Cluster Knockout Reactions Research Articles

Nuclear clustering-manifestations of non-uniformity in nuclei.

Well-developed [Formula: see text] clusters are known to exist in light [Formula: see text] nuclei, and their properties are reasonably well described with modern nuclear structure theories. However, 'modestly' developed clusters in medium to heavy nuclei remain little understood, both theoretically and experimentally. Extension of the focus to include modestly developed clusters leads us to a concept of 'generalized clusters' and 'cluster ubiquitousness'. The former includes clusters more weakly bound than an [Formula: see text] cluster, such as deuteron, triton and [Formula: see text], and even clusters partially broken owing to nuclear medium effects. The latter means the existence of clusters in any nuclei, where cluster development was not previously discussed. Effects of the tensor and the spin-orbit interactions on the coexistence of clusters with independent nucleons are discussed using recent nuclear theoretical models. A mixture of the clusters with shell-like components plays an essential role in the synthesis of elements in the universe and the origin of life, together with an [Formula: see text] decay. It is also pointed out that clustering in heavy nuclei may accelerate fission and fusion processes. Future experimental plans using cluster knockout reactions, which have the potential to extract information of 'generalized clusters' in a variety of nuclei including stable and unstable nuclei, are also discussed. This article is part of the theme issue 'The liminal position of Nuclear Physics: from hadrons to neutron stars'.

Silicon tracker for cluster-knockout reactions at intermediate energies

The cluster-knockout reaction project, ONOKORO, has been launched to elucidate the formation mechanism of clusters in atomic nuclei. For the inverse-kinetics cluster-knockout reaction experiments, a new detector array is under development to measure energies and angles of light ions emitted in the reactions. The silicon tracker tracks the particles with good angular and energy-loss resolutions. A performance test of the silicon strip detectors with a thickness of 100μm and a strip width of 100μm was performed using prototype silicon detectors. The mono-energetic proton and α-particle beams were irradiated on the silicon detectors. The energy-loss spectra in silicon detectors showed a good signal-to-noise ratio. The threshold level for signal detection is seven sigma of noise level. Their dynamic ranges were optimized wide enough to detect charge number Z= 1 and Z= 2 ions emitted in the cluster-knockout reactions.

Designing TOGAXSI: Telescope for inverse-kinematics cluster-knockout reactions

We have launched a new research project named “ONOKORO” to elucidate the formation mechanism of clusters in atomic nuclei. The project comprehensively investigates clustering phenomena in the medium-to-heavy mass region with inverse-kinematics cluster-knockout reactions at the intermediate energy facilities. The new detector array named “TOGAXSI” is under construction for this purpose. It measures scattering angles and the energies of deuterons, tritons, 3He, and α particles emitted at forward angles from the cluster-knockout reactions. It also measures the recoil protons emitted from the scattering events at large angles. High-angular and high-energy resolutions with wide solid angles are required to achieve a good cluster separation energy resolution and a reasonably high yield. The designed telescope consists of silicon trackers and GAGG:Ce calorimeters. This paper shows the required conditions and design concepts of TOGAXSI.

Search for 12 C + 12 C clustering in 24 M g ground state

In the backdrop of many models, the heavy cluster structure of the ground state of 24Mg has been probed experimentally for the first time using the heavy cluster knockout reaction 24Mg(12C,212C)12C in the quasifree scattering kinematic domain. In the (12C,212C) reaction, the direct 12C-knockout cross-section was found to be very small. Finite-range knockout theory predictions were much larger for (12C,212C) reaction, indicating a very small 12C−12C clustering in 24Mg(g.s.). Our present results contradict most of the proposed heavy cluster (12C+12C) structure models for the ground state of 24Mg.

Cluster knockout reactions

Cluster knockout reactions are expected to reveal the amount of clustering (such as that of α, d and even of heavier clusters such as12C, 16O etc.) in the target nucleus. In simple terms, incident medium high-energy nuclear projectile interacts strongly with the cluster (present in the target nucleus) as if it were existing as a free entity. Theoretically, the relatively softer interactions of the two outgoing particles with the residual nucleus lead to optical distortions and are treated in terms of distorted wave (DW) formalism. The long-range projectile–cluster interaction is accounted for, in terms of the finite range (FR) direct reaction formalism, as against the more commonly adopted zero-range (ZR) distorted wave impulse approximation (DWIA) formalism. Comparison of the DWIA calculations with the observed data provide information about the momentum distribution and the clustering spectroscopic factor of the target nucleus. Interesting results and some recent advancements in the area of (α, 2 α) reactions and heavy cluster knockout reactions are discussed. Importance of the finite-range vertex and the final-state interactions are brought out.

