Parallel Momentum Distributions Research Articles

Elastic Coulomb breakup ofNa34

Purpose : The aim of this paper is to study the elastic Coulomb breakup of $^{34}$Na on $^{208}$Pb to give us a core of $^{33}$Na with a neutron and in the process we try and investigate the one neutron separation energy and the ground state configuration of $^{34}$Na. Method : A fully quantum mechanical Coulomb breakup theory within the architecture of post-form finite range distorted wave Born approximation extended to include the effects of deformation is used to research the elastic Coulomb breakup of $^{34}$Na on $^{208}$Pb at 100 MeV/u. The triple differential cross-section calculated for the breakup is integrated over the desired components to find the total cross-section, momentum and angular distributions as well as the average momenta, along with the energy-angular distributions. Results : The total one neutron removal cross-section is calculated to test the possible ground state configurations of $^{34}$Na. The average momentum results along with energy-angular calculations indicate $^{34}$Na to have a halo structure. The parallel momentum distributions with narrow full widths at half maxima signify the same. Conclusion : We have attempted to analyse the possible ground state configurations of $^{34}$Na and in congruity with the patterns in the `island of inversion' conclude that even without deformation, $^{34}$Na should be a neutron halo with a predominant contribution to its ground state most probably coming from $^{33}$Na($3/2^{+}$) $\otimes$ $2p_{3/2}\nu$ configuration. We also surmise that it would certainly be useful and rewarding to test our predictions with an experiment to put stricter limits on its ground state configuration and binding energy.

Experimental study of the knockout reaction mechanism usingO14at 60 MeV/nucleon

Background: For the deeply bound one-nucleon removal at intermediate energies using a Be9 or C12 target, a strong reduction of cross section was observed relative to the prediction of eikonal theoretical model. The large disagreement has not been explained and the systematic trend is inconsistent with results from transfer reactions. The recently observed asymmetric parallel momentum distribution of the knockout residue indicates the significant dissipative core-target interaction in the knockout reaction with a composite target, implying new reaction mechanisms beyond the eikonal reaction descriptions. Purpose: To investigate the reaction mechanism for deeply bound nucleon removal at intermediate energies. Method: Neutron removal from O14 using a C12 target at 60 MeV/nucleon was performed. Nucleon knockout cross sections were measured. The unbound excited states of O13 were reconstructed by using the invariant mass method with the residues and the associated decay protons measured in coincidence. The measured cross sections are compared with an intra-nuclear cascade (INC) prediction. Results: The measured cross section of (O14, C11) is 60(9) mb, which is 3.5 times larger than that of (O14, O13) channel. This 2pn-removal cross section is consistent with INC prediction, which is 66 mb with the main contribution being non-direct reaction processes. On the other hand, the upper limit of the cross section for one-neutron removal from O14 followed by proton evaporation is 4.6(20) mb, integrated up to 6 MeV above the proton separation energy of O13. The calculated total cross section for such reaction processes by the INC model is 2.5 mb, which is within the measured upper limit. Conclusions: The data provide the first constraint on the role of core excitation and evaporation processes in deeply bound nucleon removal from asymmetric nuclei. The experiment results suggest that non-direct reaction processes, which are not considered in the eikonal model, play an important role in deeply bound nucleon removal from asymmetric nuclei at intermediate energies.Received 12 January 2016DOI:https://doi.org/10.1103/PhysRevC.93.044607©2016 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasLow & intermediate energy heavy-ion reactionsNuclear reactionsTransfer reactionsProperties6 ≤ A ≤ 19Nuclear Physics

