The low-energy behavior of the strength function for the $1^-$ soft dipole excitation in $^{6}$He is studied theoretically. Use of very large basis sizes and well-grounded extrapolation procedures allows to move to energies as small as 1 keV, at which the low-energy asymptotic behavior of the E1 strength function seems to be achieved. It is found that the low-energy behavior of the strength function is well described in the effective three-body "dynamical dineutron model". The astrophysical rate for the $α$+$n$+$n \rightarrow ^6$He+$γ$ is calculated. Comparison with the previous calculations is performed.
Emission of two neutrons or two protons in reactions and decays is often discussed in terms of "dineutron" or "diproton" emission. The discussion often leans intuitively on something described by Migdal-Watson approximation. In this work we propose a way to formalize situations of dineutron emission. It is demonstrated that properly formally defined dineutron emission may reveal properties which are drastically different from those traditionally expected, and properties which are actually observed in three-body decays.
Two-neutron correlation in the $^1S$ channel in quasi two-dimensional (2D) neutron systems at zero temperature is studied by means of the BCS theory with finite-range effective nuclear forces. The dineutron correlation in low density neutron systems confined in an infinite slab is investigated in a simplified model that neutron motion of one direction is frozen. When the slab is thin enough, two neutrons form a tightly bound dineutron with a small size in the quasi-2D system, and a Bose dineutron gas is found in low density limit. With increase of Fermi momentum, the neutron system changes fro…
We investigate how strong a hypothetical 1S0 bound state of two neutrons would affect different observables in the neutron-deuteron reactions. To that aim we extend our momentum space scheme of solving three-nucleon Faddeev equations to incorporate in addition to the deuteron also the 1S0 dineutron bound state. We discuss effects induced by dineutron on the angular distribution of the neutron-deuteron elastic scattering and cross sections of the deuteron breakup. A comparison to the available data for neutron-deuteron total cross sections and elastic scattering angular distributions cannot dec…
We propose a new framework by means of the dineutron condensate (DC) wave function to describe the dineutron correlation, which is characterized by the spatially strong correlation of a spin-zero neutron-neutron pair, in neutron-rich nuclei with an active deformed core surrounded by valence neutrons. Using the DC wave function for a 2$α$+2n system, which corresponds to a toy model for the $^{10}$Be system, we investigate the neutron-neutron correlation around the $2α$ core and discuss the mechanism of the dineutron formation at the surface of finite nuclei. To investigate dineutron correlation…
The nature of pairing correlations in neutron matter is re-examined. Working within the conventional approximation in which the $nn$ pairing interaction is provided by a realistic bare $nn$ potential fitted to scattering data, it is demonstrated that the standard BCS theory fails in regions of neutron number density where the pairing constant $λ$, depending crucially on density, has a non-BCS negative sign. We are led to propose a non-BCS scenario for pairing phenomena in neutron matter that involves the formation of a hidden dineutron state. In low-density neutron matter where the pairing con…
We propose a simple schematic model for two-neutron halo nuclei. In this model, the two valence neutrons move in a one-dimensional mean field, interacting with each other via a density-dependent contact interaction. We first investigate the ground state properties, and demonstrate that the dineutron correlation can be realized with this simple model due to the admixture of even- and odd-parity single-particle states. We then solve the time-dependent two-particle Schrödinger equation under the influence of a time-dependent one-body external field, in order to discuss the effect of dineutron cor…
We extend the method of antisymmetrized molecular dynamics to investigate dineutron correlation. We apply this method to $^{10}$Be as an example and investigate the motion of two neutrons around a largely deformed $^8$Be core by analyzing the two-neutron overlap function around the core. We show that the core structure plays an important role in dineutron formation and expansion from the core and that the present framework is effective for the studies of dineutron correlation.
