Neutron-Neutron Correlations in the Dissociation of Halo Nuclei
N. A. Orr
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Revised and updated version of invited contribution to the RCNP Spring Workshop on Cluster Condensation and Nucleon Correlations -- 14 pages, 5 figures
Studies attempting to probe the spatial configuration of the valence neutrons in two-neutron halo nuclei using the technique of intensity interferometry are described. Following a brief review of the method and its application to earlier measurements of the breakup of 6He, 11Li and 14Be, the results of the analysis of a high statistics data set for 6He are presented. The limitations of the technique, including the assumption of incoherent emission in the breakup and the sensitivity to the continuum states populated in the dissociation rather than the ground state, are discussed.
Status and prospects of nuclear clustering studies by dissociation of relativistic nuclei in nuclear track emulsion are presented. The unstable $^{8}$Be and $^{9}$B nuclei are identified in dissociation of the isotopes $^{9}$Be, $^{10}$B, $^{10}$C and $^{11}$C, and the Hoyle state in the cases $^{12}$C and $^{16}$O. On this ground searching for the Hoyle state and more complex $α$-particle states in the dissociation of the heavier nuclei is suggested. A detailed study of a low-density baryonic matter arising in dissociation of the heaviest nuclei is forthcoming long-term problem. An analysis o…
Results on the coherent dissociation of relativistic $^9$C nuclei in a nuclear track emulsion are described. These results include the charge topology and kinematical features of final states. Events of C-9 to 3He-3 coherent dissociation are identified.
Nuclear track emulsion is exposed to 1.2 A $^9$C GeV nuclei. Pairs of 2$^3$He nuclei having unusually narrow opening angles are observed in channel $^9$C $\rightarrow$ 3$^3$He pointing to the possible 2$^3$He resonance near the production threshold.
The charge topology of coherent-dissociation events is presented for $^{11}$C and $^{12}$N nuclei of energy 1.2~\textit{A}~GeV per nucleon bombarding nuclear track emulsions. This topology is compared with respective data for $^{7}$Be, $^{8,10}$B, $^{9,10}$C and $^{14}$N nuclei.
Dissociation of 1.2 A GeV $^{10}$C nuclei in nuclear track emulsionis is studied. It is shown that most precise angular measurements provided by this technique play a crucial role in the restoration of the excitation spectrum of the 2$α$+2p system. Strong contribution of the cascade process $^{10}$C$\rightarrow ^9$B$\rightarrow ^8$Be identified.
The dissociation features in nuclear track emulsion of $^9$Be, $^{9,10}$C, and $^{12}$N nuclei of 1.2 A GeV energy are presented. The data presented for the nucleus $^9$Be can be considered as evidence that there is a core in its structure in the form of 0$^+$ and 2$^+$ states of the $^8$Be nucleus having roughly equal weights. Events of coherent dissociation $^9$C$\rightarrow 3^3$He associated with the rearrangement of the nucleons outside the $α$-clustering are identified. A pattern of the charge fragment topology in the dissociation of $^{10}$C and $^{12}$N nuclei is obtained for the first …
Experimental data on fragmentation channels in peripheral interactions of $^8$B nuclei in nuclear track emulsions are presented. A detailed analysis made it possible to justify selections of events of the electromagnetic-dissociation process $^8$B $\to^7$Be + \emph{p} and to estimate its cross section. Events of $^{10}$C peripheral dissociation that were observed in the same exposure are described.
The dissociation of relativistic $^{12}$N nuclei having a momentum of 2 GeV/c per nucleon and undergoing the most peripheral interactions in a track emulsion is studied. The picture of charged topology of product ensembles of relativistic fragments and special features of their angular distributions are presented.
