# Dr Natalia Timofeyuk

## Research

### Research interests

Nuclear Reaction Theory

Hyperspherical Harmonics formalism

### Research projects

Usually cross sections of (d,p) reactions are calculated with local nucleon-nucleus optical potentials. We have extended the (d,p) reaction theory for the case of nonlocal nucleon-nucleus potentials.

3N force creates a novel three-body interaction involving neutron and proton in deuteron and one of the nucleons in the target. We investigated this effect in adiabatic model and in couninuum-discretized coupled-channel method.

3N force also creates an additional term in the (d,p) T-matrix. This has been studied in plane-wave Born approximation only.

To describe long-range behaviour of one particle removed from a few- or a many-body system, a hyperspherical cluster model has been developed. It has been applied to the ground and first excited states of helium drops with five, six, eight and ten atoms interacting via a two-body soft gaussian potential.

### Research collaborations

Universite Libre de Bruxelles

University of Pisa

University of Seville

University de Santiago de Compostela

## Publications

The low-lying structure of 15C has been investigated via the neutron-removal 16C(d,t) reaction. Along with the known bound neutron sd-shell states, unbound p-shell hole states have been observed. The excitation energies and the deduced spectroscopic factors of the cross-shell states are an important measure of the [(p)−1(sd)2] neutron configurations in 15C. Our results show a very good agreement with shell-model calculations using the SFO-tls interaction for 15C. However, this same interaction predicted energies that were too low for the corresponding hole states in the N=9 isotone 17O and adjustment of the p-sd and sd-sd monopole terms was required to match the 17O energies. In addition, the excitation energies and spectroscopic factors have been compared to the first calculations of 15C with the ab initio self-consistent Green's function method employing the NNLOsat interaction. The results show the sensitivity to the size of the N=8 shell gap and highlight the need to go beyond the current truncation scheme.

The low-lying structure of ¹⁵C has been investigated via the neutron-removal ¹⁶C(d,t) reaction. Along with bound neutron sd-shell hole states, unbound p-shell hole states have been firmly confirmed. The excitation energies and the deduced spectroscopic factors of the cross-shell states are an important measure of the [(p)−1(sd)2] neutron configurations in ¹⁵C. Our results show a very good agreement with shell-model calculations using the SFO-tls interaction for ¹⁵C. However, a modification of the p-sd and sd-sd monopole terms was applied in order to reproduce the N=9 isotone ¹⁷O. In addition, the excitation energies and spectroscopic factors have been compared to the first calculations of ¹⁵C with the ab initio self-consistent Green's function method employing the NNLOsat interaction. The results show the sensitivity to the size of the N=8 shell gap and highlight the need of going beyond the current truncation scheme in the theory.

Scattering of weakly bound nuclei with a pronounced cluster structure is strongly affected by their breakup. Usually, this mechanism is accounted for in a three-body model with pairwise potentials. The interaction potentials between complex systems are non-local due to the existence of excitation channels and antisymmetrization. However, a common practice is to use local optical potentials in cluster scattering studies. To assess the validity of replacing non-local optical potentials by their local equivalents, we extend the local-equivalent continuum-discretized coupled-channel (LECDCC) approach proposed by us for deuteron scattering in [Phys. Rev. C98, 011601(R) (2018)] to the case of cluster scattering. We consider the case of 6Li + 120Sn at 27 and 60 MeV, and compare the angular distributions and reaction cross sections for elastic and breakup cross sections with those obtained in the standard continuum-discretized coupled-channel (CDCC) method with local equivalents of non-local potentials. We found that while elastic scattering is not significantly affected by non-locality, the breakup observables could be affected by up to 20% depending on kinematical conditions of their observation.

When the binding energy of a two-body system goes to zero the two-body system shows a continuous scaling invariance governed by the large value of the scattering length. In the case of three identical bosons, the three-body system in the same limit shows the Efimov effect and the scale invariance is broken to a discrete scale invariance. As the number of bosons increases correlations appear between the binding energy of the few- and many-body systems. We discuss some of them as the relation between the saturation properties of the infinite system and the low-energy properties of the few-boson system.

Scattering of weakly bound nuclei with a pronounced cluster structure is strongly affected by their breakup. Usually, this mechanism is accounted for in a three-body model with pairwise potentials. The interaction potentials between complex systems are non-local due to the existence of excitation channels and antisymmetrization. However, a common practice is to use local optical potentials in cluster scattering studies. To assess the validity of replacing non-local optical potentials by their local equivalents, we extend the local-equivalent continuum-discretized coupled-channel (LECDCC) approach proposed by us for deuteron scattering in [Phys. Rev. C98, 011601(R) (2018)] to the case of cluster scattering. We consider the case of Li-6 + Sn-120 at 27 and 60 MeV, and compare the angular distributions and reaction cross sections for elastic and breakup cross sections with those obtained in the standard continuum-discretized coupled-channel (CDCC) method with local equivalents of non-local potentials. We found that while elastic scattering is not significantly affected by non-locality, the breakup observables could be affected by up to 20% depending on kinematical conditions of their observation.

A new procedure to construct hyperspherical harmonics is presented in which the matrix of the multidimensional hyperangular Laplacian is diagonalized in the single-particle oscillator basis. It is shown that this matrix can be constructed and diagonalized prior to the elimination of spurious states in small subspaces, and that calculations of only the two-body operators is required. As a result, the hyperspherical basis can be constructed much faster than in the procedure introduced earlier [N. K. Timofeyuk, Phys. Rev. C 65, 064306 (2002)], which is based on recursive elimination of hyperradial excitations. The applicability of the proposed method is demonstrated for the systems made of up to ten identical bosons with zero spin using two different two-body potentials. In particular, it has been applied to some α-particle nuclei for which the projection of their 0+ wave functions into the “condensed state wave function” have been calculated.