We discuss the correlation of the spin-singlet two-neutron pair, the dineutron correlation, in the ground and excited $0^+$ states of $^8$He by using a method to describe the dineutron correlation in neutron-rich nuclei, the dineutron condensate wave function. The shell-model configuration and the dineutron configuration compete with each other in the ground state of $^8$He. We compare the ground state structure of $^8$He with that of $^6$He and suggest that the dineutron correlation is weaker in the ground state of $^8$He than $^6$He. We also suggest the possibility of the dineutron condensat…
We study the spatial structure of four valence neutrons in the ground state of $^8$He and $^{18}$C nuclei using a core+4$n$ model. For this purpose, we employ a density-dependent contact interaction among the valence neutrons, and solve the five-body Hamiltonian in the Hartree-Fock-Bogoliubov (HFB) approximation. We show that two neutrons with the coupled spin of $S$=0 exhibit a strong dineutron correlation around the surface of these nuclei, whereas the correlation between the two dineutrons is much weaker. Our calculation indicates that the probability of the (1p$_{3/2})^4$ and [(1p$_{3/2})^…
We investigate the sensitivity of the three-nucleon system to changes in the neutron-neutron scattering length to next-to-leading order in the pionless effective field theory, focusing on the the triton-3He binding energy difference and neutron-deuteron elastic scattering. Due to the appearance of an electromagnetic three-body counterterm at this order, the triton-3He binding energy difference remains consistent with the experimental value even for large positive neutron-neutron scattering lengths while the elastic neutron-deuteron scattering phase shifts are insensitive. We conclude that a bo…
We discuss the two-neutron emission decay of $^{26}$O nucleus from a viewpoint of dineutron correlations between the valence neutrons. We first discuss how the dineutron correlation is realized both in the coordinate space and in the momentum space by employing a three-body model. We then discuss the decay energy spectrum as well as the angular distribution of emitted neutrons. We show that an emission of two neutrons in back-to-back directions is enhanced, which we interpret as a clear manifestation of the dineutron correlation between the valence neutrons.
The dineutron correlations and the crossover from superfluidity of neutron Cooper pairs in the $^1S_0$ pairing channel to Bose-Einstein condensation (BEC) of dineutron pairs in both symmetric and neutron matter are studied within the relativistic Hartree-Bogoliubov theory, with the effective interaction PK1 of the relativistic mean-field approach in the particle-hole channel and the finite-range Gogny force in the particle-particle channel. The influence of the pairing strength on the behaviors of dineutron correlations is investigated. It is found that the neutron pairing gaps at the Fermi su…
Background: Several previous studies provided contradicting results for the four-neutron system, some claiming the existence of a 0+ near-threshold resonance, others denying presence of any observable resonant states. Purpose: Since most of the studies employed enhanced two-neutron interactions to follow the evolution of an artificially bound state into a continuum one, we examine several enhancement schemes that produce a bound dineutron as well. Methods: We study the four-neutron system by solving exact four-particle equations. By varying the interaction enhancement factor we calculate two-d…
Background. Knockout reactions with proton targets provide an invaluable tool to access the properties of two-neutron halo nuclei. Recently, experimental results for the average opening angle as a function of the intrinsic neutron momentum in 11Li have shown a localization of dineutron correlations on the nucleus surface. Purpose. Study the model dependence and the effect of distortion and absorption on the opening angle distributions to assess the reliability of this observable to extract properties of Borromean two-neutron halo nuclei. Method. A quasifree sudden model is used to describe the…
We discuss a decay of unbound nuclei beyond the neutron drip-line using a three-body model with a core nucleus and two valence neutrons. We particularly discuss the role of dineutron correlation between the valence neutrons in the two-neutron emission from the ground state of $^{26}$O and $^{10}$He nuclei. Our calculations clearly indicate that the emission of the two neutrons in the back-to-back direction is enhanced due to the dineutron correlation.
We present a reaction model to describe the fast removal of the $α$-particle core in $^8$He nucleus with eventual emission of four neutrons. The obtained four neutron energy distributions allows to explain the sharp low energy peak observed by studying the missing mass spectra of four neutrons in [Nature Vol. 606, p. 678], as a consequence of dineutron-dineutron correlations.
We look for collective excitations originating from the strong surface pairing in unstable nuclei near the neutron drip-line. The soft dipole excitation is such a pairing mode as it exhibits a character of core-vs-dineutron motion. Possibility of the hydrodynamic phonon mode (the Anderson-Bogoliubov mode) is also discussed.