The charge topology in the fragmentation of $^{10}$C nuclei in a track nuclear emulsion at an energy of 1.2 GeV per nucleon is studied. In the coherent dissociation of $^{10}$C nuclei, about 82% of events are associated with the channel $^{10}$C $\rightarrow$ 2$α+$ 2\emph{p}. The angular distributions and correlations of product fragments are presented for this channel. It is found that among $^{10}$C $\rightarrow$ 2$α+$ 2\emph{p} events, about 30% are associated with the process in which dissociation through the ground state of the unstable $^9$Be$_{g.s.}$ nucleus is followed by $^8$Be$_{g.s.…
Possibilities of the nuclear emulsion technique for the study of the systems of several relativistic fragments produced in the peripheral interactions of relativistic nuclei are discussed. The interactions of the $^{10}$B and $^{9}$Be nuclei in emulsion are taken as an example to show the manifestation of the cluster degrees of freedom in relativistic fragmentation. For the case of the relativistic $^{9}$Be nucleus dissociation it is shown that exact angular measurements play a crucial role in the restoration of the excitation spectrum of the alpha particle fragments. The energy calibration of…
A role of the unstable nuclei ${}^{6}$Be, ${}^{8}$Be and ${}^{9}$B in the dissociation of relativistic nuclei ${}^{7,9}$Be, ${}^{10}$B and ${}^{10,11}$C is under study on the basis of nuclear track emulsion exposed to secondary beams of the JINR Nuclotron. Contribution of the configuration ${}^{6}$Be + $\mit{n}$ to the ${}^{7}$Be nucleus structure is 8 $\pm$ 1% which is near the value for the configuration ${}^{6}$Li + $\mit{p}$. Distributions over the opening angle of $α$-particle pairs indicate to a simultaneous presence of virtual ${}^{8}$Be$_{g.s.}$ and ${}^{8}$Be$_{2^+}$ states in the gro…
Production of ensembles of $α$-particle triples associated with the Hoyle state (the second excited state of the ${}^{12}$C nucleus) in peripheral dissociation of relativistic ${}^{12}$C nuclei is studied. Stacks of nuclear track emulsion pellicles exposed to ${}^{12}$C with an energy from hundreds MeV to a few GeV per nucleon serve as the material for studies. The Hoyle state decays are reconstructed via measurement of emission angles of $α$ particles with the precision sufficient for identification of the unstable ${}^{8}$Be nucleus. The estimate of the contribution of Hoyle's state to the $…
These lecture notes present the capabilities of relativistic nuclear physics for the development of the physics of nuclear clusters. Nuclear track emulsion continues to be an effective technique for pilot studies that allows one, in particular, to study the cluster dissociation of a wide variety of light relativistic nuclei within a common approach. Despite the fact that the capabilities of the relativistic fragmentation for the study of nuclear clustering were recognized quite a long time ago, electronic experiments have not been able to come closer to an integrated analysis of ensembles of r…
The invariant mass method is used to identify the $^8$Be and $^9$B nuclei and Hoyle state formed in dissociation of relativistic nuclei in a nuclear track emulsion. It is shown that to identify these extremely short-lived states in the case of the isotopes $^9$Be, $^{10}$B, $^{10}$C, $^{11}$C, $^{12}$C, and $^{16}$O, it is sufficient to determine the invariant mass as a function of the angles in pairs and triples of He and H fragments in the approximation of the conservation of momentum per nucleon of the parent nucleus. According to the criteria established in this way, the contribution of th…
Electromagnetic dissociation of heavy nuclei in ultra-peripheral interactions at high energies can be used to monitor the beam luminosity at colliders. In ALICE neutrons emitted by the excited nuclei close to beam rapidity are detected by the Zero Degree Calorimeters (ZDCs), providing a precise measurement of the event rate. During the 2010 Pb run, a dedicated data taking was performed triggering on electromagnetic processes with the ZDCs. These data, combined with the results from a Van der Meer scan, allowed to measure the electromagnetic dissociation cross-section of Pb nuclei at $\sqrt{s_{…
In the context of the search for triples of relativistic $α$-particles in the Hoyle state, the analysis of available data on the dissociation of the nuclei ${}^{12}$C, ${}^{16}$O and ${}^{22}$Ne in the nuclear emulsion was carried out. The Hoyle state is identified by the invariant mass calculated from pair angles of expansion in $α$-triples in the approximation of the conservation of the momentum per nucleon of the parent nucleus. The contribution of the Hoyle state to the dissociation of ${}^{12}$C $\to$ 3$α$ is 11\%. In the case of the coherent dissociation of ${}^{16}$O $\to$ 4$α$ it reach…