Overlap functions for one-nucleon removal are calculated as solutions of the inhomogeneous equation. The source term for this equation is generated by the 0ℏω no-core shell-model wave functions and the effective nucleon-nucleon (NN) interactions that fit oscillator matrix elements derived from the NN scattering data. For the lightest A⩽4 nuclei this method gives reasonable agreement with exact ab initio calculations. For 4

It has been realised recently that charge symmetry of the nucleon-nucleon interaction leads to a certain relation between Asymptotic Normalization Coefficients (ANCs) in mirror-conjugated one-nucleon overlap integrals. This relation can be approximated by a simple analytical formula that involves mirror neutron and proton separation energies, the core charge and the range of the strong nucleon-core interaction. We perform detailed microscopic multi-channel cluster model calculations and compare their predictions to the simple analytical formula as well as to calculations within a single-particle model in which mirror symmetry in potential wells and spectroscopic factors are assumed. The validity of the latter assumptions is verified on the basis of microscopic cluster model calculations. For mirror pairs in which one of the states is above the proton decay threshold, a link exists between the proton partial width and the ANC of the mirror neutron. This link is given by an approximate analytical formula similar to that for a bound-bound mirror pair. We compare predictions of this formula to the results of microscopic cluster model calculations. Mirror symmetry in ANCs can be used to predict cross sections for proton capture at stellar energies using neutron ANCs measured with stable or “less radioactive” beams.

Gamow-Teller β decay is forbidden if the number of nodes in the radial wave functions of the initial and final states is different. This Δn=0 requirement plays a major role in the β decay of heavy neutron-rich nuclei, affecting the nucleosynthesis through the increased half-lives of nuclei on the astrophysical r-process pathway below both Z=50 (for N ˃ 82) and Z = 82 (for N ˃ 126). The level of forbiddenness of the Δn=1v1g9/2 → π0g7/2 transition has been investigated from the β decay of the ground state of 207Hg into the single-proton-hole nucleus 207Tl in an experiment at the ISOLDE Decay Station. From statistical observational limits on possible γ-ray transitions depopulating the π0g-17/2 state in 207Tl, an upper limit of 3.9 x 10-3% was obtained for the probability of this decay, corresponding to log ft ˃ 8.8 within a 95% confidence limit. This is the most stringent test of the Δn=0 selection rule to date.

It is well-known that three-boson systems show the Efimov effect when the two-body scattering length a is large with respect to the range of the two-body interaction. This effect is a manifestation of a discrete scaling invariance (DSI). In this work we study DSI in the N-body system by analysing the spectrum of N identical bosons obtained with a pairwise gaussian interaction close to the unitary limit. We consider different universal ratios such as EN 0/E3 0 and EN 1/EN 0, with EN i being the energy of the ground (i = 0) and first-excited (i = 1) state of the system, for N ≤ 16. We discuss the extension of the Efimov radial law, derived by Efimov for N = 3, to general N. © 2013 Springer-Verlag Wien.

It has recently been reported [Phys. Rev. Lett. 117, 162502 (2016)] that (d, p) cross sections can be very sensitive to the n-p interactions used in the adiabatic treatment of deuteron breakup with nonlocal nucleon-target optical potentials. To understand to what extent this sensitivity could originate in the inaccuracy of the adiabatic approximation we have developed a leading-order local-equivalent continuum-discretized coupled-channel model that accounts for non-adiabatic effects in the presence of nonlocality of nucleon optical potentials. We have applied our model to the astro-physically relevant reaction 26mAl(d, p) 27Al using two different n-p potentials associated with the lowest and the highest n-p kinetic energy in the short-range region of their interaction, respectively. Our calculations reveal a significant reduction of the sensitivity to the high n-p momenta thus confirming that it is mostly associated with theoretical uncertainties of the adiabatic approximation itself. The non-adiabatic effects in the presence of nonlocality were found to be stronger than those in the case of the local optical potentials. These results argue for extending the analysis of the (d, p) reactions, measured for spectroscopic studies, beyond the adiabatic approximation.

It has been suggested recently ({____it Phys. Rev. Lett.} 91, 232501 (2003)) that the widths of narrow proton resonances are related to neutron Asymptotic Normalization Coefficients (ANCs) of their bound mirror analogs because of charge symmetry of nucleon-nucleon interactions. This relation is approximated by a simple analytical formula which involves proton resonance energies, neutron separation energies, charges of residual nuclei and the range of their strong interaction with the last nucleon. In the present paper, we perform microscopic-cluster model calculations for the ratio of proton widths to neutron ANCs squared in mirror states for several light nuclei. We compare them to predictions of the analytical formula and to estimates made within a single-particle potential model. A knowledge of this ratio can be used to predict unknown proton widths for very narrow low-lying resonances in the neutron-deficient region of the $sd$- and $pf$-shells, which is important for understanding the nucleosynthesis in the $rp$-process.

It has been suggested recently (Phys. Rev. Lett. 91, 232501 (2003)) that charge symmetry of nucleon-nucleon interactions relates the Asymptotic Normalization Coefficients (ANCs) of proton and neutron virtual decays of mirror nuclei. This relation is given by a simple analytical formula which involves proton and neutron separation energies, charges of residual nuclei and the range of their strong interaction with the last nucleon. Relation between mirror ANCs, if understood properly, can be used to predict astrophysically relevant direct proton capture cross sections using neutron ANCs measured with stable beams. In this work, we calculate one-nucleon ANCs for several light mirror pairs, using microscopic two-, three- and four-cluster models, and compare the ratio of mirror ANCs to the predictions of the simple analytic formula. We also investigate mirror symmetry between other characteristics of mirror one-nucleon overlap integrals, namely, spectroscopic factors and single-particle ANCs.

