupole deformation parameter of $^{30}$Ne is around $β_2=0.2\sim0.3$, at which the ground state takes the spin and parity of $I^π$=3/2$^-$. This state corresponds to the Nilsson level [330 1/2] in the adiabatic limit …
The Coulomb dissociation of 8B, measured with high precision by the GSI group, is in excellent agreement with the astrophysical cross section factor (S17) measured by the Weizmann group with a 7Be target. The GSI and Weizmann data are in good agreement with the Seattle data at high energies, but at low energies we observe a slight systematic (up to 2sigma) deviation, yet the Seattle group repeatedly rejects the CD method. We show that when plotting the slopes, they mis plotted one CD data point and exclude measured slopes that contradict their claim. Indeed the measured slope is essential to e…
We investigate the effects arising out of the $E1 - E2$ interference in the Coulomb dissociation of $^8$B at beam energies below and around 50 MeV/nucleon. The theory has been formulated within a first order semiclassical scheme of Coulomb excitation, in which both the ground state and the continuum state wave functions of $^8$B enter as inputs. We find that the magnitude of the interference could be large in some cases. However, there are some specific observables which are free from the effects of the $E1 - E2$ interference, which is independent of the models used to describe the structure o…
The GSI1, GSI2 (as well as the RIKEN2 and the corrected GSI2) measurements of the Coulomb Dissociation (CD) of 8B are in good agreement with the most recent Direct Capture (DC) 7Be(p,g)8B reaction measurement performed at Weizmann and in agreement with the Seattle result. Yet it was claimed that the CD and DC results are sufficiently different and need to be reconciled. We show that these statements arise from a misunderstanding (as well as misrepresentation) of CD experiments. We recall a similar strong statement questioning the validity of the CD method due to an invoked large E2 component t…
The GSI1, GSI2 (as well as the RIKEN2 and the corrected GSI2) measurements of the Coulomb Dissociation (CD) of 8B are in good agreement with the most recent Direct Capture (DC) 7Be(p,g)8B reaction measurement performed at Weizmann and in agreement with the Seattle result. Yet it was claimed that the CD and DC results are sufficiently different and need to be reconciled. We show that these statements arise from a misunderstanding (as well as misrepresentation) of CD experiments. We recall a similar strong statement questioning the validity of the CD method due to an invoked large E2 component t…
Coherent vector meson production in peripheral nucleus-nucleus collisions is discussed. These interactions may occur for impact parameters much larger than the sum of the nuclear radii. Since the vector meson production is always localized to one of the nuclei, the system acts as a two-source interferometer in the transverse plane. By tagging the outgoing nuclei for Coulomb dissociation it is possible to obtain a measure of the impact parameter and thus the source separation in the interferometer. This is of particular interest since the life-time of the vector mesons are generally much shorte…
We present S factor data obtained from the Coulomb dissociation of 83 MeV/nucleon 8B, and analyze 7Be longitudinal momentum distributions measured at 44 and 81 MeV/nucleon using a potential model, first-order perturbation theory, and dynamical solution of the time-dependent Schroedinger equation. Comparing our results with independent continuum-discretized coupled channels calculations, we study the reaction model and beam energy dependence of the E2 contribution to the dissociation cross section. By fitting radiative capture and Coulomb breakup data taken below relative energies of 400 keV wi…
We study the ground-state structure of nuclei in the vicinity of the one-neutron dripline within the latest version of the quark-meson coupling (QMC) model with a particular emphasis on 23O. For this nucleus the model predicts a [22O(0+) + n (2s_{1/2})] configuration for its ground state, with a one neutron separation energy in close agreement with the corresponding experimental value. The wave function describing the valence neutron-core relative motion was then used to calculate the Coulomb dissociation of 23O on a lead target at a beam energy of 422 MeV/nucleon. The experimental neutron-cor…
We study the breakup reactions of 8B projectiles in high energy (50 and 250 MeV/u) collisions with heavy nuclear targets (208Pb). The intrinsic nuclear wave functions are calculated using a simple model, as well as a simple optical potential. We demonstrate that nuclear effects are negligible and evaluate the contributions of various (E1, E2 and M1) multipolarities. A good agreement with measured data is obtained with insignificant M1 contribution (at 50 MeV/u) and very small E2 contribution.