Spectroscopy ofP35using the one-proton knockout reaction

The structure of $^{35}$P was studied with a one-proton knockout reaction at88~MeV/u from a $^{36}$S projectile beam at NSCL. The $\gamma$ rays from thedepopulation of excited states in $^{35}$P were detected with GRETINA, whilethe $^{35}$P nuclei were identified event-by-event in the focal plane of theS800 spectrograph. The level scheme of $^{35}$P was deduced up to 7.5 MeV using$\gamma-\gamma$ coincidences. The observed levels were attributed to protonremovals from the $sd$-shell and also from the deeply-bound $p\_{1/2}$ orbital.The orbital angular momentum of each state was derived from the comparisonbetween experimental and calculated shapes of individual ($\gamma$-gated)parallel momentum distributions. Despite the use of different reactions andtheir associate models, spectroscopic factors, $C^2S$, derived from the$^{36}$S $(-1p)$ knockout reaction agree with those obtained earlier from$^{36}$S($d$,\nuc{3}{He}) transfer, if a reduction factor $R\_s$, as deducedfrom inclusive one-nucleon removal cross sections, is applied to the knockout transitions.In addition to the expected proton-hole configurations, other states were observedwith individual cross sections of the order of 0.5~mb. Based on their shiftedparallel momentum distributions, their decay modes to negative parity states,their high excitation energy (around 4.7~MeV) and the fact that they were notobserved in the ($d$,\nuc{3}{He}) reaction, we propose that they may resultfrom a two-step mechanism or a nucleon-exchange reaction with subsequent neutronevaporation. Regardless of the mechanism, that could not yet be clarified, thesestates likely correspond to neutron core excitations in \nuc{35}{P}. Thisnewly-identified pathway, although weak, offers the possibility to selectivelypopulate certain intruder configurations that are otherwise hard to produceand identify.

One-neutron removal fromNe29: Defining the lower limits of the island of inversion

Background: Very neutron-rich isotopes, including Ne30-32, in the vicinity of N=20 are known to exhibit ground states dominated by fp-shell intruder configurations: the “island of inversion.” Systematics for the Ne-isotopic chain suggest that such configurations may be in strong competition with normal shell-model configurations in the ground state of Ne29. Purpose: A determination of the structure of Ne29 is thus important to delineate the extent of the island of inversion and better understand structural evolution in neutron-rich Ne isotopes. This is accomplished here through a combined investigation of nuclear and Coulomb-induced one-neutron removal reactions. Method: Cross sections for one-neutron removal on carbon and lead targets and the parallel momentum distribution of the Ne28 residues from the carbon target are measured at around 240 MeV/nucleon. The measurements are compared with reaction calculations combined with spectroscopic information from SDPF-M shell-model wave functions. Results: The deduced width of the inclusive parallel momentum distribution, 98(12) MeV/c (FWHM), suggests that the ground state of Ne29 has a spin parity of 3/2-. Detailed comparisons of the measured inclusive and partial cross sections of the two targets and the parallel momentum distribution of the carbon target with reaction calculations, combined with spectroscopic information from large-scale shell-model calculations, are all consistent with a 3/2- spin-parity assignment. Conclusions: The results indicate that Ne29 lies within the island of inversion and that the ground state of Ne29 is dominated by a Ne28(0+1)xp3/2 neutron configuration. Combined with recently measured interaction cross sections, it is concluded that Ne29 may exhibit a moderately developed halo-like distribution

Study of19C by One-Neutron Knockout

The spectroscopic structure of 19C, a prominent one-neutron halo nucleus, has been studied with a 20C secondary beam at 290 MeV/nucleon and a carbon target. Neutron-unbound states populated by the one-neutron knockout reaction were investigated by means of the invariant mass method. The preliminary relative energy spectrum and parallel momentum distribution of the knockout residue, 19C*, were reconstructed from the measured four momenta of the 18C fragment, neutron, and beam. Three resonances were observed in the spectrum, which correspond to the states at Ex = 0.62(9), 1.42(10), and 2.89(10) MeV. The parallel momentum distributions for the 0.62-MeV and 2.89-MeV states suggest spin-parity assignments of 5/2+ and 1/2−, respectively. The 1.42-MeV state is in line with the reported 5/22+ state.