Heavy Cluster Knockout ReactionO16(C12,2C12)He4and the Nature of theC12−C12Interaction Potential

The heavy cluster knockout reaction $^{16}\mathrm{O}(^{12}\mathrm{C},2^{12}\mathrm{C})^{4}\mathrm{He}$ performed for the first time, reveals the true nature of the $^{12}\mathrm{C}\mathrm{\text{\ensuremath{-}}}^{12}\mathrm{C}$ interaction. The observed cross section is enhanced by almost 2 orders of magnitude over the conventional zero range distorted wave impulse approximation (DWIA) predictions. An attractive $^{12}\mathrm{C}\mathrm{\text{\ensuremath{-}}}^{12}\mathrm{C}$ optical potential, as obtained in the folding model, does not explain the enhanced cross section in the finite range (FR) DWIA framework. The inclusion of a hard core of fairly long range $\ensuremath{\sim}3.65\text{ }\text{ }\mathrm{fm}$ explains the data. The present investigation of $^{16}\mathrm{O}(^{12}\mathrm{C},2^{12}\mathrm{C})^{4}\mathrm{He}$ along with the $^{12}\mathrm{C}\mathrm{\text{\ensuremath{-}}}^{12}\mathrm{C}$ elastic scattering also proves beyond doubt that the folding model's deep attractive heavy ion potentials are unsuitable to describe the highly overlapping heavy ions. The application of FR-DWIA opens up new avenues to use the heavy core knockout for the detailed investigation of heavy as well as Borromean halo nuclei.

WITNESSING THE HADRONIC COLLISION EVENTS AT CLOSE QUARTERS

It is seen that in the three body final state of a nucleon knockout reaction the residual nucleus not only bears testimony to the dynamics of the knocked out nucleon before the event but also can testify the happening at the time of the hard collision event. This arises mainly because of the distorting optical potentials of the residual nucleus with the knockout partners. In 40Ca(p, 2p) knockout reaction the optical distortion effects are large enough to be able to differentiate between strong peripheral bruising or the deep interpenetration of the two protons at the time of knockout. Similar effect is witnessed in the proton knockout using pions. Many stronger evidences of the effect of varying behaviour of the knockout vertex exist in the nucleon cluster knockout reactions which were only viewed as unexplained large anomalies. Evidences are provided where the different short distance behaviour of the knockout vertex t -matrix effective interaction produced huge differences in the finite range (FR) distorted wave impulse approximation (DWIA) predictions of various knockout reactions. These observations enhance the possibility of observing the multiquark objects (dibaryons, pentaquark eta.) through nucleon knockout reactions if they are produced at the knockout vertex by the incident hadron beam.

Analyzing power and cross section distributions of theC12(p,pα)Be8cluster knockout reaction at an incident energy of 100 MeV

The ($p,p\ensuremath{\alpha}$) reaction on $^{12}\mathrm{C}$ was investigated experimentally using polarized incident protons of 100 MeV. The scattered proton and $\ensuremath{\alpha}$ particle, from the knockout reaction, were detected in coincidence. Coincident data, which were obtained at ten quasifree angle pairs for proton angles ranging from ${25}^{\ifmmode^\circ\else\textdegree\fi{}}$ to ${110}^{\ifmmode^\circ\else\textdegree\fi{}}$, were analyzed in terms of the distorted-wave impulse approximation (DWIA). Calculated energy-sharing cross section and analyzing power distributions reproduce the data reasonably well, indicating that a quasifree knockout mechanism dominates the reaction. Since measurements of analyzing powers were made, spin-orbit distortions were included in the DWIA calculations. The effects of this were found to be very small near zero recoil momentum and did not destroy the validity of the factorization approximation where the two-body $p\text{\ensuremath{-}}\ensuremath{\alpha}$ cross section enters as a multiplicative factor in the three-body ($p,p\ensuremath{\alpha}$) cross section expression. Spectroscopic factors derived from the data are consistent with theoretical predictions. Analyzing power data also follow the trend of free $p\text{\ensuremath{-}}^{4}\mathrm{He}$ scattering data, and comparisons with DWIA predictions are in reasonable agreement. Because the two-body interaction response between the projectile and the $\ensuremath{\alpha}$ cluster was found to resemble the scattering of protons from a free $\ensuremath{\alpha}$ particle to a remarkable degree, the present results would strongly imply the existence of preformed $\ensuremath{\alpha}$ clusters in $^{12}\mathrm{C}$.