We investgate the breakup of one-neutron halo nuclei in the Coulomb field of a target nucleus. In the post-form distorted wave Born approximation theory of this reaction, with only Coulomb distortions in the entrance and the outgoing channels, an analytic solution for the breakup $T$-matrix is known. We study this $T$-matrix and the corresponding cross-sections numerically. This formula can be related to the first order semiclassical treatment of the electromagnetic dissociation. This theory contains the electromagnetic interaction between the core and the target nucleus to all orders. We show…
The Coulomb dissociation method to obtain the astrophysical S-factor, $S_{17}(0)$, for the $^7$Be($p,γ)^8$B reaction at solar energies is investigated by analysing the recently measured data on the breakup reaction $^{208}$Pb$(^8$B,$^7$Be$~p)^{208}$Pb at 46.5 MeV/A beam energy. Breakup cross sections corresponding to E1, $E2$ and $M1$ transitions are calculated with a theory of Coulomb excitation that includes the effects of the Coulomb recoil as well as relativistic retardation. The interplay of nuclear and Coulomb contributions to the breakup process is studied by performing a full quantum m…
Systematic analysis of 8B Coulomb dissociation with the Asymptotic Normalization Coefficient (ANC) method is proposed to determine the astrophysical factor S17 accurately. An important advantage of the analysis is that uncertainties of the extracted S17 coming from the use of the ANC method can quantitatively be evaluated, in contrast to previous analyses using the Virtual Photon Theory (VPT). Calculation of measured spectra in dissociation experiments is done by means of the method of Continuum-Discretized Coupled-Channels (CDCC). From the analysis of 58Ni(8B,7Be+p)58Ni at 25.8 MeV, S17=22.83…
We reply to the comments (arXiv:1605.07499 [nucl-th]) on "Structure effects in the $^{15}$N($n,γ$)$^{16}$N radiative capture reaction from the Coulomb dissociation of $^{16}$N". We have investigated the issue of "energy dependence of branching ratios" and believe that this energy dependence is due to the proper inclusion of the non-resonant continuum in the post-form reaction theory. Interestingly, this energy dependence is sensitive to the relative orbital angular momentum content of the state. We reiterate that we have attempted to resolve the discrepancy in the spectroscopic factors of low-…
Recent claims of the Seattle group of evidence of "slope difference between CD [Coulomb Dissociation] and direct [capture] results" are based on wrong and selective data. When the RIKEN2 data are included correctly, and previously published Direct Capture (DC) data are also included, we observe only a 1.9 sigma difference in the extracted so called "scale independent slope (b)", considerably smaller than claimed by the Seattle group. The very parameterization used by the Seattle group to extract the so called b-slope parameter has no physical foundation. Considering the physical slope (S' = dS…
The semiclassical, dynamical description of diffraction dissociation of weakly bound nuclei is applied to analyze the decay-energy spectra of $^{15}$C that have been measured at 68 MeV/nucleon on a Pb target. The optical potentials that are used to describe the nuclear interaction of $^{15}$C with the target nucleus are realistic because the fits to the two measured spectra, one with a small and one with a very large acceptance angle, are consistent and of similar quality. The cross section for the radiative neutron capture on $^{14}$C to the 1/2$^+$ ground state of $^{15}$C is deduced from th…
The breakup of 11Be on carbon and lead targets around 70 MeV/nucleon is investigated within a semiclassical framework. The role of the 5/2+ resonance is analyzed in both cases. It induces a narrow peak in the nuclear-induced breakup cross section, while its effect on Coulomb breakup is small. The nuclear interactions between the projectile and the target is responsible for the transition toward this resonant state. The influence of the parametrization of the 10Be-n potential that simulates 11Be is also addressed. The breakup calculation is found to be dependent on the potential choice. This le…
The 7Be(p,gamma)8B reaction is one of the major source of uncertainties in estimating the 8B solar neutrino flux and is critical for undertsanding the Solar Neutrino Problem and neutrinos. The main source of uncertainty is the existence of conflicting data with different absolute normalization. Attempts to measure this reaction rate with 7Be beams are under way by the UConn-LLN collaboration, and we discuss a newly emerging method to extract this cross section from the Coulomb dissociation of the radioactive beam of 8B. We discuss some of the issues relevant for this study including the questi…
