Post-form Distorted Wave Born Approximation Research Articles

Influence of light neutron-rich exotic nuclei in deciding abundance patterns relevant for explosive nucleosynthesis

Exotic neutron-rich nuclei play an important role in r-process nucleosynthesis. We study the effect of including proper nuclear structure to calculate neutron capture and photodisintegration rates, especially for 19C and 20N, under the aegis of post-form distorted wave Born approximation (FRDWBA). Considering a network of neutron-rich C–N–O isotopes, we show the effect on abundance calculations in a neutrino-driven wind environment of a core-collapse supernova at two critical temperatures T 9 = 3.4 and 0.62. The results are compared for nuclear physics inputs sourced from the FRDWBA, statistical estimates, and standard databases. At temperatures T 9 = 3.4, where alpha capture, or at T 9 = 0.62, where the neutron capture dominates, one can distinguish the effect of accounting for the exotic nature of the nuclei involved. Furthermore, we assess the impact of varying neutron capture and photodisintegration rates involving halo or bubble structures on the abundances within the network.

{}^{5}He({}^{3}He,{}^{4}He){}^{4}He as a three-body reaction via a continuum resonance in the n+{}^{4}He system

The {}^{5}He({}^{3}He,{}^{4}He){}^{4}He reaction involving the unstable {}^{5}He nucleus is a possible process in primordial nucleosynthesis to convert {}^{3}He into {}^{4}He in a neutron transfer reaction. Since experimental data for the reaction cross section are not available, a theoretical prediction is needed to estimate the relevance of this process in comparison to other reactions, e.g., {}^{3}He({}^{2}H,p){}^{4}He or {}^{3}H({}^{2}H,n){}^{4}He. In this work the cross section and the Maxwellian-averaged transition rate of the {}^{5}He({}^{3}He,{}^{4}He){}^{4}He reaction are calculated using a post-form distorted-wave Born approximation in a simple cluster model. For that purpose the reaction is treated as a genuine process with three particles, text{ n }+{}^{4}text{ He }+{}^{3}text{ He }, in the entrance channel proceeding through the 3/2^{-} resonance in the n-{}^{4}He scattering continuum.

Structure effects in theN15(n,γ)N16radiative capture reaction from the Coulomb dissociation ofN16

Purpose : The aim of this paper is to calculate the $^{15}$N($n, \gamma$)$^{16}$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($\gamma, n$)$^{15}$N and subsequently invoking the principle of detailed balance, the $^{15}$N($n, \gamma$)$^{16}$N capture cross section is calculated. Results : The non-resonant capture cross section is calculated with spectroscopic factors from the shell model and those extracted (including uncertainties) from two recent experiments. The data seems to favor a more single particle nature for the low-lying states of $^{16}$N. The total neutron capture rate is also calculated by summing up non-resonant and resonant (significant only at temperatures greater than 1 GK) contributions and comparison is made with other charged particle capture rates. In the typical temperature range of $0.1-1.2$ GK, almost all the contribution to the reaction rate comes from capture cross sections below 0.25 MeV. Conclusion : We have attempted to resolve the discrepancy in the spectroscopic factors of low-lying $^{16}$N levels and conclude that it would certainly be useful to perform a Coulomb dissociation experiment to find the low energy capture cross section for the reaction, especially below 0.25 MeV.

Study of breakup mechanism of a loosely bound projectile in a region of Coulomb-breakup dominance

A kinematically complete measurement of the deuteron elastic break reaction has been carried out at Ed = 140 MeV on 12 C, 40 Ca, 90 Zr, and 208 Pb targets in a wide angular range of θp , θn = 0° –8° for a detailed study of the reaction mechanism of loosely bound projectiles in kinematical regions of Coulomb-breakup dominance. A finite-range calculation of the post-form distorted-wave Born approximation is presented.