Using a three-body model, we study the dependence of spectroscopic factors for the overlap integrals ⟨core+N|core+N+N⟩ on the binding energy of the core + N subsystem, considering as prototypes He6, Be6, Li9, C9, O18, and Ne18. We show that at small N-core binding energies these spectroscopic factors can be strongly influenced by the geometrical mismatch between the two-body N-core wave function that stretches into the classically forbidden region and the spatially confined three-body function. This mismatch comes from the strong two-body correlations between the nucleons outside the core and due to the core recoil effects. The mismatch leads to symmetry breaking in mirror spectroscopic factors that in some cases can be large enough to be observed in nucleon removal reactions. It is also responsible for deviations of the ratios of mirror asymptotic normalization coefficients (ANCs) from the simple model-independent analytical estimates. We discuss the influence of such mirror symmetry breaking on the prediction of direct stellar (p,γ) reactions from the measured mirror neutron ANCs.

*a*decays, In: Physical Review C75(034302)

A one-dimensional system of bosons interacting with contact and single-Gaussian forces is studied with an expansion in hyperspherical harmonics. The hyperradial potentials are calculated using the link between the hyperspherical harmonics and the single-particle harmonic-oscillator basis while the coupled hyperradial equations are solved with the Lagrange-mesh method. Extensions of this method are proposed to achieve good convergence with small numbers of mesh points for any truncation of hypermomentum. The convergence with hypermomentum strongly depends on the range of the two-body forces: it is very good for large ranges but deteriorates as the range decreases, being the worst for the contact interaction. In all cases, the lowest-order energy is within 4.5% of the exact solution and shows the correct cubic asymptotic behaviour at large boson numbers. Details of the convergence studies are presented for 3, 5, 20 and 100 bosons. A special treatment for three bosons was found to be necessary. For single-Gaussian interactions, the convergence rate improves with increasing boson number, similar to what happens in the case of three-dimensional systems of bosons.

In a previous publication [Phys. Rev. Lett. 110, 112501 (2013)] we have proposed a generalization of the adiabatic model of (d,p) reactions that allows the nonlocality of the nucleon optical potential to be included in a consistent way together with the deuteron breakup. In this model an effective local d−A potential is constructed from local nucleon optical potentials taken at an energy shifted by ∼40 MeV with respect to the widely used Ed/2 value, where Ed is the deuteron incident energy. The effective d−A potential is shallower than that traditionally used in the analysis of (d,p) reactions within the adiabatic distorted wave approximation and this affects the calculated cross sections and the nuclear structure quantities obtained from their comparison with experimental data. In the present paper we give full derivation of the deuteron effective potential, consider its leading-order term within the local-energy approximation and discuss corrections to the leading-order term. The new method is applied to (d,p) reactions on 16O, 36Ar, and 40Ca targets and the influence of the deviation from the Ed/2 rule on the calculated cross sections is quantified.

The Perey effect in two-body channels of (d, p) reactions has been known for a long time. It arises when the nonlocal two-body deuteron-target and/or proton-target problem is approximated by a local one, manifesting itself in a reduction of the scattering channel wave functions in the nuclear interior. However, the (d, p) reaction mechanism requires explicit accounting for three-body dynamics involving the target and the neutron and proton in the deuteron. Treating nonlocality of the nucleon-target interactions within a three-body context requires significant effort and demands going beyond the widely-used adiabatic approximation, which can be done using a continuum-discretized coupled-channel (CDCC) method. However, the inclusion of nonlocal interactions into the CDCC description of (d, p) reactions has not been developed yet. Here, we point out that, similarly to the two-body nonlocal case, nonlocality in a three-body channel can be accounted for by introducing the Perey factors. We explain this procedure and present the first CDCC calculations to our knowledge including the Perey effect.

The change in mass of a nucleon, arising from its interactions with other nucleons inside the target, results in velocity-dependent terms in the Schrödinger equation that describes nucleon scattering. It has recently been suggested in a number of publications that introducing and fitting velocity-dependent terms improves the quality of the description of nucleon scattering data for various nuclei. The present paper discusses velocity-dependent optical potentials in the context of a three-body problem used to account for deuteron breakup in the entrance channel of (d, p) reactions. Such potentials form a particular class of nonlocal optical potentials which are a popular object of modern studies. It is shown here that because of a particular structure of the velocity-dependent terms the three-body problem can be formulated in two different ways. Solving this problem within an adiabatic approximation results in a significant difference between the two approaches caused by contributions from the high n–p momenta in deuterons in one of them. Solving the three-body problem beyond the adiabatic approximation may remove such contributions, which is indirectly confirmed by replacing the adiabatic approximation by the folding Watanabe model where such contributions are suppressed. Discussion of numerical results is carried out for the 40Ca(d, p)41Ca reaction where experimental data both on elastic scattering in entrance and exit channels and on nucleon transfer are available.

The nonlocal dispersive optical model (NLDOM) nucleon potentials are used for the first time in the adiabatic analysis of a (d,p) reaction to generate distorted waves both in the entrance and exit channels. These potentials have been designed and fitted in [Phys. Rev. Lett. 112, 162502 (2014)] to constrain relevant single-particle physics in a consistent way by imposing the fundamental properties, such as nonlocality, energy-dependence and dispersive relations, that follow from the complex nature of nuclei. However, the NLDOM prediction for the 40Ca(d,p)41Ca cross sections at low energy, typical for some modern radioactive beam ISOL facilities, is about 70% higher than the experimental data despite being reduced by the NLDOM spectroscopic factor of 0.73. This overestimation comes most likely either from insufficient absorption or due to constructive interference between ingoing and outgoing waves. This indicates strongly that additional physics arising from many-body effects is missing in the widely used current versions of (d,p) reaction theories.