In the events of peripheral dissociation of relativistic nuclei in the nuclear track emulsion, it is possible to study the emerging ensembles of He and H nuclei, including those from decays of unstable $^{8}$Be and $^{9}$B nuclei, as well as the Hoyle state. These extremely short-lived states are identified by invariant masses calculated from the angles in 2$α$-pairs, 2$αp$- and 3$α$-triplets in the approximation of conservation of momentum per nucleon of the primary nucleus. In the same approach, it is possible to search for more complex states. This paper explores the correlation between the…
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 technique of nuclear track emulsions is used to explore the fragmentation of light relativistic nuclei down to the most peripheral interactions - nuclear "white" stars. A complete pattern of therelativistic dissociation of a $^8$B nucleus with target fragment accompaniment is presented. Relativistic dissociation $^{9}$Be$\to2α$ is explored using significant statistics and a relative contribution of $^{8}$Be decays from 0$^+$ and 2$^+$ states is established. Target fragment accompaniments are shown for relativistic fragmentation $^{14}$N$\to$3He+H and $^{22}$Ne$\to$5He. The leading role of …
We present model results for the two-halo-neutron correlation functions, $C_{nn}$, for the dissociation process of light exotic nuclei modelled as two neutrons and a core. A minimum is predicted for $C_{nn}$ as a function of the relative momentum of the two neutrons, $p_{nn}$, due to the coherence of the neutrons in the halo and final state interaction. Studying the systems $^{14}$Be, $^{11}$Li and $^{6}$He within this model, we show that the numerical asymptotic limit, $C_{nn}\to 1$, occurs only for $p_{nn}\gtrsim$ 400 MeV$/c$, while such limit is reached for much lower values of $p_{nn}$ in …
The inelastic scattering of electrons on weakly-bound nuclei is studied with a simple model based on the long range behavior of the bound state wavefunction and on the effective-range expansion for the continuum wavefunctions. Three mechanisms have been considered: (a) dissociation of halo nuclei by high energy electrons, (b) dissociation by electrons present in a fixed target, and (c) Coulomb dissociation. It is shown that the properties of halo nuclei can be studied in electron-radioactive beam colliders using the electro-disintegration process. A comparison with fixed-target experiments is …
The results of investigations dealing with the charge topology of the fragments produced in peripheral dissociation of relativistic $^8$B nuclei in emulsion are presented. 55 events of peripheral dissociation of the $^8$B nucleus were selected from the events which do not involve the production of the target-nucleus fragments and mesons (`` white\rq\rq ~stars). A leading contribution of the $^8$B$\to^7$Be+p mode having the lowest energy threshold was revealed on the basis of those events. Information on the relative probability of dissociation modes with a larger multiplicity was obtained. The…
The differential cross section in the transverse momentum $Q$ and a total cross section of $(31\pm4)$ mb for the coherent dissociation of a 3-A-GeV/$c$ $^7$Li nucleus through the $^3$H$+^4$He channel have been measured on emulsion nuclei. The observed $Q$ dependence of the cross section is explained by the predominant supposition of the nuclear diffraction patterns on light (C, N, O) and heavy (Br, Ag) emulsion nuclei. The contributions to the cross section from nuclear diffraction ($Q\le400$ MeV/$c$) and Coulomb $(Q\le50$ MeV/$c$) dissociations are calculated to be 40.7 and 4 mb, respectively…
In the present paper, experimental observations of the multifragmentation processes of light relativistic nuclei carried out by means of emulsions are reviewed. Events of the type of "white" stars in which the dissociation of relativistic nuclei is not accompanied by the production of mesons and the target-nucleus fragments are considered. A distinctive feature of the charge topology in the dissociation of the Ne, Mg, Si, and S nuclei is an almost total suppression of the binary splitting of nuclei to fragments with charges higher than 2. The growth of the nuclear fragmentation degree is revea…
First results of an analysis to determine contribution of decays of the unstable $^{8}$Be and $^{9}$B nuclei and the Hoyle 3$α$-state to dissociation of $^{14}$N $\to$ 3He (+H) are presented. As the research material, layers of nuclear track emulsion longitudinally exposed to 2.9 $A$ GeV/$c$ $^{14}$N nuclei with at the JINR Nuclotron. Under the assumption that the He and H fragments retain momentum per nucleon of the primary nucleus, these unstable states are identified by the invariant mass calculated from the emission angles of the fragments.