Beam energy dependence of Coulomb-nuclear interference in the breakup ofBe11

Within the post-form distorted wave Born approximation wherein pure Coulomb, pure nuclear and their interference terms are treated consistently in a single setup we study the beam energy dependence of the Coulomb-nuclear interference terms in the breakup of $^{11}\mathrm{Be}$ on a medium mass $^{44}\mathrm{Ti}$ target. Our results suggest that the Coulomb-nuclear interference terms are dependent on the incident beam energy and can be as big as that of the individual Coulomb or nuclear terms depending on the angle and energy of the breakup fragments. We also calculate the relative energy spectra and one-neutron removal cross sections in the breakup of $^{11}\mathrm{Be}$ on a heavy $^{208}\mathrm{Pb}$ target at 69 MeV/nucleon for two different angular ranges of the projectile center of the mass scattering angle and compare them with recently available experimental data.

Coulomb breakup of one-neutron halo nuclei

The Coulomb breakup of one-neutron halo nuclei is studied within the postform distorted-wave Born approximation (DWBA) theory. A method of evaluation of the DWBA breakup amplitude in momentum space is presented. The theory is applied to the Coulomb breakup of the $^{11}\mathrm{Be}$ and $^{19}\mathrm{C}$ halo nuclei on $^{208}\mathrm{Pb}$ at the beam energy of $\ensuremath{\sim}70\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}∕\text{nucleon}$. Calculations for relative energy spectra are compared with available experimental data. Good agreement in shape is found for low relative energies. Comparison with the results obtained using a local momentum approximation to the DWBA amplitude shows that the effects of this additional approximation are substantial. The DWBA calculations are also compared to those of an adiabatic breakup theory. The two theories lead to significantly different results.

Theory of the Trojan-Horse Method

The Trojan-Horse method is an indirect approach to determine the energy dependence of S factors of astrophysically relevant two-body reactions. This is accomplished by studying closely related three-body reactions under quasi-free scattering conditions. The basic theory of the Trojan-Horse method is developed starting from a post-form distorted wave Born approximation of the T-matrix element. In the surface approximation the cross section of the three-body reaction can be related to the S-matrix elements of the two-body reaction. The essential feature of the Trojan-Horse method is the effective suppression of the Coulomb barrier at low energies for the astrophysical reaction leading to finite cross sections at the threshold of the two-body reaction. In a modified plane wave approximation the relation between the two-body and three-body cross sections becomes very transparent. Applications of the Trojan Horse Method are discussed. It is of special interest that electron screening corrections are negligible due to the high projectile energy.

Full quantal theory of one-neutron halo breakup reactions

We present a theory of one-neutron halo breakup reactions within the framework of post-form distorted wave Born approximation wherein pure Coulomb, pure nuclear and their interference terms are treated consistently in a single setup. This formalism is used to study the breakup of one-neutron halo nucleus 11Be on several targets of different masses. We investigate the role played by the pure Coulomb, pure nuclear and the Coulomb-nuclear interference terms by calculating several reaction observables. The Coulomb-nuclear interference terms are found to be important for more exclusive observables.

Theory of the Trojan–Horse method

The Trojan–Horse method is an indirect approach to determine the energy dependence of S factors of astrophysically relevant two-body reactions. This is accomplished by studying closely related three-body reactions under quasi-free scattering conditions. The basic theory of the Trojan–Horse method is developed starting from a post-form distorted wave Born approximation of the T-matrix element. In the surface approximation the cross-section of the three-body reaction can be related to the S-matrix elements of the two-body reaction. The essential feature of the Trojan–Horse method is the effective suppression of the Coulomb barrier at low energies for the astrophysical reaction leading to finite cross-sections at the threshold of the two-body reaction. In a modified plane wave approximation the relation between the two- and three-body cross-sections becomes very transparent. The appearing Trojan–Horse integrals are studied in detail.

Exact and approximate postform distorted-wave Born approximation amplitudes for the Coulomb breakup of neutron halo nuclei

The Coulomb breakup of neutron halo nuclei is considered within the framework of the postform distorted-wave Born approximation (DWBA). The quality of commonly used additional approximations to the DWBA theory is investigated by comparing the approximate with the exact DWBA calculations. The exact DWBA amplitude is expressed in momentum space as a three-dimensional integral and evaluated numerically. Calculations are presented for the Coulomb breakup of deuteron and ${}^{11}\mathrm{Be}$ at very forward angles at the beam energy of $\ensuremath{\sim}70 \mathrm{MeV}/\mathrm{nucleon}.$ The factorization approximation to the DWBA amplitude is studied and found to be suspected.