Motivated by the importance of P25 for the two-proton decay of S26 and for searches of the mirror analog of the island of inversion near N=16, we present the first predictions for the spectroscopy of the exotic isotope P25 obtained in the shell model, a potential model, and a microscopic-cluster model. All models predict P25 to be unbound, with an energy in the range 0.78-1.03 MeV, which favors previous mass systematics over more recent revisions. We show that P25 possesses a rich low-lying spectrum that should be accessible by experimental studies. All of the predicted states below 7 MeV, except one, are narrow. Many of them are built on the excited-core states of 24Si for which the Coulomb barrier is raised. For decays into the 24Si(g.s.)+p channel we determined the proton widths based on their link to the asymptotic normalization coefficients (ANCs) of their mirror analogs in 25Ne. We determine these ANCs from the analysis of the transfer reaction 24Ne(d,p)25Ne. The proton widths for decay into excited-state channels are obtained in model calculations. The only broad state is the intruder 3/2-, the mirror analog of which has been recently observed in 25Ne. The 25P(3/2-) energy is lower than that in 25Ne, suggesting that the island of inversion may persist on the proton-rich side. All excited states of P25 have at least two decay modes and are expected to populate variously the 21,2+ and 4+ states in 24Si, which then decay electromagnetically.

Asymptotic normalization coefficients (ANCs) for Li-8-->Li-7+n have been extracted from the neutron transfer reaction C-13(Li-7,Li-8)C-12 at 63 MeV. These are related to the ANCs in B-8-->Be-7 + p using charge symmetry. We extract ANCs for B-8 which are in very good agreement with those inferred from proton transfer and breakup experiments. We have also separated the contributions from the p(1/2) and p(3/2) components in the transfer. We find the astrophysical factor for the Be-7(p, gamma)B-8 reaction to be S-17( 0) = 17.6+/-1.7 eV b. This is the first time that the rate of a direct capture reaction of astrophysical interest has been determined through a measurement of the ANCs in the mirror system.

Extended tables are presented for spectroscopic factors, asymptotic normalization coefficients and rms radii of one-nucleon overlap functions for 0p-shell nuclei calculated in the source term approach using shell model wave functions. The tabulated data includes both new results and updates on previously published values. They are compared with recent results obtained in ab initio calculations, and with experimental data, where available. The reduction of spectroscopic factors with respect to traditional shell model values as well as its neutron-proton asymmetry is also discussed

Theoretical models of the (d, p) reaction are exploited for both nuclear astrophysics and spectroscopic studies in nuclear physics. Usually, these reaction models use local optical model potentials to describe the nucleon- and deuteron-target interactions. Within such a framework the importance of the deuteron D-state in low-energy reactions is normally associated with spin observables and tensor polarization effects - with very minimal influence on differential cross sections. In contrast, recent work that includes the inherent nonlocality of the nucleon optical model potentials in the Johnson-Tandy adiabatic-model description of the (d, p) transition amplitude, which accounts for deuteron break-up effects, shows sensitivity of the reaction to the large n-p relative momentum content of the deuteron wave function. The dominance of the deuteron D-state component at such high momenta leads to significant sensitivity of calculated (d, p) cross sections and deduced spectroscopic factors to the choice of deuteron wave function [Phys. Rev. Lett. 117, 162502 (2016)]. We present details of the Johnson-Tandy adiabatic model of the (d, p) transfer reaction generalized to include the deuteron D-state in the presence of nonlocal nucleon-target interactions. We present exact calculations in this model and compare these to approximate (leading-order) solutions. The latter, approximate solutions can be interpreted in terms of local optical potentials, but evaluated at a shifted value of the energy in the nucleon-target system. This energy shift is increased when including the D-state contribution. We also study the expected dependence of the D-state effects on the separation energy and orbital angular momentum of the transferred nucleon. Their influence on the spectroscopic information extracted from (d, p) reactions is quantified for a particular case of astrophysical significance.

Saturation properties are directly linked to the short-range scale of the two-body interaction of the particles. The case of helium is particular, from one hand the two-body potential has a strong repulsion at short distances. On the other hand, the extremely weak binding of the helium dimer locates this system very close to the unitary limit allowing for a description based on an effective theory. At leading order of this theory a two- and a three-body term appear, each one characterized by a low energy constant. In a potential model this description corresponds to a soft potential model with a two-body term purely attractive plus a three-body term purely repulsive constructed to describe the dimer and trimer binding energies. Here we analyse the capability of this model to describe the saturation properties making a direct link between the low energy scale and the short-range correlations. We will show that the energy per particle, E_N/N, can be obtained with reasonable accuracy at leading order extending the validity of this approximation, characterizing universal behavior in few-boson systems close to the unitary limit, to the many-body system.

^{207}Tl studied through

*β*decay, In: Physical Review C101(5)054311 American Physical Society

The β decay of 207Hg into the single-proton-hole nucleus 207Tl has been studied through γ-ray spectroscopy at the ISOLDE Decay Station (IDS) with the aim of identifying states resulting from coupling of the πs−11/2, πd−13/2, and πh−111/2 shell model orbitals to the collective octupole vibration. Twenty-two states were observed lying between 2.6 and 4.0 MeV, eleven of which were observed for the first time, and 78 new transitions were placed. Two octupole states (s1/2-coupled) are identified and three more states (d3/2-coupled) are tentatively assigned using spin-parity inferences, while further h11/2-coupled states may also have been observed for the first time. Comparisons are made with state-of-the-art large-scale shell model calculations and previous observations made in this region, and systematic underestimation of the energy of the octupole vibrational states is noted. We suggest that in order to resolve the difference in predicted energies for collective and noncollective t=1 states (t is the number of nucleons breaking the 208Pb core), the effect of t=2 mixing may be reduced for octupole-coupled states. The inclusion of mixing with t=0,2,3 excitations is necessary to replicate all t=1 state energies accurately.

Theories of (d,p) reactions frequently use a formalism based on a transition amplitude that is dominated by the components of the total three-body scattering wave function where the spatial separation between the incoming neutron and proton is confined by the range of the n-p interaction, Vnp. By comparison with calculations based on the continuum discretized coupled channels method we show that the (d,p) transition amplitude is dominated by the first term of the expansion of the three-body wave function in a complete set of Weinberg states. We use the 132Sn(d,p)133Sn reaction at 30 and 100 MeV as examples of contemporary interest. The generality of this observed dominance and its implications for future theoretical developments are discussed.