The Coulomb Dissociation (CD) cross sections of the stable isotopes 92,94,100Mo and of the unstable isotope 93Mo were measured at the LAND/R3B setup at GSI Helmholtzzentrum für Schwerionenforschung in Darmstadt, Germany. Experimental data on these isotopes may help to explain the problem of the underproduction of 92,94Mo and 96,98Ru in the models of p-process nucleosynthesis. The CD cross sections obtained for the stable Mo isotopes are in good agreement with experiments performed with real photons, thus validating the method of Coulomb Dissociation. The result for the reaction 93Mo(g,n) is es…
We study the break-up of 8B in collisions with heavy-ions. The process is described in terms of inelastic excitations leading to states in the continuum. The effects of the nuclear and coulomb fields are included on the same footing in the microscopic construction of the transition matrix elements. The interplay between coulomb and nuclear excitation processes differs significantly from the situation encountered in reactions involving systems close to the stability line. In particular, nuclear excitation is found to remain predominant at energies well below the coulomb barrier,
We aim to re-investigate the structure of the neutron rich exotic nucleus ^{19}C through studies of its Coulomb breakup reactions, assuming that its excitation is to states in the low energy continuum. The method used retains all finite-range effects associated with the interactions between the breakup fragments and can use realistic wave functions for this possibly halo nucleus. We apply the method to compute the longitudinal momentum distribution of ^{18}C, exclusive neutron angular distribution and relative energy spectrum of ^{19}C following Coulomb breakup of ^{19}C on heavy targets at be…
As a model of a neutron halo nucleus we consider a neutron bound to an inert core by a zero range force. We study the breakup of this simple nucleus in the Coulomb field of a target nucleus. In the post-form DWBA (or, in our simple model CWBA (``Coulomb Wave Born Approximation'')) an analytic solution for the T-matrix is known. We study limiting cases of this T-matrix. As it should be, we recover the Born approximation for weak Coulomb fields (i.e., for the relevant Coulomb parameters much smaller than 1). For strong Coulomb fields, high beam energies, and scattering to the forward region we f…
We study kaon-charmonium and eta-charmonium dissociation reactions. The K-charmonium dissociation and the eta-charmonium dissociation include 27 reactions. Cross sections for the reactions are calculated in the Born approximation, in the quark-interchange mechanism and with a temperature-dependent quark potential. The temperature dependence of peak cross sections of endothermic reactions is linked to the temperature dependence of quark-antiquark relative-motion wave functions, meson masses and the quark potential. Although the eta meson and kaon have similar masses, the energy and temperature …
The E2 cross section calculated by Langanke and Shoppa for the Riken experiment on the Coulomb Dissociation of 8B uses E2 nuclear matrix elements from one specific model. Other nuclear models predict a considerably smaller E2 cross section (by a pproximately a factor of 3 to 4), and Langanke and Shoppa appear to assume the most optimistic scenario predicting large E2 cross section. We also note that Barker has already criticised the nuclear model used by Langanke and Shoppa. A MODEL INDEPENDENT Chi-Square analysis of the Riken data, suggest the best fit for the current Riken data is obtained w…
We use the Coulomb dissociation (CD) method to calculate the rate of the $^{36}$Mg(${n,γ}$)$^{37}$Mg radiative capture reaction. The CD cross sections of the $^{37}$Mg nucleus on a $^{208}$Pb target at the beam energy of 244 MeV/nucleon, for which new experimental data have recently become available, were calculated within the framework of a finite range distorted wave Born approximation theory that is extended to include the projectile deformation effects. Invoking the principle of detailed balance, these cross sections are used to determine the excitation function and subsequently the rate o…