Postacceleration effects in the Coulomb dissociation of neutron halo nuclei

We study 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 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 that higher order effects (including postacceleration) are small in the case of higher beam energies and forward scattering. We investigate the beam energy dependence of the postacceleration effects. They are found to be quite important for smaller beam energies (slow collisions), but almost negligible at larger ones.

Four-body DWBA calculations of the Coulomb breakup of 6He

We investigate the Coulomb breakup of the two-neutron-halo nucleus 6He by extending the framework of the finite-range postform distorted-wave Born approximation theory introduced earlier for the description of the breakup of one-neutron-halo nuclei. The model can use the realistic three-body wave function for the 6He ground state. Calculations have been performed for energy, total and parallel momentum distributions of 4He fragment. The two-body 4He–neutron and neutron–neutron correlations have also been calculated. Our results are compared with those of an adiabatic model of the Coulomb-breakup reactions. The two theories lead to almost identical results. Comparisons are also made with the available experimental data. It is found that the pure Coulomb breakup can describe the bulk of the data taken at below grazing angles. However, a rigorous description of all the available data requires the consideration of the nuclear-breakup effects.

Dynamical description of the breakup of one-neutron halo nuclei11Beand19C

We investigate the breakup of the one-neutron halo nuclei ${}^{11}\mathrm{Be}$ and ${}^{19}\mathrm{C}$ within a dynamical model of the continuum excitation of the projectile. The time evolution of the projectile in coordinate space is described by solving the three-dimensional time dependent Schr\"odinger equation, treating the projectile-target (both Coulomb and nuclear) interaction as a time dependent external perturbation. The pure Coulomb breakup dominates the relative energy spectra of the fragments in the peak region, while the nuclear breakup is important at higher relative energies. The coherent sum of the two contributions provides a good overall description of the experimental spectra. Cross sections of the first order perturbation theory are derived as a limit of our dynamical model. The dynamical effects are found to be of the order of $10%--15%$ for beam energies in the range of 60--80 MeV/nucleon. A comparison of our results with those of a post-form distorted wave Born approximation shows that the magnitudes of the higher order effects are dependent on the theoretical model.

Imaginary deuteron optical potential due to elastic and inelastic breakup

The contributions to the reaction cross section from the elastic and inelastic breakup processes, calculated within the post-form distorted wave Born-approximation theory, are used as constraints to determine the contributions to the imaginary part of the deuteron optical potentials (IPDOP) due to the breakup channels. The Coulomb part of this potential due to the elastic breakup process is seen to account for the long range absorption in the optical potential. The nuclear parts of the IPDOP due to the elastic and inelastic breakup modes peak in different regions of the nuclear surface, with the latter being almost an order of magnitude larger than the former. This makes the IPDOP due to the breakup channels determined by us stronger than those calculated earlier ignoring the inelastic breakup mode.

WIDE-ANGLE α-t COINCIDENCE MEASUREMENT IN THE BREAKUP OF 7Li ON 27Al

We have performed wide-angle in-plane coincidence measurements of the alpha particles and tritons emitted in the 48-MeV 7 Li projectile breakup reaction on 27 Al . The data have been analyzed using the post-form distorted-wave Born-approximation (DWBA) theory of breakup reactions where Coulomb and nuclear breakup as well as their interference terms are included. The theory is able to provide a good description of the experimental data particularly at large relative angles between the fragments. The interference between the Coulomb and nuclear breakup modes is found to be significant.

Mechanism of the forward-angle(d,pn)reaction at intermediate energies

The elastic breakup of the deuteron has been measured in a kinematical condition of ${\ensuremath{\theta}}_{p}={\ensuremath{\theta}}_{n}=0\ifmmode^\circ\else\textdegree\fi{}$ at ${E}_{d}=140\mathrm{MeV}$ and 270 MeV on seven targets ranging from $Z=6$ to 82. A double-peaked structure with its minimum at ${E}_{p}\ensuremath{\simeq}{E}_{n}$ is observed for all the measured triple-differential cross sections, which indicates a large contribution from Coulomb breakup. While a symmetric shape is expected for an $E1$ transition, the observed proton-energy distribution is asymmetric, showing considerable dependence on both the target and the incident energy. These data and previous data at 56 MeV have been analyzed using the post-form of the distorted-wave Born approximation (DWBA) theory. Although the calculations account reasonably well for the asymmetric shape, by including the nuclear potential, they consistently overestimate the magnitudes of the cross sections over the whole measured region. Limitations of the post-form DWBA are discussed.