A powerful method of investigating proton-unbound nuclear states by tracking their decay products in flight is discussed in detail. To verify the method, four known levels in 15 F , 16 Ne , and 19 Na were investigated by measuring the angular correlations between protons and the respective heavy-ion fragments stemming from the precursor decays in flight. The parent nuclei of interest were produced in nuclear reactions of one-neutron removal from 17 Ne and 20 Mg projectiles at energies of 410–450 A MeV. The trajectories of the respective decay products, 14 O + p + p and 18 Ne + p + p, were measured by applying a tracking technique with microstrip detectors. These data were used to reconstruct the angular correlations of the fragments, which provided information on energies and widths of the parent states. In addition for reproducing properties of known states, evidence for hitherto unknown excited states in 15 F and 16 Ne was found. This tracking technique has an advantage in studies of exotic nuclei beyond the proton drip line measuring the resonance energies and widths with a high precision although by using low-intensity beams and very thick targets.

*d,p*) reactions, In: Physical Review C99(6)064612pp. 064612-1 American Physical Society

A widely accepted practice for treating deuteron breakup in A(d,p)B reactions relies on solving a three-body A+n+p Schrödinger equation with pairwise A−n, A−p and n−p interactions. However, it was shown in Phys. Rev. C 89, 024605 (2014) that projection of the many-body A+2 wave function into the three-body A+n+p channel results in a complicated three-body operator that cannot be reduced to a sum of pairwise potentials. It contains explicit contributions from terms that include interactions between the neutron and proton via excitation of the target A. Such terms are normally neglected. We estimate the first-order contribution of these induced three-body terms and show that applying the adiabatic approximation to solving the A+n+p model results in a simple modification of the two-body nucleon optical potentials. We illustrate the role of these terms for the case of 40Ca(d,p)41Ca transfer reactions at incident deuteron energies of 11.8, 20, and 56 MeV, using several parametrizations of nonlocal optical potentials.

Theoretical models of low-energy (d,p) single-neutron transfer reactions are a crucial link between experimentation, nuclear structure and nuclear astrophysical studies. Whereas reaction models that use local optical potentials are insensitive to short-range physics in the deuteron, we show that including the inherent nonlocality of the nucleon-target interactions and realistic deuteron wave functions generates significant sensitivity to high n-p relative momenta and to the underlying nucleon-nucleon interaction. We quantify this effect upon the deuteron channel distorting potentials within the framework of the adiabatic deuteron breakup model. The implications for calculated (d,p) cross sections and spectroscopic information deduced from experiments are discussed.

The low-energy reaction 14C(n,gamma)15C provides a rare opportunity to test indirect methods for the determination of neutron capture cross sections by radioactive isotopes versus direct measurements. It is also important for various astrophysical scenarios. Currently, puzzling disagreements exist between the 14C(n,gamma)15C cross sections measured directly, determined indirectly, and calculated theoretically. To solve this puzzle, we offer a strong test based on a novel idea that the amplitudes for the virtual 15C-->14C + n and the real 15F -->14O + p decays are related. Our study of this relation, performed in a microscopic model, shows that existing direct and some indirect measurements strongly contradict charge symmetry in the 15C and 15F mirror pair. This brings into question the experimental determinations of the astrophysically important (n,gamma) cross sections for short-lived radioactive targets.

This paper presents a numerical convergence study of a hyperspherical-harmonics expansion for binding energies of a system of 4≤N≤728 helium atoms using a phenomenological soft attractive two-body He-He potential and a repulsive three-body force aimed at compensating for the absence of the two-body repulsive core. Earlier calculations with such a potential have shown an improved convergence when N increases from four to six. The present study reveals that the improved convergence occurs only for a limited range of N determined by the range of the three-body repulsion. For a soft repulsive three-body force, the convergence is fast for N≤20, while for a short-range three-body repulsion it deteriorates at N≥10. The reasons for this deterioration are discussed. The range of the three-body force also determines the binding energy behavior with N, and it is also responsible for binding the excited states. The long-range force binds all first excited 0+ states but strongly underbinds the systems of N helium atoms at large N. The short-range force does not bind the first 0+ states for A≤7 but gives better predictions of binding energies as compared to the calculations of other authors though overestimating them. Some options to improve both the description of the binding energies and the convergence of the hyperspherical-harmonics expansion using phenomenological forces are discussed. It is pointed out that a fast convergence is very much needed for the reliable predictions of states with nonzero angular momentum, examples of which are also given.

The distorted-wave theory of A ( d , p ) B reactions, widely used to analyze experimental data, is based on a Hamiltonian that includes only two-nucleon interactions. However, numerous studies of few-nucleon systems and many modern developments in nuclear structure theory show the importance of the three-nucleon ( 3 N ) force. The purpose of this paper is to study the contribution of the 3 N force of the simplest possible form to the A ( d , p ) B reaction amplitude. This contribution is given by a new term that accounts for the interaction of the neutron and proton in the incoming deuteron with one of the target nucleons. This term involves a new type of nuclear matrix elements containing an infinite number of target excitations in addition to the main part associated with the traditional overlap function between A and B . The nuclear matrix elements are calculated for double-closed shell targets within a mean field theory where target excitations are shown to be equivalent to exchanges between valence and core nucleons. These matrix elements can be readily incorporated into available reaction codes if the 3 N interaction has a spin-independent zero-range form. Distorted-wave calculations are presented for a contact 3 N force with the volume integral fixed by the chiral effective field theory at the next-to-next-to-leading order. For this particular choice, the 3 N contribution is noticeable, especially at high deuteron incident energies. No 3 N effects are seen for incident energies below the Coulomb barrier. The finite range can significantly affect the 3 N contribution to the ( d , p ) cross sections. Finite-range studies require new formal developments and, therefore, their contribution is preliminarily assessed within the plane-wave Born approximation, together with sensitivity to the choice of the deuteron model.