We investigate the structure of the neutron rich nucleus ^{19}C through studies of its breakup in the Coulomb field of target nuclei. The breakup amplitude is calculated within an adiabatic treatment of the projectile excitation, which allows the use of the realistic wave functions for the relative motion between the fragments in the ground state of the projectile. The angular distribution of the center of mass of ^{19}C, longitudinal momentum distribution of ^{18}C and relative energy spectrum of the fragments (neutron - ^{18}C) following the breakup of ^{19}C on heavy targets at beam energie…
Nucleosynthesis processes involve reactions on several thousand nuclei, both close to and far off stability. The preparation of reaction rates to be used in astrophysical investigations requires experimental and theoretical input. In this context, two interesting aspects are discussed: (i) the relevant gamma transition energies in astrophysical capture reactions, and (ii) the newly discovered Coulomb suppression of the stellar enhancement factor. The latter makes a number of reactions with negative Q value more favorable for experimental investigation than their inverse reactions, contrary to …
Coulomb and nuclear dissociation of $^{17}$Ne on light and heavy targets are studied theoretically. The dipole E1 strength function is determined in a broad energy range including energies of astrophysical interest. Dependence of the strength function on different parameters of the $^{17}$Ne ground state structure and continuum dynamics is analyzed in a three-body model. The discovered dependence plays an important role for studies of the strength functions for the three-body E1 dissociation and radiative capture. The constraints on the $[s^2]/[d^2]$ configuration mixing in $^{17}$Ne and on $p…
Coulomb dissociation is an especially simple and important reaction mechanism. Since the perturbation due to the electric field of the nucleus is exactly known, firm conclusions can be drawn from such measurements. Electromagnetic matrix elements and astrophysical S-factors for radiative capture processes can be extracted from experiments. We describe the basic theory, new results concerning higher order effects in the dissociation of neutron halo nuclei, and briefly review the experimental results obtained up to now. Some new applications of Coulomb dissociation for nuclear astrophysics and n…
K*-charmonium dissociation reactions in hadronic matter are studied in the Born approximation, in the quark-interchange mechanism, and with a temperature-dependent quark potential. We obtain the temperature dependence of unpolarized cross sections for K*-charmonium dissociation reactions which produce charmed mesons and charmed strange mesons. We use the cross sections for charmonium dissociation in collisions with pion, rho meson, kaon, vector kaon, and eta meson to calculate dissociation rates of charmonium with the five types of mesons. Because of the temperature dependence of the meson mas…
Relativistic nucleus-nucleus reactions occur mainly through the Strong or Electromagnetic (EM) interactions. Transport codes often neglect the latter. This work shows the importance of including EM interactions for space radiation applications.
We discuss recent work on Coulomb dissociation and an effective-range theory of low-lying electromagnetic strength of halo nuclei. We propose to study Coulomb dissociation of a halo nucleus bound by a zero-range potential as a homework problem. We study the transition from stripping to bound and unbound states and point out in this context that the Trojan-Horse method is a suitable tool to investigate subthreshold resonances.
Purpose : The aim of this paper is to calculate the $^{15}$N($n, γ$)$^{16}$N radiative capture cross section and its subsequent reaction rate by an indirect method and in that process investigate the effects of spectroscopic factors of different levels of $^{16}$N to the cross section. Method : A fully quantum mechanical Coulomb breakup theory under the aegis of post-form distorted wave Born approximation is used to calculate the Coulomb breakup of $^{16}$N on Pb at 100 MeV/u. This is then related to the photodisintegration cross section of $^{16}$N($γ, n$)$^{15}$N and subsequently invoking th…
We review some simple mechanisms of breakup in nuclear reactions. We mention the spectator breakup, which is described in the post-form DWBA. The relation to other formulations is also indicated. An especially important mechanism is Coulomb dissociation. It is a distinct advantage that the perturbation due to the electric field of the nucleus is exactly known. Therefore firm conclusions can be drawn from such measurements. Some new applications of Coulomb dissociation for nuclear astrophysics are discussed.