The sub-barrier capture reactions following the neutron pair transfer are proposed to be used for the indirect study of neutron-neutron correlation in the surface region of nucleus. The strong effect of the dineutron-like clusters transfer stemming from the surface of magic and non-magic nuclei $^{18}$O, $^{48}$Ca, $^{64}$Ni, $^{94,96}$Mo, $^{100,102,104}$Ru, $^{104,106,108}$Pd, and $^{112,114,116,118,120,124,132}$Sn is demonstrated. The dominance of two-neutron transfer channel at the vicinity of the Coulomb barrier is further supported by time-dependent mean-field approaches.
We discuss the energy and angular distributions of two emitted neutrons from the dipole excitation of typical weakly-bound Borromean nuclei, $^{11}$Li and $^6$He. To this end, we use a three-body model with a density dependent contact interaction between the valence neutrons. Our calculation indicates that the energy distributions for the valence neutrons are considerably different between the two nuclei, although they show similar strong dineutron correlations in the ground state to each other. This different behaviour of the energy distribution primarily reflects the interaction between the …
Multi-neutron correlations in light nuclei via ab-initio lattice simulations
Forschungszentrum Jülich（于利希研究中心）；King Fahd University of Petroleum and Minerals (KFUPM)（法赫德国王石油与矿物大学）；Gaziantep Islam Science and Technology University（加济安泰普伊斯兰科学与技术大学）；Universität Bonn（波恩大学）；Beihang University（北京航空航天大学）
This is the second of two papers which investigate cold dilute neutron matter on the lattice using pionless effective field theory. In the unitary limit, where the effective range is zero and scattering length is infinite, simple scaling relations relate thermodynamic functions at different temperatures. When the second virial coefficient is properly tuned, we find that the lattice results obey these scaling relations. We compute the energy per particle, pressure, spin susceptibility, dineutron correlation function, and an upper bound for the superfluid critical temperature.
In this paper we study the renormalization of Halo effective field theory applied to the Helium-6 halo nucleus seen as an alpha-neutron-neutron three-body state. We include the 0+ dineutron channel together with both the 3/2- and 1/2- neutron-alpha channels into the field theory and study all of the six lowest-order three-body interactions that are present. Furthermore, we discuss three different prescriptions to handle the unphysical poles in the P-wave two-body sector. In the simpler field theory without the 1/2- channel present we find that the bound-state spectrum of the field theory is re…
The particle unbound $^{26}$O nucleus is located outside the neutron drip line, and spontaneously decays by emitting two neutrons with a relatively long life time due to the centrifugal barrier. We study the decay of this nucleus with a three-body model assuming an inert $^{24}$O core and two valence neutrons. We first point out the importance of the neutron-neutron final state interaction in the observed decay energy spectrum. We also show that the energy and and angular distributions for the two emitted neutrons manifest a clear evidence for the strong neutron-neutron correlation in the thre…
Radiative capture of the K-minus by the deuteron as a reaction for measurement of the Lambda-neutron scattering lengths. The use of spin information to separate the singlet and triplet scattering lengths is treated.
While diproton decay was first theorized in 1960 and first measured in 2002, it was first observed only in 2012. The measurement of $^{14}$Be in coincidence with two neutrons suggests that $^{16}$Be does decay through the simultaneous emission of two strongly correlated neutrons. In this work, we construct a full three-body model of $^{16}$Be (as $^{14}$Be + n + n) in order to investigate its configuration in the continuum and in particular the structure of its ground state. In order to describe the three-body system, effective n-$^{14}$Be potentials were constructed, constrained by the experi…
The possibility of the description of the available experimental data for cross sections of the neutron capture reaction on 10B at thermal and astrophysical energies, taking into account the resonance at 475 keV, was considered within the framework of the modified potential cluster model with forbidden states and accounting for the resonance behavior of the scattering phase shifts.
The possibility of description of the experimental data on total cross sections of the radiative neutron capture on 14C and 14N is considered within the frame of the potential cluster model with forbidden states and their classification according to Young schemes. It is shown that the using model and the potential construction methods allow to reproduce correctly the behavior of experimental cross sections at the energies from 10 meV (0.01 eV) to 1 MeV.