The low-energy reaction C14(n,γ)C15 provides a rare opportunity to test indirect methods for the determination of neutron capture cross sections by radioactive isotopes versus direct measurements. It is also important for various astrophysical scenarios. Currently, puzzling disagreements exist between the C14(n,γ)C15 cross sections measured directly, determined indirectly, and calculated theoretically. To solve this puzzle, we offer a strong test based on a novel idea that the amplitudes for the virtual C15→C14+n and the real F15→O14+p decays are related. Our study of this relation, performed in a microscopic model, shows that existing direct and some indirect measurements strongly contradict charge symmetry in the C15 and F15 mirror pair. This brings into question the experimental determinations of the astrophysically important (n,γ) cross sections for short-lived radioactive targets. © 2006 The American Physical Society.

Deuteron stripping and pick-up experiments - (d; p) and (p; d) - have been used for a long time to study the structure of nuclei. Today these experiments are often carried out in inverse kinematics in state-of-the-art radioactive beams facilities around the world, extending the boundaries of our knowledge of the nuclear chart. The nuclear structure information obtained from these experiments relies entirely on transfer reaction theory. We review the theory of (d; p) and (p; d) reactions starting from early formulations and ending with the most recent developments. In particular, we describe the recent progress made in the understanding of the three-body dynamics associated with the deuteron breakup degrees of freedom, including effects of nonlocality, and discuss the role of many-body degrees of freedom within the three-body context. We also review advances in structure model calculations of one-nucleon overlap functions - an important structure input to (d; p) and (p; d) reaction calculations. We emphasize the physics missing in widely-used standard approaches available to experimentalists and review ideas and efforts aimed at including this physics, formulating the crucial tasks for further development of deuteron stripping and pickup reaction theory

Experimental studies of one-nucleon knockout from magic nuclei suggest that their nucleon orbits are not fully occupied. This conflicts a commonly accepted view of the shell closure associated with such nuclei. The conflict can be reconciled if the overlap between initial and final nuclear states in a knockout reaction are calculated by a nonstandard method. The method employs an inhomogeneous equation based on correlation-dependent effective nucleon-nucleon interactions and allows the simplest wave functions, in which all nucleons occupy only the lowest nuclear orbits, to be used. The method also reproduces the recently established relation between reduction of spectroscopic strength, observed in knockout reactions on other nuclei, and nucleon binding energies. The implication of the inhomogeneous equation method for the physical meaning of spectroscopic factors is discussed.

The role of core excitations in exotic nuclei is discussed in the framework of a microscopic cluster model. This cluster approach is complemented by the R-matrix theory to take account of the long-range part of the wave functions. We briefly describe the model, and present two recent examples: the neutron-rich nucleus B, described by a B+n structure, and the proton-rich nucleus Na, described by a Ne+p structure. In both cases core excitations are shown to play an important role.

We present an analysis of the N-boson spectrum computed using a soft two-body potential, the strength of which has been varied in order to cover an extended range of positive and negative values of the two-body scattering length a close to the unitary limit. The spectrum shows a tree structure of two states, one shallow and one deep, attached to the ground state of the system with one less particle. It is governed by a unique universal function Δ(ξ), already known in the case of three bosons. In the three-particle system the angle ξ, determined by the ratio of the two- and three-body binding energies E3/E2=tan2ξ, characterizes the discrete scale invariance of the system. Extending the definition of the angle to the N-body system as EN/E2=tan2ξ, we study the N-boson spectrum in terms of this variable. The analysis of the results, obtained for up to N=16 bosons, allows us to extract a general formula for the energy levels of the system close to the unitary limit. Interestingly, a linear dependence of the universal function as a function of N is observed at fixed values of a. We show that the finite-range nature of the calculations results in the range corrections that generate a shift of the linear relation between the scattering length a and a particular form of the universal function. We also comment on the limits of applicability of the universal relations.

We have developed an approximate way of dealing with explicit energy dependence of nonlocal nucleon optical potentials as used to predict the (d,p) cross sections within the adiabatic theory. Within this approximation, the nonlocal optical potentials have to be evaluated at an energy shifted from half the incident deuteron energy by the n−p kinetic energy averaged over the range of the n−p interaction and then treated as an energy-independent nonlocal potential. Thus, the evaluation of the distorting potential in the incident channel is reduced to a problem solved in our previous work [N. K. Timofeyuk and R. C. Johnson, Phys. Rev. Lett. 110, 112501 (2013); Phys. Rev. C 87, 064610 (2013)]. We have demonstrated how our new model works for the case of 16O(d,p)17O, 36Ar(d,p)37Ar, and 40Ca(d,p)41Ca reactions and highlighted the need for a detailed understanding of the energy dependence of nonlocal potentials. We have also suggested a simple way of correcting the d−A effective potentials for nonlocality when the underlying energy-dependent nonlocal nucleon potentials are unknown but energy-dependent local phenomenological nucleon potentials are available.

We propose a new method for the analysis of deuteron stripping reactions, A(d,p)B, in which the nonlocality of nucleon-nucleus interactions and three-body degrees of freedom are accounted for in a consistent way. The model deals with equivalent local nucleon potentials taken at an energy shifted by ∼40 MeV from the “Ed/2” value frequently used in the analysis of experimental data, where Ed is the incident deuteron energy. The “Ed/2” rule lies at the heart of all three-body analyses of (d, p) reactions performed so far with the aim of obtaining nuclear structure properties such as spectroscopic factors and asymptotic normalization coefficients that are crucial for our understanding of nuclear shell evolution in neutron- and proton-rich regions of the nuclear periodic table and for predicting the cross sections of stellar reactions. The large predicted shift arises from the large relative kinetic energy of the neutron and proton in the incident deuteron in those components of the n+p+A wave function that dominate the (d, p) reaction amplitude. The large shift reduces the effective d−A potentials and leads to a change in predicted (d, p) cross sections, thus affecting the interpretation of these reactions in terms of nuclear structure.

