Single-nucleon Knockout Reactions Research Articles

CNOK: A C++ Glauber model code for single-nucleon knockout reactions

A C++ program package was developed to calculate parallel momentum distributions (including the stripping mechanism and the diffractive dissociation mechanism) of the heavy residue (core) in single-nucleon knockout reactions induced by intermediate-energy (around and more than tens of MeV per nucleon) beams of stable and radioactive atomic nuclei. The program implements the Glauber reaction model that is based on the eikonal approximation and the sudden approximation when dealing with the scattering process, and uses a t-ρ-ρ method to build the projectile-target scattering optical potential, where the nucleonic densities of the core and the target are needed as input. The radial wavefunction of the valence nucleon is solved by a built-in bound-wave solver driven by a globally convergent search engine for optimized potential parameters of the valence nucleon to reproduce user-specified separation energies and root-mean-square (rms) radii of the valence nucleon. The YAML file format is adopted to facilitate user input. The program is expected to especially serve the interpretation of data analysis results of single-nucleon knockout from radioactive ion beams (RIBs), where the experimental practitioners may be more conversant with C++. Program summaryProgram Title: CNOKCPC Library link to program files:https://doi.org/10.17632/dmffpbjhsh.1Developer's repository link:https://gitee.com/asiarabbit/cnokLicensing provisions: GPLv3Programming language: C++Nature of problem: This program calculates the single-particle reaction cross sections of single-nucleon removal from stable and radioactive nuclei impinging on a light composite (i.e. non-hydrogen, e.g. carbon and beryllium) target at intermediate energies (around and more than tens of MeV per nucleon), and the parallel momentum (stripping+diffractive dissociation) distributions of the core, for a pure valence configuration (bound core state+valence nucleon single-particle orbit).Solution method: The bound radial wavefunction of the valence nucleon in a Woods-Saxon (WS) potential is solved following the method of shooting to a fitting point, where the wavefunction is integrated with Runge-Kutta method from 0 and some large distance r∞ to a matching point rm near the nuclear surface. The process is iterated to optimize the eigenvalue Enlj by joining the two waves at rm “smoothly”. Most integrals are evaluated with Simpson's rules, while some with Romberg integration. Searching in the (V0,r0) space of the central WS potential to reproduce the user-specified separation energy and rms radius of the valence nucleon is done via a globally convergent Newton-Raphson root-finding routine for nonlinear systems of equations.Additional comments including restrictions and unusual features: User input is read in with YAML parser (yaml-cpp). Global parameters are readily accessed and uniformly modified in a singleton class. General algorithms (integration, interpolation, minimization, and root-finding routines) are implemented with C++ template class or functors, which adapt to different data types and/or function types. Various batch modes are wrapped in the program package to save user time. For instance, in one run, with the batch mode, one can calculate inclusive single-nucleon removal cross section involving many valence configurations, the relevant inclusive core momentum distribution, and similarly for a series of projectile+target combinations in study of systematics, as is frequently encountered in the study of quenching of single-particle-orbit occupancies (spectroscopic factors) in single-nucleon knockout reactions. Unit tests with Catch are widely deployed to facilitate debugging. C++11 support is required for compilers.

Quenching of single-particle strengths in direct reactions

A discrepancy in the asymmetry dependence of spectroscopic factors extracted with different reaction probes calls into question whether the corresponding reaction models are properly understood. In this work, we present extracted spectroscopic factors from the Ar46,34(p,d)Ar45,33 transfer reactions in inverse kinematics at a beam energy of 70 MeV/nucleon. The results are consistent with previous measurements of these reactions at a lower beam energy [Lee et al., Phys. Rev. Lett. 104, 112701 (2010)], indicating that the transfer reaction is a reliable probe for the nuclear structure of exotic nuclei across a wide energy range. Results from a large body of transfer reaction measurements, (p,pN) measurements, and theoretical nuclear structure studies make a compelling case for much weaker asymmetry dependence than what is observed with single-nucleon knockout reactions on beryllium or carbon targets.Received 19 June 2020Revised 9 November 2020Accepted 8 June 2021DOI:https://doi.org/10.1103/PhysRevC.104.024608©2021 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasDirect reactionsModels & methods for nuclear reactionsNuclear reactionsSpectroscopic factors & electromagnetic momentsTransfer reactionsNuclear Physics

Systematic study ofp-shell nuclei via single-nucleon knockout reactions

A systematic investigation of the inclusive cross sections for single-nucleon knockout reactions from $p$-shell nuclei has been performed. A total of seven reactions were studied for projectiles with masses between $A=7$ and 10, having a wide range of nucleon separation energies. Results were obtained for a range of incident beam energies and targets. These differences were found to have a minimal impact on the deduced cross sections. Experimental results were compared to theoretical predictions based on variational Monte Carlo (VMC) nuclear structure calculations, whose radial overlap functions and neutron and proton densities were included in the reaction description. These results are compared with the conventional model, developed for heavier nuclei, that uses shell-model and Hartree-Fock structure inputs. The VMC-based calculations agreed with the experimental data for several reactions where deeply bound nucleons are removed but does not describe some of the more weakly bound nucleon removal cases with comparable accuracy.