The population and decay of two-nucleon resonances offer exciting new opportunities to explore dripline phenomena. The understanding of these systems requires a solid description of the three-body (core+N+N) continuum. The identification of a state with resonant character from the background of non-resonant continuum states in the same energy range poses a theoretical challenge. It is the purpose of this work to establish a robust theoretical framework to identify and characterize three-body resonances in a discrete basis. A resonance operator is proposed, which describes the sensitivity to ch…
We consider two basic nuclear reactions: Radiative capture of neutrons by protons, $n+p\to γ+~d$ and its time-reversed counterpart, photodisintegration of the deuteron, $γ+d\to n+p$. In both of these cases we assume that the incoming beam of neutrons or photons is "twisted" by having an azimuthal phase dependence, {\it i.e.}, it carries an additional angular momentum along its direction of propagation. Taking a low-energy limit of these reactions, we derive relations between corresponding transition amplitudes and cross sections with plane-wave beams and twisted beams. Implications for experim…
It is shown that in the framework of the modified potential cluster model we succeeded in correct describing the available experimental data for neutron radiative capture on 10Be total cross-sections at low, astrophysical and thermal energies. All interaction potentials for different partial waves are constructed by describing the basic characteristics of the bound states and spectra of final nucleus. Experimental data for the total cross-sections of the neutron radiative capture on 10Be were obtained by using known data for reduced probabilities of 11Be Coulomb dissociation.
The neutron direct radiative capture (DRC) process is investigated, highlighting the role of incident p-wave neutrons. A set of calculations is shown for the 12-C(n,gamma) process at incoming neutron energies up to 500 keV, a crucial region for astrophysics. The cross section for neutron capture leading to loosely bound s, p and d orbits of 13-C is well reproduced by the DRC model demonstrating the feasibility of using this reaction channel to study the properties of nuclear wave functions on and outside the nuclear surface. A sensitivity analysis of the results on the neutron-nucleus interact…
The $({\rm n},γ)$--cross sections for neutron--rich oxygen isotopes have been calculated in the direct capture model. The experimental data for ${^{18}{\rm O}}({\rm n},γ){^{19}{\rm O}}$ can be reproduced using this model. Compared to previous work the cross section for ${^{19-21}{\rm O}}({\rm n},γ){^{20-22}{\rm O}}$ are enhanced considerably by factors between four and 300.
We formulate the Gamow shell model (GSM) in coupled-channel (CC) representation for the description of proton/neutron radiative capture reactions and present the first application of this new formalism for the calculation of cross-sections in mirror reactions 7Be(p,gamma)8B and 7Li(n,gamma)8Li. The GSM-CC formalism is applied to a translationally-invariant Hamiltonian with an effective finite-range two-body interaction. Reactions channels are built by GSM wave functions for the ground state 3/2- and the first excited state 1/2- of 7Be/7Li and the proton/neutron wave function expanded in differ…
The total cross sections of the 16O(n,gamma)17O radiative capture process is described in the framework of the modified potential cluster model with the classification of orbital states according to Young tableaux. The possibility to describe the experimental data for the total cross sections of the neutron radiative capture on 16O at the energies from 0.025 eV to 1.5 MeV is shown on the basis of E1 and M1 processes. The transitions to the bound states of 17O in the n16O channel from 2S1/2, 2P3/2 and 2D3/2 waves of the n16O scattering have been considered. These transitions have been considere…
A model-independent irreducible tensor approach to p(n,gamma)d is presented and an explicit form for the spin-structure of the matrix for the reaction is obtained in terms of the Pauli spin-matrices for the neutron and the proton. Expressing the multipole amplitudes in terms of the triplet --> triplet and singlet --> triplet transitions, we point out how the initial singlet and triplet contributions to the differential cross section can be determined empirically.