Asymmetry of the parallel momentum distribution of (p,pN) reaction residues

The parallel momentum distribution (PMD) of the residual nuclei of the 14O(p,pn)13O and 14O(p,2p)13N reactions at 100 and 200 MeV/nucleon in inverse kinematics is investigated with the framework of the distorted wave impulse approximation. The PMD shows an asymmetric shape characterized by a steep fall-off on the high momentum side and a long-ranged tail on the low momentum side. The former is found to be due to the phase volume effect reflecting the energy and momentum conservation, and the latter is to the momentum shift of the outgoing two nucleons inside an attractive potential caused by the residual nucleus. Dependence of these effects on the nucleon separation energy of the projectile and the incident energy is also discussed.

Coulomb breakup of 37Mg and its ground state structure

We calculate Coulomb breakup of the neutron rich nucleus 37Mg on a Pb target at the beam energy of 244 MeV/nucleon within the framework of a finite range distorted wave Born approximation theory that is extended to include the effects of projectile deformation. In this theory, the breakup amplitude involves the full wave function of the projectile ground state. Calculations have been carried out for the total one-neutron removal cross section (σ−1n), the neutron–core relative energy spectrum, the parallel momentum distribution of the core fragment, the valence neutron angular, and energy–angular distributions. The calculated σ−1n has been compared with the recently measured data to put constraints on the spin parity, and the one-neutron separation energy (Sn) of the 37Mg ground state (37Mggs). The dependence of σ−1n on the deformation of this state has also been investigated. While a spin parity assignment of 7/2− for the 37Mggs is ruled out by our study, neither of the 3/2− and 1/2+ assignments can be clearly excluded. Using the spectroscopic factor of one for both the 3/2− and 1/2+ configurations and ignoring the projectile deformation effects, the Sn values of 0.35±0.06 MeV and 0.50±0.07 MeV, respectively, are extracted for the two configurations. However, the extracted Sn is strongly dependent on the spectroscopic factor and the deformation effects of the respective configuration. The narrow parallel momentum distribution of the core fragment and the strong forward peaking of the valence neutron angular distribution suggest a one-neutron halo configuration in either of the 2p3/2 and 2s1/2 configurations of the 37Mg ground state.

Single-particle structure of silicon isotopes approachingSi42

The structure of the neutron-rich silicon isotopes $^{36,38,40}\mathrm{Si}$ was studied by one-neutron and one-proton knockout reactions at intermediate beam energies. We construct level schemes for the knockout residues $^{35,37,39}\mathrm{Si}$ and $^{35,37,39}\mathrm{Al}$ and compare knockout cross sections to the predictions of an eikonal model in conjunction with large-scale shell-model calculations. The agreement of these calculations with the present experiment lends support to the microscopic explanation of the enhanced collectivity in the region of $^{42}\mathrm{Si}$. We also present an empirical method for reproducing the observed low-momentum tails in the parallel momentum distributions of knockout residues.

Breakdown of theN=8magic number near the neutron drip line from parallel momentum distribution analyses

By using two theoretical models (the postform finite range distorted wave Born approximation and the adiabatic model) we calculate the parallel momentum distribution of the charged core in the Coulomb breakup of Be isotopes on a heavy target at 100 MeV/nucleon. We show that the full width at half maxima of the parallel momentum distribution can be used to study the breakdown of the $N=8$ magic number away from the valley of stability.

Direct reactions with radioactive beams

Since the first measurements in the 80's of total reaction cross sections from radioactive beams up to the most recent and advanced exclusive experiments for dripline unbound nuclei, our understanding of exotic nuclei has greatly evolved. This has been possible through a joint effort in the description of the reaction mechanisms and of the underlying nuclear structure. Most exotic nuclei are weakly bound due to the excess of either neutrons or protons and they breakup easily in peripheral reactions. We will discuss in this paper the mechanism responsible for nuclear and Coulomb breakup. Some open problems will be discussed in detail, such as kinematical effects on core parallel momentum distributions and the possibility and consequences that such cores be themselves weakly bound. A general framework for the reaction theory will be used, based on a time dependent perturbation theory approach. Its eikonal limit will be also mentioned.

Observation of a p-wave one-neutron halo configuration in (37)Mg.