To describe long-range behaviour of one particle removed from a few- or a many-body system, a hyperspherical cluster model has been developed. It has been applied to the ground and first excited states of helium drops with five, six, eight and ten atoms interacting via a two-body soft gaussian potential. Convergence of the hyperspherical cluster harmonics expansion is studied for binding energies, root-mean-squared radii and overlaps of the wave functions of two helium drops differing by one atom. It was shown that with increasing model space the functional form of such overlaps at large distances converges to the correct asymptotic behaviour. The asymptotic normalization coefficients that quantify the overlaps' amplitudes in this region are calculated. It was also shown that in the first excited state one helium atom stays far apart from the rest forming a two-body molecule, or a halo. The probability of finding the halo atom in the classically-forbidden region of space depends on the definition of the latter and on the valence atom binding energy. The total norm of the overlap integrals, the spectroscopic factor, represents the number of partitions of a many-body state into a chosen state of the system with one particle removed. The spectroscopic factors have been calculated and their sum rules are discussed giving a further insight into the structure of helium drops.

Universal behaviour in few-bosons systems close to the unitary limit, where two bosons become unbound, has been intensively investigated in recent years both experimentally and theoretically. In this particular region, called the unitary window, details of the inter-particle interactions are not important and observables, such as binding energies, can be characterized by a few parameters. With an increasing number of particles the short-range repulsion, present in all atomic, molecular or nuclear interactions, gradually induces deviations from the universal behaviour. In the present letter we discuss for the first time a simple way of incorporating non-universal behaviour through one specific parameter which controls the smooth transition of the system from universal to non-universal regime. Using a system of $N$ helium atoms as an example we calculate their ground state energies as trajectories within the unitary window and also show that the control parameters can be used to determine the energy per particle in homogeneous systems when $N \rightarrow \infty$.

Model uncertainties arising due to suppression of target excitations in the description of deuteron scattering and resulting in a modification of the two-body interactions in a three-body system are investigated for several (d,p) reactions serving as indirect tools for studying the astrophysical (p,γ) reactions relevant to rp process. The three-body nature of the deuteron-target potential is treated within the adiabatic distorted-wave approximation (ADWA) which relies on a dominant contribution from the components of the three-body deuteron-target wave function with small n−p separations. This results in a simple prescription for treating the explicit energy dependence of two-body optical potentials in a three-body system requiring nucleon optical potentials to be evaluated at a shifted energy with respect to the standard value of half the deuteron incident energy. In addition, the ADWA allows for leading-order multiple-scattering effects to be estimated, which leads to a simple renormalization of the adiabatic potential's imaginary part by a factor of two. These effects are assessed using both nonlocal and local optical potential systematics for 26Al, 30P, 34Cl, and 56Ni targets at a deuteron incident energy of 12 MeV, which is typical for experiments with radioactive beams in inverse kinematics. The model uncertainties induced by the three-body nature of deuteron-target scattering are found to be within 40% both in the main peak of angular distributions and in total (d,p) cross sections. At higher deuteron energies, around 60 MeV, model uncertainties can reach 100% in the total cross sections. A few examples of application to astrophysically interesting proton resonances in 27Si and 57Cu obtained using (d,p) reactions and mirror symmetry are given.

The direct reaction theory widely used to study single-particle spectroscopic strength in nucleon transfer experiments is based on a Hamiltonian with two-nucleon interactions only. We point out that in reactions with a loosely-bound projectile, where clustering and breakup effects are important, an additional three-body force arises due to three-nucleon (3N) interaction between two nucleons belonging to different clusters in the projectile and a target nucleon. We study the effects of this force on nucleon transfer in (d,p) and (d,n) reactions on 56Ni, 48Ca, 26mAl and 24O targets at deuteron incident energies between 4 and 40 MeV/nucleon. Deuteron breakup is treated exactly within a continuum discretized coupled-channel approach. It was found that an additional three-body force can noticeably alter the angular distributions at forward angles, with consequences for spectroscopic factors' studies. Additional study of transfer to 2p continuum in the 25F(p,2p)24O reaction, involving the same overlap function as in the 24O(d,n)25F case, revealed that 3N force affects the (d,n) and (p,2p) reactions in a similar way, increasing the cross sections and decreasing spectroscopic factors, although its influence at the main peak of (p,2p) is weaker. The angle-integrated cross sections are found to be less sensitive to the 3N force contribution, they increase by less than 20%. Including 3N interactions in nucleon removal reactions makes an essential step towards bringing together nuclear structure theory, where 3N force is routinely used, and nuclear direct reaction theory, based on two-nucleon interactions only.

The contribution of a three-nucleon (3N) force, acting between the neutron and proton in the incoming deuteron with a target nucleon, to the deuteron-target potential in the entrance channel of the A(d, p)B reaction has been calculated within the adiabatic distorted wave approximation (ADWA). Four different 3N interaction sets from local chiral effective field theory (χEFT) at next-to-next-to-leading order (N2LO) were used. Strong sensitivity of the adiabatic deuteron-target potential to the choice of the 3N force format has been found, which originates from the enhanced sensitivity to the short-range physics of nucleon-nucleon (NN) and 3N interactions in the ADWA. Such a sensitivity is reduced when a Watanabe folding model is used to generate d-A potential instead of ADWA. The impact of the 3N force contribution on (d, p) cross sections depends on assumptions made about the p-A and n-A optical potentials used to calculate the distorted d-A potential in the entrance channel. It is different for local and nonlocal optical potentials and depends on whether the induced three-body force arising due to neglect of target excitations is included or not.