Deuteron size effects on its elastic scattering from1H and4He

The effect of change in deuteron size on its elastic scattering from protons and alphas is investigated by varying the Hulthen parameters of the deuteron wave function in the scattering process. The cross sections forp-d scattering, calculated in the Born approximation, are found to increase substantially at backward angles even when the deuteron size is reduced by a small amount, whereas the shape of the angular distribution does not change significantly. For theα-d elastic scattering, interaction potential is obtained by folding the deuteron wave function and the optical potential for nucleon-scattering. The cross sections calculated atE d = 13·7 MeV, shows that the first minimum around Θcm = 60° is deepend as the deuteron size is reduced, while at 52 MeV bombarding energy, the size effects are not very distinct. These observations are useful in the interpretation of deuteron cluster knockout reactions.

Peripheral three-body coupling model for knockout reactions.

A new symmetric three-body coupling model has been developed for the description of the final state of knockout reactions. This model provides an exact description of the three-body final state when either one or both of the two distorting optical potentials vanish. Such a model gives a good description of the situation present in the knockout reactions in the extreme peripheral region, where at least one of the distorting optical potentials is ineffective. Comparison between the predictions of this model and the conventional kinematic coupling model for the 140 MeV $^{2}\mathrm{H}$(\ensuremath{\alpha},\ensuremath{\alpha}'p)n reaction and the 90 MeV $^{16}\mathrm{O}$(\ensuremath{\alpha},2\ensuremath{\alpha}${)}^{12}$C reaction are illustrative of the conclusions which could be drawn from cluster knockout reaction analyses.

Decoupling potentials for the three-body final state Schrödinger equation of knockout reactions

In the conventional distorted wave impulse approximation (DWIA) approach the three-body final state of a knockout reaction is decoupled by assuming a plane wave form for the coupling term. The influence of this decoupling approximation on the analyses of cluster knockout reactions has been investigated for a test case where the exact solution is obtainable. A proper treatment of the coupling term causes large oscillations in the effective distorting optical potentials for the decoupled Schrodinger equation. These decoupling potentials depend strongly not only on the partial wave angular momentum,l but also on their azimuthal projection,m.

(p,p alpha ) cluster-knockout reaction on 9Be at 200 MeV.

The ({ital p},{ital p}{alpha}) cluster-knockout reaction on {sup 9}Be has been investigated experimentally at a bombarding energy of 200 MeV. Coincident data were obtained at five quasifree angle pairs for proton angles ranging from 40{degree} to 80{degree}. The data were analyzed in terms of the distorted-wave impulse approximation. The calculated energy-sharing distributions reproduce the data reasonably well, indicating that the quasifree-knockout mechanism dominates the reaction. The factorization approximation employed in the calculation is found to be valid. The absolute spectroscopic factors derived from the data are in excellent agreement with lower-energy results, and compare well with shell-model predictions.

Quasielastic cluster knock-out reactions and the microscopic cluster model

The spectroscopic information contained in quasielastic cluster knock-out reactions is examined with a microscopic approach to the impulse approximation. It is shown that, because of the Pauli principle, the extracted spectroscopic factor is distinct from the probability (or amount) of clustering. A formalism is elaborated for the calculation of these quantities in a generator-coordinate model for a superposition of different clusterizations. This formalism is used to study the α + d clustering properties of 6Li described as a superposition of the α + d and 5He + p systems. The model predicts the spectroscopic factor (amount of clustering) to be 1.04 (0.97) and 1.01 (0.94) for the ground state and first excited state, respectively. The calculated spectroscopic amplitude, as a function of the αd relative momentum, is in good agreement with those extracted from high-energy 6Li(p, pd)α and 6Li(α, 2α)d experiments.

9Be(p,p alpha ) 5He cluster knockout reaction with 150 MeV polarized protons.