Cross sections of 1n-removal reactions from the neutron-rich nucleus (37)Mg on C and Pb targets and the parallel momentum distributions of the (37)Mg residues from the C target have been measured at 240 MeV/nucleon. A combined analysis of these distinct nuclear- and Coulomb-dominated reaction data shows that the (37)Mg ground state has a small 1n separation energy of 0.22(-0.09)(+0.12) MeV and an appreciable p-wave neutron single-particle strength. These results confirm that (37)Mg lies near the edge of the "island of inversion" and has a sizable p-wave neutron halo component, the heaviest such system identified to date.

Relativistic Bernstein mode instability

The classic Bernstein mode instability driven by a perpendicular momentum ring distribution function is insensitive to the parallel distribution. However, in the relativistic treatment, owing to the inexorable coupling between the parallel and perpendicular momenta through the Lorentz factor, the parallel momentum distribution may affect the instability. This paper discusses such a problem by making use of a model parallel momentum distribution function. It is found that the parallel momentum spread only leads to the modification of the real frequency, but the instability growth rate is largely unaffected.

A study of proton breakup from exotic nuclei through various reaction mechanisms in 40A - 80AMeV energy range

We have studied the single proton breakup from weakly bound exotic nuclei due to several reaction mechanisms separately and their total and the interference effects, in order to clarify quantitatively which mechanism would dominate the measured observables. We have considered: (i) the recoil effect of the core-target Coulomb potential which we distinguish from the direct proton-target Coulomb potential, and (ii) nuclear breakup, which consists of stripping and diffraction. Thus, we have calculated the absolute values of breakup cross sections and parallel momentum distributions (LMD) for 8 B and 17 F projectiles on a light and a heavy target in a range of intermediate incident energies (40A-80A MeV) for each reaction mechanism. Furthermore the interference among the two Coulomb effects and nuclear diffraction has been studied in detail. The calculation of the direct and recoil Coulomb effects separately and of their interference is the new and most relevant aspect of this work.

One-neutron knockout reaction of 17C on a hydrogen target at 70 MeV/nucleon

First experimental evidence of the population of the first 2− state in 16C above the neutron threshold is obtained by neutron knockout from 17C on a hydrogen target. The invariant mass method combined with in-beam γ-ray detection is used to locate the state at 5.45(1) MeV. Comparison of its populating cross section and parallel momentum distribution with a Glauber model calculation utilizing the shell-model spectroscopic factor confirms the core-neutron removal nature of this state. Additionally, a previously known unbound state at 6.11 MeV and a new state at 6.28(2) MeV are observed. The position of the first 2− state, which belongs to a member of the lowest-lying p–sd cross shell transition, is reasonably well described by the shell-model calculation using the WBT interaction.

Deformation effects in the Coulomb breakup of 31Ne

We present a fully quantum mechanical theory to study the effects of deformation on various reaction observables in the Coulomb breakup of neutron rich exotic medium mass nuclei on heavy targets within the framework of finite range distorted wave Born approximation by using a deformed Woods–Saxon potential. As an application of this theory, we calculate the one-neutron removal cross section, relative energy spectra, parallel momentum distributions and angular distributions in the breakup of 31Ne on Pb and Au targets at 234 MeV/u. We suggest ways to put constraints on the large uncertainty in the one-neutron separation energy of 31Ne and also argue that if 31Ne is indeed a halo nucleus then it should be a deformed one.

Reaction mechanisms in the scattering of exotic nuclei

This paper describes the evolution of our understanding of the reaction mechanisms involved in the scattering of exotic nuclei starting from the first measurements of reaction cross sections in the 1980s up to the most recent and advanced exclusive experiments for dripline unbound nuclei. We shall mainly cover nuclear and Coulomb breakup reactions, elastic scattering and total reaction cross sections measurements. Some open problems like kinematical effects on core parallel momentum distributions, the existence of a proton halo, the determination of the ground state of unbound nuclei such as 13Be, will be discussed in detail. A general framework for the reaction theory will be used, based on a time dependent perturbation theory approach and when suitable on its eikonal limit.