The phi-charmonium dissociation reactions in hadronic matter are studied. Unpolarised cross sections for 12 reactions are calculated in the Born approximation, in the quark-interchange mechanism and with a temperature-dependent quark potential. The potential leads to remarkable temperature dependence of the cross sections. With the cross sections and the phi distribution function we calculate the dissociation rates of the charmonia in the interactions with the phi meson in hadronic matter. The dependence of the rates on temperature and charmonium momentum is meaningful to the influence of phi …
Meson-charmonium dissociation reactions governed by the quark interchange are studied with temperature-dependent quark potentials. Quark-antiquark relative-motion wave functions and masses of charmonia and charmed mesons are determined by the central spin-independent part of the potentials or by the central spin-independent part and a smeared spin-spin interaction. The prominent temperature dependence of the masses is found. Based on the potentials, the wave functions, and the meson masses, we obtain temperature-dependent cross sections for fifteen pion-charmonium and rho-charmonium dissociati…
We show examples of neutron capture, photo dissociation and Coulomb dissociation processes, relevant for studying nuclear structure properties of some light nuclei. In the case of the neutron capture, we show how interference effects among the direct and resonance processes can be accounted for. The same interference effect is shown to play an important role in the photo dissociation of 9Be, for excitation energies just above the neutron emission threshold. Finally, the Coulomb dissociation of radioactive projectiles is shown to provides basic structure information on neutron rich exotic syste…
The $α$-particle production in the dissociation of $^{9}$Be on $^{209}$Bi and $^{64}$Zn at energies just above the Coulomb barrier is studied within the two-center shell model approach. The dissociation of $^{9}$Be on $^{209}$Bi is caused by a molecular single-particle effect (Landau-Zener mechanism) before the nuclei reach the Coulomb barrier. Molecular single-particle effects do not occur at that stage of the collision for $^{9}$Be+$^{64}$Zn, and this explains the absence of fusion suppression observed for this system. The polarisation of the energy level of the last neutron of $^{9}$Be and,…
We compare Path Integral Monte Carlo calculations by Militzer and Pollock (Phys. Rev. B 71, 134303, 2005) of Coulomb tunneling in nuclear reactions in dense matter to semiclassical calculations assuming WKB Coulomb barrier penetration through the radial mean-field potential. We find a very good agreement of two approaches at temperatures higher than ~1/5 of the ion plasma temperature. We obtain a simple parameterization of the mean field potential and of the respective reaction rates. We analyze Gamow-peak energies of reacting ions in various reaction regimes and discuss theoretical uncertaint…
The study of nuclear breakup of halo and weakly bound particles has been one of the key ingredients in the understanding of exotic nuclei during the last thirty years. One of the most used methods to analyse data, in particular absolute breakup cross sections, has been the eikonal approximation. Here we revise critically the formalisms used for calculating the diffraction dissociation part of nuclear breakup and show that there is a formula that can be applied to breakup on any target, while a most commonly used formula must be restricted to light targets as it contains also the effect of Coul…
A relationship between the Coulomb inclusive break-up probability and the radiative capture reaction rate for weakly-bound three-body systems is established. This direct link provides a robust procedure to estimate the reaction rate for nuclei of astrophysical interest by measuring inclusive break-up processes at different energies and angles. This might be an advantageous alternative to the determination of reaction rates from the measurement of $B(E1)$ distributions through exclusive Coulomb break-up experiments. In addition, it provides a reference to assess the validity of different theore…
The dissociation of halo nuclei through their collision with light and heavy targets is considered within the Continuum Discretized Coupled Channels theory. We study the one-proton halo nucleus $^8$B and the one-neutron halo nucleus $^{11}$Be, as well as the more normal $^7$Be. The procedure previously employed to extract the Coulomb dissociation cross section by subtracting the nuclear one is critically assessed, and the scaling law usually assumed for the target mass dependence of the nuclear breakup cross section is also tested. It is found that the nuclear breakup cross section for these v…
Indirect methods in nuclear astrophysics are discussed. Recent work on Coulomb dissociation and an effective-range theory of low-lying electromagnetic strength of halo nuclei is presented. Coulomb dissociation of a halo nucleus bound by a zero-range potential is proposed as a homework problem (for further references see G. Baur and S. Typel, nucl-th/0504068). It is pointed out that the Trojan-Horse method (G. Baur, F. Rösel, D. Trautmann and R. Shyam, Phys. Rep. 111 (1984) 333) is a suitable tool to investigate subthreshold resonances.
Within the pure Coulomb breakup mechanism, we investigate the one-neutron removal reaction of the type A(a,b$γ$)X with $^{11}$Be and $^{19}$C projectiles on a heavy target nucleus $^{208}$Pb at the beam energy of 60 MeV/nucleon. Our intention is to examine the prospective of using these reactions to study the structure of neutron rich nuclei. Integrated partial cross sections and momentum distributions for the ground as well as excited bound states of core nuclei are calculated within the finite range distorted wave Born approximation as well as within the adiabatic model of the Coulomb breaku…