Density dependence of quasifree single-nucleon knockout reactions

We address the issue whether quasifree single-nucleon knockout measurements carry sufficient information about the nuclear interior. To this end, we present comparisons of the reaction probability densities for $A(e,e'p)$ and $A(p,2p)$ in quasifree kinematics for the target nuclei $^{4}$He, $^{12}$C, $^{56}$Fe, and $^{208}$Pb. We adopt a comprehensive framework based on the impulse approximation and on a relativized extension of Glauber multiple-scattering reaction theory in which the medium effects related to short-range correlations (SRC) are implemented. It is demonstrated that SRC weaken the effect of attenuation. For light target nuclei, both the quasifree $(p,2p)$ and $(e,e'p)$ can probe average densities of the same order as nuclear saturation density $\rho_{0}$. For heavy nuclei like $^{208}$Pb, the probed average densities are smaller than $0.1\rho_{0}$ and the $(e,e'p)$ reaction is far more efficient in probing the bulk regions than $(p,2p)$.

New results from MINIBALL

Preliminary results from the study of collectivity and single-particle structure in neutron-rich nuclei are presented from selected experiments. The experiments discussed here employed the MINIBALL Germanium detector array for gamma-ray detection. Coulomb-excitation experiments at REX-ISOLDE focused on the collectivity of Cd and Xe isotopes near 132Sn as well as the shell structure near N = 20 , N = 40 , and N = 50 . Another experiment was performed to probe the single-particle structure of 47Ca, 55Ti, and 73Cu at the GSI Fragmentseparator, using single-nucleon knock-out reactions at relativistic energies.

Polarization observables and spin-dependent distortion effects in single-nucleon knockout reactions

A formalism is developed and predictions are made for selected polarization observables in one-nucleon knockout reactions within the transfer-to-the-continuum direct reaction model. The effects of nucleon-target spin-orbit distortions are also included and their importance is quantified. The calculated knockout reaction analyzing powers reach an appreciable fraction of their maximum allowed values. They are also found to be quite sensitive to the different approximation schemes used for the transfer probability amplitude within the transfer-to-the-continuum model. In contrast, they are shown to be insensitive to details of the two-body interactions assumed, including the nucleon-target spin-orbit interaction. The angular distributions of \ensuremath{\gamma}-rays, arising from the decay of heavy reaction residues produced in excited final states, are shown to be strongly anisotropic.

Dynamical core deformation effects on single-nucleon knockout reactions at fragmentation beam energies

The effects of core deformation and of its dynamical reorientation and rotational excitation on the inclusive single-neutron knockout reaction cross sections on light spherical nuclei are examined. The projectile nuclei are modeled within the framework of a weak-coupling, quadrupole-deformed core-plus-neutron two-body model. We formulate the inclusion of this non-spectator-core degree of freedom within the nonperturbative eikonal model and calculate the diffractive break up and stripping neutron-removal cross sections. We apply the methods to model the single-neutron removal reactions induced by 11Be and 17C and secondary fragmentation beams incident on a 9Be target. Our calculations indicate that dynamical deformation effects on the diffractive break up component of the knockout cross section can be significant. For the two reactions studied here, the diffractive break up cross section is significantly enhanced. This effect is found to be very surface localised, thus the importance of core deformation is increased the more tightly bound the projectile system. The quadrupole deformation parameter and excitation energy of the core also influence the magnitude of this enhancement of the diffractive cross section, which is relatively insensitive to the projectile energy. The stripping cross section is found to be virtually unchanged by the inclusion of the deformed core degree of freedom.