The (p,p\ensuremath{\alpha}) cluster knockout reaction on $^{9}\mathrm{Be}$ was investigated using polarized incident protons. Coincident data for eight quasifree angle pairs were obtained at a bombarding energy of 150 MeV. Both differential cross sections and analyzing powers were measured for the energy-sharing distribution. Distorted wave impulse approximation calculations indicate that the reaction is dominated by a quasifree knockout process, and that a D-state component of the cluster-core wave function is important for larger momentum transfer. Extracted absolute spectroscopic factors for both S- and D-state knockout are in good agreement with theoretical predictions. The analyzing power follows the trend of free p${\mathrm{\ensuremath{-}}}^{4}$He scattering and agrees with the distorted wave impulse approximation calculation reasonably well. Near zero recoil momentum, the spin-orbit interaction in the distorted waves plays little role.

Comment on a discrepancy between proton- and alpha-induced cluster knockout reactions onO16

The possibility is discussed that the enhanced clustering in the nuclear surface of some nuclei observed by Samanta et al. [Phys. Rev. C 26, 1379 (1982)] is due to the modification of the wave function of a discrete nuclear state at the nuclear surface by unbound states. The modification is formulated in a model with unified description of bound and unbound states. Experimental data from knockout reactions on odd nuclei are necessary in order to test the theoretical statements.[NUCLEAR REACTIONS Cluster knockout, light nuclei, spectroscopic factors, continuum shell model, nuclear surface.]

Distorted-wave impulse-approximation calculations for quasifree cluster knockout reactions

A formalism for distorted-wave impulse-approximation calculations of quasifree cluster knockout reactions is described. Results are presented for ($p, p\ensuremath{\alpha}$) and ($\ensuremath{\alpha}, 2\ensuremath{\alpha}$) reactions. In both cases distortion effects are large. It is concluded that incident energies between \ensuremath{\sim} 100 and \ensuremath{\sim} 200 MeV are most suitable for ($p, p\ensuremath{\alpha}$) studies of nuclear structure, whereas somewhat higher energies are more appropriate for ($\ensuremath{\alpha}, 2\ensuremath{\alpha}$) studies.NUCLEAR REACTIONS DWIA reaction theory of cluster knockout.

Medium energy cluster knock-out reactions on 6Li and their interpretation in terms of distorted waves

The 6Li(d, 2d) 4He and 6Li(d, dα) 2H reactions were performed at 27 MeV. Analyses of these and the 42.8 and 55 MeV 6Li(α, 2α) 2H reactions were performed using distorted wave and plane wave impulse approximations. The kinematic and potential coupling approximations to final state three-body Schrödinger equation and the post and prior form approximations to off-shell scattering cross section were studied for the three reactions. It was found that only the kinematic coupling and post form approximations could be used for the consistent analyses of the three reactions. The effects of distortions and localization of the reactions were investigated. Manifestations of deuteron cluster deformation were noticed in the analyses of the three reactions.

The (p, pα) and (α, 2α) reactions on 6Li and 7Li at 60 MeV

An investigation of the alpha cluster knockout reaction has been made by studying the 6,7Li(p, pα) 2,3H and the 6,7Li(α, 2α) 2,3H reactions using approximately 60 MeV incident particles. Both energy sharing and angular correlation experiments have been performed near a quasi-free angle pair, and alpha cluster momentum distributions ¦φ( q )¦ 2 extracted by means of the plane wave impulse approximation. The momentum distributions extracted from the (p, pα) reactions for the two experimental techniques are in good agreement and have the shape expected for the knockout of an L = 0 α-cluster from 6Li and an L = 1 α-cluster from 7Li. The shapes of the ¦φ( q )¦ 2 extracted from the (α, 2α) energy sharing experiments are in reasonably good agreement with the (p, pα) results; the agreement in magnitude being within the experimental uncertainties. However, the angular correlation results for 7Li(α, 2α) 3H show large discrepancies, casting doubt on the analysis of the (α, 2α) reaction with the normal impulse approximation. A discussion of the effects of various methods of making the quasi-free approximation is given.

Tests of the Peripheral Model for a Cluster Knockout Reaction

The reaction $^{6}\mathrm{Li}(\ensuremath{\alpha},2\ensuremath{\alpha})d$ was studied at 50.4, 59.0, 60.5, 70.3 and 79.6 MeV. The angular distributions and energy dependence of the off-energy-shell $\ensuremath{\alpha}\ensuremath{-}\ensuremath{\alpha}$ cross section were extracted and compared with those for free $\ensuremath{\alpha}\ensuremath{-}\ensuremath{\alpha}$ scattering. The agreement between the two is excellent, as predicted by the peripheral model in the quasifree approximation, but the quasifree approximation is not precise enough.