Nuclear breakup of8Bin a direct fragmentation model

We calculate the cross sections of the elastic and inelastic breakup modes for the inclusive breakup reaction ${}^{28}\mathrm{Si}{(}^{8}\mathrm{B}{,}^{7}\mathrm{Be})$ at beam energies between 10 and 40 MeV/nucleon within a direct fragmentation model formulated in the framework of the post-form distorted-wave Born approximation. In contrast to the case of the stable isotopes, the inelastic breakup mode is found to contribute only up to $30%$ to the total breakup cross section, which is in agreement with the recently measured experimental data. However, the high energy tail of the energy spectra of ${}^{7}\mathrm{Be}$ fragments is dominated by the inelastic breakup mode. The breakup amplitude is found to be dominated by contributions from distances well beyond the nuclear surface.

Wide-angle measurement of 48 MeV 6Li projectile fragmentation on 197Au

Abstract The 6 Li → α + d projectile breakup at E ( 6 Li) = 48 MeV with a 197 Au target is studied at large relative fragment energies. Both inclusive and exclusive measurements are carried out. The peaks corresponding to the protons and α-particles appear near the expected beam velocity positions while the deuterons and tritons are shifted to lower energy values. Calculations in the framework of both prior- and post-form distorted-wave Born approximation theories delineate an oscillatory structure for the exclusive cross section at larger α - d separation angles in consonance with the data profile. The oscillation is found to be a result of delicate Coulomb and nuclear interference. The distorted-wave analysis of the existing data at E ( 6 Li) = 75 MeV, where the Coulomb effect is smaller, show a different feature altogether having no oscillation at larger angles. At larger angles, the factorisation theory for uncorrelated events seems to hold better at 75 MeV incident energy than at 48 MeV. The implications of these results are discussed.

Coulomb dissociation of 11Li and 11Be in a direct fragmentation model

The Coulomb dissociation contribution to the two-neutron and one-neutron removal cross section of, respectively, 11Li and 11Be projectiles has been calculated in a direct fragmentation model. The model is formulated within the framework of the post form distorted-wave Born approximation. In this theory, the “post acceleration effect” of the 9Li and 10Be fragments in the final channel is accounted for properly. The Coulomb break-up can explain aprroximately upto 80% of the experimental 2n removal cross section of 11Li for the 197Au target at the incident energy of 29 MeV/ A. The beam energy dependence of the calculated cross sections is in good agreement with the few experimental points presently available. The angular distributions of the 9Li as well as of 2n system are found to be concentrated in the very forward angles.

Effect of break-up channels on (d,pn) coincidence cross section in post form break-up theories

The effect of deuteron break-up channels on the (d, pn) coincidence cross section as calculated within the framework of the post-form distorted-wave Born-approximation (DWBA) has been investigated. Expressions for the T-matrix for this reaction are derived in the post-form theory taking explicitly into account the coupling of break-up channels on the elastic deuteron channel. In this derivation the correction to the post-form DWBA T-matrix arising from coupling to the break-up channels are well separated from the latter, thus making it easier to visualize the effect of coupling clearly. Formulas are also derived for an alternate post-form T-matrix. It is shown that the final channel wave function to be used in this T-matrix does not correspond to the optical potential describing the deuteron-target elastic scattering. This makes the usefulness of the alternate post-form theories based on such potentials questionable. Numerical applications to 51V(d, pn) and 118Sn(d, pn) reactions at E d = 56 MeV show that the effect of coupling to break-up channels on the post-form DWBA (d, pn) cross section is not very significant. This is due to the fact that in this theory dominant contributions to these reactions come from the larger partial waves, in particular grazing partial waves and beyond.