Improved implementation of the transfer-to-the-continuum method for single-neutron knockout reactions and the validity of standard approximations

Approximations made in implementing the transfer-to-the-continuum model for single-nucleon knockout reactions on light target nuclei are investigated using more complete numerical calculations. The reliability of different proposed approximation schemes and their predicted cross sections are discussed. The results of the model calculations that use realistic descriptions of the distorting interactions entering the theory are also compared with available experimental data for reactions induced by $^{15}\mathrm{C}$ and $^{34}\mathrm{Si}$ secondary beams. These transitions, with different neutron orbital angular momenta, also have significantly different values of the neutron separation energy. The different approximation schemes are shown to agree most closely for the weakly bound and spatially extended, $l=0,^{15}\mathrm{C}$ ground state transition. For an $l=2$ transition in $^{34}\mathrm{Si}$, the approximation schemes are shown to be dependent on the nucleon separation energy. In all cases comparisons of even the most accurate implementation of the theory with the experimental data reveals deviations in both the magnitudes of the predicted integrated cross sections and their momentum distributions. Furthermore, the use of the different approximation schemes also produce quite significant effects on the shapes of the predicted momentum distributions and the integrated partial cross sections.

Single-nucleon knockout reactions at fragmentation beam energies

Single-nucleon knockout reactions show considerable promise as a spectroscopic tool for mapping the migration of the dominant single-particle strength in rare isotopes, produced as fragmentation beams with energies > 40 MeV/nucleon. In this paper the theoretical assumptions which underpin the eikonal theory treatment of these reactions are reviewed. Certain sensitivities to input parameters are discussed, as are the possible importance of classes of higher order corrections. The eikonal model prediction for the elastic breakup component of the nucleon removal cross sections is also compared with that from fully-quantum mechanical calculations using the discretised continuum coupled channels method. An asymmetry, manifest in the experimental longitudinal momentum distributions of the ground state residues in weakly-bound-nucleon removal, is well reproduced. 1. INTRODUCTION An ability to map the evolution of the positions and order of nuclear single particle states in rare nuclei of high isospin will be an important component in developing our understanding and the reliability of structure models in these regions. The low intensities of secondary beams of these species, combined with the small number of excited states available in lighter systems, mean that conventional (but in inverse kinematics) lightion single-nucleon transfer reaction and gamma spectroscopic methods are non-trivial. Nucleon-knockout reactions appear to offer an alternative and complementary technique which is particularly well adapted for rare isotope beams produced using fragmentation. From a reaction theory point of view, it has been extremely fortuitous that many of the first generation facilities for the production of rare unstable nuclei have been based on nuclear fragmentation. The high secondary beam energies, and fast collisions with a secondary target, have allowed a rapid development and application of reaction methods, based on the sudden/adiabatic and/or eikonal-like approximations [1–8]. These lead to considerable simplifications and also practical and accurate calculation schemes which have relatively simple and physically transparent input parameters. This has allowed new experimental results to gain feedback rapidly from theory, and vice versa. Having said this, very little of the extensive literature to date has discussed possible schemes to obtain detailed spectroscopic information from data. To a large extent,

Nuclear structure experiments with unstable fragment beams at GSI

Nuclear structure results from recent experiments at GSI using secondary beams of neutron-rich nuclei are presented. Single nucleon knockout reactions from two-neutron halo nuclei and Coulomb dissociation of unstable neutron rich oxygen isotopes are addressed in particular.

A semi-classical model for breakup reactions of light nuclei: 4He(p, pn) 3He

We introduce a new model for single-nucleon knockout reactions on light nuclei that includes multiple-scattering effects. We focus on 4He since the energy and angular distributions of the neutrons and 3He from the inelastic reaction 4He(p, pn) 3He are of astrophysical interest in the problems of accreting neutron stars, solar flares, hot ( kT ∼ MeV) plasmas, and cosmic-ray interactions with the interstellar medium. We have performed a semi-classical, Monte Carlo calculation for proton energies ranging from just above the reaction threshold (25.72 MeV) to just below the free nucleon-nucleon π production threshold (280 MeV). Our model involves only two free parameters, one that suppresses the nucleon-nucleon scattering cross sections, and another that weights the occurrence of multiple scattering. These two free parameters are fixed by comparison to a subset of the experimental data. Once fixed, the model provides total cross sections and detailed energy-angle distributions that are in excellent agreement with the available experimental data. We show that excluding multiple scattering between the outgoing nucleons and the residual nucleus leads to strong disagreement with the experimental data. We describe how to implement these results in the context of a larger problem.

Center-of-mass effects in single-nucleon knock-out reactions

Center-of-mass corrections for quantities observed in single-nucleon knock-out reactions like ($e,{e}^{\ensuremath{'}}p$) are discussed. Explicit results are obtained for the momentum distributions, occupation probabilities, and single-particle energies in the framework of the harmonic oscillator model.