The Coulomb-breakup method to extract the cross section for neutron radiative capture at astrophysical energies is analyzed in detail. In particular, its sensitivity to the description of the neutron-core continuum is ascertained. We consider the case of 14C(n, $γ$)15C for which both the radiative capture at low energy and the Coulomb breakup of 15C into 14C+n on Pb at 68 MeV/nucleon have been measured with accuracy. We confirm the direct proportionality of the cross section for both reactions to the square of the asymptotic normalization constant of 15C observed by Summers and Nunes [Phys. Re…
We discuss the possibility of the non-one-neutron emission channels in the cold fusion reaction $^{70}$Zn + $^{209}$Bi to produce the element Z=113. For this purpose, we calculate the evaporation-residue cross sections of one-proton, radiative-capture, and two-neutron emissions relative to the one-neutron emission in the reaction $^{70}$Zn + $^{209}$Bi. To estimate the upper bounds of those quantities, we vary model parameters in the calculations, such as the level-density parameter and the height of the fission barrier. We conclude that the highest possibility is for the 2n reaction channel, …
The radiative neutron capture reaction rates have been studied at very low energies which are of interest for nuclear astrophysics. The rates for many of these reactions have remained independent of temperature so far. The temperature dependence of the thermonuclear reaction rates have been explored within the statistical model. Apart from the compound nuclear contribution, the pre-equilibrium as well as the direct effects have been taken into account. The corresponding Maxwellian-averaged thermonuclear reaction rates of relevance in astrophysical plasmas at temperatures in the range from 10$^…
The semiclassical, dynamical description of diffraction dissociation of weakly bound nuclei is applied to analyze the decay-energy spectra of $^{15}$C that have been measured at 68 MeV/nucleon on a Pb target. The optical potentials that are used to describe the nuclear interaction of $^{15}$C with the target nucleus are realistic because the fits to the two measured spectra, one with a small and one with a very large acceptance angle, are consistent and of similar quality. The cross section for the radiative neutron capture on $^{14}$C to the 1/2$^+$ ground state of $^{15}$C is deduced from th…
The E1 strength functions and radiative capture cross sections for several compound Sn isotopes, including unstable 132S n and 150S n, have been calculated using the self-consistent microscopic theory. In addition to the standard RPA or QRPA approaches, the method includes the quasiparticle-phonon coupling and the single-particle continuum. The results obtained show that the phonon contribution is very noticeable for the pygmy-dipole resonance, which, as it is known, is important for a description of the radiative neutron capture. The phonon contribution to the pygmy-dipole resonance and to th…
The total cross sections of the radiative neutron capture processes on 9Be, 14C, 14N, 15N, and 16O are described in the framework of the modified potential cluster model with the classification of orbital states according to Young tableaux. The continued interest in the study of these reactions is due, on the one hand, to the important role played by this process in the analysis of many fundamental properties of nuclei and nuclear reactions, and, on the other hand, to the wide use of the capture cross section data in the various applications of nuclear physics and nuclear astrophysics, and, al…
The connection between the neutron halo observed in light neutron rich nuclei and the neutron radiative capture process is outlined. We show how nuclear structure information such as spectroscopic factors and external components of the radial wave function of loosely bound states can be derived from the neutron capture cross section. The link between the direct radiative capture and the Coulomb dissociation process is elucidated.
The path towards the production of \textit{r}-process seed nuclei follows a course where the neutron-rich light and medium mass nuclei play a crucial role. The neutron capture rates for these exotic nuclei could dominate over their $α$-capture rates, thereby enhancing their abundances at or near the drip line. We calculate the radiative neutron capture cross-section for the $^{33}$Na(n,$γ)^{34}$Na reaction via the Coulomb dissociation of $^{34}$Na as it undergoes elastic breakup on $^{208}$Pb when directed at a beam energy of 100 MeV/u using the entirely quantum mechanical theory of finite ran…
The E1 strength function for 15 stable and unstable Sn even-even isotopes from A=100 till A=176 are calculated using the self-consistent microscopic theory which, in addition to the standard (Q)RPA approach, takes into account the single-particle continuum and the phonon coupling. Our analysis shows two distinct regions for which the integral characteristics of both the giant and pygmy resonances behave rather differently. For neutron-rich nuclei, starting from $^{132}$Sn, we obtain a giant E1 resonance which significantly deviates from the widely-used systematics extrapolated from experimenta…
This paper presents an analysis of the positron capture by a neutron reaction, which is just the inverse of the well-known neutrino capture by a proton reaction. The effect of the QED radiative corrections is investigated. In particular, the analysis considers the effects of treating the neutron as a composite object that can have an electric dipole moment (nEDM). For the case of unpolarized hadrons the effects of a nEDM appear to vanish.