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 …
Using the general notion of cross section fluctuations in hadron--nucleus scattering at high energies, we derive an expression for the cross section of incoherent $J/ψ$ photoproduction on heavy nuclei $dσ_{γA \to J/ψY}/dt$, which includes both elastic $dσ_{γp \to J/ψp}/dt$ and proton-dissociation $dσ_{γp \to J/ψY}/dt$ photoproduction on target nucleons. We find that with good accuracy, $dσ_{γA \to J/ψY}/dt$ can be expressed as a product of the sum of the $dσ_{γp \to J/ψp}/dt$ and $dσ_{γp \to J/ψY}/dt$ cross sections, which have been measured at HERA, and the common nuclear shadowing factor, wh…
Clustering is a relatively widespread phenomena which takes on many guises across the nuclear landscape. Selected topics concerning the study of halo systems and clustering in light, neutron-rich nuclei are discussed here through illustrative examples taken from the Be isotopic chain.
Selected topics on halo and molecular states in light, neutron-rich nuclei are discussed. In particular, work on $xα$:X$n$ structures is briefly reviewed. The use of proton radiative capture as a probe of clustering is also presented through the example provided by the $^6$He(p,$γ$) reaction.
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.
The first measurement of neutron emission in electromagnetic dissociation of $^{208}$Pb nuclei at the LHC is presented. The measurement is performed using the neutron Zero Degree Calorimeters of the ALICE experiment, which detect neutral particles close to beam rapidity. The measured cross sections of single and mutual electromagnetic dissociation of Pb nuclei at $\sqrt{s_{\rm NN}}$ = 2.76 TeV with neutron emission are $σ_{\rm single\ EMD} = 187.4\pm0.2$ (stat.) $^{+13.2} _{-11.2}$ (syst.) b and $σ_{\rm mutual\ EMD} = 5.7\pm0.1$ (stat.) $\pm$0.4 (syst.) b, respectively. The experimental result…
Three-body correlations in the dissociation of two-neutron halo nuclei are explored using a technique based on intensity interferometry and Dalitz plots. This provides for the combined treatment of both the n-n and core-n interactions in the exit channel. As an example, the breakup of 14Be into 12Be+n+n by Pb and C targets has been analysed and the halo n-n separation extracted. A finite delay between the emission of the neutrons in the reaction on the C target was observed and is attributed to 13Be resonances populated in sequential breakup.
The CLAS collaboration at Jefferson Laboratory has compared nuclear parton distributions for a range of nuclear targets and found that the EMC effect measured in deep inelastic lepton-nucleus scattering has a strongly "isophobic" nature. This surprising observation suggests short-range correlations between neighboring $n$ and $p$ nucleons in nuclear wavefunctions that are much stronger compared to $p-p$ or $n-n$ correlations. In this paper we propose a definitive experimental test of the nucleon-nucleon explanation of the isophobic nature of the EMC effect: the diffractive dissociation on a nu…
Paring correlations in weakly bound halo nuclei $^{6}$He and $^{11}$Li are studied by using a three-body model with a density-dependent contact interaction. We investigate the spatial structure of two-neutron wave function in a Borromean nucleus $^{11}$Li.The behavior of the neutron pair at different densities is simulated by calculating the two-neutron wave function at several distances between the core nucleus $^9$Li and the center of mass of the two neutrons. With this representation, a strong concentration of the neutron pair on the nuclear surface is quantitatively established for neutron…
First searches for the coherent dissociation of relativistic oxygen nuclei into four a particles are reported. It is shown that reactions of this type are characterized by a significantly lower decay temperature than the conventional multifragmentation of residual projectile nuclei. The momentum spectra and correlations of a panicles are not reproduced by the simple statistical model of direct fragmentation. The possibility that the oxygen nucleus undergoing fragmentation acquires a nonzero angular momentum in the collision process is discussed.
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.
An experimental overview of reactions induced by the stable, but weakly-bound nuclei 6Li, 7Li and 9Be, and by the exotic, halo nuclei 6He, 8He, 8B, and 11Be on medium-mass targets, such as 58Ni, 59Co or 64Zn, is presented. Existing data on elastic scattering, total reaction cross sections, fusion processes, breakup and transfer channels are discussed in the framework of a CDCC approach taking into account the breakup degree of freedom.
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.
We present ground-state energies of helium halo nuclei based on chiral low-momentum interactions, using the hyperspherical-harmonics method for 6He and coupled-cluster theory for 8He, with correct asymptotics for the extended halo structure.