Interplay of nuclear and Coulomb effects in proton breakup from exotic nuclei

This paper gives new insight to the study of dynamical effects in proton breakup as compared to neutron breakup from a weakly bound state in an exotic nucleus. Following our recent work [Ravinder Kumar and Angela Bonaccorso, Phys. Rev. C84 014613 (2011)] there has been some discussion in the literature [B. Paes, J. Lubiana, P.R.S. Gomes, V. Guimar\~aes, Nucl. Phys. A890 1 (2012); Y. Kucuk and A. M. Moro, Phys. Rev. C86 034601 (2012)], thus in order to clarify and asses quantitatively which mechanism would dominate measured observables, we study here several reaction mechanisms separately but also their total including interference. These mechanisms are: the recoil effect of the core-target Coulomb potential which we distinguish from the direct proton-target Coulomb potential and nuclear breakup, which consists of stripping and diffraction. Direct Coulomb breakup typically gives cross sections about an order of magnitude larger than the recoil term and the amount of nuclear diffraction vs. Coulomb depends on the target. Thus for each mechanism the absolute values of breakup cross sections and parallel momentum distributions for 8B and 17F projectiles calculated on a light and a heavy target in a range of intermediate incident energies (40-80A.MeV) are presented. Furthermore we study in detail the interference among the two Coulomb effects and nuclear diffraction. The calculation of the direct and recoil Coulomb effects separately and of their interference is the new and most relevant aspect of this paper.

Nonsudden Limits of Heavy-Ion Induced Knockout Reactions

We report on the single neutron and proton removal reactions from unstable nuclei with large asymmetry ΔS = S(n)-S(p) at incident energies below 80 MeV/nucleon. Strong nonsudden effects are observed in the case of deeply-bound-nucleon removal. The corresponding parallel momentum distributions exhibit an abrupt cutoff at high momentum that corresponds to an energy threshold occurring when the incident energy per particle is of comparable magnitude to the nucleon separation energy. A large low-momentum tail is related to both dissipative processes and the dynamics of the nucleon removal process. New limits for the applicability of the sudden and eikonal approximations in nucleon knockout are given.

Evolution of the momentum distribution with mass loss in projectile fragmentation reactions

Background: Momentum distributions of fragmentation products as a function of fragment mass have been used to study the fragmentation mechanism. The parallel component of the momentum distribution has been well studied previously and modeled. The perpendicular component, however, is much less measured or understood.Purpose: Measure both components of the linear momentum of a wide range of fragmentation products and compare the widths of the momentum distributions to previous results and descriptions.Method: The parallel and perpendicular components of the momentum vector have been measured for projectile-like fragments produced in the reactions of ${}^{76}$Ge with ${}^{9}$Be and ${}^{197}\phantom{\rule{-0.16em}{0ex}}$Au at 130 MeV/nucleon in a magnetic spectrometer.Results: The measured parallel momentum distributions of all fragments follow established systematics. The perpendicular momentum distributions of fragments produced by fragmentation by the ${}^{197}\phantom{\rule{-0.16em}{0ex}}$Au target with masses near that of the projectile exhibit a clear peak near the momentum corresponding to the grazing angle that diminishes with decreasing fragment mass.Conclusions: The interplay between Coulomb and nuclear scattering can be used to describe results for the most peripheral collisions.

Physics with low energy radioactive beams

This is a review of the basic mechanisms leading to high energy breakup reactions, of the formalisms used to describe them and of some of the methods to obtain the optical potentials necessary in calculations involving exotic nuclei. Semiclassical reductions of the DWBA approximation for inclusive and exclusive breakup will be presented. The observables that can be calculated are projectile’s core parallel momentum distributions, angular distributions of nucleons from the breakup, total breakup cross sections. Methods to study resonances at threshold in unbound nuclei are also introduced. In this case the exclusive observable calculated is the neutron-core relative energy spectrum. Finally, we study the two neutron transfer to the continuum reaction between two “normal” nuclei. The observable is the continuum excitation energy spectrum of the “exotic” residual nucleus created.