We consider the astrophysical reaction rates for radiative neutron capture reactions ($n,γ$) in the crust of a neutron star. The presence of degenerate neutrons at high densities (mainly in the inner crust) can drastically affect the reaction rates. Standard rates assuming a Maxwell-Boltzmann distribution for neutrons can underestimate the rates by several orders of magnitude. We derive simple analytical expressions for reaction rates at a variety of conditions with account for neutron degeneracy. We also discuss the plasma effects on the outgoing radiative transition channel in neutron radiat…
The nn final state interaction has been investigated in d+2H->(pp)S+(nn)S->p+p+n+n reaction going through a formation and breakup of singlet diproton and dineutron in the intermediate state. In the kinematically complete experiment performed at Ed =15 MeV two proton and neutron were detected at angles close to those of emission of (pp)S and (nn)S systems. Simulation of the reaction showed that the shape of neutron energy (timing) spectrum depends on epsnn - the energy of virtual 1S0 state of nn-system. The most likely value epsnn = 0.076 +/- 0.006 MeV was obtained by fitting procedure using th…
We have investigated the implications of the neutron halo configuration, observed in the ground-state of some neutron-rich light nuclei, on neutron radiative transition processes. In particular, we have studied the influence of the neutron halo on the direct radiative capture (DRC) process. The energy dependence as well as the strength of E1 emission due to incident p-wave neutrons is strongly influenced by the halo configuration of the residual nucleus capturing state. We have compared the calculated 10Be(n,gamma)11Be DRC cross section with that derived from the experiment in the inverse kine…
Investigating the rate of $^{10}$Be(n,$γ$)$^{11}$Be radiative capture reaction within the FRDWBA framework
Amity School of Engineering and Technology, Amity University（阿米蒂工程与技术学院，阿米蒂大学）；Punjabi University Patiala（潘杰布大学帕蒂亚拉分校）；Institut für Kernphysik, Johannes Gutenberg-Universität Mainz（约翰内斯·古腾堡美因茨大学核物理研究所）；Indian Institute of Technology Roorkee（印度理工学院勒克瑙分校）；The University of Manchester（曼彻斯特大学）；Akal University（阿卡尔大学）；Research Centre for Nuclear Physics (RCNP), Osaka University（大阪大学核物理研究中心）
We discuss the energy of the excited 2$^+$ state in the unbound nucleus $^{26}$O using the three-body model of $^{24}$O+$n$+$n$. This model fully takes into account the continuum effects as well as the dineutron correlation of the valence neutrons. The present calculation yields the energy of 1.354 MeV, which is slightly smaller than the unperturbed energy, 1.54 MeV. The energy shifts for the ground and the 2$^+$ states with respect to the unperturbed energy suggest that 0$^+$ and the 2$^+$ states in $^{26}$O show a typical spectrum well described by a short-range pairing interaction acting on…
Large-scale QRPA calculations of the E1-strength are performed as a first attempt to microscopically derive the radiative neutron capture cross sections for the whole nuclear chart. A folding procedure is applied to the QRPA strength distribution to take the damping of the collective motion into account. It is shown that the resulting E1-strength function based on the SLy4 Skyrme force is in close agreement with photoabsorption data as well as the available experimental E1-strength at low energies. The increase of the E1-strength at low energies for neutron-rich nuclei is qualitatively analyze…
The importance of n-p radiative capture, utilizing polarized cold neutrons, as a means of measuring the weak pion coupling constant is reviewed. Parity conserving processes of the form k_gamma*[s_n,k_n] can contribute to the s_n*k_gamma photon asymmetry in any such experiment, if the apparatus is not perfectly symmetric. For an incident laboratory neutron energy of 0.003 eV a value of A^{PC}_{gamma}=0.67*10^{-8} is obtained for two different potential models (Argonne AV14 and Nijmegen Reid93). Serving as an extreme test case, the Reid soft core potential yields 0.61*10^{-8}, close to the resul…