The first investigation of the single-particle structure of the bound states of 17C, via the C transfer reaction, has been undertaken. The measured angular distributions confirm the spin-parity assignments of and for the excited states located at 217 and 335 keV, respectively. The spectroscopic factors deduced for these states exhibit a marked single-particle character, in agreement with shell model and particle-core model calculations, and combined with their near degeneracy in energy provide clear evidence for the absence of the sub-shell closure. The very small spectroscopic factor found for the ground state is consistent with theoretical predictions and indicates that the strength is carried by unbound states. With a dominant valence neutron configuration and a very low separation energy, the excited state is a one-neutron halo candidate.

The adiabatic distorted wave approximation (ADWA) is widely used by the nuclear community to analyse deuteron stripping ($d$,$p$) experiments. It provides a quick way to take into account an important property of the reaction mechanism: deuteron breakup. In this work we provide a numerical quantification of a perturbative correction to this theory, recently proposed in [R.C. Johnson, J. Phys. G: Nucl. Part. Phys. 41 (2014) 094005] for separable rank-one nucleon-proton potentials. The correction involves an additional, nonlocal, term in the effective deuteron-target ADWA potential in the entrance channel. We test the calculations with perturbative corrections against continuum-discretized coupled channel predictions which treat deuteron breakup exactly.

Proton capture on the excited isomeric state of ^{26}Al strongly influences the abundance of ^{26}Mg ejected in explosive astronomical events and, as such, plays a critical role in determining the initial content of radiogenic ^{26}Al in presolar grains. This reaction also affects the temperature range for thermal equilibrium between the ground and isomeric levels. We present a novel technique, which exploits the isospin symmetry of the nuclear force, to address the long-standing challenge of determining proton-capture rates on excited nuclear levels. Such a technique has in-built tests that strongly support its veracity and, for the first time, we have experimentally constrained the strengths of resonances that dominate the astrophysical ^{26m}Al(p,γ)^{27}Si reaction. These constraints demonstrate that the rate is at least a factor ∼8 lower than previously expected, indicating an increase in the stellar production of ^{26}Mg and a possible need to reinvestigate sensitivity studies involving the thermal equilibration of ^{26}Al.

One-nucleon overlap functions, needed for nucleon-removal reaction calculations, are solutions of an inhomogeneous equation with the source term defined by the wave functions of the initial and final nuclear states and interaction between the removed nucleon with the rest. The source term approach (STA) allows the overlaps with correct asymptotic decrease to be modelled while using nuclear many-body functions calculated in minimal model spaces. By properly choosing the removed nucleon interaction the minimum-model-space STA can reproduce reduced values of spectroscopic factors extracted from nucleon-removal reactions and predicts isospin asymmetry in the spectroscopic factor reduction. It is well-known that model space truncation leads to the appearance of higher-order induced forces, with three-nucleon force being the most important. In this paper the role of such a force on the source term calculation is studied. Applications to one-nucleon removal from double-magic nuclei show that three-nucleon force improves the description of available phenomenological overlap functions and reduces isospin asymmetry in spectroscopic factors.

Following recent work in which events which may correspond to a bound tetraneutron ($^4$n) were observed, it is pointed out that from the theoretical perspective the two-body nucleon-nucleon (NN) force cannot by itself bind four neutrons, even if it could bind a dineutron. Unrealistic modifications of the NN force or introduction of unreaslistic four-nucleon force would be needed in order to bind the tetraneutron. The existence of other multineutron systems is discussed.

Project of a new in‐flight fragment separator is proposed as a part of the third generation DRIBs facilities in Dubna. As compared to the existing separator ACCULINNA, beam intensity should be increased by a factor 10–15, the beam quality improved and the RIB assortment should broaden considerably at ACCULINNA‐2. Research program and structure are outlined for the new instrument.

The project of a new and more powerful in-flight fragment separator ACCULINNA-2 at U-400M cyclotron in FLNR, JINR planned to build in addition to the existing separator ACCULINNA is presented. The new separator will provide high intensity RIBs in the lowest energy range (5÷50 MeV/nucleon) which is attainable for in-flight separators. The possibilities for the astrophysics studies at the proposed device are presented. ACCULINNA-2 separator is planned to be constructed in the years 2010-2015. The current status of the project is reported.

There exists a class of nuclei that are obtained by adding one nucleon to a loosely-bound nucleon-core system, for example $^{12}$Be, $^9$C, $^{18}$Ne. For such nuclei, one-nucleon overlap integrals that represent single-particle motion can strongly differ from the standard ones due to the correlations between the two nucleons above the core. The possible non-standard overlap behaviour should be included in the interpretation of the experimental data derived from one nucleon removal reactions such as knockout, transfer and breakup, as well as the predictions of low-energy nucleon capture that leads to these nuclei. We investigate the non-standard behaviour within a three-body model and discuss the challenges associated with this problem.

A program for upgrade of existing radioactive ion beams facilities at Flerov Laboratory of Nuclear Reactions, JINR Dubna is presented. A project of a new in-flight fragment separator ACCULINNA-2 is proposed. It is expected the new instrument will be more universal and powerful than the existing nowadays. The beam intensity should be increased by factor 10-15, its optical quality greatly improved and the range of the accessible secondary radioactive beams broadened up to Z∼20. Main ion-optical characteristics, operating principles and a tentative plan for the project realization are included. An extensive research program based on local experiments made so far and international proposals for these equipments is discussed.

We present new project of fragment separator ACCULINNA-2 that is being planned to be constructed in Flerov Laboratory of Nuclear Reaction, JINR. The ACCULINNA-2 facility is not intended to compete with the new large in-flight RIB facilities. It should complement the existing/constructed facilities in certain fields. Namely, ACCULINNA-2 should provide high intensity RIBs in the lowest energy range attainable for in-flight separators.