A deformed relativistic Hartree-Bogoliubov theory in continuum has been developed for the study of neutron halos in deformed nuclei and the halo phenomenon in deformed weakly bound nuclei is investigated. Magnesium and neon isotopes are studied and some results are presented for the deformed neutron-rich and weakly bound nuclei 44Mg and 36Ne. The core of the former nucleus is prolate, but the halo has a slightly oblate shape. This indicates a decoupling of the halo orbitals from the deformation of the core. The generic conditions for the existence of halos in deformed nuclei and for the occurr…
Using a fully quantum mechanical post-form finite-range distorted-wave Born approximation theory of Coulomb breakup, I study the parallel momentum distribution of the core in the Coulomb breakup of suggested excited-state one-neutron halo nuclei considered in their different bound excited states. Narrow momentum distributions obtained in the present calculations for some cases indicate the possibilities of the excited-state halo structure in the nuclei under consideration and therefore favor the previous predictions.
We exploit the possibility of new configurations in three-body halo nuclei - Samba type - (the neutron-core form a bound system) as a doorway to Borromean systems. The nuclei $^{12}$Be, $^{15}$B, $^{23}$N and $^{27}$F are of such nature, in particular $^{23}$N with a half-life of 37.7 s and a halo radius of 6.07 fm is an excellent example of Samba-halo configuration. The fusion below the barrier of the Samba halo nuclei with heavy targets could reveal the so far elusive enhancement and a dominance of one-neutron over two-neutron transfers, in contrast to what was found recently for the Borrome…
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…
The clear separation of scales observed in halo nuclei between the extended halo and the compact core makes these exotic nuclei a perfect subject for Effective Field Theory (EFT). Such description leads to a systematic expansion of the core-halo Hamiltonian, which naturally orders the nuclear-structure observables. In this short review, I show the advantage there is to include Halo-EFT descriptions within precise models of reactions. It helps identifying the nuclear-structure observables that matter in the description of the reactions, and enables us to easily bridge predictions of nuclear-str…
Beta decay is a well-established and efficient probe of nuclear structure and provides important information also for halo nuclei. Detailed decay studies of near-dripline nuclei are challenging, but are now feasible due to the technical progress during the last decades in isotope production as well as detection capabilities. The halo structure can change the dynamics of the decay process, most noticably when decays proceed directly to continuum states as seems to be the case in beta-delayed deuteron emission, a process only observed until now for the halo nuclei $^6$He and $^{11}$Li. The prono…
It is known that nuclear deformation plays an important role in inducing the halo structure in neutron-rich nuclei by mixing several angular momentum components. While previous theoretical studies on this problem in the literature assume axially symmetric deformation, we here consider non-axially symmetric deformations. With triaxial deformation, the $Ω$ quantum number is admixed in a single-particle wave function, where $Ω$ is the projection of the single-particle angular momentum on the symmetric axis, and the halo structure may arise even when it is absent with the axially symmetric deforma…
In this short note we use a simple model to describe the dynamical effects of break-up processes in the subbarrier fusion involving weakly bound nuclei. We model two similar cases involving either a neutron or a proton halo nucleus, both schematically coupled to the break-up channels. We find that the decrease of the coulomb barrier in the proton break-up channel leads, ceteris paribus, to a larger enhancement of the subbarier fusion probabilities with respect to the neutron-halo case.
We use halo effective field theory to analyze the universal features of proton halo nuclei bound due to a large S-wave scattering length. With a Lagrangian built from effective core and valence-proton fields, we derive a leading-order expression for the charge form factor. Within the same framework we also calculate the radiative proton capture cross section. Our general results at leading order are applied to study the excited 1/2+ state of Fluorine-17, and we give results for the charge radius and the astrophysical S-factor.
Halo phenomenon in deformed nuclei is studied by using a fully self-consistent deformed relativistic Hartree-Bogoliubov model in a spherical Woods-Saxon basis with the proper asymptotic behavior at large distance from the nuclear center. Taking a deformed neutron-rich and weakly bound nucleus $^{44}$Mg as an example and by examining contributions of the halo, deformation effects, and large spatial extensions, we show a decoupling of the halo orbitals from the deformation of the core.
Essential properties of halo nuclei can be described in terms of a few low-energy constants. For neutron halo nuclei, analytical results can be found for wave functions and electromagnetic transition matrix-elements in simple but well-adapted models. These wave functions can be used to study nuclear reactions; an especially simple and instructive example is Coulomb excitation. A systematic expansion in terms of small parameters can be given. We present scaling laws for excitation amplitudes and cross sections. The results can be used to analyze experiments like ${}^{11}$Be Coulomb excitation. …
